Reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability methods for flood defences. Flooding of Caldicot Levels

Transcription

1 Reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability methods for flood defences Flooding of Caldicot Levels Failure of embankment without additional structures Failure of embankment with (new) wave return wall Failure of high grounds with masonry wall facing Failure of raised grounds along the Severn Estuary Failure of raised grounds along the Usk Failure of river banks Main report Foekje Buijs TUDelft HRWallingford February 2003

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3 Preface The underlying report contains a coverage of the research named reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability methods for flood defences. This research has been conducted as part of a project in the UK called RASP (Risk Assessment for Strategic Planning) which is carried out by among others HRWAllingford. This work represents my Msc thesis at the faculty of Civil Engineering of Delft University of Technology. This research could not have been carried out without the help of a large number of people. First of all I would like to thank the members of my supervisory committee: Prof. Vrijling (TUDelft), Prof. Vrouwenvelder (TNO/TUDelft), Mr. van Gelder (TUDelft), Mr. Wehrung (DWW, directorate-general for public works and water management), Mr. Sayers (HRWallingford) and Mr. Hall (University of Bristol). Additionally, I thank the people from HRWallingford for providing me with information, discussion and the facilities to work in the UK. The Environment Agency in Wales was very generous in lending me a large amount of reports and giving me information about the Caldicot Levels flood defences. The DWW and project bureau VNK, both connected to the Dutch directorate-general for public works and water management, helped me with the application of PC-Ring. The IHE (Institute of Hydraulic Engineering) in Delft provided me with access to and assistance with Mike11. Finally, I thank Henry Steenbergen from TNO for the implementation of two additional failure modes in PC-Ring. Foekje Buijs February 2003 i

4 Summary Introduction In the UK a number of flooding events in the last decade has caused an increasing interest in riskbased safety approach of flood defences. A risk-based safety approach takes into account the strength and the loading conditions of the flood defence system as part of the probability of inundation as well as the consequences of inundation in case of failure of the flood defence system. One of the advantages of a risk-based analysis of flood defence systems is that it points out the system s weakest links and enables the decision-maker to target maintenance activities. Another advantage is that in case of large scale flood defence improvements the decision-maker can compare different design options in terms of the actual risk reduction and the costs which are associated with the improvement options. In the light of the shift to a risk-based safety approach in the UK a project called RASP, Risk Assessment of Strategic Planning, is carried out at among others HRWallingford. This project aims to develop tiered methodologies for risk assessment of flood defence systems. These tiered methodologies consist of a high level methodology supporting national policy making, an intermediate level methodology supporting regional policy making and a detailed level approach supporting policy making at the scale of one flood defence system. Objective and main working method The objective of this Msc thesis is to apply a reliability analysis on the Caldicot Levels flood defence system in the UK using Dutch reliability methods for flood defences in order to support an evaluation of the appropriateness of these methods as part of the detailed level methodology in RASP. The main working-method is to carry out the reliability analysis by taking the following steps: Definition of the Caldicot Levels flood defence system and its components. Analysis of the failure modes connected to the components Modelling the Caldicot Levels flood defence system and expressing this model into data Calculation of the probability of flooding of the Caldicot Levels flood defence system. Two scenario s are subject to reliability analysis: The present Caldicot Levels flood defence system The same system after a number of planned improvements have been taken into account Before these steps are presented the boundary conditions and the Dutch reliability methods for flood defences which form the framework of the reliability analysis are discussed. Boundary conditions The Caldicot Levels flood defence system is located at the south coast of Wales in the UK. The system borders the Severn Estuary in the south, the river Usk in the west and a distinct line of hills in the north and east. In the Severn estuary one of the largest tidal ranges in the world occurs, a range that varies between 9 and 15 meter. The largest fetches and the most severe wind speeds are found in the south westerly wind directions. The River Usk is a small river, however the water levels can reach quite high values especially in case of high water levels at the Severn Estuary. The mean elevation of the Caldicot Levels is OD+5.5m which compares to mean tide high water levels of OD+4.8m, mean spring tide high water levels of OD+6.5m and a 200-year return period water level of OD+8.55m. The crest levels of the flood defence system vary between OD+8 and OD+10m. The embankments and soil underneath consist mainly of clay. ii

5 Finally, knowledge is available of damage caused by a number of storms which occurred in the past. Dutch reliability methods for flood defences The Dutch reliability methods for flood defences mainly consist of two parts. First software called PC-Ring which calculates the annual probability of failure of a flood defence system for a number of different failure modes: overtopping, instability of the inside slope, piping and attack of the revetment on the outside slope. PC-Ring takes into account: statistical distribution functions and correlations in time and space. Calculations amount to the calculation at the level of one reliability function and at the level of combination of a system of different reliability functions. Second a process that reduces the amount of work related to data gathering by selecting the sections that are most representative of the system s probability of failure. This process starts with dividing the system in stretches, and more detailed sections. The cross sectional and statistical properties are assumed to be constant along one section. By use of indicators, which are based on rough information, sections are selected which are considered as weak. These selected cross sections are included in the calculations with PC-Ring. Definition of the system and its components The Caldicot Levels flood defence system is defined as shown in fig.i. The line south of the locations marked A and B represents the relevant defence length for the calculation of the probability of inundation. The OD+10m relief line defines the boundary formed by the high grounds. The area between the lines suffers consequences in the form of partial or complete flooding case the flood defence system fails. For the components, see also fig.i. N B OD+10 m relief line A Lighthouse 1 = 2 = 3 = Embankment Embankment with wave return wall High grounds with masonry wall facing 4 = 5 = 6 = Raised grounds along Severn Estuary Raised grounds along the Usk River banks of the Usk Figure I. Definition of the Caldicot Levels flood defence system s boundaries. The OD+10m line represents the high grounds which do not contribute to the system s probability of flooding. Additionally, the figure includes a rough indication of the position of the main flood defence components. iii

6 Analysis of the failure modes connected to the components All of the components except for the embankment with wave return wall, are calculated with the failure modes which are present in PC-Ring. For the improved form of the embankment with wave return wall an approach is developed which takes the wave return wall into account. Erosion rear slope without reduction Failure of wave return wall Erosion rear slope Erosion rear slope Overtopping Saturation Saturation rear slope without reduction Failure of wave return wall Instability of the inside slope Saturation Etc.. Theoretically speaking, the wave return wall reduces the amount of overtopping. Failure of the wave return wall does not necessarily need to lead to failure of the complete embankment, see fig.ii. at the top. However, this approach leads to practical complications of the implementation of the wave return wall in PC-Ring. Therefore, the approach as presented at the bottom Failure of wave return wall Overtopping Failure of embankment with wave return wall Instability of the inside slope Attack of the revetment on the outside slope of fig.ii. is applied. This approach is based on the assumption that the wave return wall will fail under such conditions that consequently the complete embankment fails. Analysis of the results will point out whether the probability of failure of the wave return wall is high or low relative to that of the embankment. In the first case the probability of failure of the embankment dominates the probability of failure. In the second case the practical approach applies: the probability of failure of the wave return wall or the probability of failure of the embankment with wave return wall. Two failure modes of the wave return wall are taken into account: horizontal sliding or tilting. The force is formed by the wave impact and the strength mainly depends on the weight of the wave return wall. Modelling the Caldicot Levels flood defence system and expressing this model into data As is mentioned as part of the Dutch reliability methods for flood defences, the Caldicot Levels flood defence system is divided into stretches and more detailed sections. For each failure mode the relevancy has been determined and the weak sections have been selected according to rough indicators. The failure modes which have been taken into account are: overtopping, instability of the inside slope and attack of the revetment on the outside slope. The main obstacles in the data requirements are the models of the hydraulic boundary conditions and the statistical data availability. In case of the Severn Estuary a statistical approach is applied where a deterministic is desired. Moreover, the statistics are based on estimates. In case of the River Usk numerical problems are encountered which cannot be solved in the available time scope. Besides that, limited information about discharge statistics is available. Uplifting and piping Figure II. Fault tree of theoretical approach of wave return wall (top) and of practical approach as implemented in PC-Ring (bottom) iv

7 Results of the calculation of the annual probability of flooding of the Caldicot Levels flood defence system in its present and improved form The calculations of the annual probability of flooding of the Caldicot Levels flood defence system result in, see table I: Annual probabilities of failure of the separate included sections. Coefficients of influence that point out which random variables contribute most to the total uncertainty of the reliability function. The total annual system s probability of flooding due to one failure mode and the weakest link in the system. The total annual system s probability of flooding. The dominating failure mode turns out to be overtopping. The weak areas which result from the calculations correspond with the more severely attacked areas in the past storms. The main reasons causing these areas to be weak are a low crest level in combination with the orientation of the embankment with respect to the south westerly wind directions. The annual probability of failure of the wave return wall is dominated by failure due to tilting and Table I. Results from the calculations of the annual probability of flooding of the Caldicot Levels flood defence system in its present and improved form..w.r.w. = wave return wall. Present system Improved system Without Usk Overtopping Instability of the inside slope Attack of the revetment on the outside slope Total flood defence system Weakest link Total Weakest link Total Weakest link Total Weakest Total Pf No. β β No. β β No. β β link no. β With Usk Without Usk With Usk Failure w.r.w. Failure embankment with effect w.r.w. on overtopping Failure embankment without w.r.w *10-1 Reliability index Section no. Figure III. Reliability indices of failure due to overtopping of the present flood defence system and the improved flood defence system. For the improved flood defence system the reliability indices of embankments with and without the influence of the wave return wall on the overtopping discharges are included. v

8 is relatively high. Therefore, the assumption that the complete embankment fails if the wave return wall fails is not justified in this case. The real probability of failure is expected to be a combination between failure of the embankment with the influence of the wave return wall on wave overtopping and failure of the embankment without a wave return wall on the crest. As overtopping is the dominating failure mode, in fig.iii. the annual probabilities due to overtopping of the separate sections are given of the present and improved flood defence system. Moreover, fig.iii. points out that the planned improvements are unbalanced. Without regarding the river Usk, section 63 turns out to be the weakest link: this is one of the sections for which no improvement is planned. Conclusions and recommendations Conclusions The approach to select the sections which represent the system s weak areas most proves to be successful. PC-Ring successfully points out the system s weakest links which enables to target maintenance activities. The coefficients of influence together with the reliability functions provide the possibility to determine what causes these areas to be weak. Fig.III. points out that PC-Ring provides the possibility to compare large scale flood defence improvements in terms of annual probabilities. Therefore, the method proves to be suitable to contribute to the comparison of different design options in terms of the actual risk reduction and the costs which are associated with the improvement options. The mathematical relations are suitable to apply to different types of failure modes than the ones that are already present in the PC-Ring program. However, the implementation of the wave return wall points out that: the set up of the program causes complications when failure modes are to be incorporated on an other level than the OR-gate connecting overtopping, instability of the inside slope, piping and attack of the revetment on the outside slope. Finally, not all data requirements could be met in case of the Caldicot Levels flood defence system, it concerns mainly: statistical data and data requirements with respect to the statistical model of the hydraulic boundary conditions. Recommendations In the UK a lot of different defence types occur which are all associated with a different make-up of failure modes. The failure modes which are incorporated in PC-Ring are limited, see above. Therefore, if in the UK a computer program such as PC-Ring is set up it is recommended to research whether a tailor-made set up or a one-size-fits-all set up is desired. The tailor-made set up is based on implementing all possible failure modes in the program code, whereas the one-size-fits-all set up is based on flexibly entering the reliability functions, statistical data and the desired mathematical relations between the reliability functions. A number of typical systems can be set up default in the program, but are easier to adjust. With respect to the statistical hydraulic boundary conditions model it is recommended to research whether a method according to PC-Ring or JOINSEA provides the best results in the UK taking into account the quality and laboriousness of the model. With respect to other models it is recommended to choose models with an as wide application range as possible so that the results are comparable across different flood defence systems. vi

9 Moreover, it is recommended to research if the model which is applied in PC-Ring to the hydraulic boundary conditions can be applied to other numerical models. With respect to data gathering in relation to a method to determine the distribution of risk along across a flood plain, it is recommended to research whether an efficient time-saving method is desired to select the weak areas contributing most to the system s probability of failure. Finally, it is recommended to research what typical values of statistical data occur in general in the UK. vii

10 Table of contents Preface Summary i ii 1. Introduction 2. Problem analysis, project objective and working-method 2.1. Background leading to this project Definition of the problem Objective of this project Main working-method Boundary conditions 3.1. Location of the Caldicot Levels flood defence system Geometry of the flood defence system Geotechnical boundary conditions The structure of the soil Soil properties Groundwater Types of revetment types on the outside slope of the flood defence Hydraulic boundary conditions Local water levels: Severn Estuary Local water levels: The River Usk Local wave conditions Past events Dutch reliability methods for flood defences 4.1. PC-Ring The in PC-Ring incorporated failure modes Statistical models Available calculation methods in PC-Ring Data requirements in order to make the calculations The appropriate flood defence system s cross sections selection Detailed working-method Definition of the Caldicot Levels flood defence system and its components 5.1. The choice of the method to define the flood defence system s boundaries Short description and restrictions of available methods to define flood 5-2 defence system s boundaries Method to determine the Caldicot Levels flood defence system s 5-3 boundaries 5.2. Definition of the Caldicot Levels flood defence system s boundaries Components of the Caldicot Levels flood defence system Embankments without additional structures Embankments with wave return wall High grounds with masonry wall facing Raised grounds River banks along the Usk 5-13 viii

11 6. Analysis of the failure modes connected to the components 6.1. Failure modes connected to embankment without additional structure, 6-1 component Failure modes connected to component 1, present form Failure modes of the flood defence improvement of component Failure modes connected to embankment with wave return wall, 6-2 component Failure modes connected to component 2, present form Failure modes of the flood defence improvement of component Failure modes connected to high grounds with masonry wall facing, 6-11 component Failure modes connected to raised grounds along the Severn Estuary, 6-12 component Failure modes connected to component 4, present form Failure modes of the flood defence improvement of component Failure modes connected to raised grounds along the Usk, component Failure modes connected to river banks of the Usk Modelling the Caldicot Levels flood defence system and expressing this model into data 7.1. Available information to support the flood defence modelling process Division of the flood defence system in embankment stretches and 7-2 sections Division in embankment stretches Division in embankment sections Selection of the relevant embankment sections for each failure mode Section selection for overtopping Section selection for instability of the inside slope Section selection for uplifting and piping Section selection for attack of the revetment on the outside slope Gathering data about the relevant sections for the reliability calculations General data requirements Data requirements in connection to overtopping and the wave return wall Data requirements in connection to instability of the inside slope Data requirements in connection to attack of the revetment on the 7-20 outside slope 8. Annual probability of flooding of the Caldicot Levels flood defence system before and after improvements 8.1. Annual probability of flooding of the present Caldicot Levels flood defence 8-1 system Annual probability of flooding due to overtopping Annual probability of flooding due to instability of the inside slope Annual probability of flooding due to attack of the revetment on the 8-8 outside slope Total annual probability of flooding of the Caldicot Levels flood defence 8-11 system 8.2. Annual probability of flooding of the improved Caldicot Levels flood 8-12 defence system Annual probability of flooding due to overtopping, improved system 8-12 ix

12 Annual probability of flooding due to instability of the inside slope, 8-14 improved system Annual probability of flooding due to attack of the revetment on the 8-15 outside slope, improved system Total annual probability of flooding of the improved Caldicot Levels 8-15 flood defence system 9. Conclusions and recommendations 9.1. Conclusions Recommendations 9-2 x

13 1. Introduction In the UK a number of flooding events in the last decade has caused an increasing interest in riskbased safety approach of flood defences. A risk-based safety approach takes into account the strength and the loading conditions of the flood defence system as part of the probability of inundation as well as the consequences of inundation in case of failure of the flood defence system. One of the advantages of a risk-based analysis of flood defence systems is that it points out the system s weakest links and enables the decision-maker to target maintenance activities. Another advantage is that in case of large scale flood defence improvements the decision-maker can compare different design options in terms of the actual risk reduction and the costs which are associated with the improvement options. In the light of the shift to a risk-based safety approach in the UK a project called RASP, Risk Assessment of Strategic Planning, is carried out at among others HRWallingford. This project aims to develop tiered methodologies for risk assessment of flood defence systems. These tiered methodologies consist of a high level methodology supporting national policy making, an intermediate level methodology supporting regional policy making and a detailed level approach supporting policy making at the scale of one flood defence system. The objective of this Msc thesis is to apply a reliability analysis on the Caldicot Levels flood defence system in the UK using Dutch reliability methods for flood defences in order to support an evaluation of the appropriateness of these methods as part of the detailed level methodology in RASP. The Caldicot Levels flood defence system is located at the south coast of Wales in the UK. The system borders the Severn Estuary in the south, the river Usk in the west and a distinct line of hills in the north and east. In the Severn estuary one of the largest tidal ranges in the world occurs, a range that varies between 9 and 15 meter. The largest fetches and the most severe wind speeds are found in the south westerly wind directions. The River Usk is a small river, however the water levels can reach quite high values especially in case of high water levels at the Severn Estuary. The mean elevation of the Caldicot Levels is OD+5.5m which compares to mean tide high water levels of OD+4.8m and mean spring tide high water levels of OD+6.5m. The crest levels of the flood defence system vary between OD+8 and OD+10m. The embankments and soil underneath consist mainly of clay. The Dutch reliability methods for flood defences mainly consist of two parts. First software called PC-Ring which calculates the probability of failure of a flood defence system. Second a process that reduces the amount of work related to data gathering by selecting the cross sections that are most representative of the system s probability of failure. These selected cross sections are included in the calculations with PC-Ring. The first step in the reliability analysis is the definition of the system. This step points out the relevant defence length for the calculation of the probability of inundation and the area which suffers consequences in case the flood defence system fails. The second step is to define the system s components, or the defence types that occur in the flood defence system. Part of the second step is to determine the different failure modes which can cause failure of the components. The third step is to select for each failure mode the cross sections in the flood defence system that are regarded as the weakest compartments. These cross sections represent the flood defence system and contribute most to the total system s probability of failure. After this last step the flood defence system has been translated from reality into a model, the model has been expressed into data and the data can be used to calculate the probability of failure with PC-Ring. These results point out the weakest links in the system and which random variables contribute most to the variance of the total probability of failure. Apart from the

14 1. Introduction probability of failure of the present system, the probability of failure of the system with improvements is regarded. This points out how the probability of failure is reduced because of the improvement measures. Based on the results the evaluation can be made whether Dutch reliability methods for flood defence are appropriate to serve as a detailed level methodology in the riskbased assessment of flood defence systems in the UK. In chapter 2 the background leading to the initiative of this project, the definition of the problem and the objective of this study is given. This chapter closes with a description of the working method in main lines. Chapter 3 contains the boundary conditions of the reliability analysis of the Caldicot Levels flood defence system. Chapter 4 provides an overview of the Dutch reliability methods for flood defence systems. These methods are the tools which are used to perform the reliability analysis. From chapter 5 onward the steps of the actual reliability analysis are presented. In chapter 5 the boundaries of the Caldicot Levels flood defence system are defined together with the main components or defence types occurring in the system. In chapter 6 the processes leading to failure, or the failure modes are subject of analysis. In chapter 7 the cross sections are selected which contribute most to the system s total probability of flooding. This chapter also contains a description of the choices which have been made with respect to the data requirements in general and specifically connected to the separate failure modes. In chapter 8 the results of the calculations of the annual probabilities of failure due to the separate failure modes of the present Caldicot Levels flood defence system are presented. Additionally, the results of the calculations of the probability of failure of the Caldicot Levels flood defence system are addressed taking the application of a number of flood defence improvements into account. The latter results are compared to the results connected to the present flood defence system. Finally, in chapter 9, the conclusions and recommendations are given. 1-2

15 2. Problem analysis, project objective and approach In 2.1. the background leading to the initiative of this project is given. This leads to the definition of the problem which is presented in 2.2. The objective of this study is dealt with in 2.3. This chapter closes with a description of the working method and the structure of the report in Background leading to this project The subject of this project is a reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability methods for flood defences. First some background information about the situation in the UK is given. Second, the meaning of the term Dutch reliability methods for flood defences is explained. Background in the UK leading to this project In the past the design of flood defences in the UK was based on indicative standards of defence. These may be interpreted as tolerable risk levels roughly based on grounds such as reducing risks to people and the natural environment and to achieve best value for public money. The design according to indicative standards proceeded as follows 1 : 1. Establishing the appropriate standard for the defence (e.g. the 100 year river level), based on land use of the area protected, consistency and tradition. 2. Assessing the design load, such as the water level or wave height with the specified return period. 3. Designing (i.e. determining the primary physical characteristics such as crest level or revetment thickness) to withstand that load. 4. Incorporating safety factors, such as freeboard allowance, based on individual circumstances. More and more, the interest in risk-based design and maintenance of flood defences has grown in recent years in the UK. The main advantages of a risk-based safety approach are: It is based on the concept of risk and therefore considers all the aspects related to failure of a flood defence system: the strength and the loading conditions of the flood defence system as part of the probability of inundation as well as the consequences of inundation in case of failure of the flood defence system. It supports the process of decision-making with respect to maintenance of a flood defence system as a risk-based analysis of flood defence systems points out the system s weakest links and enables the decision-maker to target maintenance activities. In case of large scale flood defence improvements the decision-maker can compare different design options in terms of the actual risk reduction and the costs which are associated with the improvement option. To support a wide application of risk methodologies in flood defence an overarching risk-based framework is being developed that integrates decisions on different levels (e.g. national, largescale, strategy, scheme, etc) and across differing functions (local authorities, flood warning, operation and maintenance, etc..). The RASP (Risk Assessment of flood and coastal defence systems for Strategic Planning) project is carried out by, among others, HRWallingford, in the context of the above mentioned risk-based framework. See appendix 2-A for more detailed information about this project. The main objective of this project is: to develop and support the application of consistent good practice in assessing risks associated with flood and coastal defence systems, where protection for a particular area is provided by a system of defences rather than a single defence. By assessing the likely location (s), it will be possible to develop a tiered approach to identifying investment and management actions. An overview of this tiered approach is given in table 2.1. On the detailed

16 2. Problem analysis, project objective and approach level the RASP project is expected to deliver a methodology for the reliability analysis of the flood defence system. Table 2.1. Tiered risk assessment approach in RASP Level Decisions to inform Data sources Methodologies High National assessment of economic risk, risk to life or environmental risk Prioritisation of expenditure Defence type Condition grades Standard of Service Indicative flood plain maps Socio-economic data Land use mapping Intermediate Detailed Above plus: Flood defence strategy planning Regulation of development Prioritisation of maintenance Planning of flood warning Above plus: Scheme appraisal and optimisation Above plus: Defence crest level and other dimensions where available Joint probability load distributions Flood plain topography Detailed socio-economic data Above plus: All parameters required describing defence strength Synthetic time series of loading conditions Generic probabilities of defence failure based on condition assessment and crest freeboard Assumed dependency between defence sections Empirical methods to determine likely flood extent Probabilities of defence failure from reliability analysis Systems reliability analysis using joint loading conditions Modelling of limited number of inundation scenarios Simulation based reliability analysis of system Simulation modelling of inundation Dutch reliability methods for flood defences In The Netherlands a similar development with respect to risk-based design and maintenance of flood defence systems has taken place. Until recently the Dutch flood defences were expected to be able to withstand a water level with a certain frequency of exceedance. The accepted frequency of exceedance has been established for different areas. These standards of safety are mainly based on the consideration that everyone has equal rights to the same level of safety. In the last few years the emphasis in safety approaches with regard to flood defences has shifted from the frequency of exceedance approach to a risk-based approach. To support this risk-based approach, software called PC-Ring has been developed to calculate the probability of inundation of flood defence systems. These calculations are based on certain failure modes. These failure modes take both the strength of the flood defence and the local loading conditions into account. Besides the total probability of inundation the output of PC-Ring consists of the probabilities of failure of the included cross sections and the contributions of the uncertainties of random variables to the total uncertainty of reliability functions representing the failure modes. The knowledge of these probabilities provides the possibility to spot the weak elements in the flood defence system. Knowledge of the mentioned contributions indicates how the system can best be improved. In order to calculate a satisfactory probability of inundation, data sufficiently representative of the flood defence system must be entered in the software. These data are gathered after modelling the flood defence system. The PC-Ring software and the flood defence modelling methods are in this project referred to as the Dutch reliability methods for flood defences. See Appendix 2-B for more detailed information about the developments in the Dutch safety approach with regard to flood defence systems. 2-2

17 2. Problem analysis, project objective and approach 2.2. Definition of the problem The definition of the problem is: absence of a methodology to determine the reliability of flood defence systems on a detailed level in the RASP project in the UK Objective of this project The objective is to apply a reliability analysis on the Caldicot Levels flood defence system in the UK using Dutch reliability methods for flood defences in order to support an evaluation of the appropriateness of these methods as part of the detailed level methodology in RASP Main working-method Each step in the reliability analysis provides feedback on how appropriate the Dutch reliability methods for flood defences are as applied on the Caldicot Levels flood defence system. The set up of the reliability analysis of the Caldicot Levels flood defence system is given below. Risk is a function of the probabilities of undesired events and their consequences. A part of a risk analysis is the qualitative and quantitative analysis of the undesired events in a system. This part is also called a reliability analysis. In Appendix 2-C a description of the risk analysis, the position of the reliability analysis herein and some definitions with respect to the reliability analysis are presented. Table 2.2. Steps in the reliability analysis and in which chapter this step is discussed in relation to the Caldicot Levels flood defence system Reliability analysis Chapter System definition 5 Definition of components, or defence types 5 Analysis of failure modes and reliability functions 6 Modelling the flood defence system, selecting the appropriate 7 cross sections and gathering data Calculation of the probability of inundation 8 Conclusions and recommendations 9 The reliability analysis of the Caldicot Levels flood defence system eventually leads to a probability of inundation. In other words, the undesired event is partial or complete inundation of the Caldicot Levels area and the system is formed by the flood defences protecting the Caldicot Levels. The reliability analysis consists of the following main steps, see also table 2.2.: Definition of the Caldicot Levels flood defence system resulting in the boundaries of the flood defence system. The area within these boundaries suffers the consequences in case of failure of the flood defence system. Definition of the components of the system resulting in an overview of the defence types occurring in the Caldicot Levels flood defence system. Analysis of the relevant failure modes connected to each component or defence type. Analysis of the reliability function of each failure mode, comparison to the reliability functions which are included in PC-Ring. Modelling the Caldicot Levels flood defence system and expressing this model into data. In other words: the flood defence system must be expressed into a model in the form of cross sections, soil parameters, revetment properties, etc.. The cross sections which contribute most to the total probability of failure are selected and for these cross sections data are gathered in order to make the calculation with PC-Ring. 2-3

