Politecnico di Milano

Transcription

1 Politecnico di Milano Facolta di Ingegneria Civile, Ambientale e Territoriale Master of Science in Civil Engineering Ultrasonic Testing and Pulse Refraction for the Assessment of Fire Damaged Concrete Elements Thesis supervisor: Prof. Roberto Felicetti Thesis prepared by: Babak Ghaemmaghami Rad (770779) Academic year July

2 Acknowledgements I take the opportunity to express my deepest gratitude to my supervisor, Professor Roberto Felicetti for providing me with all the necessary guidelines, advices and for his kindness during all the time working on this thesis. Thanks and sincere appreciations also go to Dr. Francesco Lo Monte for his guidance which was of much help to develop this thesis. Finally, I would like to deeply appreciate my family for their support and encouragement during the years of my study in Italy. 2

3 List of Contents 0) Abstract...9 1) Chapter 1 (fire in structures) ) Definition of fire ) Fire development and fire behavior indicators ) Compartment fire development ) Fire initiation ) Fire behavior indicators ) Stages of a fire development ) Incipient stage ) Growth period ) Flashover-Transition to a Fully Developed Fire ) Fully developed stage ) Decay stage ) Burning rate ) Ventilation-controlled burning ) Fuel-controlled burning ) Standard time-temperature curve (ISO 834) ) Swedish curves ) Eurocode parametric time-temperature curves

4 1-10) Fire load density ) Rate of heat release ) Heat losses..27 2) Chapter 2 (Behavior of concrete structures in fire) ) Conduction ) Convection ) Radiation ) Thermal properties of concrete ) Density ) Thermal conductivity ) Specific heat ) Thermal diffusivity ) Mechanical properties of concrete at elevated temperature ) Compressive strength ) Tensile strength ) Modulus of elasticity ) Spalling ) Cracks ) Color change ) Chapter 3 (Fire damage assessment)

5 3-1) General approach to fire damage assessment ) Extraction of concrete cores ) Assessment methods of fire damages in concrete Tunnel linings ) General approach to fire damage assessment ) Fire scenario and global structural effect ) Local conditions of the damaged lining ) Residual properties of material ) Possible approaches to the assessment of the local lining conditions ) Average response of the concrete cover ) Point by point response of small samples ) Special interpretation techniques ) While-drilling techniques ) Ultrasonic pulse refraction ) Chapter 4 (Ultrasonic pulse refraction) ) Theory of pulse propagation through concrete ) Equipment ) Use ) Transducer arrangement ) Test calibration and interpretation of results ) Strength calibration

6 4-7) Practical factors influencing measured results ) Temperature ) Stress history ) Path length ) Moisture conditions ) Reinforcement ) Applications ) Measurement of concrete uniformity ) Detection of cracking and honeycombing ) Strength estimation ) Assessment of concrete deterioration ) Measurement of layer thickness ) Measurement of elastic modulus ) Application of ultrasonic pulse velocity tests in fire damaged structures ) The solution for a bilinear distribution of the elastic modulus ) Damage identification for the Merloni fire exposed building ) Seismic measurements within the Mont Blanc-tunnel ) Seismic refraction principle ) Seismic refraction interpretation of Mont-Blanc data ) Some considerations on seismology

7 4-16) Travel-Time curves ) Travel-time curve for a layer over a half space ) Direct waves ) Reflected waves ) Head waves ) Travel-time curves for more complicated layers ) Dipping layers ) Multiple layers ) Stepwise constant velocity distribution ) Stepwise linear distribution ) The problem of hidden and blind layers ) Nonuniqueness in case of inverse geophysical problems ) Chapter 5 (Tomographic approach to refraction travel-time inversion) ) Fundamentals of seismic tomography ) Back-projection approach ) Matrix inversion (conjugate gradient method, CG; least square method, LSQR) approach ) Iterative reconstruction(art, SIRT) approach ) Comparison of the different tomographic inversion methods ) Mathematical background of the SIRT method

8 5-7) Detailed discussion of main topic of this thesis (tomographic approach for fire damaged material) ) Obtained results ) x-t plots for both of the addition and multiplication methods ) Slowness-depth plots for both of the addition and multiplication methods ) Distance-depth plots for both of the addition and multiplication methods ) Rate of convergence of slownesses plots for both of the addition and multiplication methods ) A series of indirect UPV measurements ) Undamaged block ) Damaged block ) Chapter 6 (conclusion and recommendations) Appendix (Excel and Mathcad sheets) ) References

9 Abstract: The matter of different types of damages to the buildings is an important issue and the investigation of the intensity and effects of them to the structures can help the engineers to decide if the building under consideration have to be totally demolished or the repairing it can be a better way from economical and time-saving point of view. In the field of structural assessment there are many methods to assess the condition of a building, bridge or any other type of structures both in normal condition and in the case of being faced to a damage, generally these methods are divided in two main categories which are NDTS (non-destructive techniques) and the DTS (destructive techniques) which are discussed later. The most useful ND technique can be the ultrasonic pulse velocity testing which can make engineers to have a detailed information of the different points of a member, this technique is the main topic of this thesis through the investigation of layered materials and a damaged concrete member through performing different UPV measurements and to obtain the wave propagation traveltimes, comparing the distance-time data with the ones obtained by tomographic approach through an iterative procedure. Mainly the destructive methods are more reliable and the results are more precise but execution of these techniques is not feasible and logical in most of the cases due to the destruction and also from the economical point of view. 9

10 Chapter 1 Introductory concepts Fire in structures Definition of fire: A rapid-sustaining oxidation process accompanied by the evolution of heat and light of varying intensities. Richard Tuve. When a combustible material starts to burn, the results of this process will be heat, gases, flame and smoke. Here the fire triangle can be introduced which is built by three essential elements for the initiation and continuation of the combustion process, these elements are input heat, fuel and oxygen and the fire is continued till the proportionality between the three elements stops. During a fire process the heat transfer in three ways happens which are: conduction, convection and radiation. The heat transfer is proportional to the temperature gradients between two points. Fire development and fire behavior indicators: Building factors, smoke, air track, heat and flame are critical fire behavior indicators. Understanding the indicators is important, but more important is the ability to integrate these factors in the process of reading the fire as part of size-up and dynamic risk assessment. Compartment fire development: Fire conditions can vary considerably throughout the building with one compartment containing a fully developed fire, an adjacent compartment in the growth stage, and still other compartments yet uninvolved. Recognizing the stages of fire development and likely progression through this process allows firefighters to predict what will happen next. Fire initiation: Ignition occurs when a combustible mixture of gases is heated to temperatures that will trigger the exothermic oxidation reaction of combustion, ignition almost always requires the input of heat from an external source. 10

11 When an ignition happens inside or outside of a building and the building is engaged due to existence of air and combustive material, a fire scenario starts and the extension of this fire process and the duration is controlled by some agents which are: the openings (windows, doors), the strength of the windows to break, the fire load, the contained air in the compartment. Taking these parameters into account the damage of the members of the structure starts and as the temperature increases and the duration of the fire to the peak temperature is longer the amount and depth of damage is increased. Compartment fire development can be described as being comprised of four stages: incipient, growth, fully developed and decay. Flashover is not a stage of development, but simply a rapid transition between the growth and fully developed stages. Figure (1) shows fire development in a compartment: Figure (1). Fire development in a compartment. Figure (2) is showing the heat release rate which varies with a) fuel characteristics and b) ventilation condition. 11

12 Figure (2). Heat release rate varying with, a) fuel characteristics, b) ventilation condition. Compartment fires do not always follow the simple, idealized fire development curve illustrated in Figure (1). The speed with which the fire develops, peak heat release rate, and duration of burning are dependent on both the characteristics of the fuel involved and ventilation profile(available oxygen). Fire behavior indicators: Fire behavior indicators encompass a wide range of factors that firefighters may see, hear or feel. Some factors are relatively unchanging (i.e building construction) and others are quite dynamic changing as the fire develops (i.e smoke conditions and flames). Building: the building and its contents are present prior to ignition and can be examined during the preplanning process. The pre-fire assessment of likely fire development and spread should be compared with actual fire behavior encountered during emergency incidents to improve skill in reading building factors. Smoke and Air Track: Smoke conditions and the pattern of smoke and air movement are two of the most important indicators of fire behavior. The location and appearance o smoke can provide valuable cues related to the location of the fire, its burning regime (fuel or ventilation controlled) and the stage of fire in various areas of the building. It is critical 12

13 that firefighters begin their assessment o smoke and air track indicators from outside the building, but continue this process on an ongoing basis from both the interior and exterior of the structure. Heat: While heat cannot be observed directly, observation of the effect of heat on air track (i.e., velocity of smoke discharge), the building or exposures, and sensation of changes in temperature can be significant fire behavior indicators. It is important to remember that our personal protective equipment provides significant insulation and slows the transfer of heat and resulting sensation of changes in temperature. Flame: Flaming combustion is often the most obvious or visible indicator observed by firefighters and flame indicators such as location, volume, color, etc are important to firefighters. Stages of a fire development: Incipient stage: Ignition requires heat, fuel, and oxygen. Once combustion begins, development of an incipient fire is largely dependent on the characteristics and configuration of the fuel involved (fuel controlled fire). Air in the compartment provides adequate oxygen to continue fire development. During this initial phase of fire development, radiant heat warms adjacent fuel and continues the process of pyrolysis. A plume of hot gases and flame rises from the fire and mixes with the cooler air within the room. This transfer of energy begins to increase the overall temperature in the room. As this plume reaches the ceiling, hot gases begin to spread horizontally across the ceiling. Transition beyond the incipient stage is difficult to define in precise terms. However, as flames near the ceiling, the layer of hot gases becomes more clearly defined and increases in volume, the fire has moved beyond its incipient phase and (given adequate oxygen) will continue to grow more quickly. 13

14 The indicators for incipient stage are listed in Table 1. Building Smoke Air Track Heat Flame Size, contents, ventilation profile, and fire protection systems all have a significant influence on potential fire development and should be considered regardless of the stage of fire development. Building factors (such as size and ventilation profile) influence how other fire behavior indicators will present. The building and its contents will also influence how quickly a fire will transition from incipient to growth stage. Smoke will be limited and there will not be a well defined layer of hot gases in the upper area of the compartment. If smoke is visible from the exterior volume will generally be light in color and have limited buoyancy. Air track is generally not a major factor in recognition of incipient stage fires. However some light smoke discharge and inward air movement may be observed from openings close to the fire location. Low (near ambient) temperature within the compartment, condensation may be visible on windows in or near the fire compartment. Depending on the degree of insulation, a heat signature may or may not be visible from the exterior using a thermal imaging camera (TIC). Fire confined to a small area (i.e., the object of origin) and flames lower than ceiling height. Table (1). Indicators for incipient stage. Growth period: If there is adequate oxygen within the compartment additional fuel will become involved and the heat release rate from the fire will increase. While considerably more complex, gas temperatures within the compartment may be described as existing in two layers: A hot layer extending down from the ceiling and a cooler layer down towards the floor. Convection resulting from plume and ceiling jet along with radiant heat from the fire and hot particulates in the smoke increases the temperature of the compartment linings and other items in the compartment. As gases within the compartment are heated they expand and when confined by the compartment increase in pressure. Higher pressure in this layer causes it to push down within the compartment and out through openings. The pressure of the cool gas layer is lower, resulting in inward movement of air from outside the compartment. At the point where these two layers meet, as the hot gases exit through an opening, the pressure is neutral. The interface of the hot and cool gas layers at an opening is commonly referred to as the neutral plane. The fire can continue to grow through flame spread or by ignition of other fuel within the compartment. As flames in the plume reach the ceiling they will bend and begin to 14

15 extend horizontally. Pyrolysis products and flammable byproducts of incomplete combustion in the hot gas layer will ignite and continue this horizontal extension across the ceiling. As the fire moves further into the growth stage, the dominant heat transfer mechanism within the fire compartment shifts from convection to radiation. Radiant heat transfer increases heat flux (transfer of thermal energy) at floor level. Indicators for growth stage are listed in Table 2. Building Smoke Air Track Heat Heat Flame Size, construction, fire load and ventilation profile influence ongoing fire development. A well defined layer of hot smoke is likely to exist in the upper level of the compartment. If smoke is not confined to the compartment it will be spreading into adjacent compartments. Smoke may be visible from the exterior (see air track indicators) Air track is dependent on the ventilation profile. If the compartment has a single opening (such as a door), there will be a bi-directional air track (smoke out the top and air in the bottom). As the fire grows, air track velocity of smoke discharge and air intake will increase. Velocity is likely to be greater at openings close to the fire. However, air track at exterior openings is significantly influenced by wind, and remember to consider the influence of ambient weather conditions. Temperature inside the fire compartment and adjacent spaces will be above ambient, but will be lower in compartments located further away from the fire. Condensation disappears from windows in or near the fire compartment. Brownish staining on window glazing from pyrolysis products may become visible, heat indicators may be visible from the exterior of the compartment, particularly cracking window glass or heat at the upper level of doors, and Increasing overall temperature within the compartment. It is likely that a heat signature will be observed in the area of the fire compartment using a thermal imaging camera (TIC) from the exterior. After making entry, convection of hot gases will be visible using the TIC Fire extending beyond the object of origin and flames reaching ceiling height, bending and beginning to travel horizontally across the ceiling or through the hot gas layer. If there is an opening to the exterior in the fire compartment, flame may also be visible from the exterior. Later in the growth stage, isolated flames may be observed in the hot gas layer away from the immediate fire area (one indicator of ventilation controlled conditions). Table (2). Indicators for growth stage. Flashover-Transition to a Fully Developed Fire: Flashover is the sudden transition from a growth stage to fully developed fire. When flashover occurs, there is a rapid transition to a state of total surface involvement of all combustible material within the compartment. Conditions for flashover are 15

16 defined in a variety of different ways. In general, ceiling temperature in the compartment must reach 500o-600o C (932o-1112o F) or the heat flux (a measure of heat transfer) to the floor of the compartment must reach kw/m2. When flashover occurs, burning gases will push out openings in the compartment (such as a door leading to another room) at a substantial velocity. Recognizing flashover and understanding the mechanisms that cause this extreme fire behavior phenomenon is important. However, the ability to recognize key indicators and predict the probability of flashover is even more important. Indicators of potential or impending flashover are listed in Table 3. Building Smoke Air Track Heat Flame Flashover can occur in all types of buildings. Building factors can influence how quickly a fire will reach flashover (i.e., fire load, ventilation profile, thermal properties) and should be considered an integral part of ongoing risk assessment. Smoke indicators may or may not be visible from the exterior of the structure. However, smoke conditions indicating a developing fire are a warning sign of potential flashover conditions. After making entry, the presence of hot gases overhead and lowering of the hot gas layer are key indicators. Darkening smoke can be a flashover indicator, but do not depend on smoke color alone A strong bi-directional (air in and smoke out) air track can be a significant indicator of flashover that will move in the direction of the opening. However, any air track that shows air movement in to the fire can result in flashover. Increasing velocity of the air track when combined with other indicators can be a strong flashover indicator. Use of a thermal imaging camera (TIC) can allow more effective observation of convective heat currents within the building. Outside the fire compartment, perception of increasing temperature may not provide reasonable warning of impending flashover. However, perception of increasing temperature and observation of heat indictors such as pyrolysis of fuel packages some distance from the fire should be considered as a strong indicator of worsening fire conditions and potential for flashover. Use of a TIC allows observation of increased temperature and may allow observation of flaming combustion within the hot gas layer. Observation of the opening to the fire compartment will indicate high temperature at the top of the opening. From the exterior, increasing velocity of smoke discharge (an air track indicator) also indicates increasing temperature within the building. A TIC may allow observation of a pronounced heat signature in the area of the fire compartment. solated flames traveling in the hot gas layer (ghosting) or more substantially through the gas layer or across the ceiling (rollover). It is important to note that these flames may or may not be visible (without use of a thermal imaging camera).a later (potentially too late) indicator of impending flashover is rollover moving along the ceiling of the fire compartment and into adjacent spaces. Table (3). Indicators of flashover. 16

17 It is important to remember that flashover does not always occur. There must be sufficient fuel and oxygen for the fire to reach flashover. If the initial object that is ignited does not contain sufficient energy (heat of combustion) and does not release it quickly enough (heat release rate), flashover will not occur (e.g., small trash can burning in the middle of a large room). Likewise, if the fire sufficiently depletes the available oxygen, heat release rate will drop and the fire in the compartment will not reach flashover (e.g., small room with sealed windows and the door closed). Fully Developed Stage: At this post-flashover stage, energy release is at its greatest, but is generally limited by ventilation. Unburned gases accumulate at the ceiling level and frequently burn as they leave the compartment, resulting in flames showing from doors or windows. The average gas temperature within a compartment during a fully developed fire ranges from 700o 1200o C (1292o 2192o F), remember that the compartment where the fire started may reach the fully developed stage while other compartments have not yet become involved. Hot gases and flames extending from the involved compartment transfer heat to other fuel packages (e.g., contents, compartment linings, and structural materials) resulting in fire spread. Conditions can vary widely with a fully developed fire in one compartment, a growth stage fire in another, and an incipient fire in the other one. It is important to note that while a fire in an adjacent compartment may be incipient, conditions within the structure are immediately dangerous to life and health. Another point is that, this is burning period of the fire which impacts on structural elements and compartment boundaries. Indicators of fully developed stage are listed in Table 4. Building Smoke Air Track As with the growth stage, size, construction, and fire load influence fire development. Fire effects on the building can change the ventilation profile Smoke will darken to darker gray, brown, or black. Smoke color influenced to a substantial extent by what is burning and color may vary. Volume, optical density, and volume of smoke will increase. The height of the hot gas layer and neutral plane at openings is influenced by the ventilation profile, but if the compartment is not well ventilated, the hot gas layer will drop close to the floor as the fire progresses through this stage. Air track is dependent on the ventilation profile. However, given a single opening such as a door, smoke will exit out the top while air moves in the bottom. A fully developed fire will generally develop a well-defined and strong 17

18 Air Track Heat Flame air track. The velocity of smoke and air movement will commonly be quite high and smoke discharge will be turbulent.. In this stage of fire development, the fire is producing substantial heat. There are likely to be visual indicators of high temperature such as blackend windows, crazing window glazing. Hot surfaces (i.e., doors) may be detected using a fire stream or thermal imager. In addition high temperature can be felt, even when wearing structural firefighting clothing. Flames may be visible from the exterior, with extent indicating the area and extent of involvement to some degree. Fire will involve the entire compartment in this post flashover stage of fire development. Flames may be readily visible, but also may be obscured by smoke as the fire becomes ventilation controlled. Table (4). Indicators of fully developed stage. Decay Stage: A compartment fire may enter the decay stage as the available fuel is consumed or due to limited oxygen. As discussed in relation to flashover, a fuel package that does not contain sufficient energy or does not have a sufficient heat release rate to bring a compartment to flashover, will pass through each of the stages of fire development (but may not extend to other fuel packages). On a larger scale, without intervention an entire structure may reach full involvement and as fuel is consumed move into the decay stage. However, there is another, more problematic way for the fire to move into the decay stage. When the ventilation profile of the compartment or building does not provide sufficient oxygen, the fire may move into the decay stage. Heat release rate decreases as oxygen concentration drops, however, temperature may continue to rise for some time. This presents a significant threat as the involved compartment(s) may contain a high concentration of hot, pyrolized fuel, and flammable gaseous products of combustion. Burning rate: In a typical room fire, before flashover the burning rate depends on the type of fuel and the geometry of the burning item. The temperatures in the room can be characterized with a two-zone model. The behavior of the fire changes dramatically after flashover. The air and combustion gases become very turbulent. The high temperatures and radiant heat fluxes throughout the room cause all exposed combustible surfaces to pyrolyse, producing large quantities of combustible gases, which burn where there is sufficient oxygen. The temperatures are dependent on the heat release rate, which in turn depends on the rate of pyrolysis or evaporation of the 18

19 fuel and the available air supply to provide oxygen for combustion of the gaseous fuel. The rate of burning and consequent heat release rate may be ventilationcontrolled or fuel-controlled. Ventilation-controlled burning: In rooms with small or medium sized windows, post-flashover fires are ventilationcontrolled and the rate of combustion depends on the size and shape of ventilation openings. It is usually assumed that all window glass ( except fire resistant or wired glass) will break at the time of flashover due to the rapid rise in temperature. If the glass does not break, the fire will still be ventilation-controlled, but it will burn for a longer time at a lower rate of heat release because of smaller openings. In a ventilation-controlled fire, the rate of combustion is limited by the volume of cool air that can enter and the volume o hot gases that can leave the room. There is not sufficient air for all the combustible gases to burn inside the room, so the flames extend out the windows and additional combustion happens where the hot unburned gaseous fuels are mixed with outside air. According to Kawagoe for a room with a single opening, the rate of mass loss of burning wood fuel (m ) can be approximated by: m = (kg/s) (1) where: : the area of the ventilation opening ( ); : the height of the ventilation opening (m). The burning rate is dependent on ( opening factor ( ) as below: ), this is often expressed in terms of an = / ( ) (2) Where: : the total area of the bounding surfaces of the room ( ). Equation (1) is not always accurate, even if the burning rate is known precisely, the calculation of heat release rate is not accurate because an unknown proportion of the 19

20 pyrolysis products burn as flames outside the window rather than inside the compartment. Other sources of uncertainty arise because some proportion of the fuel may not be available for combustion, and the fire may change to fuel control after some time.equation (1) can be derived by considering the flows of air and combustion products through an opening as shown in Figure (3), for fuel of wood cribs. In a ventilation-controlled fire there are complex interactions between the radiant heat flux on the fuel, the rate of pyrolysis (or evaporation) of the fuel, the rate of combustion of the gaseous products, the inflow of air to support the combustion, and the outflow of combustion gases and unburned fuel gases through openings, the interactions depend on the shape of the fuel( cribs or lining materials), the fuel itself ( wood or plastic or liquid ), the shape of the room and the ventilation openings. Thomas and Bennetts have shown that the burning rate also depends heavily on the shape of the room and the width of the window in proportion to the wall in which it is located. If the width of the window is less than the full width of the wall, the burning rate is seen to be much higher than predicted by Equation (1) because of increased turbulent flow at the edges of the window. Equation (1) applies to a single ventilation opening in one wall of the compartment. If there is more than one opening, the same equation is often used, with being the total area of all the openings and being the average height of all the window and door openings, weighted by the area of the openings. If the openings are on several walls, the use of Eq (1) implies an assumption that the air flow is similar in all openings and there is no cross flow through the room. Figure (3). Windows flows for ventilation-controlled fire. 20

21 Fuel-controlled burning: Not all post-flashover fires are ventilation-controlled. The rate of burning may sometimes be controlled by the surface of the fuel, especially in large, well ventilated rooms containing fuel items which have a limited amount of combustible surfaces. In this case, the rate of burning will be similar to that which would occur for the fuel item burning in the open air, with enhancement from radiant feedback from the hot upper layer of gases or hot wall and ceiling surfaces. Depending on the fuel location, most fires become fuel-controlled in the decay period when the exposed surface are of the fuel decreases and the thicker items of fuel continue to burn. In fuel-controlled burning, all of the heat is released inside the room, with no flames projection out of the windows. For both ventilation and fuel-controlled burning, not all of the combustible material in the room may be available for immediate combustion. For this reason, many researchers introduce a fuel fraction or combustion efficiency factor by which the heat of combustion or available fuel is reduced. Babrauskas suggests a value in the range of Standard time-temperature curve (ISO 834): According to the Eurocode 1(EN ), the standard time-temperature curve for post-flashover fires is represented as the below equation and Figure (4): Where = gas temperature [ c] t= time [min] 21

22 Figure (4). Standard time-temperature curve (ISO 834). In order to investigate the changes of a structural component, it can be put under the condition of a fire in a test instrument such that the temperature in the apparatus is increasing according to the above figure until a failure happens either structural or insulation. There is a positive point for these series of tests such they are independent from different parameters affecting the fire intensity like: fire load, ventilation condition and building thermal properties. Swedish Curves: These series of curves are able to represent the short term effects of post-flashover fire but concerning the long term effects of exposure it can be said that they are not so reliable. The most reliable and widely used time-temperature curves for real fire exposure are Magnusson and Thelandersson (1970) which are depicted in Figure (5). They applied a similar approach to that one by Kawagoe and Sekine using a combination of theory with calibration against experimental data. They are derived from heat balance calculations using the equation by Kawagoe for the burning rate of ventilation controlled fires. As it can be seen in Figure (5) each group of Swedish curves are related to one specific ventilation factor and a range of different fuel loads(mj/ )of total surface area). 22

23 Figure (5). time-temperature curves by Magnusson and Thelandersson (1970). The ventilation factor is constant for each group of curves thus the burning rate is the same because it is dependent on the size of opening, now as the fuel load increases, it leads to longer and hotter fires before it reaches to the decay period. Now considering the Figure(6) showing the situation of changing ventilation factors for a constant fuel load it is seen that fires with high ventilation factors burn faster with higher temperature and the burning duration of this condition is shorter compare to poor-ventilated fires. 23