18 2. Problem analysis, project objective and approach Calculation of the probability of inundation of the Caldicot Levels flood defence system with PC-Ring. The probability of inundation of the current system points out which stretches of the flood defence system can be improved to significantly decrease the current system s probability of failure. Additionally, the probability of inundation is calculated for the flood defence improvements which are planned for the Caldicot Levels flood defence system. The current and improved system s probabilities of failures are compared. 1 HRWallingford, Risk, Performance and uncertainty in Flood and Coastal defence, Volume 1- A Review, Report SR 587, Wallingford

19 3. Boundary conditions Introduction As is mentioned in the Introduction, the actual flood defence system must be translated into a model, this model must be expressed into data and these data are used to perform calculations. This chapter contains the boundary conditions which form the context of the reliability analysis of the Caldicot Levels flood defence system. Set-up of chapter The following boundary conditions are discussed in this chapter: The location implies the elevation of the by the flood defence system protected area in relation to the water levels. Apart from that, the location determines the assets at risk. See 3.1. The geometry determines the shape of the flood defence system, a boundary condition which is indispensable to the calculation of the probability of failure of an arbitrary failure mode. See 3.2. The geotechnical boundary conditions determine the properties of the material the flood defence system is made of and the foundation of the flood defence system. See 3.3. The type of revetment can reduce the overtopping discharge and determines the resistance of the flood defence in relation to wave attack. See 3.4. The hydraulic boundary conditions are the driving force behind the loading side of all of the failure modes. These hydraulic boundary conditions are expressed in the local water level, the significant wave height and wave period. See 3.5. The occurrence of past events is a check point for the order of magnitude of the system s probability of inundation that results from the calculations. See Location of the Caldicot Levels flood defence system General The Caldicot Levels flood defence system is located between Newport and Caldicot at the south coast of Wales in the UK, see fig and 3.2. The flood defence system borders the Severn Estuary in the south, the River Usk in the west and a distinct line of hills in the north and east. In the Severn Estuary one of the largest tidal ranges in the world occurs. The tidal ranges in this estuary reach values Severn Estuary N Caldicot Levels Figure 3.1. Location of the Caldicot Levels and the Severn Estuary in the UK

20 3. Boundary conditions between on average 9 meter and at maximum 15 meter. The shallow banks across the upper estuary and the fact that this area is not directly exposed to Atlantic waves cause the wave heights and periods in the upper estuary to be significantly lower than on the open coast of the outer estuary. The River Usk is a small river which can pose a threat to parts of Newport. The Usk is a river with mean discharges of between 40 and 50 m 3 /s and a 100 year return period discharge of 910 m 3 /s. Newbridgeon-Usk Highway M4 A 10 km River Usk A N = Length of available cross sections along Severn Estuary = Length of available cross sections along River Usk Figure 3.2.: The location of the Caldicot Levels between Newport and Caldicot, south of the highway M4. Figure 3.3. Approximate elevation profile across the Caldicot Levels from South (left of the figure) to North (right of the figure), corresponding with A-A in fig Elevation profile The flood risk area is about 7000 ha wide and is typically OD +5.5 m. This level compares with a mean high water level of OD+4.8 m, a mean high water spring level of OD+6.5 m and a current 200-year return period still water level of OD m. The crest level of the flood defences along the southern border of the Caldicot Levels with the Severn Estuary varies between OD m to OD m. See fig for an approximate elevation profile across the Caldicot Levels from South to North. 3-2

21 3. Boundary conditions Under mean high water circumstances the water level in the estuary does not reach the outside toe of the embankment along large lengths of the flood defence system. The mean elevation of the Caldicot Levels, the area at risk, is higher than the mean high water level. If breach occurs, the water level is higher than the mean elevation less than half the time each month. Land use The majority of this flood risk area is currently in agricultural use. However, there has been significant industrial and infrastructure development in recent times (see Table 3.1.). These developments include: industrial and retail parks (including the Tesco distribution Centre at Magor); the towns of Caldicot, Magor and Undy; the agricultural villages of Nash, Goldcliff, Whitson and Redwick; the M4 motorway; London to South and West Wales railway plus key strategic electricity transmission lines including two or three main lines feeding south and east Wales. 1 Table 3.1: Capital Value Estimates for properties subject to blight in 2000 (from Chatterton, 2001) Land use Number Capital value ( ) Residential 303 detached houses 46,505, non detached 43 farm houses Agricultural buildings 43 farms 7,417,500 Retail 12 (20,273 m 2 ) 5,520,880 Vehicle services 15 (8,838 m 2 ) 2,594,930 Pubs/cafes 10 no. 2,500,000 Contractors etc.. 19 (7,921 m 2 ) 1,742,620 Storage/Wholesale 21 (19,387 m 2 ) 4,265,150 Offices 2 (1095 m 2 ) 240,900 Leisure services 3 (11,926 m 2 ) 3,697,060 Manufacturing 10 (8,157 m 2 ) 1,880,560 Llanwern Steelworks 1 no. 1 billion Tesco Dit. Centre,Magor 1 no. 2 billion 3.2. Geometry of the flood defence system The geometry of the flood defence system at the borders of the Caldicot Levels with the Severn Estuary and the River Usk is represented by a number of cross sections. The flood defences bordering the Severn Estuary consist of embankments. These embankments are described by 127 cross sections which are indicative of nature. The length of the flood defences is approximately 20 km. About every 150 to 250 meter one cross section is available. In fig the black line represents the length of the flood defence which is described by the above mentioned 127 cross sections. For the largest length of the embankments bordering the Severn Estuary, improvements are planned. For each of the 127 indicative cross sections describing the current flood defences along the estuary, the planned improvements are available. Most embankments are improved, either by raising the crest level and rear slope or the latter and an additional wave return wall. In some cases the current flood defence is not improved. The Caldicot Levels border the River Usk by quays, wharfs, ship docks or river banks. These borders reach elevations high enough to form a barrier between Newport and the river Usk. 3-3

22 3. Boundary conditions After reaching these elevations the land slopes slightly down to levels of about OD+6.8 m or more. An impression of the elevations of the river banks of the Usk are presented in fig From the mouth of the River Usk to the upstream located Newbridge-on-Usk 110 cross sections are available. This length is represented in fig 3.2. with the red line. Figure 3.4. Impression of elevations along the River Usk in Newport 3.3. Geotechnical boundary conditions The geotechnical boundary conditions are formed by the soil of the Caldicot Levels on which the flood defences are founded and the ground which the flood defences are made of. The soil consists of several different types of layers and these layers occur in certain thicknesses, this is discussed in In the properties of the different layers are presented. In information is given about the groundwater level The structure of the soil The structure of the soil consists of the types of soil layers that occur and the thickness of these layers. Types of soil layers In connection to the Caldicot Levels sea defence system improvements a survey of the available soil data has been done 2. According to this report the soil of the Caldicot Levels is roughly build up in the following way, from the crest of the embankment down: The layer formed by the embankment Upper cohesive formation: silty clay or clayey silt, occasionally small sand partings Peat layer, which can also occur in between two upper and lower cohesive layers. The peat layer sometimes does not occur at all. Lower cohesive formation: like the upper cohesive formation silty clay or clayey silt, however sandier, more sand partings and sand lenses. Sand layer below lower cohesive layer. This layer is not always present. Rockhead Thickness of soil layers Regarding the thickness of the soil layers two sources of information are available: A mean ratio of the soil layers that has been given in the report containing the survey of the available soil data from which the layer types are derived as mentioned above. This mean ratio is 1.6 :1: 2.6 = upper cohesive : peat : lower cohesive. A report containing information about bore holes 3 at a number of locations along the Caldicot Levels flood defences. The information on the bore holes varies: at some locations a 3-4

23 3. Boundary conditions complete list is given of the soil layer thicknesses from the flood defence level down to the rockhead layer. At other locations only the depth of the rockhead is known. Determining the structure of the soil at an arbitrary location Often at an arbitrary location along the flood defences the thickness of the layers have not been completely listed in the bore hole report, and/or near the desired location no bore hole is close by. In that case the following approach has been applied in this project to derive the structure of the soil: Look up the bore holes situated nearest to the desired location. Estimate a rockhead depth and a sand layer thickness based on the bore hole(s) that are as close as possible. Determine the thickness of the total soil layer between the sand layer and the soil surface. Based on the above mentioned mean ratio of 1.6:1:2.6 the thickness of the upper cohesive, peat and lower cohesive layers can be estimated by splitting up the total soil layer according to that ratio Soil properties The following soil properties are of importance in the context of this project: Drained angle of internal friction, φ' ( ) Drained cohesion, c (kpa) Unit weight of the dry soil, γ dry (kn/m 3 ) Two types of calculations are distinguished for which different values of the soil properties are required: Mstab: calculations of the stability factor according to Bishop in the two dimensional cross sectional plane with software called Mstab. Usually in The Netherlands for Mstab calculations the characteristic values of the soil properties are used. These characteristic values indicate in case of the parameters at the loading side the values that are exceeded with a probability of 5%, and at the strength side the values that are lower with a probability of 5%. MPROSTAB: Calculations of the probability of failure due to instability of the inside slope given a certain water level using software called MPROSTAB. To this end the mean values and standard deviations of the soil properties are required. Available information for Mstab calculations In this project characteristic values of the soil properties are not available. However, for some parameters ranges of highest and lowest values found in the soil tests and accompanying mean values are given. In case of the Mstab calculations for the strength parameters the lowest value of this range is taken, for the loading parameters the highest value of the range is taken Another problem is that not all of the required data are available. At some points the data have been completed with indicative data for certain soil types from literature 4. In table 3.2. the values of the soil properties are listed. The differences in drained cohesion of the upper and lower cohesive soil types are explained by the difference in the amount of sand present in the layers. Weak sandy clay has been chosen to represent the soil properties of the upper cohesive soil type. In case of the lower cohesive soil type, strong sandy clay has been chosen. 3-5

24 3. Boundary conditions Available information for MPROSTAB calculations If information is available for soil properties in case of MPROSTAB calculations the mean values are chosen. If the values are indicative from literature, the same values have been applied as in the Mstab calculations. In table 3.2. the applied values are listed. Table 3.2. Soil parameters as applied in the Mstab and the MPROSTAB calculations Soil layer φ' ( ) c' (kpa) γ dry (kn/m 3 ) Made ground/ Mstab 27 2* 20.2 embankment MPROSTAB 29 2* 18.9 Upper cohesive Mstab 25 10* 11 formation MRPOSTAB 29 10* 15.7 Peat layer Mstab 15* 5* 5.8 MPROSTAB 15* 5* 6.4 Lower cohesive Mstab 26 0* 12.4 formation MPROSTAB 29 0* 13.9 Sand layer both Mstab and MPROSTAB 30* 0* 17* * = indicative values from literature Groundwater No direct information is available on groundwater levels in the Caldicot Levels. However, the Caldicot Levels are supplied with a system of drainage canals, called reens. These canals drain superfluous water at the Severn Estuary. Water levels that are known to occur in this system have values of OD+5.5 m. This water level is regarded as relatively high, but is the best available information. The ground water level is assumed to be the same level as the water level in the reens, in other words OD+5.5m Types of revetment on the outside slope of the flood defence Three types of revetment of the outside slope of the flood defences occur in the Caldicot Levels flood defences: Placed stone revetment is present at two locations. In both situations the maintenance is in a moderate condition. Grass occurs along large stretches of the flood defences. The overall condition of the grass is good. Rock armour revetment is applied along large stretches of the flood defences. The overall condition of the rock armour is good. The sizes of the stones vary between 0.75 and 1.5 meter Hydraulic boundary conditions The loading side of the reliability function at each location along the flood defence system is determined by the local hydraulic boundary conditions, i.e. the local water levels and the local wave conditions (significant wave height and wave period). The loading of the Caldicot Levels flood defences is formed by two different hydraulic regimes: the Severn Estuary and the River Usk. The local water levels at both the Severn Estuary and the River Usk are determined by use of Mike11. This model uses the de Saint Venant equations to predict the propagation of a tidal wave into a network of rivers. The local water levels are a function of the following basic factors: Water levels occurring at the mouth of the estuary/river 3-6

25 3. Boundary conditions Discharge occurring upstream of the estuary/river at a point where the tidal fluctuations have no influence on the local water levels Geometry of the estuary/river Wind speed Wind direction In the end the results of these models are discussed The local wave conditions are determined by the use of Bretschneider s model 5. The significant wave height and the significant wave period are a function of the following factors: Wind speed Wind direction Fetch of the wind Water level along the fetch The above mentioned basic factors are discussed below, in case of: The Severn Estuary, see The River Usk, see The local wave conditions, see An overview of the Severn Estuary and the location of the River Usk can be found in fig River Usk Network line as entered in Mike11 Caldicot Levels Mouth of the estuary N (0,0) 150 km Figure 3.5. Location of the mouth of the estuary as applied in the Mike 11 model. Additionally, a part of the network and the location of cross sections as entered in MIKE11 for the lower and middle Severn Estuary Local water levels: Severn Estuary As is mentioned above the hydraulic regime at the Severn Estuary consists of the local water levels and the local wave conditions. The factors influencing the local water levels are discussed below. The factors influencing the local wave conditions are the subject of

26 3. Boundary conditions Water levels at the mouth of the Severn Estuary The basis of the water levels at the mouth of the estuary/river is as follows: Water level = astronomical tide + surge U F = the wind speed [m/s] = the fetch of the wind [m] Astronomical tide is the consequence of α = the angle of the wind speed with the the relative movements of the earth, the length direction of the shore [ ] moon and the sun. The predictions of the c = a coefficient which is calibrated astronomical tide are accurate because of according to the desired situation [-]. In the regularity of the earth and moon The Netherlands a value of 3.5*10-6 is movements. Consequentially, the applied astronomical contribution to the water d = the mean depth along the fetch [m] level is deterministic. g = the gravitational constant [m/s 2 ] Surge is the part of the actual occurring water level at a certain moment which is caused by the wind speed and barometric Figure 3.6. Expression for the calculation of surge effects. The latter factor can be neglected. The wind surge can be determined with the function 6 presented in fig From the expression in fig follows that a smaller depth means higher surges. Therefore, large surges can especially be found at shallow seas and lakes or rivers. The upper estuary, near the Caldicot Levels is shallow and large surges are known to occur there. s = Astronomical tide Astronomical tide levels at Milford Haven are presented in table 3.3. Milford Haven is located approximately at the mouth of the Severn Estuary, see fig Surge For two reasons the contribution of surge to the total water level at the mouth of the estuary is neglected: First of all, no direct information is available with regard to the surges at the mouth of the estuary. Second, including this contribution of the s F cos( α) gd = the surge [m] Table 3.3. Astronomical tide at Milford Haven (approximately mouth of Severn Estuary) Tide (in m OD) at Milford Haven neap Hw 1.49 neap Lw mean Hw 2.39 mean Lw spring Hw 3.29 spring Lw surge in the reliability analysis is in this project not relevant to the objective of supporting the evaluation the Dutch reliability methods for flood defences. Notes with respect to negligence of surge To form an impression of the order of magnitude of the surges the expression according to fig is used. For the variables approximate values are chosen. The fetch and the depth are derived as follows: From the 200 m depth line seaward, the depths increase steeply to values of 2000 m. The contribution to the surge from this point seaward is negligible. The maximum distance from the mouth of the Severn Estuary to the 200m depth line, or the fetch, is about 600 km, see fig. U c 2 3-8

27 3. Boundary conditions 3.7. The 50 meter depth line is located in the mouth of the estuary. At about ⅓ of the 600 km fetch length from the mouth of the estuary the 100 meter depth line is present 7. An estimate of the depth along the 600 km fetch length is ⅓*75+⅔*150 = 125 m. The values of the remaining variables, c, F and g of the expression in fig are given in fig The value of cos α is left out for the moment. Fig shows the values of the surge at varying wind speeds and three different depths. Two important wind speeds are marked in fig. 3.7.: U = 20 m/s and U = 30 m/s. Often the annual maximum wind speed at the Severn Estuary approximately takes the value of the first. The latter wind speed represents the largest annual maximum value that occurred in the past 29 years at the Severn Estuary. The following notes are made with respect to the above: Fig points out that in case of a mean depth of 125 meter, the value of the surge takes on values of between 0.6 and 1.5 meter for wind speeds varying between U is 20 and 30 m/s. For depths larger than 125 m, the applied expression to determine surges still implies significant surges. The 3.5*10-6 coefficient can be differently calibrated in the situation of the Severn Estuary. The surges are not calculated at a shore but at a North to South line at the mouth of the estuary. If the angle of for instance the western wind direction with the southern shore of the estuary is taken, which amounts to an angle of <45, the surges have to be corrected with a factor > This still results in significant surges. In case of wind speeds from the westerly directions, the shear of the wind with the water surface causes the water to be pushed into the funnel shaped estuary. Concluding: according to the in fig mentioned expression to determine values of the surge, the influence of surge on the total water level cannot be neglected. However, in the light of the objective of this project, the influence of surge on the total water level at the mouth of the estuary is neglected. Total water level As a result of the above mentioned reasons the water level at the mouth of the Severn Estuary is considered as a function of the astronomical tide only. Discharge occurring upstream of the Severn Estuary Below the influence of the discharge on the local water levels at the Severn Estuary is discussed. If the discharge would make a difference, it should be defined at a location upstream where the local water level is independent of the tidal variations at the mouth of the estuary. The Severn Estuary is the extension of the River Severn. Apart from the River Severn several other rivers are discharging at the estuary, among others the River Usk. However, these Surge [m] Figure 3.7. Surge as a function of U in case of d is 125, 150 or 175 Wind speed U [m/s] c = 3.5*10^-6 F = 600 km g = 10 m/s^2 d = 125 m d = 150 m d = 175 m 3-9

28 3. Boundary conditions discharges are assumed to have a negligible influence on the local water levels at the estuary compared to the discharges due to the tidal variations. The discharges due to tidal variations are expected to be high for two main reasons: the large tidal ranges occurring at the estuary; the large size of the estuary. The basis of the above mentioned assumption is supported by plans that have existed in the past to exploit the large tidal ranges in the context of hydropower. Geometry of the Severn Estuary Another important factor influencing the local water levels is the geometry of the estuary/river. This determines the size of the system. The geometry is defined by a number of cross sections at regular distances. Including a large number of cross sections in the Mike11 model is beneficial to the accuracy of the predictions of the local water levels. Below the following matters are discussed with respect to the geometry of the Severn Estuary: The location of the cross sections. The sources of information which have been used to estimate the dimensions of the cross sections. The resulting cross sections. The consequences of the applied geometry to the accuracy of the Mike11 model. Location of the cross sections The geometry of the Severn Estuary has been defined in the Mike11 model by 35 cross sections. The location of the first 27 cross sections are presented in fig Cross sections 28 to 35 are shown in fig The locations of the cross sections are chosen such that the shape A1 = at the mouth of the Usk, but is referred to as Newport A2 = Goldcliff A3 = Magor Pill A4 = Sudbrook Mean high water line 25 km Mean low water line Figure 3.8. Cross sections 28 to 35 defining the geometry of the upper Severn Estuary ( map from ABP Research 2000) 3-10

29 3. Boundary conditions of the estuary in the plane of the water surface is properly represented. The distance between the cross sections describing the lower and middle estuary is approximately five km. The distance between the cross sections describing the upper estuary is smaller than five km as the presence of shallow areas is more dominant. Sources of information The following sources of information have been used to derive the dimensions of the cross sections: A regular atlas provides insight of the size of the water surface, see fig.3.5. And the presence of islands. Atlas of the seas around the British Isles contains the following relevant information: The location of the OD-50 meter line in the mouth of the Severn Estuary, see fig This OD-50 m line curves along the shores of the mouth of the estuary and provides an impression of how the shores of the estuary slope down. The OD-50 m line is between 20 and 30 km from the shore. One location in the estuary with a depth of OD-34m enables an estimation of how the depth changes from the mouth up the estuary. Research has been done on the sediment layers at the bottom of the estuary 9 in the context of plans to build a barrage to generate hydro power. The used information narrows down to: Severn Estuary OD-50 m line Figure 3.9. Map showing the OD-50 m line in the mouth of the Severn Estuary. Additionally, the depth at a location in the estuary is included. A figure which presents the depth of the rockhead soil layer. This is combined with approximate thicknesses of sediment layers covering the rockhead soil layer. On the basis of this combination an estimate can be done of the depth of the bottom. A figure which shows the limit of the Lowest Astronomical tide in the middle part of the estuary, in the area of cross sections 25 to 27. This limit points out three locations of very shallow areas or islands. The map from ABP Research 8 in fig contains the mean high water and mean low water lines for the shallow upper estuary area. The report about bore holes 3 includes information to construct one bathymetry, located near Sudbrook (A4 in fig. 3.8.). This bathymetry provides an impression of the shape of the shore between the mean high water and mean low water lines. Combined with the at the previous bullet mentioned map in fig this supports estimates of the shores in the upper estuary. Cross sections and the used source of information Below for the cross sections the applied source of information is mentioned and an example is given of the result. The numbers of the cross sections can be found in fig and fig

30 3. Boundary conditions Cross sections 1 to 6: based on the OD-50 m line as presented in fig and the presence of the island Lundy from an atlas. See fig for cross section 5. Cross sections 7 to 11: cross section 11 is approximately located at the point of the OD-34m depth in fig The cross sections between 6 and 11 are of gradually decreasing depths. See fig for an example. Cross section 11 to 20: Cross section 20 falls in the scope of the figures taken from the barrage plans. The depths of the cross sections between 11 and 20 are assumed to change gradually from OD-34m to OD-30m. The latter value is estimated from the figures of the barrage plans. See fig for an example. Depth (m OD) North South [meter] SEVERN /1/ m [meter] Distance from the northern shore Figure Cross section 5, the island Lundy Depth (m OD) North South [meter] SEVERN /1/ m [meter] Distance from the northern shore Depth (m OD) [meter] North South SEVERN /1/ m [meter] Distance from the northern shore Figure Cross section 11 North South [meter] SEVERN /1/ Figure Cross section 19 North South [meter] SEVERN /1/ Depth (m OD) m [meter] [meter] Distance from the Distance from the northern shore northern shore Depth (m OD) m Figure Cross section 27, Cardiff Figure Cross section 32, Magor Pill Cross sections 21 to 27: all these cross sections are in the scope of the figures from the barrage plans. The shallow areas that are indicated in the figures caused by sediment layers or by islands have been taken in account. See fig for an example. 3-12

31 3. Boundary conditions Cross sections 28 to 35: the shape of the cross sections have mainly been determined by the mean high water and mean low water lines as indicated in fig Assumptions of the depths have roughly been based on the bathymetry that is available near location A4 in fig See fig for an example. Accuracy of the model of the estuary A number of 35 cross sections does not provide an accurate description of the estuary. However, in the context of this project this number is sufficient for the following two reasons: The emphasis is on how this type of model can be used in a reliability analysis of a flood defence system. It is therefore sufficient to get an impression of how the local water levels change as a function of different tidal boundary conditions and wind field. The amount of information with respect to the geometry of the estuary is limited. It makes no sense to include a large amount of cross sections at locations where hardly any information is available. Wind speed As is mentioned above in relation to the total water level the wind speed causes an additional surge on top of the astronomical tide at the shallow estuary. The magnitude of the wind speed therefore has an important influence on the local water levels. To give an impression of the magnitude of the wind speeds, a list is given of the annual maxima that have occurred in the past 29 years in table 3.4. (ABP Research, 2000) Table 3.4. Annual maxima of wind speeds at the Severn Estuary for the past 29 years Annual maxima Wind speed (m/s) Wind direction See fig for an impression of the relative frequencies of the wind directions divided in 30 degree sectors. Surge is a function of the wind direction for two reasons. First, the magnitude of the wind speeds is dependent of the wind direction: this is supported by the fact that all but two of the above mentioned 29 annual maxima have Figure Relative frequencies of the wind directions for 30 degree sectors 3-13

32 3. Boundary conditions occurred in the southwesterly wind directions. Second, the occurrence of surge depends on the angle of the wind speed with respect to the geometry of the estuary. For example, off-shore wind speeds cause negative surges. Conversely, on-shore winds cause positive surges with magnitudes as a function of among others the angle of the wind with the shore and the depth of the estuary along the fetch. The dependency between the wind speeds and wind directions is taken into account by using statistical wind speed distributions given a number of different wind directions. The effect of the geometry is included in the simulation of the local water levels by entering a wind field consisting of wind speeds and wind directions into the Mike11 model. Discussion of the Mike11 model of the local water levels at the Severn Estuary First the results of the Mike11 are presented. Second, the limitations of these results are discussed. Presentation of the results Three types of results are addressed: First in table 3.5. below the results of the predictions of local water levels by use of Mike11 are listed and compared with local tidal water levels from the Admiralty tide tables. The model under predicts the high water levels of the spring tide. Based on this information the model is expected to under predict in case of extreme events. However, the available information is not enough to confirm this expectation. Table 3.5. Predictions of local water levels from Mike11 compared with the information from the Admiralty tide tables. Root mean square values for the different high water and low water events. Milford Haven (mouth of estuary) Cardiff tide table Mike11 prediction Newport tide table Mike11 prediction Avonmouth tide table Mike11 prediction neap Hw neap Lw mean Hw mean Lw spring Hw spring Lw RMS Hw neap RMS Lw neap RMS Hw mean RMS Lw mean RMS Hw spring RMS Lw spring total total

33 3. Boundary conditions Second: to provide an impression of the influence of the wind speed in terms of surge, table 3.6. is included. According to this table the largest wind speed annual maximum of 30 m/s causes a surge of 1.2 meter at Cardiff. This is compared to the 1.4 meter event that is known to have occurred at Cardiff. However, it is unknown during what circumstances the latter value has occurred. Table 3.6. The effect of wind speed on the local water level at Newport according to the Mike11 model Wind speed (m/s) Wind direction (degrees from the north) Astronomical tide at the mouth of the estuary (m OD) Mike 11 output of local water level at Cardiff (m OD) Third: in fig the variation in time of the local water levels is given in case of mean spring tide together with the astronomical tide at the mouth of the Severn Estuary according to Mike11. This gives an impression of the differences in water levels and phase differences between the locations according to the model in Mike11. There is no information available to compare the results of the phase differences. Water level (m OD) [meter] Time Series Water Level (SPRING V IS 0.res11) Water Level Milford Haven Cardiff Newport Goldcliff Magor Pill Sudbrook 00:00: :00:00 06:00:00 09:00:00 12:00:00 15:00:00 18:00:00 21:00:00 00:00: :00:00 06:00:00 09:00:00 12:00:00 Time (hours) Figure Time series of mean spring tide at respectively Milford Haven (=Severn 0.00), Cardiff, Newport, Goldcliff, Magor Pill and Sudbrook 3-15

34 3. Boundary conditions Limitations of the results With respect to the model and the results a number of remarks are made: In relation to the cross sections: The shape of the cross sections is based on little information. This implies a certain freedom to vary the shape of the cross sections in order to get closer predictions of the available actual tides at Cardiff, Newport and the port of Bristol. It is unclear how reliable the model predicts for extreme events. The same comment applies to the roughness of the cross sections. The roughness factor of Chézy is used, and the roughness factor values are taken between 25 and 30 m 0.5 /s these are not uncommon values. Then again, arbitrary roughness values are applied to the cross sections to get a closer prediction of the actual tidal events. More detailed information on the bathymetry of the estuary should be retrieved if the predictions of the local water levels are in the light of a different objective than in case of this project. In relation to the results: The phase differences between Milford Haven and the locations along the Caldicot Levels have not been checked against actual occurring values. The peak shaped tides in fig are caused by the tidal boundary condition at Milford Haven which has been implemented with time steps of 15 minutes between defined water levels. For more detailed results, the tidal boundary condition should be entered with smaller time steps. The root mean square differences in table 3.5. are solely meant to indicate the order of magnitude of the differences between the actual tides and the predictions. The root mean square values are not presented to indicate the quality of the model. To indicate the quality of the model, the predictions should be tested against a larger amount of tide events and the root mean squares should be regarded with respect to each location. In general: A disadvantage of the Mike11 model is that for the cross sections the water level is constant over the whole length. Implicitly the assumption is made that the lines with the same tide levels are directed from south to north in the estuary. However, in the Atlas of the seas around the British Isles a map indicates that these lines with equal tidal levels are shifted in the direction of south west to north east. Concluding The Mike11 model is sufficiently suitable to be used in the light of the objective of this project: The model provides results which are in the order of magnitude of the actual occurring water levels. The model includes the required basic factors that influence the total water level at the estuary: the wind speed, wind direction and the geometry of the estuary. However, the main limitations of the Mike11 model of the Severn Estuary are: An insufficient amount of information to base the model on. Hardly any information to validate the results of the model and to form an impression of the quality of the results. 3-16

35 3. Boundary conditions Local water levels: The River Usk The hydraulic boundary conditions of the River Usk are discussed below. This is done in a similar manner as the hydraulic boundary conditions of the Severn Estuary. In fig an overview of the Usk is given. Environment Agency has supplied the complete Mike11 model of the Usk: the geometry, four different discharge boundary conditions, simulation files and the results of the simulations based on these four different peak discharges. The factors influencing the local water levels are discussed below. The factors influencing the local wave conditions are the subject of Water levels at the mouth of the River Usk The mouth of the River Usk is located in the upper Severn Estuary. Therefore the water levels at the mouth of the River Usk are a function of the same basic factors as the local water levels in the Severn Estuary. N 1 km Contours of Newport St. Julian s Glebelands recreation grounds in Newport George Street bridge Mouth of the River Usk Newbridge-on Usk Figure The River Usk with the boundaries of the Mike11 model: mouth of the Usk and Newbridge-on-Usk upstream. Astronomical tide The mouth of the River Usk is located south of Newport. The astronomical tide at the mouth of the Usk is given in table 3.7. The values of the astronomical tide at the mouth of the Usk are a function of: Astronomical tide at the mouth of the Severn Estuary. Geometry of the Severn Estuary amplifies the tidal wave that propagates upstream into the estuary. Table 3.7. Astronomical tide at the mouth of the River Usk in m OD Uskmouth neap, mean Hw 2.99 neap, mean Lw mean Hw 4.64 mean Lw spring, mean Hw 6.29 spring, mean Lw

36 3. Boundary conditions Surge The contribution of surge to the water levels at the mouth of the River Usk is determined by the wind field at the Severn Estuary. The occurrence of wind over the shallow Severn Estuary can cause significant surges. A maximum surge of 1.4 m is known to have occurred near Cardiff. Total water level The total water level, astronomical tide and surge, occurring at the mouth of the River Usk is determined with the Mike11 model of the Severn Estuary. In the latter model the astronomical tide at the mouth of the estuary and the wind field (wind speed and direction) are entered. The simulation of the local water levels in the Severn Estuary points out the water level that occurs at the mouth of the Usk. These results are entered as the tidal boundary condition at the mouth of the river in the Mike11 model of the River Usk. Discharge occurring upstream of the River Usk Below the influence of the discharge on the local water levels at the River Usk is discussed. In case that the discharge makes a difference, it should be defined at a location upstream where the local water level is independent of the tidal variations at the mouth. At Newbridge-on-Usk (see fig ) located upstream at the River Usk the local water levels are not influenced by the tidal variations at the mouth of the river. In table 3.8. an impression of peak discharges is given that can occur at the Usk during a period of high water. Table 3.8. Peak discharges occurring at the River Usk with a ten year, twenty year, fifty year and hundred year return period Q m 3 /s Q m 3 /s Q m 3 /s Q m 3 /s The Mike11 model of the Usk has been supplied by the Environment Agency. Apart from the Usk a number of branches that mouth at the Usk are included in the model: some branches of the drainage system and a small river, the Llwyd, with discharges about 6 times smaller than the Usk. See fig Discharge in m3/s Time in hours Usk SorBrook Cryndau Pill Spytty Pill Llwyd Figure Behaviour of the discharge in time of the Usk and four branches mouthing at the Usk 3-18

37 3. Boundary conditions Geometry of the River Usk The geometry of the River Usk is available in the Mike11 model that has been supplied by the Environment Agency. This is contrary to the Mike11 model of the Severn Estuary which has been set up completely in this project. 110 cross sections describe the geometry of the River Usk. The cross sections that are part of the supplied model of the Usk are very detailed. An example is given in fig The cross section in this figure consists of 36 different points. All elevations with respect to 0 m OD Figure Example of a cross section of the River Usk located near George Street Bridge Wind speed The wind speed influences the magnitude of the surge at the mouth of the Usk. Apart from that the wind can cause local surges at the River Usk. The wind field over the River Usk is equal to the wind field over the Severn Estuary. For an indication of the magnitude of the occurring wind speeds see table 3.4. which shows the annual maxima for the last 29 years. Wind direction The wind direction of the wind influences the occurring surge at the mouth of the Usk and the local surges at the river. This influence depends on the magnitude of the wind speeds given the wind direction and the geometry of the river. The wind field over the Severn Estuary is equal to the wind field over the Severn Estuary. For an indication of the relative frequencies of the wind directions at the Severn Estuary see fig Discussion of the Mike11 model of the local water levels at the River Usk First an example of the results is presented. Second the limitations of the model are given. Presentation of the results In fig.3.20 the variation in time of the local water levels at a number of locations along the Usk are given. The downstream boundary condition, the water level at the mouth of the Usk is shown in the same figure. The upstream boundary condition, the discharge at Newbridgeon-Usk is presented in fig The variation in time of the water level at Newbridge-on-Usk can be recognised in the variation in time of the discharge at Newbridge-on-Usk. The shape of the variation of the discharge in time can also be recognised in the variations of the water levels at locations in between the mouth of the Usk and Newbridge-on-Usk. 3-19

38 3. Boundary conditions [meter] 11.0 Time Series Water Level (Q4 V10 R270 MEAN.res11) Water level (m OD) Water level at Newbridgeon-Usk Water level at St. Julian s Glebelands recreation grounds in Newport :00: :00:00 12:00:00 18:00:00 00:00: :00:00 12:00:00 18:00:00 00:00: Time (hours) 06:00:00 12:00:00 18:00:00 Figure Result of the Mike11 model of the River Usk for neap tide and Q10 Water level at mouth of Usk Discharge (m 3 /s) Usk Sor Brook Cryndau Pill Spytty Pill Llwyd 0:00 5:00 10:00 15:00 20:00 1:00 6:00 11:00 16:00 21:00 2:00 7:00 12:00 17:00 Time (hours) Figure The discharge at Newbridge-on-Usk (or Usk) and the other branches mouthing at the Usk Limitations of the Mike11 model of the Usk During the use of the above outlined Mike11 model of the Usk, a number of problems are encountered: Simulations have been made based on the original supplied Mike11 model of the Usk. Problem: The results of these simulations are different from the results that have been supplied together with the model. Possible explanation: the choice of the numerical time step. However, variation of this time step does not solve the problem. 3-20

39 3. Boundary conditions From the supplied result files the variations in time of the water surface along a certain length of the Usk have been regarded. Problem: At one or two locations abrupt changes in water levels occur. Possible explanation: a straightforward explanation for these sudden changes is not at hands. One explanation might be that the peak discharge at the branches is responsible. On the other hand the discharges at the branches vary gradually in time. The numerical time step does not seem to be the likely cause. Other simulations have been based on different discharge and tidal boundary conditions from those that have been supplied. Problem: During these simulations problems occur with the results: the simulation does not finish the calculation during the total entered period of simulation or very high, unlikely water levels appear. Possible explanation: These problems can definitively be attributed to the choice of the numerical time step. However, decreasing the time step increases the time that the simulation takes. No time is available for this solution in the light of the total number of simulations that has to be done in this project. Examples of the results in case of the third type of problems can be found in Appendix 3-D. Concluding Irrespective of the problems with the results, the Mike11 model is sufficiently suitable to be used in the light of the objective of this project: Detailed geometry is available. The model includes the required basic factors that influence the total water level at the River Usk: the wind speed, wind direction and the detailed geometry of the river. The main limitations are: In relation to the model: the inability to generate the same results as those that have been supplied with the same model and the inexplicable abrupt water level differences at one or two locations. The problems with the numerical time step in case of the in the light of this project required discharge and tidal boundary conditions. Especially the second mentioned limitation has considerable consequences for the results. This problem with the numerical step can result in very high or low water levels. These numerical problems cannot be solved within the time scope of this project, they cannot be neglected either. Solution The numerical problems with the simulations with neap tide as the tidal boundary condition are relatively small. Regarding one location: in case of neap tide the difference between the local water levels at the relevant upstream location and the water level at the mouth is taken. Next, for a different tidal boundary condition the difference between the local water level at the upstream location and at the mouth is assumed to be equal to the difference in water level during neap tide. The same approach is applied for each desired location. 3-21

40 3. Boundary conditions Local wave conditions The local wave conditions consist of: The significant wave height The significant wave period From an analysis of the wave climate at the Severn Estuary, carried out by ABP Research 8, the following can be concluded: long-period swell waves from the Bristol Channel, the contribution of wave diffraction is negligible and the wave climate is dominated by the locally generated wind waves. This supports the choice of Bretschneider s model which predicts significant wave heights and wave periods of wind generated short waves at shallow areas. Hs (m) Ts (s) Wind speed (m/s) Depth = 12m Fetch = 50km Depth = 4 m Fetch = 8km Depth = 12m Fetch = 50km Depth = 4 m Fetch = 8km The factors at the basis of the local wave conditions according to Bretschneider s model are discussed below. These factors point out that the south-westerly wind directions are related to the severest wave loading conditions. Examples of the local wave conditions according to this model are given in fig Wind speed (m/s) Figure The significant wave height Hs (top) and the significant wave period (bottom) as a function of the wind speed. Impression of conditions in two wind directions: South-western: Mean depth= 12m; Fetch= 50km South-eastern: Mean depth= 4m; Fetch= 8km Wind speed and wind direction Higher wind speeds cause larger wave heights and wave periods. As is mentioned above in the context of the local water levels at the Severn Estuary and the River Usk the relative high wind speeds are related to the south-westerly wind directions. Off-shore wind speeds of course cause off-shores directed waves and the flood defence does not experience loading by these off-shore waves. For an impression of the magnitude of the wind speeds and the relative frequencies of the wind directions see respectively table 3.4. and fig Fetch of the wind The larger the fetch of the wind, the larger the significant wave heights and the loading of the sea defences. As can be seen from fig the large fetches are related to the south-westerly wind directions. 3-22

41 3. Boundary conditions Water level along the fetch Deep seas cause higher wave heights and wave periods. In fig.3.8. the location of the shallow areas south of the Caldicot Levels flood defence system can be seen. In the south-westerly directions of the large fetches the sea is less shallow. Bretschneider in perspective In fig significant wave heights and mean wave periods according to measurements between 1978 and 1980 are presented. The values of fig are in the same order of magnitude as the values in fig For instance a H s of 1.5 m in fig in case of depth = 12m; fetch = 50km gives T s is 4.5 s. This compares to a H s of 1.5 m in fig which has been simultaneously measured with mean values of the wave period between 3.3 s and 5.3 s. (the mean wave periods are lower compared to the significant wave periods which represent the mean value of the highest one third of the wave periods). H s = 1.5m Concluding, Bretschneider s model provides sufficient predictions of the local wave conditions at the Severn Estuary to support the objective of this project. If more accurate Figure3.23. Significant wave height (indicated as H 3 ) and the mean wave period at the Severn Estuary south of Cardiff according to measurements during two years (from Severn Barrage, 1981). predictions are desired, it is recommended to make predictions of local wave conditions with models such as HISWA or SWAN Past events Knowledge of past events is used to shed some light on the results of the calculation of the flood defence system s probability of failure. The following events are known to have occurred in the years between 1990 and : 26 February 1990: Blowhole at the crest, erosion and substantial overtopping discharges at the flood defences just west of Goldcliff (A2) in fig December 1999: Damage to the front face of the embankment at the flood defences in the middle between Magor Pill (A3) and Sudbrook (A4) in fig Initiation of damage of the flood defence revetment of the outside slope just west of Goldcliff in fig

42 3. Boundary conditions 1 Chatterton, J.B., Caldicot Sea Defence Strategy Plan: Benefit Assessment, JCA, January WS Atkins, Caldicot Levels sea defence improvements, Ground investigation, interpretative report and wave return wall condition survey, Swansea WS Atkins, Gwent Levels foreshore management plan, Geological database, Swansea Tol, van A.F., Oostveen, J.P., CUR 162, Constructing with ground. Structures made of ground on and in soil with little bearing capacity and strong compressible subsoil (in Dutch), Delft Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PC-Ring, part A: description of the failure modes (in Dutch), Delft TAW, Guidelines for the design of river dikes, part2-lower river area (in Dutch), Delft Directorate of Fisheries research,maff (DEFRA), Atlas of the Seas around the British Isles, London ABP Research, Gwent Levels hydraulic study, Objective A: Joint probability surge and tide wave analysis, Southampton Institution of Civil Engineers, Severn Barrage, Proceedings of a symposium organised by the Institution of Civil Engineers, held in London on 8-9 October 1981, London WS Atkins, Caldicot Levels sea defence improvements, Design parameters report, Swansea

43 4. Dutch reliability methods for flood defences Introduction As is mentioned in the Introduction, the actual flood defence system has to be translated into a model, this model has to be expressed into data and these data are used to perform calculations. This chapter serves to provide an impression of the tools that are available to support this process of modelling the flood defence system and making the calculations of the system s probability of failure. Set-up of this chapter The main tools are: PC-Ring: software that calculates the system s probability of failure, this is the subject of 4.1. An approach to select the appropriate cross sections of the flood defence system that contribute most to the total probability of failure. This approach limits the amount of work: instead of modelling the complete flood defence system and gathering data for the total length of flood defence, a limited amount of cross sections is selected. This approach is presented in 4.2. At the end of the chapter, in 4.3., the information about these tools is incorporated in a more detailed working-method than the rough working-method which is presented in chapter PC-Ring The following subjects are regarded: The in PC-Ring incorporated failure modes, this is discussed in The statistical models of the random variables that are part of the reliability functions, this is subject of The calculation methods to come to a system s probability of failure, this is presented in Impression of the data requirements in order to make the reliability calculations with PC- Ring, this is addressed in The in PC-Ring incorporated failure modes First of all a division is made between structural and non-structural failure of the flood defence system: Structural failure is: inundation of the by the flood defence system protected area after a flood defence has breached. Non-structural failure is: inundation of the by the flood defence system protected area as a consequence of large overtopping discharges without breaching of a flood defence. PC-Ring only includes failure modes concerned with structural failure. As this project among others serves to apply PC-Ring, non-structural failure is not part of the analysis. The following failure modes of embankments are included in PC-Ring: Overtopping/running over. Instability of the inside slope. Piping. Damage of the revetment on the outside slope and consequently erosion of the embankment body. The fault tree of these failure modes related to an embankment is given in fig. 4.1.

44 4.Dutch reliability methods for flood defences Failure of embankment Non-structural failure not included in PC-Ring Structural failure Non-structural failure Overtopping/ flowing over Instability of inside slope Heave/piping Damage of revetment and erosion of the dike body Overtopping Running over Piping Erosion of the dike body Erosion inside slope Saturation Erosion inside slope Instability of the inside slope Saturation Uplifting Instability of the inside slope Damage of revetment on outside slope Saturation with water of pores in clay of inside slope Saturation with water of pores in clay of inside slope = OR gate = AND gate = INHIBIT gate. The event at the right hand side of the gate can only occur if the basic event below the gate has taken place Figure 4.1. Failure modes of the embankment as applied in PC-Ring Overtopping/running over Water discharges passing the crest of the embankment either due to overtopping or running over are the cause of loading of the inside slope. Water discharges due to running over are in PC-Ring only assumed to be relevant in case of off-shore wind or wave heights smaller than 1 mm. In the other situations the water discharges are assumed to occur due to wave overtopping 1. Failure of the inside slope due to the loading by the overtopping/running over discharges can occur in two ways: Erosion of the inside slope. Saturation of the pores in the clay and consequently instability of the inside slope. These failure modes are discussed below. 4-2

45 4.Dutch reliability methods for flood defences Erosion of the inside slope Water discharges due to overtopping or running over respectively hit or scour the inside slope of the embankment. Due to this loading of the inside slope the grass gets damaged. After the grass has been damaged, the embankment body is exposed to the overtopping/running over water. In the end, if this erosion process continues long enough, the embankment breaches. The duration of this erosion process depends on the duration of the storm. In case of discharges due to overtopping the reliability function is: Z = m qc q c - m qo q o / P t In which q c is the critical discharge expressing the limit discharge for which almost damage of the grass occurs, q o is the actual occurring overtopping discharge due to the hydraulic boundary conditions in combination with the geometry of the embankment, m qc is the model uncertainty with respect to the critical discharge q c, m qo is the model uncertainty with respect to the actual discharge and P t is the percentage of time that overtopping occurs, this variable is applied to take the pulsating character of overtopping in account. The critical discharge q c can be determined in two ways: either a model based on the strength of the grass or the desired limit discharge can be entered manually. For the model of q c or reasonable manual threshold values see Appendix 4-A. The actual overtopping discharge q o is calculated with the overtopping equations according to Van der Meer, revised version 1. In case of discharges due to running over the reliability function is: Z = h d + Δh h c In which h d is the crest level of the embankment, Δh c expresses the critical height for which almost damage of the grass occurs and h is the actual occurring water level. The critical height Δh c is derived from the critical overtopping discharge q c, see Appendix 4-A. The latter is represented by the model based on the grass strength as is applied in case of failure due to overtopping. The actual occurring water level h is available from the hydraulic boundary conditions. Saturation Water from the overtopping or running over discharges infiltrates the pores of the clay soil of the crest and inside slope of the embankment. Increasing water pressures in the pores of the clay cause decreasing effective stresses and therefore, a decreasing shear strength. If the pores of the clay are completely saturated with water from the overtopping or running over discharges the shear strength is at its lowest and the inside slope is most susceptible to instability. This description points out that failure consists of two events: the process of saturation of the pores in the clay and instability of the inside slope due to low shear strength. The reliability function describing the process of saturation of the pores in the upper clay layer is: 4-3

46 4.Dutch reliability methods for flood defences Z I = q cv m qo q o In which q cv is the critical discharge for which within a few hours during a storm complete saturation of the upper layer of the inside slope occurs. The value of this q cv depends on whether the water discharge is caused by running over or wave overtopping, see Appendix 4-A. A water discharge due to running over infiltrates the upper layer more progressively than due to wave overtopping. The extent of infiltration of the latter depends on the wave height. q o is the actual overtopping discharge according to Van der Meer revised. m qo is the model uncertainty with respect to the actual discharge. The reliability function describing the process of instability of the inside slope due to the low shear strength caused by the high water pressures is: Z II = tan( αc) tan( αi ) In which tan (α c ) expresses the strength of the with water saturated clay layer at the inside slope, if this value is lower than the actual slope then instability of the inside slope occurs. Instability of the inside slope First, below a general description is given of how the stability of an embankment slope can be modelled. Second, the failure mode instability of the inside slope is presented. Background information: stability according to Bishop Instability of an embankment slope occurs if part of the embankment slides away along a slip plane. According to Bishop s approach this slip plane is circular and the stability is expressed in the form of a stability factor. To determine this stability factor the embankment is divided into vertical slices. The stability factor consists of a ratio between two moments that are taken with respect to the centre of this slip circle: The first moment is formed by the weight of the slices and the arm of this weight with respect to the centre of the slip circle. This moment represents the loading side of the ratio. The second moment is formed by the shear force along the slip plane of each slice and the arm of this shear force with respect to the centre of the circle. This moment represents the resisting part of the ratio. Embankment M = centre of slip circle Slip circle Figure 4.2. Slip circle model according to Bishop (From CUR162, 1999) A lower stability factor implies a lower stability. The embankment slope is considered to be instable if the stability factor reaches a value smaller than 1. The slip circle approach according to Bishop is shown in fig

47 4.Dutch reliability methods for flood defences Failure mode: instability of the inside slope If the water level outside the embankment increases, the water heads in the embankment body increase as well. These increasing water heads in the embankment body influence the ratio between the shear strength, the water pressures and the weight of the embankment. Eventually, the ratios are influenced to such an extent that part of the embankment becomes instable and slides away. According to Bishop s model this is defined as the situation in which the stability factor drops below a value of 1. Software called MPROSTAB is available to calculate the probability of failure due to instability of the inside slope given a certain outside water level. The following reliability function is applied: Z = Γ - q In which Γ is the stability factor according to Bishop and q is the threshold value of the stability factor for which instability occurs. Theoretically speaking, this threshold value q is equal to 1. MPROSTAB takes the Figure 4.3. The Bishop method in the three dimensional spatial correlations plane between soil properties into account and becomes a three dimensional approach instead of a two-dimensional approach, see fig MPROSTAB is used to calculate the probability of failure due to instability given a water level in three different situations: for instance an average water level, an extreme water level with a return period of 1 in 1000 years and the latter extreme water level minus one meter. In PC-Ring the output of MPROSTAB is used to calculate the total probability of failure due to instability of the inside slope. To this end, the reliability indices and the alfa values are used in the following reliability function in PC-Ring: n MPROSTAB Z = β ( h) + α ( h) i= 1 i u i In which β(h) is the reliability index given the water level resulting from the MPROSTAB calculations, α i (h) are the influence coefficients given this water level and u i are variables with a standard normal distribution. Piping First uplifting causes openings in the impervious clay layer covering the sand layer. Second, a flow of water through these openings initialises an erosion process. This process can progress from the point of the openings caused by the previous uplifting behind the embankment towards the water outside. The erosion process takes the form of pipes undermining the foundation of the embankment. These pipes can eventually cause failure. 4-5

48 4.Dutch reliability methods for flood defences Uplifting Uplifting occurs if the difference between the local water level h, and the water level inside, h b is larger than the critical water level h c, see fig This is expressed in the reliability function as: h Clay Klei h b d Z = m o h c m h ( h h b ) In which m o takes the model uncertainty of the model which determines h c in account and m h the level of damping. The critical water level expresses the limit water level for which almost uplifting occurs. This water level is based on the properties of the impervious layer. Piping The embankment fails as a consequence of piping if the difference between the local water level h and the inside water level h b, reduced with a part of the vertical seepage length d, exceeds the critical water level h p. L Sand Zand Clay Klei Figure 4.4. Parameters for uplifting/piping (from Vrouwenvelder et al., 2001) D Z = m p h p h 0.3d h ) ( b In which m p is the model uncertainty of the model with which h p is described. The critical water level h p is described by Sellmeijer s model of piping, see Appendix 4-B. Damage of revetment on the outside slope and erosion of the embankment body The types of revetments that are relevant to this project are discussed below: Grass. Placed stone revetment directly on clay. Partially penetrated riprap revetment. Grass The waves load the outside slope of the embankment. If the grass gets damaged the body of the embankment is fully exposed to the loading by the waves and starts to erode. The body of the embankment consists of two parts: the clay cover layer and the embankment core. If both components are eroded, the embankment breaches. This failure mode is represented by the following reliability function: Z = trt + trk + trb ts In which t RT is the time that a storm takes to damage the grass, t RK is the time that a storm takes to erode the clay cover layer and t RB is the time that a storm takes to erode the rest of the embankment body. For the models of these three components see Appendix 4-C. t s is the duration of the storm. Placed stone revetment directly on clay The waves load the revetment on the outside slope of the embankment. If the placed stones are damaged the body of the embankment is fully exposed to the loading by the waves and 4-6