24 Figure(6). Different ventilation factors for constant fuel load. Eurocode parametric time-temperature curves: Parametric fires consider the factors which affect the fire growth and intensity like: fire load density, compartment and ventilation size. It can be mentioned that these curves have the aim to reach to a more realistic prediction of changes of time and temperature compare to the standard approaches. Parametric curves are not based on the real calculations of head transfer and gas flow rates but on the observations of test fires. When dealing with parametric fire models there are three parameters which are taken into account: the available fire load in the compartment, the openings and the last one is the type and nature of the different walls of the compartment. The following data are needed in order to figure out these models: fire load density, rate of heat release and heat losses. Fire load density: Fire load density is the total amount of combustion energy per unit of floor area and is defined as the source of the fire development. The fire load includes the existing furniture, wall and ceiling linings of the building. The characteristic value of the fire load density is derived from the following relationship: 24

25 Where: : the combustible material [kg]; : the net calorific value [MJ/kg]; : assuming the complete combustion is the total amount of energy contained in material and released; : the optional factor to protected fire load; A : the floor area. If the moisture content is considered the net calorific values are determined according to EN ISO 716:2002. Where: : the moisture content; : the net calorific value of dry materials. In order to calculate the designed fire load density the following formula should be taken into account which is based on characteristic fire load. Where: : characteristic fire load; m : combustion factor; : takes into account the fire activation risk due to the compartment size; : factor related to the type of occupancy. Tables (5, 6, 7) are available to find the values for (for 80% fractile),, : 25

26 Table (5). 80% fractile for different types of occupancy. Table (6). Values for,. Table (7). Values for. 26

27 Rate of heat release: Rate of heat release is dependent on the condition of the fire which may be fuel controlled or ventilation controlled, when the fire is ventilation controlled the size of the openings determines the amount of the available oxygen in the compartment and in case of having enough air for the burning, the burning process will be dependent on the amount of available fuel in the compartment. 1) calculation of burning rate (m/[kg/s]) when the fire is controlled by ventilation condition( according to Kawagoe (1958)): Where: : area of the openings ( ); : height of the openings (m). The above equation comes from the experiments for a room with a single opening. 2) Calculating rate of heat release for the case of facing a fuel controlled burning: If the duration is not known the rate of heat release is estimated based on the fuel information and the compartment fire temperature. Heat losses: Heat losses should be considered when facing the temperature development of a compartment fire and the losses occur through convection, radiation and the heat flow from openings. 27

28 In order to calculate the heat losses from compartment boundaries the concept of thermal inertia of the wall material is taken into account. λ : heat conductivity ( ; c : heat capacity ( ); ρ : mass density (. Chapter 2 Behaviour of concrete structures in fire From previous experiments about different reinforced concrete structures it can be told that this category of structures have good behaviours when exposed to fire and in many cases reinforced concrete structures have been able to gain the required strength capacity to utilize. Concrete is not combustible and has a low thermal conductivity. When a reinforced concrete member is exposed to a fire the temperature of both concrete and steel starts rising and dependidng on the restrains and loading condition deformations increase, previous observations show that most of structural failures of buildings exposed to a fire have not been due to the strenght reduction of concrete material but due to the other parts of the structures bearing the horizontal deformations and lead to shear or buckling failures of columns and walls. The behaviour of concrete in case of fire is dependent on the changes of material properties in increasing temperature condition. The thermal diffusivity of concrete is low compared to steel, the temperature gradients in a reinforced concrete member is great, form the other side because of high thermal inertia it takes a long time for the inneral parts of the member to get hot. In order to be able to analyse the failure time and condition of member, response of the whole structural element in high temperature condition should be considered. Another important phenomenon that should be investigated is spalling which is explosive separation of concrete pieces from the surface of the member when the tensile strenght of the material at outer 28

29 layer is decreased. Spalling can happen due to thermal stresses or fast expansion of the moisture in the concrete element which leads to increase of pore water pressure. There are different methods, tests and procedures to investigate the condition of the reinforced concrete structure exposed to a fire, these assessments and investigations are performed with the aim of collecting the required data to know the residual bearing capacity of each element, to decide if retrofitting of damaged structure is feasible and if yes which method is applicable for strenghtening it. In this section thermal and mechanical properties of concrete are discussed which are: thermal conductivity, specific heat, thermal expansion and mass losses. Mechanical properties are more affected by fire than the thermal properties which can be a good point for concrete members exposed to fire. the propagation of heat happens slowly in concrete but the amount of damages to the concrete is remarkable, to this when a concrete member is exposed to a fire different investigations should be done to know the durability condition of the member,to this purpose the first investigations are the visual ones which control color change, cracking and spalling. As a overal view the part of the concrete exposed to over 500 C temperature is not bearing any load and usually the color of this part of the concrete changes to red or pink. the concrete member exposed to strong fires may suffer different degradation processes like thermal expansion or softening, drying shrinkage and internal pore pressure. Heat transfers throughout the fire exposed concrete member through convection and conduction and makes changes in both chemical and physical properties also in porous concrete member the pore pressure changes and the result will be first the reduction of mechanical properties like strength and stiffness and second change of physical properties such as thermal conductivity, permeability and porosity. Definition of the conduction, convection and radiation as the mechanisms through which the heat is moved from the hot gasses in the compartment to the structural elements : Conduction: Transmission of kinetic energy among the molecules without matter transport. conduction is the most common way of heat transfer which happens due to the 29

30 changes of liquid and gases density. Conduction is important for the ignition of solid surfaces. Considering the Figure (7), heat transfer through conduction can be defined: Figure (7). Heat transfer through conduction. Where: q = thermal flux (W); = thermal conductivity (W/m c). Values of for concrete is in the range of 0.8 to 1.4 (W/m c) and for steel from 10 to 70. For transient heat flow when temperatures are changing with time, the amount of heat required to change the temperature of the material must be included. For 1-D heat transfer by conduction in a material with no internal heat being released: 30

31 Where: D : the thermal diffusivity. As the thermal diffusivity of the material is lower the conduction is higher. Convection: Convection is the transfer of thermal energy between a solid and a moving fluid. There are two types of convection. First one is the Forced convection and the second one is the free convection. Forced convection is the one when a fluid is forced to flow through the motion of heated matter. And free convection is due to the buoyancy effects. The convection heat transfer is an important factor in the upward transport of hot gases and smoke to the ceiling and also outward movement from windows. The velocity of the fluid which surrounds the solid material is deeply affecting the heating and cooling rate. Where: q = thermal flux (W); = thermal convection coefficient (W/ c). Radiation: Radiation is the transfer of thermal energy between two objects through electromagnetic waves which can travel through vacuum, transparent solid or liquid. Conduction does not require a medium and the effect of gases is not seen in this type of heat transfer. There is a high level of importance for radiation in case of fire, because the role of this type of heat transfer from flames to fuel surfaces, from hot smoke to building objects and from a burning building to the next one is significant. Through following relation the heat flux from one surface to the other one can be calculated. 31

32 Where: = absolute temperature of receiving surface; = absolute temperature of emitting surface; ϕ = configuration factor. Thermal properties of concrete: In order to calculate temperatures of structural members the thermal properties of material should be known. 1) Density: the density of concrete depends on the aggregates and mix design. Density of a dense concrete is about 2300 kg/. But to make a light weight concrete member porous material should be used to reduce the density of concrete. When a concrete member is heated up to 100 C the density of it reduces up to 100 kg/ because of evaporation of free water and its effect is not that much on thermal response. Other than moisture changes, density of concrete does not change much at elevated temperature except for limestone aggregate concrete which decomposes above 800C with a corresponding decrease in density. Density changes of concrete can be considered as below: ρ(t) = ρ(20 c) for 20 c < t <115 c ρ(t) = ρ(20 c). ( (t-115) / 85) for 115 c < t < 200 c ρ(t) = ρ(20 c). ( (t-200) / 200) for 200 c < t < 400 c ρ(t) = ρ(20 c). ( (t-400) / 800) for 400 c < t < 1200 c 2) Thermal conductivity: Thermal conductivity is the ratio of the flux of heat to temperature gradient or in another word can be defiend as the ability of material to conduct heat.this property is temperature dependent and varies in a wide range based on the type of the aggregates Figure (8).Based on (EC2, 1993) for design purposes these values can be 32

33 considered as approximate values: 1.6 W/mK for siliceous concrete, 1.3 W/mK for calcareous (limestone) aggregate concrete and 0.8 W/mK for light weight concrete. Thermal conductivity is measured in joules per second per square meter of area of the member when the temperature deference is 1 c per meter thickness of the member. Figure (8). Variations of thermal conductivity with temperature for different aggregate types. 3) Specific heat: Specific heat is defined the quantity of heat required to raise the temperature of a unit mass of a material by one degree centigrade and varies in a wide range based on the moisture content. According to the specific heat diagram of concrete according to the (Eurocode2, 1993), the peak between 100 and 200 c allows for water being driven off during the heating process, according to EC2,1993 the design values are given as approximate values which are 1000J/kg.K for siliceous and calcareous aggregate concrete also 840 J/kg.K for lightweight concrete. According to Eurocode 2 the changes of specific heat with temperature is as below: Cp(t) = 900 ( ) for 20 c < t < 100 c Cp(t) = (t-100) ( ) for 100 c < t < 200 c 33

34 Cp(t) = (t-200) / 2( ) for 200 c < t < 400 c Cp(t) = 1100 ( ) for 400 c < t < 1200 c 4) Thermal diffusivity: Diffusivity represents the rate at which temperature changes within the concrete mass. This parameter changes in the range of to The relation of diffusivity with conductivity, density and heat capacity is defined based on the following simple relationship. Diffusivity = Where: C : the specific heat; ρ : the density of concrete. Mechanical properties of concrete at elevated temperature: Change in the mechanical properties of a concrete in case of being exposed to a fire is dependent on the aggregates properties and the thermal compatibility between cement paste and the aggregates, therefore in order to make a resistant concrete against high temperature condition type and compatibility of material should be investigated. When a concrete member is exposed to high temperature condition the mechanical properties of it such as elastic modulus, strength and volume deformation undergo a value of reduction and causes the overall structural quality reduction of the member and due to the durability and strength reduction the concrete member may goes to failure zone. When a concrete member heated up to high temperature both chemical composition and physical structure of the concrete change considerably. Dehydration which is defined as the release of chemically bound water from calcium silicate hydrate, happens above 110 c. 34

35 1) Compressive strength: When a concrete exposed to fire the temperature of it starts rising and the changes by time will be like this: above 100 c the physically contained water is released from concrete which causes a reduction of the modulus of elasticity up to 20% but there is not a significant change in strength of the member. When the temperature goes beyond 300 c the silicate hydrates decompose and above 500 c the portlandite is dehydrated. The reduction process of concrete happens slowly when the temperature is lower than 500 c and will be rapid when upper than 500 c and rising the temperature to upper values of 600 c the aggregates suffer the decomposition process it means decomposition of limestone. Having all mentioned above, the residual bearing capacity of the concrete member is directly dependent to the maximum temperature which concrete experienced and the loading condition while heating process. In a simple word, the part of concrete exposed to temperature higher than 500 c does not have a considerable strength to bear any type of loading because it contains a large amount of calcium oxide (cao). Figure(9) Coefficient kc(ɵ) allowing for decrease of characteristic strength ( ) of concrete. 35

36 2) tensile strength: The tensile strength of concrete is important because it determines the ability of concrete to resist cracking. At room temperature, tensile strength of concrete generally varies from 7 to 11% of its compressive strength. From the limited tensile test data it can be conclude that the type and mixture proportions have a significant effect on the tensile strength versus temperature relationship, the decrease in tensile strength of calcareous aggregate concrete is twice as high as that of siliceous aggregate concrete at 500 c. concretes with lower cement content have lower reduction in tensile strength than those with higher cement content. The rate of heating has minimal effect on tensile strength at high temperature and the residual tensile strength is somewhat lower than the tensile strength measured at elevated temperature. Comparing compression and tensile results, the splitting-tensile strength appears to be more sensitive to the effect of moisture content as well as to microcracking caused by temperature exposure. A comparison of the effect of elevated temperature exposure on residual compressive, tensile (splitting-tension), and bend strengths (notched beams) for a siliceous gravel concrete exposed to temperature up to 600 c is presented in Figure (10). From the results it can be conclude that the residual tensile strength, either splitting-tensile or notched beam, is affected more significantly as the temperature increases than the compressive strength. Figure(10) comparison of the effect of elevated-temperature exposure on residual compressive, tensile (splitting-tension), and bend strengths (notched beams) of siliceous aggregate concrete. 36