49 4.Dutch reliability methods for flood defences starts to erode. If the body of the embankment is eroded, breach occurs. The failure mode damage of the placed stone revetment is represented by the reliability function: Z = c k Δ D - r H s In which c k is a coefficient for the strength of the placed stones, Δ the relative density and D the thickness of the placed stones. Apart from this, the reduction factor r and the significant wave height H s are part of the reliability function. Erosion of the embankment is represented by the following reliability function: Z = t RK + t RB - t s In which t RK is the time that a storm takes to erode the clay cover layer and t RB is the time that a storm takes to erode the rest of the embankment body. t s is the duration of the storm. The models that are used to determine these values are equal to those applied in the failure mode of revetment type grass. Partially penetrated riprap revetment Partially penetrated riprap revetment is part of the group of asphalt revetments. Asphalt revetment fails either due to water overpressures or due to wave impacts, see fig After failure of the revetment the embankment body is fully exposed to loading by the waves. The embankment breaches after the body of the embankment has completely eroded. The strength component of the reliability function of failure of the asphalt due to water over pressures is among others formed by the thickness of the asphalt. Apart from this note the rest of this reliability function is not relevant in the context of this project. The reliability function of failure due to impact of waves is relevant in the context of the project: Z = D n50 - Δ m ψ Φ u H s b ξ sw p cos(α) Failure asphalt due to water overpressures Failure asphalt due to wave impacts Among others partially penetrated riprap revetment Figure 4.5. Failure mode damage asphalt and erosion core of embankment in PC-Ring In which D n50 is the nominal diameter for which 50% of the weight of the grains is larger or smaller than this value, ξ p is the breaker parameter, Δ m is the relative density, ψ u is a parameter for penetration of the asphalt, Φ sw is the stability factor and α is the angle of the outside slope. The reliability function of the erosion of the embankment body after being fully exposed to the wave loading is: 4-7

50 4.Dutch reliability methods for flood defences Z = t RB - t s In which t RB is the time needed to erode the core of the embankment and t s is the duration of the storm Statistical models The statistical models that are applied for the random variables in PC-Ring are described below. First the statistical models of random variables in PC-Ring in general are discussed. Second the statistical models of the hydraulic boundary conditions are presented separately. Statistical models of random variables in PC-Ring in general The statistical models consist of the following components: Statistical distribution functions. Spatial correlation function. Model representing the correlation in time. These components are discussed below. Statistical distribution functions For each variable in the above mentioned reliability functions a choice has to be made whether the variable is of a deterministic or random nature. In the latter case the distribution functions have already been established in the computer code and cannot be altered by means of input. However, the parameters accompanying the distribution function in the form of mean values and standard deviations have to be defined. Instead of the standard deviation regularly the expression of the variation coefficient, V = σ/μ, is used. Apart from the random variables related to the hydraulic boundary conditions, most random variables in PC-Ring are normal or lognormal distributed. Figure 4.6. Shape of the correlation function (from Vrouwenvelder et al., 2001) Spatial correlation function The in PC-Ring applied spatial correlation function is 3 : 2 Δx ρ ( Δx) = ρ x + (1 ρ x ) exp 2 d x In which ρ x is a constant correlation and d x is the correlation distance. In fig an impression is given of the shape of the function. Model representing correlation in time In PC-Ring the Borges Castanheta model is applied to represent the correlation in time. According to this model the time is divided into intervals Δ t in which complete correlation is assumed. Between the time intervals a Figure 4.7. Representation of the Borges Castanheta model (from Vrouwenvelder et al., 2001) 4-8

51 4.Dutch reliability methods for flood defences constant correlation d t is taken. An impression of this model is given in fig.4.7. Statistical models of hydraulic boundary conditions In PC-Ring a number of models for different situations of hydraulic boundary conditions are incorporated. In the context of this project only one model is relevant. In case of the Caldicot Levels flood defence system the model of a tidal river is applied. In fig and fig the model that is applied to determine the local hydraulic boundary conditions and the data Basic random variables for the hydraulic boundary conditions (h sea, Q, U, statistics) Model: Mike11 Local water levels (h) Model: Bretschneider Z-function F and d Local wave conditions (H s, T s ) h sea Q U F d h H s T s = water level at the mouth of the Severn Estuary (m). = river discharge upstream at a point where the local water levels are independent of the tidal variations (m 3 /s). = wind speed (m/s). = fetch of the wind (m). = depth along the fetch (m). = local water level (m). = significant wave height (m). = significant wave period (s). Figure 4.8. Model that is applied to determine the local hydraulic boundary conditions in the Z-functions Data requirements at the mouth of the river 1. Water levels, h sea 2. Wind speeds, U 3. Statistics of water levels given the wind direction φ F(h sea <h sea φ) 4. Statistics of wind speeds given the wind direction F(U<U φ) 5. Probability of the wind directions P(φ) A B C Flow direction D Data requirements upstream of the river 1. Discharges Q at a location upstream independent of tidal influences. 2. Statistics of Q 3. The magnitude of Δ t according to the Borges Castanheta model. 6. Correlation between h sea and U Figure 4.9. The data requirements of the basic random variables and the statistics that are used to determine the local hydraulic boundary conditions at for instance locations A, B, C and D 4-9

52 4.Dutch reliability methods for flood defences requirements for this model are presented. Below the following aspects of this model are further explained: The way in which the local water levels are determined in PC-Ring. The statistics that are mentioned in fig Local water levels To explain the model for the tidal river as applied in PC-Ring fig is used as an example. The basic random variables h sea, Q and U can occur in various different combinations. Each different combination results in a different local water level. The local water levels at for instance locations A, B, C and D are predicted as a function of different combinations of the basic random variables using Mike11. The results of these calculations are laid down in one table for each location A, B, C and D. To determine the local water level for flood defences situated for example between A and B, PC-Ring linearly interpolates between the water level at A and the water level at B. This linear interpolation takes place according to the distance of the location of the flood defence with respect to A and with respect to B. The combinations of the basic random variables are formed by: Nine different discharges. The discharge values are chosen such that the range of occurring discharges is sufficiently represented. The extreme values are emphasised in this choice. Five different wind speeds. The wind speed values are chosen such that the range of occurring wind speeds is sufficiently represented. A number of wind directions: those wind directions are chosen that are relevant to the probability of flooding. Six different water levels at sea. The water level values are chosen such that the range of occurring water levels is sufficiently represented. The extreme values are emphasised in this choice. For a thorough description of these Mike11 models, see chapter 3, under the title of the hydraulic boundary conditions. Statistics The following statistics are applied in PC-Ring with respect to the hydraulic boundary conditions: Water levels at sea given the wind direction: For F h weibull sea ( h > m sea d : ϕ) = P( h sea < h sea α α h m ) 1 exp sea d ϕ = p c + σ σ In which h sea is the water level at the sea, φ is the wind direction and p c, m d, σ, α are variables that determine the shape of the distribution function. Wind speeds given the water level and the wind direction: F( u h sea, ϕ) = P( u < u h sea K, ϕ) = exp exp ϕ ( u) + ρ w ( h m w sea A h ) / B h K φ (u)=a w u 2 +b w u+c w 4-10

53 4.Dutch reliability methods for flood defences In which u is the wind speed, h sea is the water level, φ is the wind direction, ρ w is the correlation between the wind speed and the water level given a wind direction, A h, B h and m w are fitting parameters. This model for the correlation between the wind speed and water level originates from the model developed by Volker. This model is explained in Appendix 4-D. The probability of the wind directions: The wind direction is a discrete random variable. The statistics consist of a probability of each of the 16 wind directions. The discharge Q: the statistics of the discharge Q are represented by Q as a function of the return period. This function is in the form of: Q = a*ln(r) + b In which Q is the discharge and R is the return period of Q. a and b are fitting parameters. The statistics of Q can consist of more than one connecting functions of the same form as presented above. The statistics of Q cannot be entered as variables in PC- Ring but are fixed in the computer code Available calculation methods in PC-Ring First an overview is given of the main steps that PC-Ring takes to come to an annual probability of flooding of a flood defence system. Second the main calculation methods are mentioned that are applied. The information below is taken from [4]. Main steps taken in PC-Ring calculations The following steps are taken in the calculation of the flood defence system s probability of flooding: 1. Calculation of the probability of failure of one flood defence cross section for one tide, one partial failure mode (for instance failure mode overtopping, partial failure mode saturation), given the wind direction. 2. Combination of the partial failure modes resulting in the probability of failure of one total failure mode. 3. Taking the probability of the wind directions into account. 4. Determining the probability of failure due to one failure mode for the total flood defence stretch for which the under step 1 mentioned flood defence cross section is representative. 5. Combining the probabilities of failure of all the wind directions. 6. Determining the probability of failure for the total regarded period. 7. Combining the probabilities of the different failure modes. 8. Combining all the flood defence stretches to find a total flood defence system s probability of flooding. Calculation methods as applied in PC-Ring When regarding the above mentioned eight steps to calculate the system s probability of flooding, two main calculation methods occur: The calculation of the probability of failure represented by one reliability function, as in the above mentioned step 1. The combination of different reliability functions taking mutual correlations into account, as in the above mentioned steps 2 to

54 4.Dutch reliability methods for flood defences Probability of failure of one reliability function In PC-Ring the below mentioned main methods are available to calculate the probability of failure of one reliability function: FORM (First Order Reliability Method) SORM (Second Order Reliability Method) MC (Crude Monte Carlo) DS (Directional Sampling) A number of combinations of the above mentioned methods: for instance an option that PC-Ring automatically switches to DS if convergence does not occur in a calculation with FORM or SORM. Other options involve the combination of DS and FORM, the latter method is then used to find the design point. Combination calculations Consider a system consisting of n elements. An element can for instance be: a cross section, a tide, a wind direction, a stretch, a failure mode. Each element is represented by one Z- function. Two elements of the system are picked and are combined to form one equivalent representative element. In other words two Z-functions are combined to one. The total amount of elements in the system is reduced from n to n-1. Repeating this procedure over and over again will eventually reduce the amount of elements in the system to one. In other words, the system is wrapped up. The procedure to find one equivalent representative Z-function is according to the method of Hohenbichler 5. This procedure calculates P(Z 1 <0 AND Z 2 <0) taking the mutual correlation into account. If this probability is known, then P(Z 1 <0 OR Z 2 <0) can be determined Data requirements in order to make the calculations Below a rough impression is given of the data requirements of PC-Ring for the calculation of the system s probability of failure of each of the four failure modes. First the data are given that are equally required for the different failure modes. Second the data requirements specifically connected to the failure modes are described. General data requirements Some of the data requirements are equal for the different failure modes: Statistical data of the wind speeds and water levels at sea. The statistical data that are required to define the distribution function of the wind speed given the wind direction, the water level at sea given the wind direction, water level given the wind direction, the probabilities of the wind directions and the correlation between wind speed. Statistical data of the discharges at the river. The statistical data that are required to define the distribution function of the discharges. Second, the time interval of the Borges Castanheta model connected to the discharge. Data with respect to local water levels. A number of locations is selected for which the local water levels are determined as a function of the discharge at the river, the wind speed, wind direction and water level at sea. For each selected location one list with local water levels is made. This type of approach enables an approach with an as high level of accuracy as desired: a high level of accuracy is achieved by a high number of different locations. For flood defences between two of those selected locations the local water level is linearly interpolated between the two defined lists of local water levels. 4-12

55 4.Dutch reliability methods for flood defences Fetches. For each cross section that is taken into account the fetches and the mean depths along these fetches are defined for the different wind directions. It is possible to split up one fetch into a number of compartments with different mean depths. Geometry. An embankment cross section can be defined by at maximum seven pares of coordinates containing chainage and elevation. Seven pares represent a cross section with a verge in the outside slope. Six pares represent a cross section with a bend in the outside slope. Five pares stand for a cross section without one of the two former mentioned features. Additionally, information with respect to the roughness of the slope is required, the length of the section, how the cross section is orientated with respect to the North and the river axis, the two hydraulic locations from which the local water levels at the cross section is derived and the percentage of influence of the locations in connection to the linear interpolation. Overtopping The following types of data are required to make a calculation of the system s probability of failure due to overtopping: Information related to the reliability functions of overtopping and running over. Statistical data with respect to the variables that are part of these reliability functions: whether the variable is random or deterministic of nature, correlation in time and space, correlation lengths, mean values and standard deviations. Other type of data requirements are choices that have to be made with respect to: the type of overtopping model or whether the critical discharge should be calculated according to the grass strength model or according to a manually entered value. Numerical data. These data are required to operate the calculation process: the choice of the calculation method, how many iterations must be made before the conclusion is made that the results will not converge and the choice with respect of the starting point of the calculations. Instability of the inside slope The following types of data are required to make a calculation of the system s probability of failure due to instability of the inside slope: Information related to MPROSTAB. This concerns software independent of PC-Ring: Geometry of the embankment and length of the section. The structure of the soil below the embankments: soil types, thickness of the layers. Soil properties: volumetric weight, angle of internal friction, cohesion. The ground water level in the embankment in case of three different water levels. With respect to the soil properties: mean values and standard deviations, vertical and horizontal spatial correlation, correlation lengths. Statistics with respect to the water pressures and the Bishop safety factor. In PC-Ring: the general data requirements and the numerical data. Attack of the revetment on the outside slope The following types of data are required to make a calculation of the system s probability of failure due to attack of the revetment on the outside slope : Information related to the reliability functions of attack of the revetment on the outside slope. Statistical data with respect of the variables that are part of these reliability functions: whether the variable is random or deterministic of nature, correlation in time and space, correlation lengths, mean values and standard deviations. Other type of data requirements are choices that have to be made with respect to: the type of revetment or the type of model that represents the erosion process of the remaining embankment after damage of the revetment. Numerical data. See failure mode overtopping for a description. 4-13

56 4.Dutch reliability methods for flood defences Uplifting and piping The following types of data are required to make a calculation of the system s probability of failure due to uplifting and piping: Information related to the reliability functions of uplifting and piping. Mainly, statistical data with respect of the variables that are part of these reliability functions: whether the variable is random or deterministic of nature, correlation in time and space, correlation lengths, mean values and standard deviations. Numerical data. See failure mode overtopping for a description The appropriate flood defence system s cross sections selection The process of flood defence modelling and data gathering presents time-consuming activities in practice. The main thought behind solving this practical problem is considering the flood defence system as a serial system. This main thought results in a practical approach to select the appropriate cross sections for the calculations with PC-Ring. Practical problem: laborious flood defence modelling and data gathering In order to make the calculations with PC-Ring, the flood defence system must be translated into a model. This model can be expressed in data, and these data are used in the calculations. Ideally, the complete flood defence system is thus expressed in data and taken into account in the probability calculations. However, in practice this takes a lot of time in terms of flood defence modelling and data gathering. This time is usually not available. Serial system and weakest link A way to deal with this problem is to regard the flood defence system as a serial system. The weakest link in a serial system dominates the total system s probability of failure. Therefore, only the cross sections are taken into account that are expected to contribute most to the total system s probability of failure. Practical approach of flood defence modelling and data gathering The process of cross section selection and data gathering is as follows: 1. Division of the water defence system in defence types. 2. The next step is to divide the water defence system in embankment stretches. To this end rough information and insights are used. The division is based on the external physical characteristics and not yet on the characteristics directly connected to the failure modes, although implicitly the connections are there. The following characteristics are important for this selection 6 : Orientation to the wind directions: embankment stretches that are orientated differently will be loaded by different wave regimes and therefore must be discerned as different embankment stretches. High water regimes, differences in extreme water levels: lengths of the water defence system for which different high water regimes are relevant must be discerned as separate embankment stretches. Geometrical characteristics foreshore: Embankment stretches with significant different sizes of the foreshore in terms of height and width. External geometry of the water defence: lengths of the water defence system with significant differences in height and (external) construction are discerned as different embankment stretches. Differences in geometry will lead to differences in loading conditions due to the same hydraulic boundary conditions. 4-14

57 4.Dutch reliability methods for flood defences 3. The water defence system has now been divided into rough stretches with the same type of characteristics. However, cross sections have to be determined which can be regarded as representative of the total embankment stretch. If still significant differences between cross sections in an embankment stretch are present, then the stretches need to be divided into further parts: the embankment sections. A first insight with regard to weak spots in the water defence system can be given by managing authorities. These authorities can also help to determine the relevant failure modes for certain embankment sections. The following failure mode related considerations can form a basis for a division in embankment sections: Different types of outside slope revetment (types and construction), this will lead to a further division for the failure mode: damage of the revetment on the outside slope and erosion of the embankment body. Differences in geometry on a detailed level has consequences for each of the failure modes. Differences in the foundation soil can have a considerable effect on the contributions to the probability of failure of geotechnical failure modes. For these failure modes a further division has to be made. Differences in the inside slope revetment of embankments (quality of the grass, thickness and qualification of the clay cover layer on the inside slope, the angle of the inside slope, etc.), this kind of information is especially useful for the division in embankment sections for the failure modes overtopping and consequently erosion of the inside slope or instability of the inside slope. Information about the construction of the embankment (clay embankment, sand embankment with a clay core, etc ) and information about the soil layers underneath and directly next to the embankment (in front of and behind the embankment), this information is relevant to the failure modes heave and piping, instability of the inside slope and damage to the revetment and erosion of the embankment body. 4. After step 3 the water defence system has been divided in embankment sections. The following step is to select the relevant sections for the reliability analysis. The procedure to come to this selection of sections is given below: Regard a failure mode for which it is desirable to reduce the number of dike sections. The first logical step is to eliminate all the embankment sections for which the mode is not relevant, or in other words: the contribution of the section to the probability of failure due to a certain mode is negligible in advance. Well known weak spots can provide valuable first insight in which sections contribute significantly and which ones do not. For the remaining sections, indicators are used to rank them. These indicators are related to the failure modes. The number of selected sections can be limited based on this ranking. Apart from the selected weak sections based on the indicators, sections from the middle and strong categories have to be chosen. This is done because it is practical to be able to make an estimate of the probability of flooding after eliminating the weak spots in the probability of failure calculations. The former three steps have to be performed for all failure modes, which can result in a different selection of embankment sections for each mode. Check the spreading of the sections along the water defence system with respect to the magnitude of the expected consequences. The sections with substantial consequences that fall out off the analysis should be added or shift a bit with the choice in the middle and strong sections. With the total risk analysis in mind, a strong section with extensive consequences can contribute just as much or even more to the total risk as a weak section with hardly any consequences. 4-15

58 4.Dutch reliability methods for flood defences 5. The first selection of embankment sections has been finished. For each section it is clear which failure modes are regarded. The next step is to gather data for the regarded failure modes and embankment sections. 6. After the first calculations of the probability of failure with PC-Ring a check is made if sections have to be added or adjusted: First the contribution of the failure modes to the total probability of failure is regarded. For the mode with the largest contribution a check has to be made if the last selected sections still have a significant contribution to the probability of failure. If they do an additional selection of sections for that mechanism has to be made. This check needs to be made for all the failure modes with an emphasis on the ones with the largest contribution. This process has to be repeated until no more sections need to be included in the analysis. The number of cycles depends on the number of embankment sections which are chosen initially and after expansion Detailed working-method In 2.4. a rough working-method has been presented based on a reliability analysis of a flood defence system. The in 4.2. described approach for practical flood defence modelling and data gathering provides the possibility to refine the rough working-method as presented in 2.4. For the detailed working-method that combines flood defence system s reliability theory and practice, see fig

59 4.Dutch reliability methods for flood defences Subject of Stages in detailed working-method Information/ calculation tools Chapter 5 Definition of the flood defence system Definition of the flood defence system s components Maps/ relief lines/ site visit Available reports/ geometry/ site visit Chapter 6 Analysis of failure modes connected to the system s components Literature in general and associated with PC-Ring Division in embankment stretches Rough external characteristics Division in embankment sections Failure mode related considerations Chapter 7 Overtopping Section selection for each failure mode Damage of revetment and erosion of embankment body Instability of inside slope Uplifting and piping Indicators/ theory/ knowledge of past events/ Mstab Flood defence modelling & data gathering Flood defence modelling & data gathering Flood defence modelling & data gathering Flood defence modelling & data gathering Available reports/ cross sections Chapter 8 System s probability of flooding due to overtopping System s probability of flooding due to damage to revetment etc.. System s probability of flooding due to instability of inside slope System s probability of flooding due to uplifting and piping PC-Ring/ MPROSTAB Total flood defence system s probability of flooding Combin/ check with past events Chapter 9 Conclusions and recommendations Results from work Figure Detailed working-method 4-17

60 4.Dutch reliability methods for flood defences 1 Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PC-Ring, Part A: descriptions of failure modes (in Dutch), Nr. 98-CON-R1430, Delft Tol, van A.F., Oostveen, J.P., CUR 162, Constructing with ground. Structures made of ground on and in soil with little bearing capacity and strong compressible subsoil (in Dutch), Delft Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PC-Ring, Part B: Statistical models (in Dutch), Nr. 98-CON-R1431, Delft Vrouwenvelder, A.C.W.M., Theoretical manual of PC-Ring, Part C: Calculation methods (in Dutch), 98- CON-R1204, Delft M. Hohenbichler & R. Rackwitz, First-order Concepts in System Reliability, Structural Safety, 1, 1983, pages Calle, E., Jonkman, B., Lassing, B., Most, van der, H., Data gathering and flood defence modelling to support the calculation of probabilities of flooding of ring dike systems (in Dutch), Manual (version 3.2), Delft

61 5. Definition of the Caldicot Levels flood defence system and its components Introduction In order to carry out the reliability analysis of the Caldicot Levels flood defence system, the system is first translated into a model, this model is expressed in data and with these data reliability calculations are made. The first step in the translation of the Caldicot Levels flood defence system to a model is to define the boundaries of the flood defence system. This step points out the relevant defence length for the calculation of the probability of inundation and the area which suffers consequences in case the flood defence system fails. Below the system definitions in general and the system definitions as applied on the Caldicot Levels flood defence system are regarded. These definitions serve as a basis to determine the flood defence system s boundaries. System definitions In Appendix 2-C.2. the following definitions are mentioned with respect to a system: A system is defined as an assembly of elements or processes with a common purpose. The reliability of a system is defined as the extent to which the system fulfils its requirements. System definitions in practice Applying the above mentioned system definitions to the Caldicot Levels flood defence system leads to: The common purpose of the Caldicot Levels flood defence system is to protect the area within the boundaries from flooding. The nature of the Caldicot Levels flood defence system is a serial system. In other words: if failure occurs at one or more locations along the flood defences then the area within the boundaries of the system suffers consequences in the form of partial or complete flooding. The reliability of the Caldicot Levels flood defence system is to what extent the flood defences of the system can protect the area within the boundaries from flooding. Set-up of this chapter First a choice is made about which method is used to define the flood defence system s boundaries, this is done in 5.1. For more detailed background information the reader is referred to Appendix 5-A and Appendix 5-B Second, this method is applied to determine the Caldicot Levels flood defence system s boundaries in 5.2. Finally an impression is given of the Caldicot Levels flood defence system in 5.3. An additional impression is given in Appendix 5-C by the photos of the site visit Choice of the method to define the flood defence system s boundaries A method to define the Caldicot Levels flood defence system s boundaries can be derived from the following possibilities: The method according to the Benefit Assessment which has been performed in the light of flood defence improvements that are planned along the Caldicot Levels flood defence system 1. To this method is referred in the text as: the method according to the Benefit Assessment. See Appendix 5-A. The method which is applied in The Netherlands to define the boundaries of flood defence systems 2. See Appendix 5-B.