37 Figure(11). Coefficient (Ɵ) allowing for decrease of tensile strength of concrete at elevated temperatures. 3) Modulus of elasticity: The elastic modulus defined as the ratio of the elastic modulus at a specific temperature to that at room temperature. When the temperature reaches to 100 c the elastic modulus will be about 80 to 90% of the room temperature strength. A temperature of 300 c marks the beginning of a higher rate of decrease in modulus of elasticity for all concretes and it is because of the dehydration progress and loss of bond between materials. Lightweight aggregate concretes retain higher proportions of the original modulus of elasticity at high temperature than normal weight aggregate concretes. Spalling: Base on Khoury spalling is defined as the violent or non-violent breaking off of layers or pieces of concrete from the surface of a structural element, when it is exposed to high and rapidly rising temperatures as experienced in fires high internal stresses caused by water evaporation or temperature gradients inside the concrete are the main factors leading to explosive spalling. Controlling the sensitivity of concrete to its explosive spalling behavior during fire exposure is one of the most important issues in the design and construction of concrete structures. Developments in concrete mix 37

38 design have lead to new types of concrete such as high strength, ultra-high strength and self-compacting concrete which besides an increased structural performance, also have shown a different sensitivity to spalling due to fire exposure. Figure(12). Explosive spalling of a high performance concrete slab after 119 min ISO fire, sudden explosive spalling leading to a loss of 60mm concrete cover (Eike Wolfram Heinrich Klingsch). Factors leading to explosive spalling: 1) Material related parameters: Researches on concrete spalling at high temperatures identifies several material related parameters which affect the spalling for instance silica fume lowers the permeability and increases the possibility of explosive spalling due to the reduced release of high vapor pressure. 2) Structural or mechanical parameters: As an example the tensile strength effects the spalling so a high tensile strength lowers the risk of explosive spalling because it offers a high resistance against spalling due to a high pore pressure and resistance of corner spalling. 3) Heating characteristics: Heating rate and the caused temperature gradients have strong effects on explosive spalling. As an example high temperature gradients (ΔT > 1.0 K/mm) promote the risk of explosive spalling due to thermal stresses. 38

39 Spalling can be classified as: 1) Aggregate spalling (splitting of aggregates); 2) Corner spalling (corners of column or beam members fall off); 3) Surface spalling (outer layer of the concrete member fall off). Explosive spalling happens just in concrete columns, beams and girders within a limited range of stresses and moisture content and generally occurs during the first 30 minutes of fire exposure and goes on as a step by step process removing layers of shallow depth. The result of spalling is the removal of surface layer of the concrete member and it makes deeper layers to be exposed to high temperature and finally the reinforcing rebars are exposed to fire and maximum temperature. Cracks: The first effects of temperature rise in concrete will occur between 100 and 200 c when evaporation of free moisture contained in the concrete mass, happens. Instant exposure can result in spalling through generation of high internal steam pressures. Spalling of concrete and surface cracking have been observed under laboratory and real fire conditions (Diederichs et al., 1995; Kodur et al., 2003; Bilodeau et al., 2004,). As the temperature approaches 250 c, dehydration or loss of non-evaporable water or water of hydration begins to take place. The first significant degradation in compressive strength is usually experienced between 200 and 250 c. at 300 c, strength reduction will be in the range of 15 to 40%. At about 550 c, the reduction in compressive strength will be in the range of 55 to 70% o its original value (Gustafero, 1983). There will be the critical situation when temperature is about 550 c because calcium hydroxide dehydration occurs. Calcium hydroxide is a hydration product of most Portland cement, the amount being dependent upon the particular cement being used. Limestone aggregates also begin to deteriorate at about 750 c. at higher temperatures in the range of 1200 c, concrete specimens suffer melting. 39

40 Figure(13) Surface state of concrete heated at different temperatures (Belkacem Toumi and Musa Resheidat). Figure(14) Surface cracks density versus heating temperature. Figure(15) Residual relative compressive strength. 40

41 Surface concrete cracking is a visible type of damage that has significantly adverse effects on the mechanical properties and durability properties of concrete. At high temperatures, the unrestrained thermal expansion of steel reinforcement is larger than that of most concretes and this causes high thermal stresses and cracking around the steel in reinforced concrete members. From the previous experiences it can be conclude that such cracks concentrate where before the fire exposure incipient cracks were present due to drying shrinkage and flexural loading, also the thermal incompatibility of aggregate and cement paste causes stresses which frequently lead to cracks. Color change: It is generally agreed that when heated to between 300 c and 600 c concrete containing siliceous aggregates will turn red, between 600 c and 900 c whitish-grey and between 900 c and 1000 c a buff color is present. The color change of heated concrete results principally from the gradual water removal and dehydration of the cement paste but also transformations occurring within the aggregates. The most intense color change, the appearance of red coloration, is observed for siliceous riverbed aggregates containing iron. This coloration is caused by the oxidation of mineral components. While siliceous aggregates turn red when heated, the aggregates containing calcium carbonate get whitish. Due to calcinations process turns to lime and give pale shades of white and grey. Chapter 3 Fire damage assessment General approach to fire damage assessment: Concrete can sustain various degrees of damage depending on the severity of the fire and the high temperature levels reached. The effects on concrete components of high temperature fire includes: 1) reduction in compressive strength; 2) micro-cracking within the concrete microstructure; 41

42 3) color changes consistent with strength reductions; 4) reduction in the modulus of elasticity; 5) various degrees of spalling; 6) loss of bond between concrete and steel; 7) possible loss of residual strength of steel reinforcement and possible loss of tension in prestressing tendons. The more severe fire damage would also involve the total exposure of main bars, significant exposure of prestressing tendons, significant cracking and spalling, buckling of steel reinforcement and even significant fracture and deflection of concrete components. The main objective of fire damage assessment in concrete structures is to provide the information required to evaluate the residual bearing capacity and durability of the structure and to design any strengthening or repair intervention. There are many documents with the approach of assessment and repair of fire damaged structures with the aim of defining the criteria of ability to repair and recognition the suitable assessment procedures based on the collection of event data, the inspection of the structural members and the analysis and classification of the material damage. In order to achieve this goal, different disciplines of Civil Engineering should be involved which is named Structural Design, Fire Engineering and Non-Destructive Testing (NDT). For instance having the maximum temperature reached in some significant points helps to validate a numerical model of the gas temperature in the compartment and extending the results to other parts. The structure should be observed and investigated at different scales from the whole fire scenario to the identification of the residual material properties at a point. The investigation and assessment of fire damaged concrete comprises both visual inspection and apply of various tests to establish the full extent of damage and the residual quality of the in-situ concrete. The visual inspection should be supplemented with consideration of temperature effects of fire damage on concrete, the physical properties, petrographic examination, temperature effects on reinforcing steel and prestressing strands and the temperature effects on the concrete-steel interaction. 42

43 Extraction of Concrete Cores: During the inspection, concrete cores may be extracted from both fire damaged areas and from sound concrete further away from the damage Figure (16). The purpose of obtaining the concrete cores is to: 1) Enable compressive strength testing and relative comparison between fire-affected and unaffected areas, and petrographic examination of the fire damaged concrete; 2) Establish visually the depth of fire-affected concrete with respect to both steel reinforcement and prestressing tendons Figures(17, 18); Cores are usually 75 mm or 100 mm diameter for strength and petrology testing, although they can be smaller. Cores as small as 20 mm may be required from between pre-stressing tendons, often located at 50mm centers both vertically and horizontally. Accurate positioning of the drilling equipment must be achieved, probably within an accuracy of better than 2 mm. 3) Enable a visual inspection of any internal surfaces of voided superstructure components using suitable lighting through adjacent cored holes. Figure(16) 43

44 Figure(17) Figure(18) Assessment methods of fire damages in concrete Tunnel linings: Fire in tunnels is one of the main open issues concerning the safety of infrastructures, as testified by a number of recent events occurred in road, rail and metro tunnels. Focusing just on structural point, one important aspect to be considered is the high severity of the fire scenarios that may develop in these underground traffic systems. The considerable fire load due to the tailed-back vehicles and the transported goods, the effective confinement of the released heat and the lack of active control measures are the main factors which may cause high temperatures and long fire duration. In most cases the thermal impact is the highest at the top of the tunnel, due to the direct flame impingement, and becomes smaller at the benches. When dealing with the assessment of fire damage in concrete tunnels, the following aspects are worthwhile to be taken into account: 1) A wide range of material conditions can be encountered, with the most severe heating above the heaviest burnt vehicles, maximum temperatures from a few hundreds degrees up to concrete melting (_1200_C) and a deterioration depth from a few centimeters to an important share of the lining thickness. 2) The exposed surface may be considerably rough, because of either the original finish (shotcrete linings) or the incidence of explosive spalling. This makes the implementation of some Non-Destructive Testing (NDT) techniques quite difficult. 3) The signs of any incipient collapse are seldom visible, due to the stiffness of the tunnel cross-section. Also the implementation of global static or dynamic load tests is hardly practicable. 4) The most significant parts to be inspected are difficult to access, being generally located at the crown of the concrete vault. This entails some limitations on the choice of the investigation techniques and on the number of test points. 44

45 5) There are stringent time limitations, due to the high cost of traffic disruption during the assessment and repair works. General Approach to fire damage assessment: a) Fire scenario and global structural effects: in order to have comparisons with published data concerning real scale tests or similar accidents some data can be obtained from the fire service operational reports which are the course of the fire, the nature and quantity of the fire load, the ventilation conditions and the steps of the extinguishing and rescue work. Further information on the fire severity can be obtained by examining the conditions of the remaining debris before their removal. melting of plastic material, softening and melting of metals like aluminium lamp reflectors, softening of lamp bulbs are helpful evidents to reach to the maximum temperature experienced during the fire. In order to detect any incipient collapse the global effects of fire should be considered at the structural level and through comparing the geometry of the concrete vault with the shape of the tunnel cross-section in undamaged parts the deformations can be detected. b) local conditions of the damaged lining: When dealing with lining cross section the effect of thermal gradients and the interaction between concrete and reinforcement such as cracking, spalling and rebar buckling can be taken into account. When a concrete member is heated the microcracks are distributed due to the diverging thermal strains of cement matrix and aggregates. Numerous cracks may be visible on the surface after cooling, as a result of the irreversible plastic contraction due to the restrained thermal dilatation in the hot phase. Due to the thermal gradients or any local failure, it is probable that larger isolated cracks develop through the lining not radial fractures as those ascribable to the hoop tension at the extrados of circular tunnels, are hardly detectable through NDTs for concrete structures. The depth of surface-opening cracks can be determined by means of ultrasonic pulse diffraction method or more advanced wave propagation analyses. Another possible defect which is probable to happen are the delamination cracks running parallel to the exposed surface, a good method for detection of the type of cracks can be tapping the structure with a hammer and checking the acoustic response by ear. This approach takes roots in the low frequency flexural vibrations governing the impact response of the detached concrete for a sufficiently low 45

46 thickness/extent ratio. When the defects are small and deep a different vibration mechanism in the ultrasonic range should be used which is based on the propagation of short pulses ( µs) which are partly back-reflected by any sizeable discontinuity in the material and then detected in the form of delayed echoes via sensor applied on the hit surface ( impact and pulse-echo techniques). Using the latter approach the local thickness of the concrete lining and the effective grouting of the outer annulus in segmental tunnels can be detected. Residual properties of material: Considering the smallest scale of observation, the residual material properties at a point of the member is the aim of investigations. The thermal diffusivity of the concrete is low and because of it the steep thermal gradients during a fire develop, and the lining has to be taken into account as a strongly layered element. This applied both to the mechanical response (compressive and tensile strength, young s modulus, hardness) and to a number of chemo-physical properties that are affected by the exposure to high temperature (velocity and attenuation of elastic waves, density of micro-cracks, porosity, humidity, chemical composition, color, etc). Possible approaches to the assessment of the local lining conditions: The methods of the material damage assessment can be divided into 3 categories: a) Average response of the concrete cover: Hammer tapping, Schmidt rebound hammer, Cut and Pull out test, Ultrasonic pulse velocity (UPV), etc; b) Point by point response of small samples: Small scale mechanical testing, while drilling tests, Ultrasonic pulse velocity, water absorbtion, X-ray diffraction (XRD), Spectroscopy (LIBS), etc; c) Special interpretation techniques: Sonic refraction, Impulse response, velocity and transmission, refraction ( WARR), Quantitative impulse-thermograohy, etc. The approaches of category (a) consists in the evaluation of the average response of the lining surface through well established techniques. For instance the Schmidt s 46

47 rebound hammer is a tool to sound the elastic and inelastic deformability of the first mm layer. And releasing a damage severity map is possible by using this method. This method is sensitive to a heavy material decay and not applicable to spalled or delaminated concrete. The category (b) includes the approaches based on the point-by-point analyses of concrete cores. Taking advantage of a number of chemo-physical properties that can be measured on very small samples or thin slices, a profile of the material deterioration and increasing depth can be the result. For instance the While drilling techniques in which the operation of cutting a core or drilling a hole is performed as a way to continuously scan the material soundness at increasing depth. The category (c) methods of assessment are a series of advanced techniques for the interpretation of the overall response of the concrete lining under different kinds of input (mechanical pulses, electromagnetic waves, electric fields, etc) and they are considered as the application at a smaller scale of the methods that are usually used in geophysics to investigate the layers of soils. a wide assortment of tools for the assessment of fire damaged tunnel linings is available, ranging from well established and relatively simple techniques to the latest and rather sophisticated test methods. While-drilling techniques: Extraction of a core through drilling the tunnel lining is a good way to investigate the concrete soundness at increasing depth which is a common practice in geophysical prospection. Application of the core-drilling resistance to the inspection of the damaged concrete is investigated with a set of sensors for measuring the main functioning parameters (rotational speed, longitudinal stoke, exerted thrust and electric power consumption). A quantity which is measured through this test and certifies the quality of the material is the time taken for a unit advance of the tool (s/mm), this value is influenced by the exerted thrust and the peripheral speed of cutting tool. Also the net work done per unit notched volume (J/ ) could be calculated as work = power * time). This quantity is not so affected by the working variables, because any change of the exerted thrust or the peripheral speed has opposite effects on the power input and the drilling time. The only limitation of the method regards its viability for the extensive testing of a tunnel ceiling, because of 47

48 relatively heavy drill and to the need for water and AC power supply. One advantage of this technique is the very fast and easy implementation, even in the case of spalled concrete or roughly finished shotcrete, as was proved in the assessment of a motorway tunnel following a series of hydrocarbon pool fire tests. A drawback is the initial opposite trend of the material response, since a higher work is required to drill slightly damaged concrete and a sizeable decrease can be recognized just for a decay of the compressive strength exceeding 50%. Figure(19). Sensitivitiy to thermal damage of different drilling resistance indicators (Roberto Felicetti). More studies have been recently performed in order to find a solution for this limitation by monitoring other working parameters of the hammer-drill. One direction considers the propagation along the bit body of the compression pulses induced by the hammering mechanism. The stress-wave produced by each impact propagates towards the tip of the drill bit and it is reflected in the form of a tensile stress-wave Figure (20). The procedure is captured using strain gages glued on the bit shank and connected to a wide band signal conditioner via a slip-ring. 48

49 Figure(20). Working principle of the Hammer-Drill Pulse Propagation method; modified chuck for strain signal transmission and pulse time of flight through a thermally damaged concrete panel Ultrasonic pulse refraction: (Roberto Felicetti). The velocity of sound in concrete is one of the most responsive indicators of the thermal damage, due to the pronounced temperature sensitivity of the Young s modulus and to the synergistic effect of pore drying. Considering a strongly layered material, needed information on the pulse velocity profile is obtained via the indirect UPV technique, which is based on the refraction of ultrasonic compression waves. Putting the emitting and the receiving probes on the same side of the element which is under the test, the pulse arrival time is achieved Figure (21). 49

50 Figure(21). Minimum travel-time path in the Ultrasonic Pulse Refraction method and shape parameters of the experimental X-T. c curve.obtained from a thermally damaged concrete panel; onset time picking and first peak amplitude for different distance between the probes (Roberto Felicetti). Performing the test after a fire exposure the assumption is that the material velocity rises at increasing depth, also the curved trajectory of the sound wave corresponding to the minimum travel time is considered as the best compromise between reducing the path via the shallow layer and exploiting a longer but faster way through the deep but undamaged layers. It can be understood that the maximum depth involved in pulse propagation is a function of the distance X between the probes, and by performing a series of repeated measurements of the pulse arrival time T at increasing distance the deeper layers of the structure are involved in the test, doing this test a X-T plot is derived. One property of this diagram is that the final slope corresponds to the reciprocal of the asymptotic velocity of the deepest layer of 50

51 concrete which has been inspected and tends to the value of velocity at 20 c in the undamaged material for a thick member exposed to a relatively short fire duration. multiplying the time T by velocity in pristine concrete, the geometric properties of this normalized plot are controlled just by the profile of the relative velocity V(z)/ c. among them, the intercept of the final asymptote at X=0 is of particular interest, because it is a measure of the time delay accumulated in the slow shallow layers and it is strongly related to the thickness of the damaged concrete. Considering the arrival time with adjacent transducers (X= 100mm) is related to the pulse velocity in the most damaged concrete at the surface. Chapter 4 Ultrasonic pulse refraction For the first time the measurement of the pulses velocity through concrete was performed in USA in the mid 1940s, and it was found that the velocity is dependent on the elastic properties of material and not on the geometry. A few years later more developments were performed in France, Canada and United Kingdom using electroacoustic transducers, which were found to offer greater control on the type and frequency of pulses generated. The result of these developments was the modern ultrasonic method, employing pulses in the frequency range between 20 to 150 KHz, produced and recorded by electronic circuits. This procedure of testing when is applied to metal members employs a reflective pulse technique with much higher frequencies and cannot be applied to concrete due to the high scattering which occurs at matrix/aggregate interfaces and microcracks. Theory of pulse propagation through concrete: When applying an impulse to a solid mass, three types of waves are generated. The first series of waves are surface waves having an elliptical particle displacement which are the slowest ones, the second series are directed to the shear or transverse waves with particle displacement at right angles to the direction of travel and they are faster than the first series. And finally the third series are longitudinal or compression waves 51

52 with particle displacement in the direction of travel, these series of waves are the fastest ones and need more notice because generally make more useful information. It is worthwhile to mention that the electro-acoustical transducers produce waves of this type. As the wave velocity depends on the elastic properties and mass of the medium, having the mass and velocity of wave propagation the elastic properties can be defined. For an infinite, homogeneous, isotropic elastic medium, the compression wave velocity is the outcome from below formula: V = Where: V : the compression wave velocity (Km/s); K = ; = dynamic modulud of elasticity (kn/ ); ρ= density (kg/ ); υ = dynamic Poisson s ratio; Pulse velocity equipment and use: Equipment: As it is shown in Figure (22), the test equipment works somehow that provides a means of generating a pulse, transmitting it to the concrete, receiving and amplifying the pulse and measuring and displaying the time taken. 52

53 Figure(22). Typical Ultrasonic pulse velocity testing equipment. Transducers with natural frequencies between 20 khz and 150 khz are the best ones where the item under the test is concrete, and these may be of any type, although the piezo-electric crystal is most popular. Time measurement is performed according to detection of the compressive wave pulse, the first part of which may have only a very small amplitude. In case of using an oscilloscope, the received pulse is amplified and the onset taken as the tangent point between the signal curve and the horizontal time-base line, but for digital instruments the pulse is amplified and shaped to trigger the timer from a point on the leading edge of a pulse. Use: One important issue which should be controlled during the test, is good acoustical coupling between the concrete surface and the face of the transducer, and this is obtained through using a medium like petroleum jelly, liquid soap or grease. Air 53

54 pockets should be eliminated, and just a thin separating layer exists, any surplus must be squeezed out. The other point necessary to be taken into account is repeating of the readings by complete removal and reapplication of transducers to obtain a minimum value for the transit time. The path length must be measured to an accuracy of ±1%. And this makes difficulty for paths over about 500 mm, but for shorter paths the use of calipers is suggested. Transducer arrangement: There are three possible arrangements for transducers as shown in Figure(23): 1) opposite faces (direct transmission); 2) adjacent faces (semi-direct transmission); 3) same face (indirect transmission). (1) (2) (3) Figure(23). Types of reading, direst(1); semi-direct(2); indirect(3). 54

55 The maximum pulse energy is transmitted at right angles to the face of the transmitter, thus the direct method is the most reliable method form the transit time measurement point of view. Also the path is clearly defined and wherever the use of this method is possible, it should be done in order to investigate the quality of the concrete. In case of using the semi-direct method the angle between the emitter and receiver should not be too great also the path length should not be so large in order to achieve satisfactory results. When the only possibility to perform the test is the third method i.e. indirect method, the results are the least satisfactory because the received signal amplitude may be less than 3% of that for a comparable direct transmission. When there are discontinuities in the sample under the test, the pulse is scattered and the received signal is subject to errors. The pulse velocity is mainly affected by the influence of the surface zone concrete, which may not be representative of the body, and the exact path length in uncertain. To fix this problem a series of readings are performed somehow that the transmitter is fixed at a point and the receiver located at a series of fixed incremental points along a chosen radial line Figure (24), and the results are plotted in Figure(25) and the mean pulse velocity is considered as the slope of the best straight line. Figure (24). Indirect reading with fixed transmitter and incremental changing receiver. 55

56 Figure (25). Indirect reading, results plot. Existence of any discontinuity in this plot could be because of surface cracking. Test calibration and interpretation of results: The issue is that the material under test are complex of two separate constituents, matrix and aggregate, which have different elastic and strength properties, through performing resonance tests on prisms, the relationship between pulse velocity and dynamic elastic modulus of the composite material is defined Figure (26). this relationship is affected by the value of dynamic Poisson s ration but for most practical concretes made of natural aggregates the estimate of modulus of elasticity has to be accurate within 10%. Figure (26). Pulse velocity vs. dynamic elastic modulus. 56

57 Strength calibration: In order to define the relationship between elastic modulus and strength of the composite material the following items should be properly taken in to account: 1) properties of individual constituents; 2) influence of aggregate particle shape; 3) efficiency of the aggregate/matrix interface; 4) variability of particle distribution; 5) water/cement ratio. Strength calibration should normally be performed for a particular mix in the laboratory taking into account the factors mentioned above. Pulse velocity readings are performed between both pairs of opposite cast faces of cubes knowing the moisture condition, which are then crushed in the usual way. Practical factors influencing measured results: There are some parameters influencing the results of the tests on in-situ concrete. 1)Temperature: Considering Figure() the effects of extreme temperature conditions can be estimated, which according to the work by Jones and Facaoaru are the microcracking at high temperatures and the water freezing within the concrete at very low temperatures. 2) Stress history: Generally it can be considered that the pulse velocity of laboratory cubes is not affected until a stress of approximately 50% of the crushing strength is reached. Then at higher stress levels, a considerable reduction in pulse velocity happens because of the formation of internal microcracks which influences the path length. Under service conditions in which stresses will not exceed cube strength the influence of compressive stress on pulse velocity is not significant, and that pulse velocities for prestressed concrete members can be used with confidence. When a member is overstressed, the pulse velocities are affected. Tensile stresses are not going to affect 57

58 the pulse velocities that much but potentially cracked regions should be considered accurately, even when measurements are parallel to cracks. 3) Path length: Physical limitations of the time-measuring equipment may introduce errors where short path lengths are involved as shown in Figure (27) as a result of a laboratory test on a specimen incrementally reduced in length by sawing. Based on BS 1881: Part 203, the minimum path lengths for concretes with maximum aggregate sizes of 20 and 40 mm should not be less than 100mm and 150 mm respectively. Also for unmoulded surfaces a minimum length of 150mm should be taken for direct, or 400mm for indirect readings. This is obvious that the pulse velocity decreases with increasing path length, and a typical reduction of 5% for a path length increase from approximately 3m to 6m usually happens. This is because attenuation of the higher frequency pulse components results in a less clearly defined pulse onset. Figure (27). Effect of short path length. 58

59 4) Moisture conditions: The pulse velocity through saturated concrete may be up to 5% higher than through the same concrete in a dry condition, and the influence will be less for high-strength than for low-strength concretes. The moisture effect on both pulse velocity and concrete strength is a factor which should be considered in strength calibration. The pulse velocity of a moist specimen is higher than a dry one but lower measured strength than a comparable dry specimen, so that drying out results in a decrease in measured pulse velocity relative to strength as shown in Figure (28). Figure (28). Effect of moisture conditions. Tomsett has introduced an approach which permits calibration for actual in-situ concrete strength to be obtained from a correlation based on standard control specimens. The relationship between specimens cured under different conditions is as below: 59

60 = k ( - ) Where: : the strength of a standard saturated specimen; : the actual strength of the in-situ concrete; : the pulse velocity of the standard saturated specimen; : the pulse velocity of the in-situ concrete; K: a constant reflecting compaction control ( the suggested value for normal structural concrete is 0.015, and if it is poorly compacted the value is 0.025). 5) Reinforcement: As the pulse velocity is higher in steel than concrete, considerable uncertainties are introduced for heavily reinforced regions. Where the situation is somehow that avoiding the reinforcing steel close to the pulse path is impossible, the corrections to the measured value will be necessary, although these corrections are not easy to establish. It should be considered that, the velocity along a bar embedded in concrete is more affected by the velocity of pulses in the concrete and the condition of the bond between steel and concrete. Roughly speaking, any sharp increase in pulse velocity through a concrete member depends upon the proximity of measurements to reinforcing bars, the diameter and number of bars and their orientation with respect to the propagation path. An increase happens when the first arriving pulse at the receiving transducer travels partly in concrete and partly in steel. Applications: The applications of pulse velocity tests are so wide-ranging and the principal applications are mentioned below which can be performed both in the laboratory and on site with equal success. 1) Measurement of concrete uniformity: There are many published reports of the use of ultrasonic pulse velocity surveys to investigate the strength variations within members. The statistical analysis of results, coupled with the production of pulse velocity contours for a structural member, may 60