62 5. Definition of the Caldicot Levels flood defence system and its components Below a short description of both methods is given together with their limitations in Finally the method that is derived from these methods in order to apply to the Caldicot Levels flood defence system is presented in Short description and restrictions of available methods to define flood defence system s boundaries Method according to the Benefit Assessment First a short description is given of this method, for more detailed information see Appendix 5-A. Second the restrictions of this method are discussed in short. Short description The approach according to the Benefit Assessment has been based on the former indicative flood plain approach in the UK. This former approach amounts to assuming absence of water defences and consequently determining the indicative flood plain which would be affected by respectively a 100 year return period water level for fluvial areas and a 200 year return period water level for tidal areas. The extent of the inundation is in this approach determined as a function of inundation depth and inundation speed given that breach occurs for a water level with that particular return period. Sometimes due to lack of information concerning the relief, the outer flood plain boundary is formed by the lowest relief line for which information is available. Restrictions This method according to the Benefit Assessment has one general restriction and one restriction specifically connected to the Caldicot Levels flood defence system: General restriction: Often in the UK it is impossible to find a closing system of flood defences surrounding a by flooding threatened area. If so, it is difficult to define exactly which flood defences contribute to the probability of flooding of a certain area. Restriction specifically connected to the Caldicot Levels flood defence system: The Benefit Assessment which has been carried out in the light of the Caldicot Levels flood defence system s improvements only regards the flood defences along the Severn Estuary. The influence on the system s boundaries by the flood defences along the River Usk are not taken into account. Method as applied in The Netherlands First a short description is given of the method which is applied in The Netherlands to define the boundaries of flood defence systems. For more detailed information see Appendix 5-B. Second the main restrictions of this method are given. Short description In The Netherlands the flood defence systems are quite straightforward to recognise. The flood defences enclose the low-lying polder areas. The system is formed by following the line of the flood defence until it hits high grounds. High grounds are defined by an elevation level, the NAP +2m line in case of threat from the sea. Follow this level until it connects to the flood defences. Consequently follow the flood defences until the starting point is reached. Restrictions The above described method has one general restriction and one restriction specifically connected to the Caldicot Levels flood defence system: 5-2

63 5. Definition of the Caldicot Levels flood defence system and its components General restriction: The same restriction as the method according to the Benefit Assessment: often in the UK it is impossible to find a closing system of flood defences surrounding a by flooding threatened area. If so, it is difficult to define exactly which flood defences contribute to the probability of flooding of a certain area. Restriction specifically connected to the Caldicot Levels flood defence system: The level of NAP +2m that is applied in The Netherlands to define the high grounds is not transferable to the Caldicot Levels flood defence system as the mean elevation is OD+5m Method to determine the Caldicot Levels flood defence system s boundaries The method to determine the Caldicot Levels flood defence system s boundaries is to follow the flood defence until it connects to high grounds. Then the high grounds are followed around the low-lying Caldicot Levels area on an elevation level of OD+10 m. From the point where this elevation line connects back to the flood defences, the latter are followed until the starting point is reached. A number of remarks are made with regard to this method: The limit of the area at risk of flooding is represented by the OD+10 m relief line. The elevation from this OD+10m limit outside the area at risk increases sharp in case of the Caldicot Levels. The exact boundaries of the area at risk of flooding formed by the high grounds are not important in the light of this project s objective. These boundaries depend on the extent of the possible flooding events. This method provides the opportunity in case of the Caldicot Levels flood defence system to form a closed system of defences Definition of the Caldicot Levels flood defence system s boundaries The Caldicot Levels are bounded in the north and the east by high grounds, in the west by the River Usk and in the south by the Severn Estuary. The River Usk and the Severn Estuary form the hydraulic boundary conditions and pose the threats of flooding of the Caldicot Levels. The Caldicot Levels flood defence system s boundaries are defined according to the method presented in The definition process starts at an arbitrary point at the flood defences along the Severn Estuary. The first step is to follow the flood defences along the Severn Estuary in the direction of the east until the OD+10m elevation line is encountered at location A, see fig The second step is to follow the OD+10 m line from location A in fig in the direction of the west along the high grounds. In fig the connection between the OD+10m line and the flood defences along the Usk is shown. This connection is represented by location B. The last step is to follow the flood defences along the Usk from location B southward. Follow the flood defences until the arbitrary chosen starting point at the flood defences along the Severn Estuary. The definition of the flood defence system is now completed and is presented in fig.5.3. The high grounds do not contribute to the system s probability of flooding. The flood defence system that is subject of the reliability analysis is therefore formed by the southern line between location A and B. 5-3

64 5. Definition of the Caldicot Levels flood defence system and its components 10 OD+10m line 15 OD+15m line Flood defences Location A, where the flood defences along the Severn Estuary connect to the OD+10m elevation line A 1000 m N Figure 5.1. The location where the flood defences along the Severn Estuary connect to the OD+10m line in the east. The figure on top provides an overview of the Caldicot Levels. The figure at the bottom provides a magnified view of the black rectangle in the top figure. 5-4

65 5. Definition of the Caldicot Levels flood defence system and its components 10 OD+10m line B 20 Location B, where the flood defences along the Usk connect to the OD+10m elevation line OD+20m line 1000 m N Figure 5.2. The location where the flood defences along the Usk connect to the OD+10m line in the west. The figure at the bottom provides a magnified view of the black rectangle in the top figure. 5-5

66 5. Definition of the Caldicot Levels flood defence system and its components B OD+10m line A N 10 km Figure 5.3. The Caldicot Levels flood defence system s boundaries. The locations A and B correspond with the locations A and B in fig.5.1. and fig.5.2. The OD+10m line represents the high grounds which do not contribute to the system s probability of flooding Components of the Caldicot Levels flood defence system In order to provide a first impression of the shape of the Caldicot Levels flood defence system the following aspects of the system are discussed: Six main components or defence types, that are subject of the reliability analysis. Flood defence improvements that are planned along large parts of the Severn Estuary flood defences. These flood defence improvements are subject of the reliability analysis. Three structure types that occur in the flood defence system but are not included in the reliability analysis. Six main components The six main components, or defence types, of the Caldicot Levels flood defence system are shown below in fig.5.4.: 1. Embankment without additional structures, component 1, see Embankment with wave return wall, component 2, see High grounds with masonry wall facing, component 3, see Raised grounds along Severn Estuary, component 4, see Raised grounds along the Usk, component 5, see River banks of the Usk, component 6, see The Dutch reliability analysis methods for flood defences which are discussed in chapter 4 provide the possibility to calculate the probability of failure of these six defence types. In to the six components are presented by pictures from a site visit and an indication of the dimensions. Flood defence improvements The flood defence improvements are part of the reliability analysis. The probability of flooding of the system without improvements will be compared with the probability of flooding of the system with flood defence improvements. This comparison provides an impression of the suitability of the Dutch reliability methods for flood defences to support decisions with respect to improvement 5-6

67 5. Definition of the Caldicot Levels flood defence system and its components options. In to the flood defence improvements linked to the six main components are addressed. N B A Lighthouse 1 = 2 = 3 = Embankment Embankment with wave return wall High grounds with masonry wall facing 4 = 5 = 6 = Raised grounds along Severn Estuary Raised grounds along the Usk River banks of the Usk Figure 5.4. Rough indication of the position of the main flood defence components Three defence types that are excluded from the reliability analysis To three defence types that are present in the Caldicot Levels flood defence system the Dutch reliability methods for flood defences cannot be applied and are therefore excluded from the reliability analysis. These three defence types are addressed in short below. Culverts, which are called Pills in the Caldicot Levels flood defence system. Bridge abutments of the new Severn Bridge. This bridge enters land near location A in fig.5.4. A masonry wall that is known to be present in the core of some of the flood defences. However, where this wall is present in the flood defence is not known. Culverts or Pills Several culverts called Pills, see fig.5.5., provide the drainage of the system of drainage canals, called reens, present in the Caldicot Levels. The drainage through these pills are managed by a steel flap door. This door closes and opens due to the hydraulic head difference over the embankment during respectively high and low water. These culverts also contribute to the probability of failure of the system. The failure mode which occurs most is blockage of the flap door by all sorts of objects (even shopping cars). Inspection is performed frequently to try to prevent this type of failure from occurring. Figure 5.5. Caldicot Pill, example of a culvert draining the 'reens' 5-7

68 5. Definition of the Caldicot Levels flood defence system and its components Bridge abutments The foundation of the new Severn Bridge is present near location A in fig.5.4. In fig.5.6. a picture is give of the bridge abutments. From the points where the embankments of the flood defence system connect to the ramp of the bridge the flood defences are included in the reliability analysis. Figure 5.6. Bridge abutments Masonry wall allegedly present in the core of flood defences In the Wave overtopping analysis, Caldicot sea defence improvements 3 it is remarked that Much of the sea defences that front the Caldicot Levels have a masonry wall through the core of the structure (much originates from the 19 th century) with a visible example at Peterstone, Wentlooge Levels. This masonry structure is likely to decrease the likelihood of breaching of the defence. Possible approach The influence of this masonry wall in the core of some stretches of the embankment can be approached by assuming an embankment core which can hardly be eroded. This assumption has consequences for the failure modes erosion of the rear slope due to overtopping and attack of the revetment on the outside slope and consequently erosion of the core of the embankment. Limitations and considerations An approach as mentioned above does not take the failure modes of the masonry wall into account. Another limitation is that there is no information available with regard to where these masonry walls are present. Below some considerations are given with respect to the presence of the masonry wall in the core of the embankment: The embankments which protect the Caldicot Levels have a history as far as the Roman times. The masonry walls might have been constructed as a revetment to protect the embankments from erosion. This would mean that the masonry walls are rather masonry facings closed in by an embankment slope than a gravity based masonry wall with two earth slopes. This supports an approach to assume a core of the embankment that hardly erodes, instead of a complete different flood defence structure. An assumption with respect to the location of masonry walls along the embankments of the Caldicot Levels is that these walls are present at the places where the old wave return wall has been applied. The fact that these wave return walls have been applied at certain locations indicates that these parts of the embankments are under heavier attack than other locations and that extra protection against this attack is required. Despite of these assumptions with respect to the structure of an embankment with masonry wall and the locations of these masonry walls, the influence of this structure on the probability of failure is not taken into account in this study. 5-8

69 5. Definition of the Caldicot Levels flood defence system and its components Embankments without additional structures Below in fig a picture is given of an embankment without additional structures according to component 1. The picture is taken near location A in fig. 5.4., in other words west of Sudbrook and just south of Caldicot. In fig.5.8. an indication is given of the dimensions of this component. An indication of the dimensions of the flood defence improvement is given in fig Figure 5.7. Picture of an embankment according to component 1, near Location A Sea side Land side Chainage Elevation (meter OD) Figure 5.8. Indication of dimensions of embankments according to component 1. Improvement Land side Sea side Chainage Elevation (meter OD) Figure 5.9. Indication of dimensions of flood defence improvement of component 1 5-9

70 5. Definition of the Caldicot Levels flood defence system and its components Embankments with wave return wall Below in fig a picture is given of an embankment with wave return wall according to component 2. The picture is taken east of Goldcliff in fig In fig an indication is given of the dimensions of this component. An indication of the dimensions of the flood defence improvement is given in fig Figure Picture of an embankment according to component 2, near Goldcliff Sea side Land side Chainage Elevation (meter OD) Figure Indication of dimensions of embankments according to component 2. OD+ 11.4m = flood defence improvement Figure Indication of dimensions of flood defence improvement of component

71 5. Definition of the Caldicot Levels flood defence system and its components High grounds with masonry wall facing Below in fig a picture is given of high grounds with masonry wall facing according to component 3. The picture is taken at Goldcliff in fig In fig the dimensions are given of this component, as this component is represented by one cross section. For this component no flood defence improvements are planned. The crest behind the slope with the masonry wall facing is formed by naturally present high grounds. The width of this crest reaches values of 200 meter. Figure Picture of an embankment according to component 3, at Goldcliff Land side Sea side Chainage Elevation (meter OD) Figure Dimensions of embankment according to component

72 5. Definition of the Caldicot Levels flood defence system and its components Raised grounds Below in fig a picture is given of raised grounds according to component 4. The picture is taken near the lighthouse as shown in fig In fig an indication is given of the dimensions of this component. An indication of the dimensions of the flood defence improvements of this component is given in fig The raised grounds are not improved along the complete length but when improved, the plans are similar as shown in fig Component 5 represents flood defences with the same shape as component 4 but border the Usk: a different hydraulic regime. The picture in fig shows the extensive width of the crest of the raised grounds. The crest of the raised grounds is present from the lighthouse to the left in the picture. From the lighthouse to the right in the picture the raised grounds slope down to the sea. The same can be concluded about the width of the crest in the drawing in fig : the width is indicated to be at least 15 meter, after this the drawing is cut short and the rear-slope is not drawn. This is because the width is too extensive to completely include in the drawing. Figure Looking in the direction of the sea from the land formed by the raised grounds. The lighthouse is approximately at the top of the slope of the raised grounds down to the sea. Sea side Land side Chainage Elevation (meter OD) Figure Indication of the dimensions of embankment according to component

73 5. Definition of the Caldicot Levels flood defence system and its components Land side Sea side Chainage Elevation (meter OD) Figure Indication of dimensions of flood defence improvement of component River banks of the Usk Below in fig an indication of the dimensions are given of the river banks of the River Usk, component 6. For this component no flood defence improvements are planned and no pictures are available. River side Land side Chainage Elevation (meter OD) Figure Indication of the dimensions of river banks of the Usk according to component

74 5. Definition of the Caldicot Levels flood defence system and its components 1 Chatterton, J.B., Caldicot Sea Defence Strategy Plan: Benefit Assessment, JCA, January TAW, Guideline of safety testing, Meinema drukkerij, August WS Atkins, Wave overtopping analysis, Caldicot sea defence improvements, Swansea

75 6. Analysis of the failure modes connected to the components Introduction As is mentioned in the Introduction, the actual flood defence system must be translated into a model, this model must be expressed into data and these data are used to perform calculations. The first step in this modelling process has been taken in chapter 5. In this chapter the Caldicot Levels flood defence system s boundaries and its components have been defined. This step has pointed out the relevant defence length for the calculation of the probability of inundation and the area which suffers consequences in case the flood defence system fails. The first set up of the fault tree is given in fig Flooding of Caldicot Levels Failure of embankment without additional structures Failure of embankment with (new) wave return wall Failure of high grounds with masonry wall facing Failure of raised grounds along the Severn Estuary Failure of raised grounds along the Usk Failure of river banks Figure 6.1. Fault tree of the Caldicot Levels water defence system on the level of the system s components The next part of the system that must be modelled in the light of the reliability analysis is formed by the processes that lead to failure: the failure modes connected to the components of the Caldicot Levels flood defence system. Set-up of this chapter This chapter presents that next step in the modelling process: the analysis of the failure modes down to the level of the reliability functions. Each component is regarded separately with respect to the failure modes: Embankment without additional structures, see 6.1. Embankment with wave return wall, see 6.2. High grounds with masonry wall facing, see 6.3. Raised grounds along Severn Estuary, see 6.4. Raised grounds along the Usk, see 6.5. River banks of the Usk, see 6.6. Overtopping Wave Overtopping Slip circle inner slope Micro instability Piping Settlement Slip circle outer slope Liquefaction Drifting ice Ship collision 6.1. Failure modes connected to embankment without additional structures, component 1 The failure modes of the present form of this component are discussed in The failure modes of the flood defence improvements of this component are presented in Failure modes of component 1, present form Introduction In fig.6.2. a number of possible failure modes of an embankment Sliding Tilting Erosion outer slope Erosion foreshore Figure 6.2. Overview of a number of possible failure modes of an embankment without additional structures (from CUR 169)

76 6. Analysis of the failure modes connected to the components without additional structures are given. However, this study focuses on failure modes that are incorporated in PC-Ring. In chapter 4 these failure modes are listed and briefly introduced. It appears that in PC-Ring with respect to embankments four main failure modes are part of the reliability calculations. These failure modes contribute according to experience significantly to the total system s probability of failure. Besides that, for these failure modes (suitable) models are available to make reliability calculations. Failure modes For the sake of completeness the failure modes that are included in PC-Ring and thus subject to this study are given below: Overtopping or running over, consisting of: Damage of the grass on the inside slope and consequently erosion of the embankment body. Saturation of the pores of the clay cover layer on the inside slope of the embankment and consequently instability of the inside slope. Instability of the inside slope. Damage of the revetment and consequently erosion of the embankment body. Uplifting and consequently piping. See fig for the matching fault tree. The relevancy of these failure modes in case of the Caldicot Levels flood defence system is treated in chapter Failure modes of flood defence improvement of component 1 In 5.3. the flood defence improvement to component 1 is given in case of the Caldicot Levels flood defences. After the application of this flood defence improvement the component type remains the same: an embankment without additional structures. The only difference with the present situation is that the magnitude of the embankment has increased. Therefore, the same failure modes are applied as to the embankment without additional structures in its present form, as discussed in Calculation of the system s probability of flooding of the present system and of the system after the application of the flood defence improvements provides an impression of the increase of the safety related to flooding Failure modes connected to embankment with wave return wall, component 2 The failure modes of the present form of this component are discussed in The failure modes of the flood defence improvements of this component are presented in Failure modes of component 2, present form Introduction Component 2 is an embankment with an additional wave return wall. The presence of this extra structure, embodied by the wave return wall, influences the performance of the embankment as a whole. In order to determine the probability of failure of this component the following aspects need to be considered: The function of the wave return wall and the effect(s) of the presence of the structure. The failure modes of the wave return wall. The performance of the embankment with wave return wall as a whole. These aspects are discussed below. 6-2

77 6. Analysis of the failure modes connected to the components Function of wave return wall and the effects of its presence in the present form The function of the wave return wall is to reduce the amount of (wave) overtopping. This reduction is primarily dependent on the height of the wave return wall and the discharge that is incident upon it 1. The effects of the presence of the wave return wall in its present form are known to be limited. This is among others a result of its small height and the low quality of the structure s material. In other words, the reduction of the overtopping discharge by the presence of the present wave return wall is limited. Failure modes of the wave return wall As the effect of the wave return wall in its present form is small, the question whether the wall fails or not is not relevant. The performance of the embankment with wave return wall as a whole The presence of the wave return wall in its present form has limited influence on the performance of the embankment as a whole. In this study this influence is assumed to be negligible in the reliability calculations of embankments with wave return wall in its present form. Therefore, the same failure modes as for an embankment without additional structures are applied to calculate the probability of failure of embankments with wave return wall in its present form. Thus, for failure modes of the embankment with wave return wall in its present form, see However, one note must be made: the small wave return wall introduces a jump in the geometry of the embankment. This can cause problems with the calculation of the actual overtopping discharges with Van der Meer. These problems are the result of the Irribarren number i which is part of the formulas. They are solved by replacing the wave return wall by a 1:1 slope which starts at the outside toe of the wave return wall and reaches as high as the level of the top of the wave return wall Failure modes of flood defence improvement of component 2 Introduction The flood defence improvement of component 2 is an embankment with an additional wave return wall. The presence of this extra structure, embodied by the wave return wall, influences the performance of the embankment as a whole. In order to determine the probability of failure of this component the following aspects need to be considered: The function of the wave return wall and the effect(s) of the presence of the structure. The failure modes of the wave return wall. The performance of the embankment with wave return wall as a whole. These aspects are discussed below. Function of wave return wall and the effects of its presence in case of the flood defence improvements The function of the wave return wall as a part of the flood defence improvements and the effects of its presence on the surroundings are given below. These aspects are the basis of the analysis of the performance of the embankment with wave return wall as a whole in case of the flood defence improvements. i The Irribarren number indicates whether the incoming waves on a slope break or not. In case that the waves break, the number indicates the type of breaking waves. 6-3

78 6. Analysis of the failure modes connected to the components The function The function of the wave return wall is to reduce the amount of (wave) overtopping. This reduction is primarily dependent on the height of the wave return wall and the discharge that is incident upon it (HRWallingford, 1998). The effects The effects of the presence of the wave return wall can in the case of the flood defence improvements not be neglected. Some effects of a wave return wall with significant dimensions are as follows (from CUR 169): First of all a positive effect: reduction of the overtopping discharges. Examples of negative effects are: The presence of a wave return wall leads to increased attack on the armour layer due to wave reflection. Overtopping water becomes more concentrated into a jet, and is a potential danger to the rear slope. The wave return wall represents a rigid element in a structure, which is flexible by nature. Uneven settlements may lead to great problems for the elements of the wave return wall. The wave return wall increases the danger of excessive pore pressures in the mound; If the wave return wall fails, the overtopping discharges are either no longer reduced or less reduced. The latter occurs in case that the failed wave return wall is partly blocking the opening. If the wave return wall fails this completely (or again partly) takes away the negative effects. In this study only the effect of reduction of the overtopping discharge is regarded. The reduction of the overtopping discharges is assumed to stop completely if the wave return wall fails. Failure modes of the wave return wall First the failure modes of the wave return wall in general are discussed. Second two of the failure modes are selected. Finally the reliability functions of these two failure modes are described. Failure modes of wave return wall in general In fig a number of possible failure modes are given of the wave return wall. These are explained below: Horizontal sliding: the horizontal forces are larger than the friction force as a result of the weight of the wave return wall. Tilting of the wave return wall: the resulting force is not within the core of the foundation plane. Instability of the soil on which the wave return wall is founded, and as a result occurrence of a slip circle. Sliding Tilting Instability Piping Structural failure Figure 6.3. Possible failure modes of the wave return wall 6-4

79 6. Analysis of the failure modes connected to the components Piping underneath the structure. Structural failure of the wave return wall: the stresses in the concrete are larger than the structure can bear. Including these failure modes in the fault tree of the wave return wall leads to fig In this fault tree the top event is failure of the wave return wall. The consequence of this failure is no more reduction of the overtopping discharges. Failure wave return wall Sliding Tilting Instability Piping Structural of soil failure Figure 6.4. Fault tree of wave return wall Selection of failure modes in case of the Caldicot Levels flood defences A selection of the failure modes of the wave return wall as mentioned above is made. These failure modes are added to the ones already present in PC-Ring. The following failure modes are selected: sliding, tilting. Not included are: instability, piping and structural failure. Instability of the soil on which the wave return wall is founded is not included because this failure mode has a strong correlation with the failure mode sliding. In both cases the soil fails after loading of the wave return wall by the wave impact. Besides this, another argument is that there is no simple model to represent this type of failure. Moreover, instability can also occur along different kinds of slip circles than indicated in fig Piping underneath the wave return wall can occur if the water level reaches as high as the wave return wall long enough to initiate the erosion process. The level of the toe of the wave return wall as part of the flood defence improvements is in all cases higher than OD+9.5m. A water level as high as that level or higher can only be accomplished by a high water event combined with a strong wind. Such an event persists for about two hours, this is not long enough to cause piping. Moreover, the embankments consist of clayey soil with a low permeability and the wave return wall is founded 30 cm deep in the embankment. The failure mode piping is not included because of these arguments with respect to persistence of the loading event, material of the embankment and the foundation plane of the wave return wall in the embankment. Structural failure is not included in the selection of failure modes that are added to PC-Ring. Some examples of processes that can lead to structural failure of the wave return wall are: failure of the steel in the reinforced concrete due to wave impact, failure of the concrete due to the shear stresses caused by the wave impact, decreasing quality of the reinforced concrete because of the maritime climate. The shape of the wave return wall and the nature of the loading (wave impact) make it difficult to model structural failure of the wave return wall. Apart from that there is, to support such a model, no information available about the wave return wall s structure in terms of material properties or whether or where reinforcement steel is present. Reliability functions of failure due to sliding or tilting of the wave return wall The reliability functions of failure due to sliding and tilting of the wave return wall are presented below. The model of the wave impact pressures is described in Appendix 6-A. 6-5

80 6. Analysis of the failure modes connected to the components Reliability function of sliding Failure of the wave return wall due to sliding occurs when the resulting horizontal forces are larger than the friction force as a result of the weight of the wave return wall. This is expressed in the following reliability function: 2 Z = tan( ϕ )ΣV ΣH 3 In which 2 / 3 tan(φ) represents the friction angle δ. ΣV is the resulting vertical force and ΣH is the resulting horizontal force. Wall The expression of ΣV is as follows: Foundation ΣV = Weight foundation + weight wall = A w *l*γ b + h f *l*b f * γ b In this expression the elements which are called respectively the foundation and the wall can be found in fig The following parameters can also be found in this figure: A w [in m 2 ] is the area of the wall, l [in m] is the length of the wave return wall element (the elements are not linked), γ b [kn/m 3 ] is the volumetric weight of the concrete, h f [in m] is the height of the foundation and b f is the width of the foundation [in m]. The expression of the resulting horizontal forces is: Figuur 6.5. Relevant dimensions of the wave return wall ΣH = H wave H p;g In which H wave is the resulting horizontal force[in kn] of the pressures that are exerted on the wall by the wave impacts and H p;g is the resulting force of the passive ground pressures that is exerted by the soil behind the foundation of the wave return wall [in kn]. The resulting horizontal force of the wave impact pressure consists of the following components: H wave = cos 2 (β)*p so *l*h m In which p so is the wave impact pressure, this pressure is constant over the surface of the wall, see Appendix 6-A. cos 2 (β) takes the angle of the incoming waves into account. β is the angle of the incoming waves with the normal axis of the embankment. The cos 2 is applied because it concerns an energy approach. For a description of the wave impact model, see Appendix 6-A. l is the length of the wave return wall element and h m is the height of the wall. The force that is exerted by the passive soil pressures at the inside of the wave return wall foundation is given in the expression below. The water is assumed to overtop to such an extend that the embankment soil is saturated down to the level of the foundation plane. 6-6

81 6. Analysis of the failure modes connected to the components H p;g = 3*0.5*h d 2 *(γ g -10)*l+0.5*h d 2 * γ w *l In which h d is the depth of the foundation plane of the wave return wall with respect to the crest of the embankment body [in m], γ g is the volumetric weight of the with water saturated soil [in kn/m 3 ], l the length of the element [in m] and γ w the volumetric weight of water 10 kn/m 3. Reliability function of tilting The failure mode tilting is described above in the context of the general description of the failure modes of the wave return wall. Failure of the wave return wall due to tilting occurs when the resulting force is not within the core of the foundation plane. This is expressed by the following reliability function: Z = 6 1 b f ΣM ΣV b f is the width of the foundation [in m], see fig. 6.5., ΣM is the resulting moment of the horizontal forces with respect to the centre of the foundation plane. Theoretically speaking the eccentric weight of the wall also contributes to this moment. However, the arm of the eccentric weight of the wall appears to be small in case of the Caldicot Levels flood defences. Therefore, the eccentric weight of the wall does not make a significant contribution to the moment and is not taken into account. ΣV is the total weight of the wave return wall. The resulting moment is represented by the following expression: ΣM = H wave * (0.5*h m +h f ) - H p;g * 1/3* h d + A w *l*γ b *a z In which H wave is the horizontal wave impact force [kn] according to the expression mentioned above in relation to the failure mode sliding. h m is the height of the wall, see fig.6.5., h d is the depth of the foundation with respect to the crest level of the embankment, H p;g is the horizontal passive force [in kn] according to the expression mentioned above in relation to failure due to sliding. A w *l*γ b is the weight of the wall and a z is the eccentricity of this weight with respect to the centre of the foundation plane (as is mentioned above this contribution is negligible in this case). ΣV is equal to the expression mentioned above in relation to the failure due to sliding. The performance of the embankment with wave return wall as a whole in case of the flood defence improvements To this point the function of the wave return wall is defined, the effects of this wave return wall on its surroundings are known and the reliability functions of the failure modes of the wave return wall are defined. In other words, only the wave return wall has been subject to analysis up until now. Therefore, the next step before implementing these failure modes in PC-Ring is to determine how the two structures, the embankment and the wave return wall, cooperate. First the performance of the embankment with wave return wall is discussed on a theoretical level. Second the performance of the embankment with wave return wall as implemented in PC- Ring is presented. 6-7

82 6. Analysis of the failure modes connected to the components The theoretical performance of the embankment with wave return wall Main thought Failure of the wave return wall does not necessarily lead to failure of the embankment as well. This depends on the probability of failure of the wave return wall in relation to the probability of failure of the embankment. If the probability of failure of the wave return wall is high relative to that of the embankment, then the embankment is not expected to fail after failure of the wave return wall. However, if the probability of failure of the wave return wall is small relative to that of the embankment, then the embankment may fail directly after failure of the wave return wall or without failure of the wave return wall prior to that of the embankment. The effects on the surroundings of the wave return wall is limited to the reduction of overtopping. The failure modes of the embankment other than overtopping remain equally relevant. In other words: the embankment either fails due to attack of the outside slope or due to instability of the inside slope or due to uplifting and piping or finally due to overtopping. In the latter case complications caused by the presence of the wave return wall must be taken into account. This matter is addressed below. Considerations with respect to embankment with wave return wall and fault tree The above main thought leads to the following considerations: Overtopping over embankment with wave return wall damage of grass on the inside slope and consequently erosion of the embankment breach of the embankment. Failure of the wave return wall no more reduction overtopping extra erosion of the inside slope breach of the embankment. Overtopping over embankment with wave return wall saturation of the clay cover layer on the inside slope and consequently instability of the inside slope breach of the embankment. The wave return wall fails no more reduction overtopping saturation of the clay cover layer on the inside slope breach of the embankment. The bullets in the list above can be replaced by the OR-gate. This leads to the fault tree in Etc.. Overtopping Instability of the inside slope Erosion rear slope without reduction Erosion rear slope Erosion rear slope Saturation Saturation rear slope without reduction Saturation Failure of wave return wall Failure of wave return wall Figure 6.6. Place of wave return wall in failure mode overtopping 6-8