61 also produce valuable information concerning variability of both material and construction standards. Readings should be taken on a regular grid over the member. A spacing of 1m may be suitable for large uniform areas, but this should be reduced for small or variable units. Typical pulse velocity contours for a beam constructed from a number of batches are depicted in Figure (29). Figure (29). Typical pulse velocity beam contours (km/s), (J.H.Bungey). 2) Detection of cracking and honeycombing: The application o ultrasonic pulse velocity in detection of cracking and honeycombing is an independent process from any other property of material because it can be easily considered that the pulse cannot travel through air and presence of any void on the path will increase the path length and the pulse goes around the flaw and the result will be a higher attenuation and a longer transit time will be recorded. One problem can be for the water filled cracks or voids, because the compression waves are able to travel through water and in this condition the recognition of cracks faces to uncertainties. Tomsett with deeper studies on this issue concluded that although water-filled cracks are not detected, the pulse velocity through water-filled voids is lower comparing the surrounding concrete. When studying the situation of cracks, it can be properly assumed that even micro-cracking of concrete is able to disrupt the path taken by the pulses, and at compressive stresses in excess of 50% of the cube crushing strength, the measured pulse velocity may be expected to drop because of disruption of both path length and width. Having the pulse velocity of a sound concrete member, It is possible to detect overstressing, or the onset of cracking by continual monitoring during load increase. Using an indirect surface reading, an estimate of crack depth is obtained as shown if Figure (30). Putting the transducers at 61

62 equidistant points from a know crack and having the pulse velocity through sound concrete as V km/s, then: Path length without crack = 2x Path length around crack = 2 Surface travel time without crack = = Travel time around crack = = Crack depth, h = x Figure (30). Crack depth measurement (J.H.Bungey). Applying direct measurements through the member under test with readings taken on a specific grid, the location of honeycombing can be determined and if thickness of the member is constant in all parts, a contour map of transit times will illustrate the location and extent of areas of poor compaction. 3) Strength estimation: Through applying pulse velocity measurements on a part of in-situ concrete the prediction of absolute strength is impossible. Although it is possible to obtain reasonable correlations with both of compressive and flexural strength in the laboratory, enabling the strength of comparable specimens to be estimated to ±10%, the problems of relating these to in-situ concrete are considerable. The most reliable method could be the use of cores to establish the calibration curve coupled with 62

63 Tomsett s moisture correction. If a reliable calibration chart is existing, coincide with good testing conditions, it is possible to achieve 95% confidence limits on a strength prediction of ±20% relating to a localized area of interest. 4) Assessment of concrete deterioration: The application domain of ultrasonic pulse velocity tests is very wide when the strength reduction or deterioration process of a concrete member due to a fire exposure or mechanical, frost or chemical attack is under the investigation. A simple method to assess the depth of fire or surface chemical attack has be produced by Tomsett. In this approach the assumption is that the pulse velocity for the sound interior regions of the concrete can be determined from unaffected areas, and that the damaged surface velocity is zero. A linear increase is assumed between the surface and interior to enable the depth to sound concrete to be calculated from a transit time measured across the damaged zone. For example, if a time T is obtained for a path length L including one damaged surface zone of thickness t, and the pulse velocity for sound concrete is, then the thickness is defined as following: T = (T - L) Although this process results in a rough estimate of damage depth but there are many reasonable results from a number of fire damage investigations. 5) Measurement of layer thickness: Performing indirect reading methods the layer thickness can be obtained based on the fact that as the path length increases the pulse will travel deeper in concrete member. This is appropriate for application to slabs in which a surface layer of different quality exists due to construction, weathering or other damage such as fire. Briefly reviewing the procedure of an indirect test, when the transducers are close together the pulse travels in the surface layer, but at greater distances the path includes the deeper layers. And these layer changes are determined by discontinuities In the plot of transit time v. having the transducer spacing, the pulse velocities through two layers with different slopes Figure (31), the thickness t of the upper layer which is related to the velocities and, the following relation is true although this is most suitable for a distinct layer of uniform thickness, the value obtained is just an estimate and it should be considered that there will be a maximum thickness of layer that can be detected. 63

64 t = ; 6) Measurement of elastic modulus: Figure (31). Layer thickness measurement. This property can be measured through ultrasonic pulse velocity test with high accuracy. Values of pulse modulus are calculated theoretically using an assumed value of Poisson s ratio to obtain a value within ±10%, or more commonly an estimate of dynamic modulus can be obtained from the reliable correlations with resonant frequency values. These measurements may be valuable in the laboratory when performing a test on a model but they are not so useful on site, although they may be used to provide an estimated static elastic modulus value for use in calculations relating to load tests. 64

65 Application of ultrasonic pulse velocity tests in fire damaged structures: According to a preliminary evaluation of the mechanisms involved in terms of damage mechanics performed by Benedetti (1995), the property reduction in concrete is considered to be a consequence of the diffuse microcracking generated by the combination of load, thermal strains, and moisture migration. As a result of the intrinsic irreversibility of damage, a different mechanical behavior after cooling. When dealing with ultrasonic testing on fire damaged concrete structures, the relation between sound speed and elastic modulus, and the slow down of ultrasonic waves because of microcracking should be determined. The velocity of sound in concrete is strongly affected by the thermal damage, because of drying of pores and the pronounced temperature sensitivity of the Young s modulus. However, detecting the residual velocity profile within a member submitted to strong temperature gradients is a difficult process. Based on the refraction of longitudinal ultrasonic waves, useful information on the damage depth and severity can be provided through the indirect UPV technique. In this method, the measurement of the pulse arrival time is performed by applying both the emitting and receiving probes on the same face of the element under testing Figure (32). Figure (32). Position of receiver and emitter and the X-T plot. The assumption is that the pulse velocity rises at increasing depth (the same assumption is considered after a fire), the path of sound waves corresponding to the minimum travel time is the best compromise between reducing the covered distance 65

66 via a shallow path and exploiting the faster deep layers then, the maximum depth of the material involved in this pulse propagation is a function of the distance X between the probes. As a consequence, a series of repeated measurements of the pulse arrival time T at increasing distance X allows deeper and deeper material layers to be investigated. The result of this process is the X-T plot. The important property of this experimental diagram is that the reciprocal of the final slope corresponds to the asymptotic velocity of the deep concrete layers, which is normally equal to the velocity c in the pristine material for thick members and relatively short fire duration. After multiplying the ordinate by the asymptotic velocity (T => T ) the final slope is normalized to a unit value and the shape of the plot is controlled only by the profile of the relative velocity V(z) /. The intercept of the final asymptote at X=0 is an important feature, because it is a measure of the time delay accumulated in the slow shallow layers and it is strongly related to the thickness of the sizeably damaged concrete (a 20% velocity decay threshold is considered usually). It is worthwhile to mention that no preliminary information on the member under investigation is required for the application of this method. Several tomographic ultrasonic techniques have been proposed to map the consistency of a concrete section. However, due to the complexity of the scanning apparatus and the cost, these techniques are not suitable for field characterization of large fire damaged buildings. The simplest hypothesis that allows evaluation of the thickness of the damaged external layer of a concrete section is based on the assumption that both the outer layer and the internal core have the same elastic modulus. Assuming that for a certain measurement length the time spent by a pulse to travel from one probe to the other is equal either running at the surface or in the inner core Figure (33), the below formula can be produced: = (1) 66

67 Figure (33). Path equivalence concept for the ultrasonic travelling pulses. Where the pulse velocities of the layer and the core can be estimated from a distance-time plot similar to the Figure (34). Figure (34). Schematic view of a bilinear spacing-time plot. The problem is that, the evaluation of the parameters of Equation (1) is not practically so simple because the plot is not usually as is shown in Figure (34). On the other hand, fire alters a concrete section with a high gradient continuous damage pattern, which is difficult to represent with average values. As an assumption, near the surface the elastic modulus distribution is linearly changing. In this case we can construct a solution using the calculus of variations in order to establish the minimal time path analytical form. This is a modification of the well known problem of the brachistochrone first solved by Jacob Bernoulli in the 18 th century. 67

68 Figure (35). Set of functions describing the possible paths in a damaged concrete section. Considering the Figure (35), and taking the ƞ(x) which is the path of the travelling pulse, the function that evaluates the transit time is defined, under the condition that the path runs only on the external layer where the elastic modulus is linearly distributed: (ƞ) = From the previous data based on fire analysis: =, = We obtain the condition that defines the true path as the minimal one: = ƞ( :: Min { τ(ƞ) = d } The solution is given by the Euler-Lagrange formula: ƞ = 0 68

69 Being: = Where: a and b: the yet unknown coefficients of the linear approximation of the elastic modulus. The solution method makes use of the substitution a + bƞ = ζ. Then the implicit form is obtained: - arctan - = The trajectory can be expressed in a parametric representation posing ζ( ) = sin. Then it is obtained: = Ƞ(a) = ( -1) The integration constants are to be fixed through the limit conditions: Ƞ(a) = 0 where = 0 Ƞ(a) = 0 where = L From the statement of null ƞ(a) we extract the limit value of the parameter a: = arcsin, = π - = π - arcsin Substituting in the parametric representation of the path, summing and subtraction the two formulas for the starting and ending points, we have: = L 69

70 = This system of transcendental equations has no closed form solution, so we must resort to an iterative solution computing in turn the two constants and the two elastic parameters (a) and (b). For common distributions of elastic properties resulting from fire damage, and for usual probe spacing (with less accuracy for close spacing), the denominator of the first equation is very close to π; so we can construct an approximate solution, which is needed for the most part in situations occurring in practice: = = Substituting now these values in the representation of the path, and introducing the moduli and for the constants (a) and (b), we can obtain the approximate closed form solution: Ƞ(a) = And: = (2a sin2a) arcsin a π - arcsin we recognize that the evaluated path is a trocoid,i.e., a part of a cycloid curve. Finally, performing the integral: Τ = da, 70

71 with: = arcsin We determine the minimum travelling time of a ultrasonic pulse: = 2 ( π 2arcsin ) The solution for a bilinear distribution of the elastic modulus: When considering the inner cold core, the damage index is equal to zero, based on Figure (36), the bilinear pattern for the distribution of elastic modulus can be taken into account as a good assumption. In this case paths that remain in the high gradient layer have the minimal travelling time and paths entering in the constant modulus core have the fastest path defined by a straight line running on the edge of the core. While the solution of the variational problem is an exact one, the mixed solution composed of a straight line and two parts of trocoid is just a good approximation. Considering the unknown core modulus as zone will be defined as:. Then the thickness of the damaged = Through computing the maximum depth for a trocoidal path which is tangent to the core it is obtained: ( ) = - = Then the angle at which it crosses the core boundary can be computed, and following it the total time spent by a pulse to run inside it: = - Solving for (a) and substituting we have: = arcsin 71

72 The total travel time is evaluated summing up the two contributions: = 2 ( arcsin - arcsin ) = [ -2 ( 2 - sin2 ) Doing some simplifications: = [ 2 ( 2 - ) arcsin - 4arcsin + π +2 ] The above relation is valid for L >. Figure (36). Bilinear modulus distribution for a damaged concrete section. As an example the damage identification for the Merloni fire exposed building can be taken into account: Considering the condition of a real fire environment it is not usually feasible to use the laboratory simulated tests for comparison purposes. But from the other side, the ability of concrete to memorize the most severe situation through diffuse microcracking, can allow one to characterize the damage locally. 72

73 Briefly discussing on Merloni fire, the main problem has been the separation of the damaged area in homogeneous zones requiring passivation, restoration and demolition (Benedetti and Barboni [1993]). In order to collect the required information in the case of Merloni fire, several different NDTs was performed on reinforced concrete elements. For the columns which are in the selected part for restoration works Figure (37), a series of tests have been performed as bellow: - UPV direct and side measurements at three distinct locations in each column. - Sampling of one 70 mm core cut along the shortest side of the column. - Performing UPV direct tests along the core with fine spacing, running with the probes onto two orthogonal diametrical planes containing the core axis. - Performing compression tests for the standard height cylinders (B=H), obtained cutting the core. Figure (37). Subdivision of the damaged area into homogeneous parts (Benedetti and Barboni [1993]). There were two ways to draw the residual elastic modulus profile inside the columns (Benedetti [1995]) : (1) directly, through performing UPV tests on the core, (2) 73

74 through calculation, starting from the UPV side data of the columns and applying the reconstruction techniques. There is a main problem when taking core samples which is the cutting and testing the two parts of the cylinders resting near the column surface. Because of damage level of these zones and porous condition of the material, the cutting process causes to deterioration of these areas of sampling and finally the results of UPV measurements are not so satisfactory. The figure (38) illustrates the experimental UPV side plots used to deal with the proposed procedure, in comparison with the transit time curves obtained by using the reconstructed residual modulus distribution and a shortened trocoidal path. As a result of the test, two different curves relating each one to one side of the column were obtained as a consequence of different temperature boundary conditions. There are some local sharp deviations on these diagrams which can be the result of the flaws diffracting the ultrasonic pulse travel. Figure (38). Time-spacing plots for the Merloni columns D2, F2, H2, I3, M2, M3 (square : side1; circle : side 2; _ : reconstructed optimal diagram ), (Benedetti and Barboni [1993]). 74

75 Seismic measurements within the Mont Blanc-tunnel: On March 26, 1999, a fire in the Mont-Blanc tunnel happened and following it, considerable reinforcement work was required in order to reopen the tunnel. To plan and perform the restoration work, a complete diagnosis of tunnel walls was necessary. The major consequence of fire is the decrease of the Young s modulus and shear modulus o concrete. The extent of damage with respect to depth varies along the tunnel with distance from the center of both the main fire and local hightemperature vehicle fires. Considering the figure(39), three zones on a sidewall of the tunnel were selected in order to study the condition of tunnel: - A sound zone (SZ); - A moderately damaged zone (MZ); - A heavily deteriorated zone (HZ). Figure (39). Section of the Mot-Blanc tunnel for the SZ, MZ and HZ zones (Odile Abraham, Xavier De robert). The objective of the seismic method was to recover the mechanical characteristic of the concrete as a function of depth. 75

76 Since fire causes a decrease in the mechanical moduli of concrete, it will make the reduction of the compression ( ) and shear ( ) wave speeds according to the following relations: = and = Where: λ & µ : Lame coefficients; ρ : the density. then young s modulus will be : E = Then the wave speeds measured along the tunnel for the same concrete can be compared and as a result the walls with different degrees of deterioration will be separated. In order to do the measurements, for each of the three zones mentioned above (SZ, MZ and HZ), a horizontal measurement line has been considered and one source point and 70 sensor points has been located on it. This experimental set-up was not designed for extensive surveying and should be optimized for this purpose. The source is a steel ball, which hits a 1 steel anvil glued to the concrete. The ball is maintained at rest a fixed distance from the anvil by an electromagnet to ensure reproducibility of the excitation. Its diameter is equal to m. the receivers are 15 accelerometers pre-amplified by 15 preamplifiers. Both the source and receiver signals are recorded on a 32-channel data acquisition system with a sampling frequency of 500 khz over 8192 time steps. The coupling of sensors is ensured using cyanolite glue. In order to collect data from 70 sensor points, five series of measurements have been performed. Spacing between the sensors increases with distance from the source. For the first series, spacing is equal to 1 cm; it moves to 2 cm for the second through fourth series, and then to 4 cm for the last. For each series, 10 source impacts have been recorded. Data from each series are obtained and then presented on seismograms. The horizontal axis is related to the offset distance between source and receiver, and the vertical axis representing the time. Figure (40) 76

77 shows the average of the 10 seismograms measured on each zone (SZ, MZ and HZ). The signals are quite noisy due to: Numerous reflections stemming from the concrete-to-rock interface, visible cracks on the walls near the measurement line, and joints. This noise unfortunately made difficulties for obtaining reliable results with surface waves. Two general comments can be mentioned from these seismograms: -Frequency content is higher in the sound zone (SZ) than in MZ and HZ. Paradoxically, in assuming that damage and attenuation rise together, the MZ appears more heavily deteriorated than HZ. - The first arrival of the compression waves indicates clear slope changes varying from one zone to the next, which suggests that the mechanical properties of concrete do not progressively evolve as a function of depth. A classical seismic refraction procedure can be applied to determine the corresponding layer thickness and compression wave speeds. Figure (40). Recorded seismograms (from left to right : zone SZ, zone MZ, zone HZ) (Odile Abraham, Xavier De robert). Seismic refraction principle: Whenever a wave reaches to an interface, it is reflected and refracted. Seismic refraction is based on Huygen s principle and uses refracted waves. This refraction is only valid when wave speed increases with depth. The figure (40.a) explains the underlying principle for one plane layer of thickness, with a compression wave speed equal to, on top of an infinite medium of compression wave speed (with > ). In order to determine the values of, and the information required consists of the arrival time of the compression wave as a function of source receiver 77

78 distance (Figure 40.b). When the offset is less than a given distance is the direct wave., the first wave = 2 The slope of the straight line before determines the. The first arrival refracted wave and the slope of the next straight line yields. The intersection of this line with the y-axis,, is applied to calculate the thickness of the first layer: = This principle can be extended to several layers, also to inclined layers, in which case several source points are required to recover the 2D geometry of the medium. Figure (40). Seismic refraction principle : (a) description of the medium; (b) measurement (Odile Abraham, Xavier De robert). 78

79 Seismic refraction interpretation of Mont-Blanc data: For each of the zones, the time of the first wave arrival can be plotted as a function of source-receiver distance similar to the Figure (41). The selection of seismograms is performed individually for each source impact, instead of considering the average seismogram, in order to prevent from producing an artifact from any trigger discrepancy. Results for the MZ are more dispersed because source diameter was increased in order to record a proper signal for the last series, i.e. the larger offsets. Source energy was calibrated on HZ but, MZ is in worse condition. Figure (41). Time versus offset plots (from left to right : zone SZ, zone MZ, zone HZ) (Odile Abraham, Xavier De robert). A one-layer model has been considered to interpret data as only one source point was available. To obtain a more detailed model with a high level of confidence, at least five source points are needed. The obtained results have been summarized in Table (8). Table (8). Seismic refraction results using a one-layer model (Odile Abraham, Xavier De robert). 79

80 The compression wave speed of a sound concrete is at least 3500 m/sec. according to the data in table (8) and regardless of the zone considered, the quality of the first few centimeters of concrete is poor. This low-velocity layer has been observed both on cores and with spectral analyses of surface waves, this issue is due to the normal carbonation of older concrete. An analysis of values shows that the mechanical characteristics of this first layer significantly from one zone to another. The level of damage has been greater in MZ than HZ and the compression wave speed for the MZ equal to 870 m/sec compare to the HZ with that of 1130 m/sec. also the damaged zone thickness is larger for MZ than for HZ, i.e., 0.13 m versus 0.09 m. Some considerations on Seismology: Travel-Time curves: Considering the following Figure, there are a number of receiver stations at certain distances away from a source: Figure (42). Showing a source and a series of receiver stations to apply in seismology (MIT OpenCourseWare, spring 2008). 80

81 The wave front will arrive at the closest station to the source and following it to the next stations. The seismograms recorded at each station is like the following Figure: Figure (43). Example of recorded seismograms (MIT OpenCourseWare, spring 2008). By connecting the same point on each seismogram, the travel-time curve is obtained as below: Figure (44). Producing travel-time curve from recorded seismograms. (MIT OpenCourseWare, spring 2008). 81

82 Travel-Time curve for a layer over a half space: When considering a layer over a half space, there are three types of recognized waves as illustrated in Figure (45). A. Direct waves B. Reflected waves C. Head waves Figure (45). Depicting three types of waves (Direct wave, Reflected wave, Head wave), (MIT OpenCourseWare, spring 2008). A. Direct waves: The travel time for a direct wave is calculated as below: = According to the above simple relationship, the travel-time curve should be a straight line as below: 82

83 Figure (46). Travel time for a direct wave, (MIT OpenCourseWare, spring 2008). B. Reflected waves: The travel time for a reflected wave is divided in two parts, first, the travel time from the surface to the layer and the second, the travel time from the layer back to the surface: = + = The travel-time curve for reflected waves is a hyperbola. The asymptote is the traveltime curve for direct waves. 83

84 Figure (47). Travel time for a reflected wave, (MIT OpenCourseWare, spring 2008). C. Head waves: Head waves produce when the incident angle is greater that the critical angle. The critical angle is the incident angle for which the refracted wave travels along the interface. This angle is determined by through Snell s Law considering that the refracted wave travels along the interface when its angle is. = = ( ) The travel time for a head wave is obtained from three parts: =

85 = + The form of this equation is y = mx+b, and its result is a straight line. This line is not continuous because head waves do not develop until the critical angle is reached. As a result, the line starts at the critical distance, which is defined as: = 2h tan The following Figure shows the travel-time curve for all the three wave types: Figure (48). Travel time for reflected, Direct and Head waves, (MIT OpenCourseWare, spring 2008). As an important point, at the critical distance the direct wave arrives before the head wave. Since the velocity of the head wave is higher than the velocity of the direct wave, the slope of the head-wave curve is smaller and the two curves eventually cross. This distance namely crossover distance is given by: 85

86 = 2h Beyond this distance, the head wave arrives before the direct wave. Travel-time curves for more complicated layers: Considering a layer which is not flat or there are multiple layers, the travel-time curves get complex. Dipping layers: A dipping layer changes the slope of the travel-time curve for head waves. Then the slope is not given by the reciprocal of the velocity and it will have a slope as below: Slope = => Slope = Where is the apparent velocity. The apparent velocity changes according to the dip direction. For a layer dipping downward at an angle Ɵ relative to the surface, it is defined as: = And for a layer dipping upward, it is defined as: = Multiple layers: When there are multiple layers, each layer will have its own reflected waves and head waves. In practice, as the number of layers increases it becomes more difficult to identify each of the individual straight-line segments of the travel-time plot, in addition, with increasing numbers of layers, there is less likelihood that each layer will be bounded by strictly planar horizontal interfaces, and a more complex model may be necessary. It would be unusual to make an interpretation using this method for more than four layers. Considering the condition of two layers, the travel-time curves will be like: 86

87 Figure (49). Travel-time curves for a two layer medium. considering a series of layers of constant velocity (stepwise constant velocity distribution) like Figure (50): Figure (50). A series of layers of constant velocity. In the above Figure, (h) is the index of the deepest layer involved in that path, Δ is the thickness of i-th layer, is its velocity and the parameter = is considered as the ray parameter for the path whose deepest horizontal segment propagates at the interface between (h-1) and the h layers at the velocity. 87

88 The inclined distance of the i-th segment of the propagation path is obtained as: = = = The total propagation time up to the inversion point will be: = + = + Where: : one half of the length of the horizontal path between the layers (h-1) and (h). Having: =. =. = [1 + ] = + The propagation time could be written as bellow: = + = +. Where: : the total horizontal range of the ray path reaching the (h-1) to (h) interface. Considering the deepest layer (h) values from (zero) to (N) and following it the ray parameter =, the result will be a series of lines as shown in Figure(51). Figure (51). Travel-time curves for different number of layers. 88

89 Going through the equations of these lines it can be understood that in some cases the head waves produced in a layer may not lead to any first arrival which could be the problem of hidden waves. Figure (52). A three layered medium, and the X_T plot showing the arrival reflections form different layers. Approximation of the velocity profiles by means of a series of layers with linear velocity functions (stepwise linear distribution): Considering the Figure (53): Figure (53). A layered medium with linear velocity profile. 89

90 According to the Snell s Law of refraction: = p which is the ray parameter and is constant for a given path. The inclination of the secant (s) is the average of the inclinations at the extremities of the arc as below: = Then the horizontal propagation of the refracted pulse thickness of the layer : is calculated from the =. tan( ) The radius of the i-th arc can be obtained through following formula: = = And the time of flight Δτ along the arc will be: Δ = dɵ =. p. dɵ =. p. {ln[tan( ) ln[tan( )]} It is worthwhile to mention some points: - If is not in a monotonically increasing trend, the formulas are still valid (with negative radius R) - If = the radius R is infinite and the formula for the time of flight will not be determined, being the propagation path as a straight line Δτ = = = - A pulse can reach to the surface if the initial inclination is so that sin ( ) namlely p, having this condition there is layer with = at which the ray will be horizontal, i.e. (Ɵ = ). - Since the initial inclination can take any value in the above range, the inverse point may be located also within a layer, and not necessarily at the interface between two layers (as in the case of stepwise constant velocity distribution). 90