83 6. Analysis of the failure modes connected to the components fig.6.6. In this figure erosion rear slope means: damage of the grass on the inside slope and consequently erosion of the embankment body. In the same figure saturation means: saturation of the pores of the clay cover layer on the inside slope and consequently instability of the inside slope. Discussion of this theoretical approach in relation to implementation in PC-Ring The implementation of the system in PC-Ring as suggested in the fault tree in fig.6.6. brings some complications. One complication is the combination of the failure modes that are already part of PC-Ring, erosion of the rear slope and saturation, with the probability of failure of the wave return wall. Another complication is the length effect of the wave return wall. The performance of the embankment with wave return wall as implemented in PC-Ring The above mentioned complications have lead to an other implementation of the system in PC-Ring than in fig.6.6. The following is explained below: The implementation of the system of the embankment with wave return wall in PC-Ring. The approach of the influence of the wave return wall on the overtopping discharges. The context of the results. Implementation of the system in PC-Ring The assumption which is the basis of the implementation of the system of the embankment with wave return wall in PC-Ring is: that the wave return wall fails under such severe loading conditions that failure of the wave return wall must cause failure of the whole embankment. This assumption makes failure of the wave return wall to an equally important failure mode as for instance overtopping, instability of the inside slope, attack of the revetment on the outside slope or uplifting and piping. This leads to the system s fault tree as shown in fig.6.7. Failure of embankment with wave return wall Failure of wave return wall Overtopping Instability of the inside slope Attack of the revetment on the outside slope Uplifting and piping Figure 6.7. Fault tree of embankment with wave return wall as implemented in PC- Ring The failure modes of the wave return wall are failure due to sliding or failure due to tilting. The reliability functions of these failure modes that have been presented earlier in this text have been implemented in PC-Ring. The eight steps that are taken to calculate the probability of failure are the same as in case of the failure modes that are already present in PC-Ring. These steps can be found in

84 6. Analysis of the failure modes connected to the components Influence of the wave return wall on overtopping discharges The main function of the wave return wall is reduction of the overtopping discharges. The overtopping discharges are in PC-Ring determined with the wave overtopping model according to Van der Meer. With this model it is possible to take the reducing effect into account of a vertical wall which is integrated in the embankment slope. The above mentioned approach of the reduction of the wave return wall according to Van der Meer amounts to: 2 Replace the vertical wall by a 1:1 slope. This slope starts at the outside toe of the vertical wall and reaches a height that is equal to the level of the top of the vertical wall. Add a coefficient of 0.65 to the existing set of reduction coefficients. These reduction coefficients are not directly multiplied with the overtopping discharge. Therefore, this additional coefficient of 0.65 does not imply a 35% reduction of the discharge. A limitation of the above mentioned approach is that the wave return wall is a vertical wall which is not integrated in the slope of the embankment. The wave return wall is placed on the crest of the embankment. Because of this limitation, the by the presence of the wave return wall reduced overtopping discharges according to Van der Meer have been compared. The model that has been used for this comparison is the wave overtopping model according to Owen (HRWallingford, 1998). This model is based on a wave return wall which is shaped similarly to those planned at at the Caldicot Levels flood defences and which is placed on the crest of an embankment. The comparison between the model according to Van der Meer and the model according to Owen is described in Appendix 6-B. The comparison points out that the differences between overtopping according to Van der Meer and Owen are large in case of an embankment without wave return wall. Consequently, using Van der Meer in case of embankments without wave return wall and Owen in case of embankments with wave return wall, leads to probabilities of failure which cannot be compared. Moreover, the model according to Van der Meer is already part of PC-Ring. The Van der Meer overtopping model is therefore preferred to take the reduction of the overtopping by the wave return wall into account. However, two limitations must be kept in mind: Van der Meer actually applies to a vertical wall integrated in the slope of the embankment. Additionally, Van der Meer might provide too high overtopping discharges. Context of the calculation results The results of the reliability calculations will point out whether the assumption holds that the embankment breaches if the wave return wall fails. If the probability of failure of the wave return wall is high relative to the probability of failure due to overtopping of the embankment then the assumption is not justified. However, if the probability of failure of the wave return wall is of the same order of magnitude as or smaller than the probability of failure due to overtopping of the embankment, then the assumption is justified. 6-10

85 6. Analysis of the failure modes connected to the components 6.3. Failure modes connected to high grounds with masonry wall facing, component 3 Introduction The high grounds with masonry wall facing are regarded in this study as an embankment with a very wide crest and a masonry wall revetment on the outside slope. This approach leads to the same failure modes as the embankment without additional structures as discussed in How these failure modes are regarded in the context of this component is discussed below. No flood defence improvements are associated with this component. Failure modes of high grounds with masonry wall facing The failure modes that are incorporated in PC-Ring are addressed separately in the context of high grounds with masonry wall facing: Overtopping Overtopping of the high grounds with masonry wall facing can occur. However, the likelihood that this overtopping will lead to breach of the 200 meter wide embankment is small. Overtopping discharges on the other hand will cause damage to the houses on the crest of the high grounds. Moreover, large discharges may not lead to breach but they can flood the area behind the high grounds. When overtopping discharges do not cause breach but do lead to flooding this has been called non-structural failure in chapter 4. A reliability function of non-structural failure is in the form of: the actual overtopping discharge versus a limit discharge causing flooding. This limit discharge should be linked to a certain storage volume plus an additional volume of water. The storage volume depends on the amount of water that seeps into the ground and the number of drainage canals that are available in the area. The additional volume of water is the part of the overtopping discharge that cannot be stored and which presence causes direct damage. Such a failure mode is not available in PC-Ring. The proposed approach of this problem is therefore to choose a value of the limit discharge. This critical discharge is chosen such that it is expected to initiate damage to the high grounds. In one of the reports from the Environment Agency 3 a summary is given of the limit discharges which are expected to initiate damage. In case of the category broad embankments with shallow backslopes, grass embankment with rock armour a limit discharge of m 3 /s/m is applied. A limit discharge marking the initiation of damage is actually a serviceability limit state and not an ultimate limit state. This choice has been made deliberately because the volume of water connected to this discharge might be enough to cause ULS damage to the houses on and the land behind the high grounds. Instability of the inside slope The inside slope is approximately 200 meter away from the outside water levels. A change in outside water level hardly has any effect on the water pressures near the inside slope. The relevancy of this failure mode is therefore very small. Attack of the revetment on the outside slope of the embankment The masonry wall revetment on the outside slope of the high grounds is a very well maintained structure. The revetment is located such that it is expected to be under heavy 6-11

86 6. Analysis of the failure modes connected to the components attack from waves. If the revetment fails and the erosion process progresses land inward the houses on the crest of the high grounds are in danger. For two reasons this failure mode is not taken into account in this project: The failure modes related to the masonry wall are not incorporated in PC-Ring. However very important to the buildings located on top of the high grounds, the probability of failure of the structure is expected to be very low. Moreover, The probability of flooding of the Caldicot Levels due to failure of the masonry wall and consequently erosion of the 200 meter wide embankment is low or negligible. Uplifting and piping Due to the width of the embankment the seepage length is large. Therefore this failure mode is not taken into account Failure modes connected to raised grounds along Severn Estuary, component 4 The raised grounds along the Severn Estuary are regarded in this study as an embankment with a very wide crest. The width of this crest varies along the flood defences. This approach leads to the same failure modes as the embankment without additional structures as discussed in How these failure modes are regarded in the context of this component is discussed below. Flood defence improvements are planned for this component Failure modes connected to component 4, present form As is mentioned above, the same failure modes as for embankment without additional structures apply to this component. Overtopping Overtopping of the raised grounds along the Severn Estuary can occur. However, the likelihood that this overtopping will lead to breach of the embankments with varying large widths is small. Overtopping discharges on the other hand may not lead to breach but they can flood the area behind the raised grounds. The area behind the raised grounds is used for industrial purposes. When overtopping discharges do not cause breach but do lead to flooding this has been called non-structural failure in chapter 4. The type of reliability function which should be applied, is addressed above in 6.3. in the light of failure of the high grounds with masonry wall facing. The same type of approach is proposed as in 6.3.: the choice of a limit discharge connected to initiation of damage. In case of the category broad embankments with shallow backslopes, grass embankment without rock armour a limit discharge of m 3 /s/m is applied. This limit discharge is connected to a serviceability limit state and not an ultimate limit state. This choice have been made deliberately as the industrial area behind the raised grounds might suffer significant damage long before the raised grounds breach. Instability of the inside slope The inside slope is very far away from the outside water levels. A change in outside water level hardly has any effect on the water pressures near the inside slope. The relevancy of this failure mode is therefore very small. 6-12

87 6. Analysis of the failure modes connected to the components Attack of the revetment on the outside slope of the embankment The raised grounds are very wide embankments. Even if the revetment is damaged, the likelihood is very small that the erosion process progresses long enough to cause breach of the embankment. Uplifting and piping Due to the width of the embankment the seepage length is large. Therefore this failure mode is not taken into account Failure modes of flood defence improvement of component 4 At some points the raised grounds are improved with a wave return wall to evidently reduce the amount of overtopping. The reducing effect of the wave return wall on the actual overtopping discharges is taken into account. The choice of the limit discharge remains the same. Another note is that failure of the wave return wall will not lead to failure of the complete embankment. Therefore, the assumption that is made with respect to the implementation of failure of the wave return wall in PC-Ring does not hold in this case Failure modes connected to raised grounds along the River Usk, component 5 The raised grounds along the River Usk are of the same nature as the raised grounds along the Severn Estuary. The only difference is the different hydraulic regime that poses the hydraulic loading conditions. Apart from that, no flood defence improvements are planned for these flood defences. For the approach of the failure modes, see Failure modes connected to the river banks of the Usk, component 6 North of the raised grounds along the River Usk no embankments are present. The river banks consist of docks, wharfs, quays or just high river banks. For none of these mentioned cases failure modes are available. To approach this problem simply the probability is regarded that the highest point of a cross section of the river bank is exceeded. The lower cross sections along the River Usk have been selected. During this selection the near presence of residential or industrial areas (the Usk passes through Newport) has been taken into account. 6-13

88 6. Analysis of the failure modes connected to the components 1 HRWallingford Ltd., Wave overtopping of seawalls, Design and assessment manual, R&D Progress report W5/006/2, Environment Agency Van der Meer, J.W., Wave run up and wave overtopping of embankments, H 2458/H 3051, Waterloopkundig Laboratorium WS Atkins, Caldicot Levels Sea defence improvements, Design Parameters Report, Swansea

89 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Introduction As is mentioned in the Introduction, the actual flood defence system must be translated into a model, this model must be expressed into data and these data are used to perform calculations. Finished part of the analysis The first step in this modelling process has been taken in chapter 5. In this chapter the Caldicot Levels flood defence system s boundaries and its components have been defined. This step has pointed out the relevant defence length for the calculation of the probability of inundation and the area which suffers consequences in case the flood defence system fails. The second step has been taken in chapter 6. In this chapter another part of the system that is part of the reliability analysis has been modelled, namely, the processes that lead to failure. In other words: the failure modes connected to the components. Objective of this chapter The next step is to translate the relevant defence length that has been defined in chapter 5 into a model which can be used in the reliability calculations. This model is finally expressed into data which can be used in those reliability calculations. Set-up of this chapter The set up of this chapter is as follows: The chapter starts with mentioning the information that is available to support the flood defence modelling process in 7.1. The first step in the process of modelling the flood defences is the division of the flood defence system into embankment stretches and sections, see 7.2. The result of this first analysis is a flood defence system that consists of sections which are represented by one cross section. The second step is to select the embankment sections that are expected to contribute most to the probability of failure, see 7.3. This selection is done based on rough indicators for each separate failure mode. This assembly of sections represents the flood defence system in connection to the reliability calculations. Ideally, the complete flood defence system should be included in the reliability calculations. However the section selection is applied to reduce the amount of work with respect to data gathering. The third step is to express this assembly of sections into data which can be used in the reliability calculations, see 7.4. The selection of sections of the flood defence improvements is equal to the selection representing the present flood defence system. The aim is after all to compare the probability of flooding of the present flood defences with the improved flood defences. For the reason above, the flood defence improvements are not addressed in the modelling process in 7.1. to 7.3. However, they are part of the description of the process of data gathering.

90 7. Modelling the Caldicot Levels flood defence system and expressing this model in data 7.1. Available information to support the flood defence modelling process Information is available on the following topics: The location, in the form of maps and land use. The geometry of the flood defences, in the form of 116 cross sections describing the flood defences along the Severn Estuary and 76 cross sections of the river banks along the River Usk. The general geotechnical condition of the Caldicot Levels flood defence system, in the form of the soil structure and the soil properties. Revetments that are present along the flood defence along the Severn Estuary. The hydraulic boundary conditions: water levels, wind speeds, wind directions, waves. This information is described more detailed in chapter 3, the boundary conditions Division of the flood defence system in embankment stretches and sections Division in embankment stretches In chapter 4, the following rough external characteristics that must be applied to make the division in embankment stretches are mentioned: Orientation to the wind directions. High water regimes, differences in extreme water levels. Geometrical characteristics foreshore. External geometry of the water defence. For a detailed general description of these characteristics, see chapter 4. The application of these rough characteristics to the Caldicot Levels flood defence system results in 45 stretches and is addressed below. A description of the results from the division in embankment stretches can be found in Appendix 7-A. The embankment stretches are indicated at a map in Appendix 7-B. Orientation to the wind directions Significant changes in orientation to the wind direction of the flood defences along the Severn Estuary have been taken into account. In case of the Severn Estuary the westerly wind directions are associated with more severe wave conditions than the easterly wind directions. This is caused by a combination of high wind speeds that are more likely to come from the westerly wind directions, large fetches and relatively large mean depths along these fetches. In case of the River Usk the orientation of the river banks with respect to the wind direction varies significantly. However, in case of the Usk, only the frequency of exceedance of the local water levels is regarded. High water regimes Along the Caldicot Levels flood defence system a clear difference is present between the hydraulic regime formed by the Severn Estuary and the hydraulic regime formed by the River Usk. The flood defences along the River Usk, are represented by two components: the raised grounds along the River Usk and the river banks of the Usk. The remaining four components are located along the Severn Estuary. Geometrical characteristics foreshore In case of significant changes in the width of the foreshores of the embankments a division in stretches has been made. 7-2

91 7. Modelling the Caldicot Levels flood defence system and expressing this model in data External geometry The most important differences in geometry are of course the differences between the components. However, flood defences of one component type have been into stretches which contain cross sections which are similar of shape and dimensions. Apart from that differences in revetment have been taken into account in the division in stretches according to external geometry Division in embankment sections The division in embankment sections must be made based on failure mode related considerations, for instance: Different types of outside slope revetment (types and construction). Detailed geometrical differences. Differences in the foundation soil. Differences in the inside slope revetment of embankments (quality of the grass, thickness and qualification of the clay cover layer on the inside slope, the angle of the inside slope, etc.). Information about the construction of the embankment (clay embankment, sand embankment with a clay core, etc ). For a detailed general description of these characteristics, see chapter 4. The application of these failure mode related considerations to the Caldicot Levels flood defence system points out the following: First, the different types of revetment have already been taken into account in the division in embankment stretches. Second, as for the considerations with respect to the foundation soil and the construction of the embankment: the geotechnical data are limited to information that is generally applicable to the Caldicot Levels flood defence system. Detailed local information is not available. This does not support a more detailed division in embankment sections. Finally, it is assumed that the revetment on the inside slope of the embankment consists of grass with good quality at all locations along the flood defences. An exception is made for those locations for which information is available by means of the site visit. Therefore, the division into embankment sections has been based on the detailed differences in geometry. This results in 116 sections along the Severn Estuary and 76 sections along the River Usk. Each of the sections is represented by one cross section. These cross sections are equal to those that have been mentioned in chapter 3 which describes the boundary conditions. The division into embankment sections can be found in Appendix 7-B Selection of the relevant embankment sections for each failure mode For each failure mode the following is addressed: The general relevancy of a failure mode in case of the Caldicot Levels flood defence system. The indicator which has been used for the selection of the relevant sections. This indicator must provide the possibility to rank the sections in relation to a certain failure mode. The weakest sections are selected. These sections are expected to contribute most to the probability of failure of a certain failure mode. 7-3

92 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Section selection for overtopping Relevancy of the failure mode overtopping The failure mode overtopping is expected to contribute significantly to the system s probability of failure for three reasons: The fact that a new wave return wall is an important element of the flood defence improvements of the Caldicot Levels flood defence system. Needless to say that the function of these wave return walls is to reduce overtopping discharges. According to the past storm events which have been mentioned in chapter 3, problems connected with the failure mode overtopping have occurred. Along the Usk problems with flooding of the river have occurred in the past as well. The indicator for the selection in connection to overtopping Two indicators are regarded in this context: The indicator of the section selection along the Severn Estuary for the failure mode wave overtopping/running over. The (similar) indicator which has been applied for the selection of the river bank sections along the River Usk. In this context overtopping/running over is regarded as equal to a probability of exceedance by the river water level of a certain elevation. Indicator of the section selection for overtopping along the Severn Estuary As the failure mode overtopping is expected to contribute significantly to the total probability of flooding a large selection of sections is made. The following considerations have been made with respect to this selection: From each of the 45 embankment stretches at least one section is selected in the reliability calculations. The section that is chosen to represent one stretch is the section with the lowest crest level. The crest level is a very important factor in the model which is applied to determine the overtopping discharges. Therefore, the crest level is used as the indicator for overtopping. Finally, stretches which have been involved in the overtopping damage by the past storm events are represented by more than one section. It is possible that one stretch points out to contribute significantly to the total probability of failure. In that case it is recommended to include more sections from that stretch in a second calculation round. The latter is not part of this study. Indicator of the section selection for overtopping along the Usk The probability of failure is considered to be equal to the probability that the river water level at the Usk exceeds a certain elevation. This elevation is taken equal to the highest point of the river bank. See fig.3.4. in chapter 3, a general impression of the elevation profile along the Usk is given. This elevation profile points out that the river bank slopes down in the direction of Newport. Therefore the selection of the river bank sections has been based on: The relative height of the river bank given a certain hydraulic event. For instance a discharge with a ten year return period in combination with an extreme tide event. The relative height can be found by subtracting the occurring river water levels from the levels of the highest points of the river banks. The river bank sections with the lowest relative height have been chosen in combination with the following: The distance of the residential or industrial areas from the river banks. 7-4

93 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Therefore, the indicator can be described as: the river bank sections with the lowest relative height and the nearest threatened residential or industrial areas. It is possible that one stretch points out to contribute significantly to the total probability of failure. In that case it is recommended to include more sections from that stretch in a second calculation round. The latter will not be part of this study. The selection has resulted in a high number of sections. In Appendix 7-H the cross sections that are included in the overtopping reliability calculations are presented Section selection for instability of the inside slope Relevancy of the failure mode instability of the inside slope There are no past events which indicate problems with damage due to instability of the inside slope. However, this failure mode is included for two reasons: The inside slopes of the embankments appear to be steep. This is an indication that the failure mode might be relevant. To compare the results from the calculations of the failure modes that are expected to be relevant: the probability of failure due to instability of the inside slope is expected to be lower than the probability of failure due to more relevant failure modes. The indicator for the selection in connection to instability of the inside slope For instability of the inside slope two selection rounds have been applied: First one section of each stretch Value nominator and denominator Bishop against increasing crest level has been selected according to a rough indicator. Second the sections representing one stretch are compared according to a more detailed indicator It is possible however, that after the first reliability calculation one stretch crest level points out to contribute significantly to the total probability of failure. In that case it is recommended to include SF Bishop against increasing crest level more sections from that stretch in a second calculation round. The latter is 5 not be part of this study. Indicator used in first selection round The indicator which has been used to compare the sections forming one embankment stretch is the crest level. A high crest level increases the probability of failure due to instability of the inside slope. See fig.7.1. value numerator or denominator Stability factor Bishop crest level numerator denominator Figure 7.1. Reaction of numerator and denominator of Bishop stability factor to increasing crest levels SF 7-5

94 7. Modelling the Caldicot Levels flood defence system and expressing this model in data In this figure the Stability Factor according to Bishop is shown against increasing crest levels. In the lower figure the stability factor is seen to decrease given higher crest levels. Lower stability factor means lower stability of the inside slope. An explanation of the method according to Bishop is given in Appendix 7-C. Indicator used in second selection round The sections that have been selected in the first round are now compared based on the Bishop stability factor from calculations with software called Mstab. The weakest sections have been chosen. To this number some strong sections have been added which can be used to compare the results from the weak sections. Moreover, these sections have been chosen such that the sections are spread over the length of the flood defence. The results from this selection is presented in table 7.1. The numbers of the selected cross sections correspond with the numbers of the cross sections as supplied by the Environment Agency, see Appendix 7-A and 7-B Section selection for uplifting and piping Relevancy of the failure mode uplifting and piping There are no past events that prove that problems with uplifting and piping have occurred. There is no evidence either that indicates that piping might occur: The impervious cohesive layers are thick along the complete length of the Caldicot Levels flood defence system. Therefore, the occurrence of uplifting is not likely. The seepage lengths are large. This is in the first place caused by the extensive foreshores and shallow areas in front of the flood defences. These foreshores or shallow areas consist of thick cohesive layers. Thus, the distance between the inside toe of the embankment to the point where the sand layer is in direct contact with the water at the Severn Estuary is very large. Take for instance the bathymetry that is given in Appendix 3-B. The distance of the embankment to the end of the mud layer can be as high as 980 meter. According to the description of the cohesive layers in occasional small sand partings and lenses can occur. A conservative scenario that includes the presence of these sand partings and layers could be applied. However, in this study such a scenario does not contribute to achieving the objectives. Because of the above mentioned three reasons the failure mode uplifting and piping is not included in the reliability calculations. The indicator for the selection in connection to uplifting and piping If, however, in other cases, the failure mode uplifting and piping is expected to be relevant then the following set of indicators can be used to rank the sections 1. F opb γ = γ γ nat w w d 0.8(H h binnen ) Table 7.1. The cross sections which have been selected for instability of the inside slope Selected cross sections Stability factor In which F opb is the indicative safety in connection to heave, γ nat = is the mean wet unit weight of the impervious layer covering the sand layer (kn/m 3 ), γ w is the unit weight of the water (kn/m 3 ), d is the thickness of the impervious layer, H is the water level outside, h binnen is the water level at the inside of the embankment. If F opb < 1, then F opb is taken

95 7. Modelling the Caldicot Levels flood defence system and expressing this model in data The indicative safety in connection with piping is determined with: F pip L = 18 (H h binnen 0.3d) In which L is the estimated seepage length, if F pip < 1 then F pip is taken 1. The combined indicator for the selection of the embankments is: I opb / pip = 3(F opb 1) + (F pip 1) Cross sections are ranked according to increasing indicator. Cross sections with I opb/ pip =0 for sure have to be taken in account. Other sections can be selected by taking the lowest indicator values Section selection for attack of the revetment on the outside slope Relevancy of the failure mode attack of the revetment on the outside slope For the following reasons failure due to attack of the revetment on the outside slope is expected to be relevant: The occurrence of for instance the masonry wall at Goldcliff and the armour revetment along extensive stretches of the flood defences indicates that the outside slopes of the embankments are severely attacked. This should be regarded in combination with the relative small width of the embankments. The latter indicates little remaining resistance against the erosion process after the revetment has been damaged. According to the past storm events which have been mentioned in chapter 3, damage of the revetment on the outside slope has occurred. The indicator for the selection in connection to attack of the revetment on the outside slope The sections have been selected according to the following strategy: First a selection is made based on the strength of the revetment. To this end the three different revetment types are discerned: Grass Rock armour revetment Placed stone revetment Second a selection is made based on the remaining strength in relation to the erosion process. Therefore, for each type of revetment the five weakest sections are selected according to the following indicator: L B = L BK + ( h d 1 1 h) + tanαu tanαi Table 7.2. Selection of the cross sections for attack of the revetment on the outside slope and the L b values for a 10 year return period water level Placed stone revetment Selected cross sections Selected cross sections In which L B is the width of the embankment at the height of the outside water level h. L bk is the width of the crest. h d is the crest level. α u is the angle of the outside slope and α i is the angle of the inside slope. For all the sections the same hydraulic Grass L B (m) Riprap Selected cross sections L B (m) S

96 7. Modelling the Caldicot Levels flood defence system and expressing this model in data event has been chosen in connection to the outside water level: a ten year return period water level. This takes the spatial variations in water level into account. Only two sections with placed stone revetment appeared to occur. The results of the selection process are given in table 7.2. The numbers of the selected cross sections correspond with the numbers of the cross sections as supplied by the Environment Agency, see Appendix 7-A and 7-B Gathering data about the relevant sections for the reliability calculations In chapter 4, paragraph a general impression of the data requirements is given. The same set-up is applied in the description of the data gathering. The data requirements of the wave return wall are added: General data requirements. See Statistical data of the wind directions. Statistical data of the wind speeds. Statistical data of the water levels at sea Statistics of the discharge. Data with respect to local water levels. Geometry of the flood defence system in its present and improved form (including geometry of wave return wall). Fetches. Overtopping and the wave return wall. See Instability of the inside slope. See Among others, information related to MPROSTAB Attack of the revetment on the outside slope. See General data requirements Statistical data of the wind directions First the available information is addressed. Second, the adaptation of this information to the data requirements in PC-Ring are discussed. Third, the results of this adaptation are presented. N Available information A list is available containing the number of wind speed events in twelve different wind directions during a period of 29 years 2. The probability of each one of those twelve wind directions has been determined by taking the number of events in one wind direction and dividing them by the total number of events. See fig and Appendix 7-D for the resulting relative frequencies. Adaptation of available information to data requirements in PC-Ring This study is based on sixteen wind directions. Moreover, the sectors that represent the wind directions are differently arranged than in the available information. See fig.7.2. The available probabilities of the twelve wind directions have been adjusted proportionally to the different arrangement and magnitude of the sixteen wind direction sectors. The proportionality is based on the extent of overlapping of the 22.5 sectors by the 30 sectors. An N Figure 7.2. Change of division in twelve to sixteen wind direction sectors in case of the available information (top) and after adaptation (bottom) 7-8

97 7. Modelling the Caldicot Levels flood defence system and expressing this model in data example is given in Appendix 7-D. Results of this adaptation See Appendix 7-D for the results from the above performed adaptation of the available information. Fig and fig.7-d.2. in the appendix point out that the westerly wind directions have the highest probability of occurrence. Statistical data of the wind speeds First the available information is addressed. Second, the adaptation of this information to the data requirements in PC-Ring are discussed. Third, the results of this adaptation are presented. Available information Weibull distributions of the wind speed given the wind direction and an omnidirectional wind speed distribution are available. The wind directions concern 30 sectors. The North sector is represented by -15 to 15 with respect to the North. Adaptation of available information to data requirements in PC-Ring The distribution which is applied in PC-Ring is, see chapter 4: F( u h sea, ϕ) = P( u < u h sea K, ϕ) = exp exp ϕ ( u) + ρ w ( h m w sea A h ) / B h K φ (u)=a w u 2 +b w u+c w In which u is the wind speed, h sea is the water level, φ is the wind direction, ρ w is the correlation between the wind speed and the water level given a wind direction, A h, B h and m w are fitting parameters. In chapter 3 the correlation between the wind speed given the wind direction and the water level at sea given the wind direction is assumed to be negligible. Therefore, ρ w = 0. With M w =1 the following distribution is found: sea sea 2 [ exp( ( a u + b u c )] F ( u h, ϕ ) = P( u < u h, ϕ) = exp + w This distribution function resembles a Gumbel distribution function. Combining this with the available information leads to the following required adaptation steps: The available wind speed distributions given the 30 sectors must be transferred to a division in 22.5 sectors. The available Weibull distributions have to be transformed to the above mentioned Gumbel shaped distribution functions. Comparison between the available omnidirectional distribution and the omnidirectional distribution which is derived from the adapted conditional wind speed distributions. These three steps are described in Appendix 7-E. Results of this adaptation The comparison between the available omnidirectional distribution function and the omnidirectional distribution which has been derived from the adapted conditional distributions is shown in fig.7.3. The difference between the two functions for the highest wind speeds (u>35m/s) varies between 1 and 2.5 times the probability of exceedance at that wind speed as calculated with the actual available omnidirectional distribution function. w w 7-9

98 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Fig.7.4. is added to provide an impression of the difference between the westerly and easterly wind directions. The westerly wind directions are represented by the light lines, the easterly wind directions are represented by the dark lines. Most of the distribution functions of the westerly wind directions are shifted to the right with respect to the easterly wind directions. Such a shift to the right indicates that the probability of exceedance of the high wind speeds is relatively higher. The highest wind speeds are therefore more likely to come from the west. comparison betw een actual and derived omnidirectional distributions F(u) Wind speed (m/s) derived actual Figure 7.3. Comparison between the available omnidirectional distribution function and the omnidirectional distribution which has been derived from the adapted conditional distributions. F(U<u) Wind speed (m/s) Figure 7.4. All the conditional distribution functions. The dark coloured lines represent the easterly wind directions, the light coloured lines represent the westerly wind directions Statistical data of the water levels at sea First the available information is addressed. Second, the adaptation of this information to the data requirements in PC-Ring are discussed. Third, the results of this adaptation are presented. Available information There is no information available about distribution functions given the wind direction of the water levels at the mouth of the Severn Estuary. In chapter 3 the water level at the mouth of the Severn Estuary is assumed to be independent of the wind speed. Therefore, the variations at the mouth of the Severn Estuary are assumed to be the result of astronomical tidal variations only. 7-10

99 7. Modelling the Caldicot Levels flood defence system and expressing this model in data If the water levels at the mouth of the Severn Estuary solely vary due to the tidal variations, the water levels are deterministic of nature. However, in PC-Ring the following Weibull distribution function must be defined with respect to the water levels at the mouth of the Severn estuary (see chapter 4): For h sea > m d : α α h m ( ) ( ) 1 exp sea d F weibull h ϕ = P h sea < h ϕ = p + sea sea c σ σ Figure 7.5. Impression of variations in the astronomical tide at a location at the southwest coast in The Netherlands (Vlissingen) (from d Angremond et al., 1999) Adaptation of available information to data requirements in PC-Ring Thus, a statistical distribution of the water levels at the sea is required in order to make calculations with PC-Ring possible where a deterministic approach is actually preferred. Therefore, the above mentioned Weibull distribution function is defined, based on the high water level during three tidal events. Fig.7.5. provides an impression of tidal variations at a location at the Dutch coast. Mean tide, High water: OD+2.39 m exceeded in about 0.5 of the tide events, therefore, probability of exceedance 0.5. Spring tide, High water: OD+3.29m at the mouth of the estuary. Spring tide occurs twice a month, approximately 25 times a year, probability of exceedance in the order of magnitude of 25/707= This number of 707 is derived from the number of tides that occurs in a year: period of a tide is hours, 365*24/12.42 = 707. Literature source [2] points out that a lunar nodal cycle with a period of 18.6 years occurs. In connection to this cycle the following is mentioned in relation to the Severn Estuary: Annual variations in mean High water of 0.15m and annual variations in the tidal ranges of 0.30m. At Newport during one of the 18.6 year cycles, a peak of a highest spring tide of 7.5m has occurred. This water level corresponds with a high water at the mouth of the Severn Estuary of about OD+4.5m according to the Mike11 model which is described in chapter 3. The probability of exceedance of the peak high water value of OD+4.5m in the 18.6 year lunar nodal cycle is estimated with 1/(18.6*707) = 7.6*

100 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Results of this adaptation The high water levels of the above mentioned three tidal events and the accompanying probabilities of exceedance have been fitted with the Weibull distribution function. The results are shown in fig.7.6. The focus of the distribution is on the spring tide and the peak spring tide. In the context of the reliability which aims to find the system s probability of flooding, the extreme water level events are emphasised. Finally, as the water levels are assumed to be independent of the wind speed, the water level statistics given the wind direction are equal for each different wind direction. The three mentioned events hardly form a basis to fit a realistic distribution. A data set that covers at least three years is required to fit a statistical distribution which can be used in applications. Moreover, the deterministic nature of the astronomical tide is approached with a statistical distribution function. LN( P(h sea h sea )/p c ) Three tidal events -5 Weibull "fit" Water level at mouth Severn Estuary (m OD) P(h sea h sea ) Water level at mouth Severn Estuary (m OD) Three tidal events Weibull "fit" Figure 7.6. "Fit" of the weibull distribution for water levels to few available events. In the left plot the probabilities have been transformed according to LN(probability of exceedance/p c ) to achieve a better fit. In both plots the weibull distribution only applies for the tidal events with a high water level > m d = 2.7. In the left plot this equals the intersection with the horizontal axis. In the right plot the intersection equals the P(h sea >h sea ) = 1.0 level. α = 0.8 σ = p c = 1.0 m d = 2.7 Statistics of the discharge at the River Usk First the available information is addressed. Second, the adaptation of this information to the data requirements in PC-Ring are discussed. Third, the results of this adaptation are presented. The discharges of the rivers mouthing at the Severn Estuary are assumed to be negligible. Therefore, below only the discharges at the river Usk are addressed. Available information In chapter 3, paragraph , table 7.3. is presented as available information with respect to peak discharges and the accompanying return periods at the River Usk. The required statistics of the discharge have been discussed in chapter 4, paragraph The statistics of the discharge Q are represented as a function of the return period. This function is in the form of: Q = a*ln(r) + b Table 7.3. Peak discharges occurring at the River Usk with a ten year, twenty year, fifty year and hundred year return period Q m 3 /s Q m 3 /s Q m 3 /s Q m 3 /s Adaptation of available information to data requirements in PC-Ring The discharge values in table 7.3. have been fitted with a regression line. The result is the following equation: 7-12

101 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Q = *Ln(R) In which Q is the discharge at the River Usk and R is the accompanying return period of the discharge. Results of this adaptation The fit of the discharge statistics is given in fig.7.7. The amount of information in case of the discharge at the Usk is more than in case of the water levels. However, the amount is still very low. Like in the case of the water levels, the discharge statistics must be regarded with scepsis. Q values Statistics of Q at Usk y = Ln(x) Return periods Figure 7.7. Statistics of Q at the River Usk Q regression line Data with respect to local water levels points out that the local water levels must be determined for a number of locations. The number of locations represents the level of accuracy (the latter is discussed in 4.1.4). For each one of those locations one table is constructed which contains the local water levels. The local water levels are determined as a function of a combination of the following: Nine different discharges. Five different wind speeds. A number of wind directions. Six different water levels at sea. Before discussing the boundary conditions which are mentioned above, the following notes are made: The discharges only apply to the hydraulic model of the River Usk as the discharges of rivers mouthing at the Severn Estuary are assumed to be negligible. In chapter 3, paragraph the set-up of the Mike11 model of the River Usk is presented. The water levels at the mouth of the Usk are a function of the local water levels near Newport at the Severn Estuary. The latter are determined with Mike11 as a function of the water levels at the mouth of the estuary and the wind speed which causes surge. See fig.7.8. for an additional explanation. Water levels at the mouth of the Severn Estuary Wind speed above the Severn Estuary Mike11 model of the Severn Estuary Local water level at Newport in the Severn Estuary Discharge at the Usk Local water levels at Usk Mike11 model of the Usk Figuur 7.8. Process which is applied to determine the local water levels at the Severn Estuary and the River Usk. 7-13

102 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Therefore, the entries for the wind speeds and water levels at sea for the local water levels at the Usk are equal to those that are applied to the Severn Estuary. Number of locations A location serves to define the local water levels. A relatively high level of accuracy can be achieved by for instance defining the local water levels every 1000 meters along the river Usk or the Severn Estuary. However, to limit the amount of work but at the same time to support the objectives of this study a lower number of locations has been chosen: In case of the Severn Estuary: four locations. This implies a location approximately every 6 km. The locations can be found in fig.3.8. as A1 (=Newport), A2 (=Goldcliff), A3 (Magor Pill), and A4 (= Sudbrook). In the context of this report it is easier to number these locations oppositely: location 1 = Sudbrook, location 2 = Magor Pill, location 3 = Goldcliff, location 4 = Newport. In case of the River Usk: five locations: location 5, location 6, location 7, location 8 and location 9. This implies a location approximately every 2 km. All the above mentioned locations can be found in Appendix 7-B. Nine different discharges With respect to the discharges two aspects are relevant: The choice of the nine different peak values of the discharges. The shape of the behaviour of the discharge in time. The discharges of the rivers mouthing at the Severn Estuary are assumed to be negligible. The discharges at the River Usk are addressed below: Choice of the nine different peak discharges The discharges must be chosen such that the complete range of possible occurring discharges at the Usk is represented. The emphasis of this range of discharges is on the extreme values. The choice of values has been based on the regression line in fig.7.7. The resulting values are presented in table 7.4. Shape of the behaviour in time of the discharge In chapter 3, paragraph , in fig the behaviour of the discharge in time is given of the data which have been supplied by the Environment Agency. A similar shape has been applied in case of the calculations with the nine discharges which are mentioned above. The values in table 7.4. represent the peak values that are reached in the behaviour in time of the discharge. Applying the peak shaped behaviour of the discharge in time implies that the phase difference between the tidal water levels at the mouth of the Usk and the peak discharge should be taken into account. However, a possibility to take phase differences into account is not incorporated in PC- Ring. The possibility to take the peak discharge as a constant value in time during the calculations has not been applied. In the this case the Mike11 model of the Usk provides more Table 7.4. Discharge values at the Usk as chosen for the reliability calculations Discharges at the Usk (m 3 /s)

103 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Table 7.5. Wind speeds above the Severn Estuary as chosen for the reliability calculations Wind speeds (m/s) Table 7.6. Wind directions at the Severn Estuary as chosen for the reliability calculations Wind directions at Severn Estuary Table 7.7. Wind directions at the River Usk as chosen for the reliability calculations Wind directions at Usk Table 7.8. Water levels at the mouth of the Severn Estuary as chosen for the reliability calculations Discharges at the Usk (m 3 /s) problems of numerical nature than in case of the peak shaped behaviour in time of the discharges. Five different wind speeds The wind speeds must be chosen such that the complete range of possible occurring wind speeds above the Severn Estuary is represented. The extreme values must be emphasised. The annual maxima of the wind speeds are on average 20 m/s. The largest known annual maximum is about 30 m/s. The wind speeds that have been chosen are presented in table 7.5. A number of wind directions The following wind directions have been chosen: Severn Estuary: Eight wind directions have been chosen. See table 7.6. The shore of the Severn Estuary is facing the southern wind directions. The wind directions are chosen such that the surge caused by the wind speed is expected to appear. The calculations with Mike11 point out that the largest surges occur in the wind direction of The wind directions to all cause negative surges. The river Usk: is differently orientated to the wind directions. The shores of the Usk along the Caldicot Levels are generally speaking facing the western wind directions. To limit the amount of calculations with Mike11, four wind directions are chosen. See table 7.7. Six different water levels at sea The water levels that have been chosen to represent the variations at the mouth of the Severn Estuary are listed in table 7.8. The first and second values represent respectively neap and mean tide. The third value represents a water level between mean tide and spring tide. The fourth water level is spring tide. The fifth and sixth water levels are chosen in the light of the lunar nodal cycle of 18.6 years which has been mentioned above. Results of the calculations of the local water levels The results of the calculations of the local water levels at the Severn Estuary with Mike11 are presented in Appendix 7-F. The results of the calculations of the local water levels at the River Usk with Mike11 are presented in Appendix 7-G. 7-15

104 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Geometry of the flood defence system in its present and improved form The sections which have been selected according to the in 7.2. mentioned strategy are represented by one cross section. These cross sections are defined by their geometry and their location. Below some aspects in relation to the geometry of the cross sections are addressed for both the present flood defence system and the improved flood defence system. Flood defence system in its present form The following aspects are mentioned in chapter 4, in relation to the geometry of the flood defence system in its present form: Five, six or seven coordinate pares which contain chainage and elevation. These pares define the geometry of the cross section up to the edge of the crest which is located on the landside. Roughness coefficients which describe the roughness of each of the planes which form the outside slope. Length of the section which is represented by the defined cross section. The nearest two locations where the tables with local water levels are defined and between which the cross section is situated. The percentage of interpolation of the above mentioned two locations associated with the local water level at the cross section. Orientation of the cross section with respect to the north These aspects are presented for the sections that have been selected for the reliability calculations in Appendix 7-H. Improved flood defence system The same aspects as mentioned above are presented in Appendix 7-H in relation to the flood defence system after the application of the improvements. In addition, the new wave return walls as part of the flood defence improvements are addressed. In chapter 6, fig 6.5. the main dimensions of the wave return wall are shown. For the sake of clearness this figure is again presented here in fig.7.9. Wall In the Caldicot Levels flood defence system three main types of wave return walls can be found. The dimensions of these types and where they are located are presented in Appendix 7-H. Foundation Figuur 7.9. Relevant dimensions of the wave return wall Fetches The fetches are required in order to calculate the wave height and wave period according to Bretschneider s model. This has been discussed in chapter 3, paragraph In the light of the same model the mean depth along the fetch is required in order to determine the local wave conditions. In PC-Ring for each off-shore wind direction the fetches and the mean depths along these fetches are entered. Moreover, it is possible to split up one fetch in several parts with 7-16

105 7. Modelling the Caldicot Levels flood defence system and expressing this model in data different mean depths. Fig.3.5. provides an impression of which wind directions imply the largest fetches: the south westerly wind directions. Additionally, these fetches are located in the direction of the deeper parts of the Severn Estuary. Relative large fetches and mean depths imply more severe local wave conditions in case of wind from the south westerly directions. At a number of locations along the Severn Estuary breakwaters are present. Influence of wind coming from wind directions which are blocked by these breakwaters is assumed to be negligible. Information with respect to the fetches can be found in Appendix 7-I. Information with respect to the breakwaters can also be found in this appendix Data requirements in connection to overtopping and the wave return wall Below first the data requirements in connection to the failure mode overtopping in general are mentioned. Second these data requirements are discussed in the light of the flood defence improvements. Required data in connection to overtopping in general Data requirements The failure mode overtopping requires data additional to the data requirements which have been mentioned above in These additional data requirements are: Statistical data in connection to the parameters which form the reliability function of overtopping: The mean value and standard deviation which define the distribution function of the parameters. The correlation length and the spatial correlations in relation to the spatial correlation model. The time interval and the correlation in time in relation to the Borges Castanheta model of the variations in time. Information with respect to the type of critical discharge model: either the model based on the strength of the grass or the manually entered critical discharge values. The statistical data in connection to the wave return wall. The above mentioned information is given in Appendix 7-J. Note with respect to data requirements availability The mean value of the above mentioned statistical data has been derived from the available information of the Caldicot Levels flood defence system. Due to lack of information with regard to the rest of the statistical data, these data have been derived from typical values which are applied in The Netherlands. Data requirements of the flood defence improvements in relation to overtopping One main difference in relation to the failure mode overtopping between the present and the improved flood defence system is the difference in geometry. A second main difference is the presence of the wave return wall. The geometrical data of the present and the improved system are given in Appendix 7-H. The statistical data in connection to the wave return wall are given in Appendix 7-J. It is noted that the influence of the wave return wall on the overtopping discharges has already been included in the 7-17

106 7. Modelling the Caldicot Levels flood defence system and expressing this model in data information of the geometry. The rest of the statistical data with respect to overtopping remains unchanged in case of the flood defence improvements Data requirements in connection to instability of the inside slope Below first the data requirements in connection to the failure mode instability of the inside slope in general are mentioned. Second these data requirements are discussed in the light of the flood defence improvements. Required data in connection to instability of the inside slope in general Below first the data requirements are mentioned in connection to instability of the inside slope. Following, the data requirements that need additional explanation are addressed. Data requirements MPROSTAB requires the following data: Geometry of the embankment and length of the section in case of both the present flood defence system and the flood defence improvements, see Appendix 7-H. The structure of the soil below the embankments: soil types, thickness of the layers. See chapter 3, paragraph Soil properties φ, c, γ and the accompanying statistical data. See below. The piezometric levels in the embankment in case of three different outside water levels. Statistical data with respect to the deflection of the piezometric level. See below. Model uncertainty of the Bishop method. See below. Soil properties In table 3.2. an overview is given of the most important soil properties which have been applied in the MPROSTAB calculations. These soil properties and the accompanying statistical data are listed in Appendix 7-K. The piezometric levels in the embankment Two types of piezometric levels in the embankment and in the soil layers located beneath the embankment are of importance: The groundwater level. The piezometric level in the sand layer which is located below the impermeable layers formed by the upper cohesive formation, the peat layer and the lower cohesive formation. The water pressures have been determined in case of three different outside water levels: First, a water level with a 1000 year return period. Second, the latter water level minus 1.0 meter. Third, the water level in an average situation. Below an explanation is given how the two types of piezometric levels have been determined in case of the Caldicot Levels flood defences. The ground water level The ground water level in the embankment is approached in a conservative way: the ground water level in the embankment connects to the outside water level and heads in a straight line for the ground water level at the inside of the embankment. This straight line is tangent to the inside toe of the embankment. The groundwater level at the inside of the embankment has been presented in chapter 3, paragraph and is assumed to be OD+5.5m. See fig for an example of the ground water level in an embankment. 7-18

107 7. Modelling the Caldicot Levels flood defence system and expressing this model in data This approach is conservative. Within the duration of the storm the ground water level in the embankment must adjust to the outside water level, while the permeability of the cohesive soil forming the embankment is low: in the order of magnitude 6*10-9. Moreover, the outside water levels change quite rapidly in case of the Caldicot Levels flood defence system. On the other hand, water levels in embankments made of cohesive soil are known to be higher than expected considering the simultaneously occurring outside water level. This supports the application of the approach which is described above. Water head in the sand layer Outside water level OD+5.5m Embankment Tangent of the groundwater to the inside toe of the embankment Upper cohesive Lower cohesive Peat Sand Figure Example of the approach of the piezometric levels in the MPROSTAB calculations The piezometric level in the sand layer In fig apart from the groundwater level in the embankment, an example is given of the piezometric level in the sand layer. This piezometric level has been derived from a model which provides an analytical solution to the piezometric level of a sand layer located between two impermeable layers 3. From calculations appears that the piezometric level in the sand layer does not significantly influence the Bishop stability factor. However, the levels have been taken into account in the MPROSTAB calculations. Model uncertainty of the Bishop method In Appendix 7-C the method according to Bishop is described. Moreover, in chapter 4, paragraph , a general explanation is given of how the probability of failure due to instability of the inside slope is calculated. In these descriptions the Bishop stability factor is 7-19

108 7. Modelling the Caldicot Levels flood defence system and expressing this model in data provided with a limit of 1.0 which indicates that a lower stability factor leads to instability. In Appendix 7-K the uncertainty which is taken into account with respect to this limit value is given. Data requirements of the flood defence improvements in relation to instability of the inside slope The calculations of the failure due to instability of the inside slope have also been done in case of the improved flood defence system. The geometry is different with respect to the calculation of the present system. The rest of the information remains the same: the soil properties, the soil structure, the method to determine the piezometric levels and the choice of outside water levels Data requirements in connection to attack of the revetment on the outside slope Below first the data requirements in connection to the failure mode attack of the revetment on the outside slope in general are mentioned. Second these data requirements are discussed in the light of the flood defence improvements. Required data in connection to attack of the revetment on the outside slope in general First the data requirements in general are discussed. Following, the requirements in connection to the different types of revetment are presented. Data requirements The following information is required in relation to the failure mode attack of the revetment on the outside slope: Statistical data in connection to the parameters which form the reliability function of overtopping: The mean value and standard deviation which define the distribution function of the parameters. The correlation length and the spatial correlations in relation to the spatial correlation model. The time interval and the correlation in time in relation to the Borges Castanheta model of the variations in time. Information with respect to the type of revetment: either grass, placed stone revetment or rock armour revetment. Grass For some mean values such as the depth of the grass roots, the duration of the storm or the quality of the grass and the clay of the embankment typical values have been chosen. These typical values are default available in PC-Ring. In case of the grass a good quality has been chosen. In case of the clay of the embankment a moderate quality has been assumed. This assumption is based on the information that along some stretches of the Caldicot Levels flood defence system the cohesive soil from the foreshore has been used to construct the embankments. Other mean values can be derived from available information. For the rest of the statistical data also typical default values in PC-Ring have been chosen. The data requirements can be found in Appendix 7-M. 7-20

109 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Placed stone revetment The same applies to for instance mean values for the quality of clay of embankments with placed stone revetment and the coefficient in relation to the strength of the placed stones: typical default values in PC-Ring have been chosen. Other mean values can be derived from available information. For the rest of the statistical data also typical default values in PC-Ring have been chosen. The data requirements can be found in Appendix 7-M. Rock armour revetment In The Netherlands rock armour revetment is hardly used to protect the outside slope of embankments. Therefore, this revetment is not included in the reliability functions of PC- Ring. To solve this problem, the reliability function of partially penetrated riprap revetment is adjusted. Below first the required reliability function is derived. Next, this function is compared to the reliability function of partially penetrated riprap revetment. Required reliability function of failure of the rock armour revetment The reliability function for rock armour revetment is derived in Appendix 7-L. The result is as follows: Z = D n50 Δ m H 6.2 p s 0.18 ξ p Sd ( ) N 0.2 (plunging waves) The next step is to connect this to the possibilities in PC-Ring. Comparison with partially penetrated riprap revetment In chapter 4, paragraph the reliability function of partially penetrated riprap revetment has been described. Additionally, in it is noted that failure of the partially penetrated riprap revetment consists of two parts: failure due to water overpressures or failure due to wave impact. The first step is to eliminate the reliability function of failure due to water overpressures. This is done by taking a large thickness of the asphalt layer. The consequence is a negligible probability of failure due to water overpressures. The second step is to find out how the reliability function mentioned above of rock armour revetment compares to the partially penetrated riprap revetment failure mode. To this end, the partially penetrated riprap revetment is presented again: Z = D n50 - Δ m ψ Φ u H s b ξ sw p cos(α) In which D n50 is the nominal diameter for which 50% of the grains is larger or smaller than this value, ξ p is the breaker parameter, Δ m is the relative density, ψ u is a parameter for penetration of the asphalt, Φ sw is the stability factor and α is the angle of the outside slope. 7-21

110 7. Modelling the Caldicot Levels flood defence system and expressing this model in data Adjustments to the partially penetrated riprap revetment reliability function The required reliability function for riprap can be found by substituting the following values for the variables in the function for partially penetrated riprap: b = 0.5 ψ u *Φ sw = 6.2 *p 0.18 (S/ N) 0.2 = in which p=0.1, S=2.5, N=7500 α cannot be separately entered in PC-Ring. It is therefore not possible to enter cos α =1 with α = 0. Consequently, the value must be divided by cos α of the regarded cross section. The main disadvantage of this approach is that the damage level S, the permeability parameter P and the number of waves N cannot be separately entered as statistical variables. The data requirements can be found in Appendix 7-M. 7-22

111 7. Modelling the Caldicot Levels flood defence system and expressing this model in data 1 Calle, E., Jonkman, B., Lassing, B., Most, van der, H., Data gathering and modelling for the calculation of the probability of flooding of flood defence systems, Manual (version 3.2), Delft ABP Research, Gwent Levels hydraulic study, Objective A: Joint probability surge and tide wave analysis, Southampton TAW, Guideline for the design of river dikes, part 1- the upper river area, Delft

112 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Introduction As is mentioned in the Introduction, the actual flood defence system must be translated into a model, this model must be expressed into data and these data are used to perform calculations. Finished part of the analysis The first step in this modelling process has been taken in chapter 5. In this chapter the Caldicot Levels flood defence system s boundaries and its components have been defined. This step has pointed out the relevant defence length for the calculation of the probability of inundation and the area which suffers consequences in case the flood defence system fails. The second step has been taken in chapter 6. In this chapter another part of the system that is part of the reliability analysis has been modelled: the processes that lead to failure have been modelled. In other words: the failure modes connected to the components. The third step has been to translate the relevant defence length that has been defined in chapter 5 into a model which can be used in the reliability calculations. This model has finally been expressed into data which can be used in those reliability calculations. The latter two steps have been taken in chapter 7. Objective of this chapter In this chapter the results of the reliability calculations of both the present Caldicot Levels flood defence system and the improved system are given. In all calculations the method according to SORM is applied. All the section numbers correspond with those applied in Appendix 7-H. Set-up of this chapter The set up of this chapter is as follows: Discussion of results of the calculation of the annual probability of flooding of the present flood defence system. Annual probability of flooding due to overtopping, see Annual probability of flooding due to instability of the inside slope, see Annual probability of flooding due to damage of the revetment and consequently erosion of the embankment body, see Discussion of results of the calculation of the probability of flooding of the improved flood defence system. Annual probability of flooding due to overtopping, see Annual probability of flooding due to instability of the inside slope, see Annual probability of flooding due to damage of the revetment and consequently erosion of the embankment body, see Annual probability of flooding of the present Caldicot Levels flood defence system Annual probability of flooding due to overtopping First the results of the reliability calculations in connection to the failure modes saturation or erosion are presented. Second these results are discussed and compared to the past damage events which are mentioned in chapter 3, paragraph 3.6.

113 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Results of reliability calculations of overtopping The following results are discussed: The total annual probability of flooding of the Caldicot Levels flood defence system. The α-values of the random variables which are incorporated in the reliability calculations. The annual probability of failure of the separate selected sections. Effect on the system s annual probability of failure by calculating with different models or more random variables. Total annual probability of failure due to overtopping The total annual probability of flooding of the Caldicot Levels flood defence system due to saturation or erosion is The probabilities of flooding due to overtopping (saturation or erosion of the inside slope with remaining strength) and the accompanying reliability indices of the for overtopping selected sections are represented by the blue columns in fig.8.1. The dominating annual probability of flooding is 0.26 contributed by section no. 68: the weakest link in the serial system. This section is part of the river banks along the Usk. See Appendix 8-A for the list of reliability indices and annual probabilities of failure on which fig.8.1. is based. In fig.8.1. additionally the reliability indices and annual probabilities of failure are included which are related to erosion by the overtopping discharges without remaining strength and to the limit discharges causing the initiation of damage according to the Environment Agency. Annual probability of failure Section no. Reliability index Section no. Figure 8.1. The annual probability of failure (top) and the reliability indices (bottom) of the for overtopping selected sections. The numbers of the sections correspond with those in Appendix 7-H. Section no. 1t/m 19 and no. 49 t/m 52 = embankment without additional structures Section no. 20 t/m 48 and no. 53 t/m 57 = embankment with wave return wall Section no. 41 and 42 = high grounds with masonry wall facing Section no. 58 t/m 62 = raised grounds along the Severn Estuary Section no. 62 t/m 67 = raised grounds along the river Usk Section no. 68 t/m 78 = Usk river banks 8-2

114 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements The α-values The α-values show the contribution of a basic random variable to the total variance of the reliability function. The α-values which are the result of the calculation of the annual probability of flooding due to overtopping of the Caldicot Levels flood defence system are given in table 8.1. The five random variables that contribute most to the total variance are: the water level at the mouth of the Severn Estuary, the wind direction, the error in the model of the local water levels, the wind speed and the discharge of the Usk. Table 8.1. α-values of the basic random variables resulting from the calculation of the annual probability of failure due to saturation or erosion. Random variable α-value m qc, model uncertainty critical discharge m qa, model uncertainty actual discharge k, roughness coefficient f b, Empirical coefficient of actual discharge due to breaking waves f n, Empirical coefficient of actual discharge due to not breaking waves c, cohesion of the embankment soil φ', effective angle of internal friction ρ, mass density of the embankment soil d k, thickness of the clay cover layer m Hs, model uncertainty of Bretschneider H s m Ts, model uncertainty of Bretschneider T s Dh zw, error in model of local water levels β*, deflection in wave direction t s, duration of the storm h sea, water level at the mouth of the Severn Estuary U, wind speed Discharge Usk Wind direction The annual probability of failure due to overtopping of the separate selected sections As mentioned above, the annual probabilities of failure and the reliability indices of the accompanying selected sections are shown in fig.8.1. Apart from the weakest link, represented by section 68, a number of areas with relatively high annual probabilities of failure attract attention: Section Section Section Section Section Section The reasons why these sections turn out to be weak are discussed in general below. A more detailed analysis can be found in Appendix 8-B. The sections along the Severn Estuary are discussed separately from the sections along the Usk. Weak sections along the Severn Estuary The three main reasons why the above mentioned sections which are located along the Severn Estuary turn out to be weak are as follows: Sections which have significantly lower crest levels, see fig.8.2. Sections which are exposed to wind directions with large fetches, such as the southwesterly wind directions. The extent to which the sections face these wind directions with large fetches: the orientation to the wind direction. If the orientation of the normal of the embankment is practically in one of these wind directions, then the incoming waves have full 8-3

115 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements West (Newport) Distance (m) East (Caldicot) Crest level (m OD) 1. represents section no. 3 in fig.8.1. in connection to the bridge over the Severn. 2. represents section no represents section no represents section no. 32 and represents Goldcliff, the high grounds with masonry wall facing, section no. 41 and represents section no. 49 and represents section no. 62 to 64 Figure 8.2. The crest levels of the flood defences along the Severn Estuary. The numbers 1 to 7 indicate points of interest and are explained to the right of the figure. effect on the overtopping discharges. If the waves come in under an angle, the effect is lower in proportion to the angle. Weak sections along the river Usk The high annual probability of failure of the river banks along the Usk can be explained by the following reasons: The low elevation of the selected sections. The strong limitations of the model which has been applied to determine the local water levels along the Usk. These limitations are mainly the result of numerical problems. No time is available to eliminate these numerical problems. The limited information on which the statistics of the discharge are based. Effect of changes on the system s annual probability of failure due to overtopping The following situations are regarded: The system s annual probability of flooding due to damage of the revetment on the inside slope and consequently erosion of the embankment body, see fig.8.1. (purple columns) The system s annual probability of flooding in case of self implemented critical discharge values, see fig.8.1. (light columns) For these critical discharges the limit discharges marking the initiation of breach according to the Environment Agency have been taken. The system s annual probability of flooding taking all possible random variables with respect to the geometry into account. The results are presented in table 8.3. Table 8.3. System s annual probability of failure and the weakest link for three different situations. In none of the calculations section 68 to 78 is taken into account. The first result, saturation or erosion without 68 to 78, is added as a reference Variation System s probability of flooding (without 68 to 78) Section with highest annual probability of failure (without 68 to 78) Section no. Annual probability of failure Saturation or erosion (with remaining strength) Damage of inside slope and erosion (without remaining strength) Self implemented critical discharges Extra random variables, saturation or erosion

116 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements These results point out that saturation is in almost all cases associated with a higher annual probability of failure than erosion. Sections 68 to 78, the river banks of the Usk, are insensitive to the above mentioned variations. Therefore, in these calculations sections 68 to 78 are excluded. Saturation of the clay cover layer and consequently instability of the inside slope which has been discussed above is added in table 8.3. without 68 to 78 as a reference. Discussion of results of reliability calculations of overtopping The results with respect to the failure mode overtopping are discussed according to the past events which have been mentioned in chapter 3, paragraph 3.6. Additionally, the order of magnitude of the annual probability of failure due to overtopping is compared to Dutch annual probabilities of failure due to overtopping. Past events related to failure due to overtopping at the Caldicot Levels flood defence system Analysis of the results in the light of the past events related to the Caldicot Levels flood defence system delivers the remarks mentioned below. See for the past events chapter 3, paragraph 3.6. System s annual probability of flooding due to overtopping in the light of past events The system s annual probability of failure is high: an annual probability of flooding of 0.30 taking the Usk river banks into account and an annual probability of flooding of 0.18 (see table 8.3) without taking these river banks into account. In the past ten years at least once damage has occurred in the form of the blowhole in the crest of the embankments. Therefore, the annual probability of damage might be in the above mentioned order of magnitude of However, the annual probability of flooding, or actual breach, is expected to be lower according to the past events. Another limitation of the results is the high annual probability of flooding of saturation and consequently instability of the inside slope. No problems due to this failure mode are known to have occurred in the past. Causes of these high results can be: The model which has been applied to determine the local water levels as well as the water level statistics are based on limited information. Considering the high α-value of the water level at the mouth of the Severn Estuary, , the water levels are of great influence on the results. It is possible that the models related to the failure mode overtopping in PC-Ring provide conservative results. The limit discharges in case of the raised grounds are conservative: they are based on the serviceability limit state. The presence of breakwaters have been taken into account as much as possible. However, in case of section 12 a possibility is for instance that the breakwater does not only block wind direction 225 but also wind direction Such a small change can have a large effect on the annual probability of failure. Do the weak links from the calculations correspond with problem areas? The calculations mark the weak links: the six groups of sections which have been discussed above. All of these groups of sections correspond with locations where problems have occurred in the past. The models of the failure mode overtopping in 8-5

117 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements combination with the α-values of the reliability calculations provide the possibility to explain why these sections form a weak link. Annual probability of flooding due to overtopping of the Caldicot Levels flood defence system compared to Dutch probabilities The annual probability of flooding due to overtopping of the Caldicot Levels flood defence system compared to four Dutch flood defence systems 1 is given in table 8.4. Table 8.4. The reliability index related to the failure mode overtopping of the Caldicot Levels flood defence system (with section 68 to 78) compared to four Dutch flood defence systems Reliability index Flood defence system (overtopping) Caldicot Levels flood defence system (with Usk river banks) 0.51 Betuwe, Tieler- en Culemborgerwaarden 3.1 Groningen-Friesland 3.6 Centraal Holland 4.3 Hoeksche waard Annual probability of flooding due to instability of the inside slope First the results of the reliability calculations in connection to the failure mode instability of the inside slope are presented. Second these results are discussed and compared to the past damage events which are mentioned in chapter 3, paragraph 3.6. Results of reliability calculations of instability The following results are discussed: The total annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system. The α-values of the random variables which are incorporated in the reliability calculations. The annual probability of failure of the separate selected sections. System s annual probability of failure due to instability of the inside slope The annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system is The weakest link is section 79 with a annual probability of failure of and a reliability index of The annual probabilities of failure and the reliability indices related to instability of the inside slope of the separate sections are shown in fig.8.3. The annual probability of failure of section 79 is not included in fig.8.3., otherwise, the annual probabilities of failure of the other sections are not visible. Elimination of section 79 delivers a system s annual probability of flooding due to instability of the inside slope of 0.12*10-2. Section 55 is the weakest link after elimination of section 79. Section 55 has a annual probability of failure of 0.7*10-3. The α-values The α-values show the contribution of a basic random variable to the total variance of the reliability function. The α-values which result from the calculation of the annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system are given in table

118 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Table 8.5. α-values of the basic random variables resulting from the calculation of the annual probability of failure due to instability of the inside slope Random variable α-value Fluctuations cohesion Uncertainty mean value cohesion Fluctuations tan(φ) Uncertainty mean value tan(φ) Uncertainty water overpressures 0.00 Uncertainty groundwater surface 0.00 Model uncertainty Error in local water level Water level at the mouth of the Severn Estuary Wind speed Wind direction The annual probability of failure due to instability of the separate selected sections With exception of section 55 the stability factors resulting from the calculations with Mstab in chapter 7 reflect the mutual differences in annual probability of failure. The high annual probability of failure of section 79 can be explained by a relatively high crest level combined with an inside slope of Discussion of results of reliability calculations of instability The results with respect to the failure mode instability of the inside slope are discussed according to the past events which have been mentioned in chapter 3, paragraph 3.6. Additionally, the order of magnitude of the annual probability of failure due to instability of the inside slope is compared to Dutch annual probabilities of failure due to instability of the inside slope. Probability of failure Section no. Reliability index Section no. Figure 8.3. Annual probabilities of failure and reliability indices related to instability of the inside slope of the separate sections 8-7

119 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Past events related to failure due to instability of the inside slope at the Caldicot Levels flood defence system Considering the annual annual probability of failure of 12% the expectation is that instability of the inside slope should have caused problems. However, in the past ten years no problems have occurred with instability of the inside slope. The high annual probability of failure is dominated by section 79. It is possible that the drawing is incorrect and that the actual inside slope is less steep than Elimination of section 79 then leads to a system s annual probability of failure of 0.12*10-2. This might be more realistic, even more because the drawings are regarded to be indicative of nature. However, it is also possible that the annual probability of failure is indeed 12%. Annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system compared to Dutch probabilities The annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system compared to four Dutch flood defence systems 1 is given in table 8.6. Table 8.6. The reliability index related to the failure mode instability of the inside slope of the Caldicot Levels flood defence system compared to four Dutch flood defence systems Reliability index Flood defence system (overtopping) Caldicot Levels flood defence system 1.2 Betuwe, Tieler- en Culemborgerwaarden 4.2 Groningen-Friesland 4.0 Centraal Holland 5.1 Hoeksche waard Annual probability of flooding due to attack of the revetment on the outside slope First the results of the reliability calculations in connection to the failure mode attack of the revetment on the outside slope are presented. Second these results are discussed and compared to the past damage events which are mentioned in chapter 3, paragraph 3.6. Results of reliability calculations of attack of the revetment on the outside slope The following results are discussed: The total annual probability of flooding due to attack of the revetment on the outside slope of the Caldicot Levels flood defence system. The α-values of the random variables which are incorporated in the reliability calculations. The annual probability of failure of the separate selected sections. System s annual probability of failure due to attack of the revetment on the outside slope The annual probability of flooding due to attack of the revetment on the outside slope of the Caldicot Levels flood defence system is 0.95*10-2. The weakest link is section 14 with an annual probability of failure of 0.94*10-2. The annual probabilities of failure and the reliability indices related to attack of the revetment on the outside slope of the separate sections are shown in fig

120 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements The α-values The α-values show the contribution of a basic random variable to the total variance of the reliability function. The α-values which are the result of the calculation of the annual probability of flooding due to attack of the revetment on the outside slope of the Caldicot Levels flood defence system are given in table 8.7. Dominant α-values are respectively wind speed, wind direction, model factor of H s according to Bretschneider and water level. The annual probability of failure of the separate selected sections The selected sections of the three different types of revetment are discussed below. Placed stone revetment Placed stone revetment, no. 14 and no. 19: section 14 is the section with the highest annual probability of failure, see fig.8.4. Section 19 has a relative high annual probability of failure. The total annual probability of failure consists of two contributions: the damage of the revetment and consequently erosion of the embankment body. The wind direction and therefore the angle of the incoming waves with the normal of the embankment have a large influence on both contributions to the annual probability of failure. The higher annual probabilities of failure occur in the wind direction which is relatively close to the orientation of the normal of the embankment and is associated with Annual probability of failure Reliability index Section no. Section no. Figure 8.4. Annual probabilities of failure and reliability indices related to attack of the revetment on the outside slope of the separate sections. Section 14 and 19 = placed stone revetment Section 10, 12, 17, 18 and 51 = grass Section 19, 26, 29, 32 and 33 = rock armour revetment Table 8.7. α-values of the basic random variables resulting from the calculation of the annual probability of failure due to attack of the revetment on the outside slope Random variable α-value d w, depth of the grass roots 0.00 L BK, width of the embankment core D, thickness of the placed stone revetment Tan (α u ) Tan (α i ) Δ s, Relative density stone c k, coefficient strength of stone placement c RB, coefficient erosion of the embankment Angle in reduction factor which takes the angle of the incoming waves into account D, Nominal diameter of the riprap Model factor of Bretschneider for H s Modelfactor of Bretschneider for T s 0.00 Error in local water level Deflection of the wave direction Duration of the storm Water level at the mouth of the estuary Wind speed Wind direction

121 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements larger fetches. Section no.14 is more orientated to the west than section no. 19. Grass Grass, no.10, 12, 17, 18, 51: these are the sections with the lowest annual probability of failure, see fig.8.4. The total annual probability of failure consists of two contributions: the damage of the revetment and consequently erosion of the embankment body. The lowest of the two contributions influences the annual probability of failure most as both events must occur before the embankment breaches. The annual probability of failure is dominated by the lower annual probability of failure of the remaining strength of the embankment. The annual probability of failure of the remaining strength is determined by the orientation of the sections to the wind and the volume of the embankment which represents the remaining strength. Rock armour revetment Rock armour revetment involves sections 26, 29, 32, 33 and 48, see fig.8.4. The total annual probability of failure consists of two contributions: the damage of the revetment and consequently erosion of the embankment body. The lowest of the two contributions influences the annual probability of failure most as both events must occur before the embankment breaches. The annual probability of failure is dominated by the lower annual probability of failure of the remaining strength of the embankment. Again, the annual probability of failure of the remaining strength is determined by the orientation of the sections to the wind and the volume of the embankment which represents the remaining strength. Discussion of results The results with respect to the failure mode attack of the revetment on the outside slope are discussed according to the past events which have been mentioned in chapter 3, paragraph 3.6. Additionally, the order of magnitude of the annual probability of failure due to attack of the revetment on the outside slope is compared to Dutch annual probabilities of failure due to attack of the revetment on the outside slope. Past events related to the Caldicot Levels flood defence system According to the past events, section 12 should be among the weaker links. However, this part of the embankment is among the stronger sections, see fig.8.4. An explanation follows below. PC-Ring calculates the total annual probability of flooding. This probability consists of a combination between damage to the revetment and erosion of the embankment leading to breach. The probability of erosion of the embankment turns out to be the lowest and therefore is dominant over the probability of damage to the revetment. Therefore, the volume of the embankment and the orientation to the wind is more important than the type of revetment which protects the outside slope. However, considering the probability of damage to the grass on the outside slope of section 12 is relatively high compared to the other sections with grass. The same applies to the rest of the sections: the locations with the highest probability of damage do not necessarily have to be the locations with the highest annual probability of flooding. 8-10

122 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Annual probability of flooding due to instability of the inside slope of the Caldicot Levels flood defence system compared to Dutch probabilities The annual probability of flooding due to attack of the revetment on the outside slope of the Caldicot Levels flood defence system compared to four Dutch flood defence systems 1 is given in table 8.8. Table 8.8. The reliability index related to the failure mode attack of the revetment on the outside slope of the Caldicot Levels flood defence system compared to four Dutch flood defence systems Reliability index Flood defence system (overtopping) Caldicot Levels flood defence system 3.1 Betuwe, Tieler- en Culemborgerwaarden 4.5 Groningen-Friesland 5.5 Centraal Holland 5.6 Hoeksche waard Total annual probability of flooding of the Caldicot Levels flood defence system The total annual probability of flooding of the Caldicot Levels flood defence system is the combination of the annual probabilities of failure due to the discussed failure modes. Calculation of this system s annual probability of failure results in Section 68 contributes the dominating annual probability of failure of This section is part of the river banks of the river Usk. The failure mode which contributes most to the total system s annual probability of failure is therefore overtopping. Elimination of the river banks of the Usk in the calculations results in a system s annual probability of failure of Section 28 contributes the dominating annual probability of failure of Again the failure mode which contributes most to the total annual probability of failure is overtopping. Flood defence improvements should therefore mainly be directed to reduce failure due to overtopping. The groups of weak sections have been discussed in Decisions with respect to flood defence improvements must be based on the causes of weakness of these groups of sections. These causes can be found in for instance the contributions of the α-values and knowledge of the models forming the failure mode. Another section which attracts attention is section no.79 which has a high annual probability of failure due to instability of the inside slope (0.12). This section is also an ideal candidate for flood defence improvements. 8-11

123 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Reliability index Section no. Figure 8.5. Reliability indices of the for the failure mode overtopping selected sections. Three different calculations have been done: the first, taking failure of the wave return wall into account as a failure mode equal to saturation or erosion of the inside slope. The second calculation: including the influence of the wave return wall on the overtopping discharges, but excluding the possibility of failure of the wave return wall. The third calculation: leaving any kind of influence of the wave return wall out, in other words, no wave return wall present on crest of embankment. The abbreviation w.r.w. stands for wave return wall Annual probability of flooding of the improved Caldicot Levels flood defence system Annual probability of flooding due to overtopping, improved system In fig.8.5. the results of the annual probability of failure due to overtopping are shown in case of the improved Caldicot Levels flood defence system. No known improvements are planned for the river banks of the Usk. Therefore, the annual probability of failure of the river banks of the Usk are equal to those presented in fig.8.1. and will not be discussed here. The following is addressed with respect to failure due to overtopping of the improved Caldicot Levels flood defence system: Results, in the form of three different reliability calculations. Discussion of the wave return wall as part of the improved flood defence system. Comparison of the results of the present and improved Caldicot Levels flood defence system. Results of reliability calculations of overtopping, improved system In fig.8.5. three different results are presented. In Appendix 8-C the values can be found of the reliability indices and annual probabilities of failure on which fig.8.5. is based. The following sections are improved with a new wave return wall: 21 to 24, 27, 28, 31 to 33, 35, 36, 38, 40, 43, 53, 54, 57, 60, 62. Calculation 1: failure of wave return wall and its influence on overtopping The results according to the practical approach mentioned in chapter 6, paragraph This approach considers the wave return wall as an equal failure mode compared to saturation or damage of the grass on the inside slope and erosion of the embankment. Section 31 turns out to have the highest annual probability of failure with a value of This is the annual probability of failure due to tilting of the wave return wall. Calculation 2: influence of wave return wall on overtopping, no failure of wave return wall The annual probability of failure due to overtopping assuming that the wave return wall does not fail. This is achieved by taking the reduction of overtopping by the wave return wall into account and not calculating the annual probability of failure of the wave return wall. Section 8-12

124 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements 63 turns out to have the highest annual probability of failure with a value of 0.4*10-1. Section 31 is still the weakest link of the sections with a wave return wall. The annual probability of failure of section 31 is in this case 0.35*10-3. Calculation 3: no wave return wall present on crest of embankments The annual probability of failure due to overtopping assuming embankments without wave return wall. This leads to: no reduction of the overtopping discharges and not taking the annual probability of failure of the wave return wall into account. Section 63 turns out to have the highest annual probability of failure with a value of 0.4*10-1. Section 62 is the weakest link of the sections with a wave return wall. The annual probability of failure of section 62 is in this case 0.33*10-1. Discussion of the wave return wall as part of the flood defence improvements First the practical approach of failure of the wave return wall in the reliability calculations as mentioned in chapter 6 is discussed. Second the effect of the presence of the wave return wall on the annual probability of failure due to overtopping is addressed. Discussion of practical approach of wave return wall in reliability calculations Considering failure of the wave return wall as an equal failure mode as saturation or erosion of the inside slope leads to a high system s annual probability of failure: 0.14 (without taking the river banks of the Usk into account). This is the result according to the practical approach of the annual probability of failure of the wave return wall as suggested in chapter 6, paragraph The theoretical approach is also explained in chapter 6, paragraph This approach considers the annual probability of failure of the embankment with wave return wall as follows: a combination between either the wave return wall fails and consequently the embankment fails, or the wave return wall does not fail and the embankment fails while the wave return wall reduces the overtopping discharges by its presence. In case of all the sections mentioned above, the wave return wall has a higher annual probability of failure than the embankment with or without the wave return wall, see fig.8.5. This leads to the expectation that the embankment will not necessarily fail if the wave return wall fails. Therefore, the assumption on which the practical approach is based in chapter 6 is not justified. Concluding: the annual probability of failure due to overtopping of the embankment with wave return wall must have a value between the result from calculation 2 and calculation 3 in fig.8.5. The degree of influence of these two calculations depends on the magnitude of the annual probability of failure of the wave return wall: a relative low annual probability of failure wave return wall means higher degree of influence of calculation 2, conversely, a relative high annual probability of failure wave return wall means higher degree of influence of calculation 3. Effect of wave return wall on overtopping See fig.8.5. for the effect of the wave return wall in terms of reduction of failure due to overtopping. The effect is visualised by the difference between the reliability indices according to calculation 2 (purple coloured columns) and calculation 3 (light coloured columns). 8-13

125 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Reliability index Section no. Figure 8.6. Reliability indices of failure due to overtopping of the present flood defence system and the improved flood defence system. For the improved flood defence system the reliability indices of embankments with and without the influence of the wave return wall on the overtopping discharges are included. Comparison of overtopping results of improved and present flood defence system In fig.8.6. the reliability indices of the present flood defence system and the improved flood defence system are presented. The annual probability of failure of the wave return wall is not included in the figure. The annual probability of failure of the improved system is expected to have a value between the annual probability of failure due to overtopping of an embankment with and without a wave return wall on the crest. Fig.8.6. points out that the improvements to the approximately equally weak areas formed by sections 1 to 19, 20 to 47 and 61 to 64 are unbalanced: The improvements to sections 1 to 19 are more effective than the improvements to 20 to 47. No improvements are planned for sections 61, 63 and 64. These sections therefore form the new weakest link in the improved flood defence system. Additionally, the sections which form the river banks along the Usk are not improved either although these seem to Section no. introduce the weakest links of the total Caldicot Levels flood defence system. Reliability index Annual probability of flooding due to instability of the inside slope, improved system The reliability indices of failure due to instability of the inside slope of the present and the improved flood defence system are presented in fig.8.7. The annual probability of failure due to instability of the inside slope of the improved Caldicot Levels flood defence system is 0.95*10-4. Section 46 turns out to have the highest annual probability of failure of 0.95*10-4. Annual probability of failure Section no. Figure 8.7. The reliability indices of failure due to instability of the inside slope of the present (blue columns) and improved flood defence system (purple columns) (top). The annual probability of failure due to instability of the inside slope of the improved flood defence system (bottom) 8-14

126 8. Probability of flooding of the Caldicot Levels flood defence system before and after improvements Fig.8.7. points out that the flood defence improvements are effectively reducing the annual probability of failure due to instability of the inside slope except for section Annual probability of flooding due to attack of the revetment on the outside slope, improved system The reliability indices of failure due to attack of the revetment on the outside slope of the present and the improved flood defence system are presented in fig.8.8. The annual probability of failure due to attack of the revetment on the outside slope of the improved Caldicot Levels flood defence system is 0.66*10-5. Section 29 turns out to have the highest annual probability of failure of 0.34*10-5. Fig.8.8. points out that the flood defence improvements are effectively reducing the annual probability of failure due to attack of the revetment on the outside slope for sections 12 and 14. The effect of the improvements on the annual probability of failure of the rest of the sections is relatively low. Section no. Annual probability Reliability index Section no. Figure 8.8. Reliability indices of attack of the revetment on the outside slope of the present (blue columns) and improved flood defence system (purple columns) (top). The annual probability of failure due to attack of the revetment on the outside slope of the improved flood defence system (bottom) Total annual probability of flooding of the improved Caldicot Levels flood defence system The total annual probability of flooding of the improved Caldicot Levels flood defence system is the combination of the annual probabilities of failure due to the discussed failure modes. Calculation of this system s annual probability of failure results in Section 68 contributes 8-15