91 The waves whose turning point (the deepest point reached by a ray travelling on a curved path) is located within a layer with gradually increasing velocity are called diving waves (Cerveny & Ravindra 1971). Refracted arrivals from such buried layers are not true head waves since the associated rays do not travel along the top surface of the layer but along a curved path in the layer with a turning point at some depth below the interface. Methods of interpreting refraction data in terms of diving waves are generally complex, but include raytracing techniques. Some ray-tracing programmes require velocity gradients to be introduced into all layers of an interpretation model in order to generate diving waves rather than true head waves. - For a generic initial inclination in the above interval, the inversion point of the propagation path is positioned at the point where = =. then (p) will be also the slowness of the deepest layer which the ray path has been reached. It is also the local slope of the corresponding point in the X-T plot. - Rays of gradually decreasing initial inclination (gradually decreasing p) lead to points where the X-T curve exhibits gradually decreasing slope. However, this doesn t guarantee that X and T are monotonically increasing functions of. The problem of hidden and blind layers: It is possible for some layers not produce any refracted first-arrival waves. In this case the layers will not be detected in a simple first arrival refraction survey. The above methods for the interpretation of the X-T plot would yield a self-consistent but wrong solution. Because of it, the possibility of undetected layers should always be taken into consideration. In practice, there are two different types of problem. In order to be detected in a first arrival refraction survey, a layer must (a) be underlain by a layer of higher velocity so that head waves are produced, and (b) have a thickness and velocity such that the head waves become first arrivals at some range. A hidden layer is a layer which, whilst producing head waves, does not give rise to the first arrivals. Rays travelling to deeper layers arrive before those critically refracted at top of the layer in question. 91

92 Figure (54). A hidden layer: a thin layer that does not give rise to first arrivals. This may result from the thinness of the layer, or from the closeness of its velocity to that of the overlying layer. In such a case, a method of survey involving recognition of only first arrivals will fail to detect the layer. It is good practice to examine the seismic traces for possible arrivals occurring behind the first arrivals.these should then be examined to ensure they are compatible with the structural model derived from the first arrivals. In case the soil presents a region with high velocity gradients, rays whose turning point is either above or below this region behave so the corresponding portions of the travel time and ray parameter curve show travel time increasing with distance. By contrast, rays that bottom in the region of high velocity gradient are bent upward more and emerge at smaller values of distance that would otherwise be the case. As a result, three rays with different ray parameters emerge at the same distance, and the curve has three distinct branches, giving a characteristic triplication. A blind layer presents a more insidious problem, resulting from a low-velocity layer, as illustrated in Figure (55). Rays cannot be critically refracted at the top of such layer and the layer will therefore not give rise to head waves. Hence, a low-velocity layer cannot be detected by refraction surveying which is a critical problem in geophysics, but it can generally be ruled out in case of fire damaged concrete. It is worth mentioning, the top of the low-velocity layer gives rise to wide-angle reflections that may be detected as later arrivals during a reflection survey. 92

93 Figure (55). A blind layer: a layer of low velocity that does not generate head waves. The problem of hidden layers may be of interest in the case of fire damaged concrete since the gradient of the velocity profile is the combination of two distributions: - The temperature distribution, with steepest gradients at the surface of the member exposed to fire; - The thermal sensitivity of waves velocity in concrete which tends to saturate at high damage levels (the velocity may gradually approach that of compression waves in air). As a result, in some cases the steepest velocity gradient may occur at an intermediate depth. This is a point to be considered, since the experimental results available at high damage levels are scanty and not very reliable. 93

94 Figure (56). Shows: Temperature Depth, relative UPV Temperature, and Relative UPV Depth changes in case of a fire exposed concrete member. Nonuniqueness in case of inverse geophysical problems: The existence of different forms of nonuniqueness on the realm of inverse geophysical problems should be investigated and the type of the related nonuniqueness should be determined in order to understand what type of a priori information is necessary to find a realistic solution. Usually nonuniqueness is considered as a whole and is approached by applying smoothing constraints, damping constraints with respect to the solution increment and rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when dealing with geophysical problems different types of nonuniqueness exist and following it different ways to solve the problem are available. A general approach for solving nonunique problems is the inclusion of additional, socalled, a priori information. Such information is introduced as of smoothing and damping constraints and is usually applied to the facing problem without considering the nonuniqueness complexity of the problem. Discussing about geophysical nonuniqueness, the finite number of data measurements and infinite dimensional parametrization of the earth can be considered as one of the main reasons of it (Backus and Gilbert, 1967). Such nonuniqueness can be referred to as indeterminacy nonuniqueness and the cause of this nonuniqueness is the fact that there could not be always enough data as the number of parameters needed to be characterized. The finite number of data 94

95 measurements can make us only finite resolving power to the solution of an inverse problem. Nonuniqueness usually deals with the problems that are ill-posed, and it can be mentioned that most of the problems are ill-posed. A well-posed problem requires the following conditions (Hadamard, 1932): 1) The equation has a unique solution. 2) The solution is stable,i.e., small perturbations in the data do not make substantial changes in the solution. Due to the nonuniqueness problem, a direct inverse solution cannot be found using the traditional mathematical approach. X = d (1) When the forward problem is expressed as: A X = d (2) Where: d: the observed data (or ), X: symbolizes the model parameters & : symbolize the forward and inverse mathematical operators, respectively. Usually (X) and (d) are vectors and ( ) and ( ) are matrixes as in the above two equations. Since a solution to the problem is not possible using formula (1), a different approach must be taken. Using a parameter model X (say ) and the forward mathematical operator A, the calculated data formula (2). If the difference between the calculated data 95 is obtained through and the observed data is zero then the proposed model could be a solution to the inverse problem: - = 0 (3) Practically, due to the model errors, inherent errors in the observed data, and inaccuracies in mathematical formulations (like simplification assumptions), the result of the equation (3) can go to a minimum value instead of a perfect match and it can be written as: - = min (4) square operators are a good way to find a minimum value, especially when there are more data than parameters to be solved during the inversion. Thus, generalized solutions of equation (1), i.e. pseudosolutions (Tikhonov and Arsenin, 1977), can be calculated by minimizing the error of the following system: E(X) = (5)

96 Where: E : the mismatch error or the misfit functional E(x) (Zhdanov, 2002). This is the norm for measuring the error. Because the least-squares method weights large errors excessively if the data errors do not have a Gaussian distribution, then just a very few (even one) data samples could significantly overinfluence the solution (Menke, 1984). The quadratic norm for measuring the misfit error in equation (5) will be used further in the discussions for the ease of argument, although other norms might be better suited for specific geophysical areas. The shape of the misfit functional E(x) for a simple mathematical earth model X with a fixed number of parameters is of special interest because E can have different values for different values of the model X. Nonuniqueness can be expressed in different forms. Even if we assume that the available data is exact, i.e., there is not nonuniqueness caused by error in the data, when dealing with nonlinear problems, on the whole, there may be one, two, many or specific ranges of solutions. Those solutions, in which the error function E(X) has the smallest minimum value, are considered as global minima. There might be local minima also, in which the error function E(X) has values that are locally low although not as low as the global minimum. There are two major approaches applied for solving ill-posed problems: statistical (global) and deterministic (local). Statistical methods divide the range for each of the possible parameter values into a set of N possible values and each parameter of the model can be assigned any of these N possible values. Then calculated values are compared with the observed ones. As an advantage of the statistical method it can be mentioned that by doing an exhaustive searching of the model space the probability of reaching to the true solution is high. It is possible that many solutions are obtained which each of them are candidates to be the solution, hence the nonuniqueness problem and the additional information are needed to decide which of them is the exact solution. Deterministic (local) methods require significantly less number of models because they look for solutions in a controlled way. The mathematical tool for finding a solution to equation (5) in a deterministic manner ( equivalent to solving equation (1)), was developed at the beginning of the 19 th century which is named the leastsquare (Gauss, 1809; Legendre, 1806). Deterministic methods use an initial model and then logically change the model to minimize the difference between calculated and 96

97 observed data. After each iteration the model is appropriately modified and the process continues until convergence, that is when further model updates do not affect the mismatch error E(X) difference between the observed and calculated data). Deterministic methods are applied to provide stable solutions to inverse problems such as surface wave dispersion-curves inversion to find S-wave velocities (Xia et al., 1999,2003) and surface wave attenuation-curve inversion to find quality factors of near-surface materials (Xia et al., 2002) and to improve stability of inverse processing to an inverse problem of reflection travel time (Xia and Miller, 2000). There are various iterative schems that may be applied to converge on a solution. Censor (1981) discusses the common iterative methods of the stationary iterative reconstruction technique (SIRT) and the algebraic reconstruction technique (ART). The conjugate-gradient algorithm methods, such as LSQR (Paige and Saunders, 1982), are preferred because they are more stable in an ill-conditioned system and converge more rapidly. It can be said that neither of the two statistical and deterministic methods alone can overcome nonuniqueness generally. Depending on the type of nonuniqueness, appropriate type and amount of a priori information should be available for the inversion process to obtain a true solution to an inverse problem. In general, there are five major factors that contribute to nonuniqueness. One is indeterminacy when no data are available to resolve some of the parameters (indeterminacy nonuniqueness). For example, when dealing with refraction tomography there might be cells through which first-arrival-time rays do not pass because of a complex velocity structure. A second factor is based on the inverse problem itself (problem of exact-data nonuniqueness) as in the case of the hiddenlayers problem (low or high velocity) in refraction analysis (BURGER, 1992; IVANOV et al., 2005). Numerous same-number-of-parameter models can generate the same data because the hidden layer does not generate first arrivals. This can happen when there is no refracted energy (as in the low-velocity hidden-layer case) or because the refraction arrival times are not first arrivals (as in the high-velocity hidden-layer case) and are therefore undetectable due to interference with other waves arriving after the first arrivals (the surface wave, guided, reflected waves, etc.). The third factor that contributes to nonuniqueness are data and model errors (error nonuniqueness). The fourth factor occurs (extension of the third) when the errors of the overdetermined observed data have no Gaussian distribution in which case a single data sample can overinfluence the final solution (MENKE, 1984). Finally a fifth factor relates to numerical error and instability. For example, when using a deterministic inversion, the LSQR algorithm is better for solving large sparse matrices than the SVD method (NOLET, 1987). 97

98 The inverse refraction/tomography problem is linked to Snell s law of refraction and is a nonlinear problem. For that reason, nonuniqueness often exists even when exact refraction/tomography data are available. To show the nonuniqueness of more general cases, three simple three-layer model cases are considered in which the second layer is hidden having higher Figure (57a), equal Figure (57b), or lower velocity Figure (57c) than the first layer and lower velocity than the third layer. In the case in which the first and second layers have equal velocities, the problem becomes a twolayer model but it is regarded as a general case of a three-layer model. This threelayer example Figure (57) is derived from BURGER (1992). It is clear that there are no refractions from the low velocity second layer Figure (57c) however there are refractions from the second hidden layer that has higher velocity than the first layer Figure (57a). However, these refractions are not first arrivals; they arrive after the direct wave or the refractions from the third layer and are likely to be undetectable because of the interference of other types of seismic waves such as the Rayleigh wave, reflected waves, guided waves, etc. Each model in this example Figures (57a, b, c) produces the same first-arrival times. Hence, if we measure the exact first arrivals Figure (57) and try to use only those measurements to find a solution to the inverse problem, any of the models would be a solution. 98

99 Figure (57), graphic description of the refraction nonuniqueness problem. Three different layer models produce the same first arrivals. Layers 1 and 3 have the same thickness and velocity parameters, but the layer 2 is different. (a) layer 2 is a high-velocity layer. (b) layer 2 has the same velocity as layer 1. (c) layer 2 is a low-velocity layer. The figure is derived from Burger (1992). The second-layer thickness is rounded for display purposes. This example demonstrates the essence of exact-data nonuniqueness. Using a 1-D representation of the same model Figure (58) in which the first arrivals from the previous example Figure (57) are measured, it becomes necessary to make an assumption about the true model. As can be seen in Figure (58), such an assumption can strongly influence the depth of the third layer. Due to nonuniqueness, the third layer can be mapped correctly over a range of depths. The depth of the third layer can be estimated at depths as shallow as 10 m or as deep as 18 m. Additionally, there are multiple equally plausible geological settings that would place the third layer at quite 99

100 different depths. The purpose of Figure (58) is to provide a better feel for the vertical gradient changes of the possible models. The lower bound is a maximum verticalvelocity-gradient model and the upper bound is a minimum vertical-velocity-gradient model. Figure (58), 1-D display of nonunique models from Figure 1. Close to the lower bound a low-velocity (250 m/s) hidden layer (dots), same-velocity (500 m/s) hidden layer (dots and dashes), high-velocity (1400 m/s) hidden layer (dashes), and highest-possible-velocity (2090 m/s, upper bound) hidden layer (solid) still preserving the same first arrivals. The lowest possible velocity of the hidden layer (lower bound) is a maximum vertical-gradient velocity model, while the highest possible velocity of the hidden layer (upper bound) is a minimum vertical-gradient velocity model. Given the two obvious linear first-arrival trends, the simplest case would be to assume a two-layer model Figure (57). Using that model, the depth to the third layer Figure (57b) would be 11.7 m. In the best situation this model would be the true model. An example of this simple model would be when the third layer is high velocity granite bedrock covered by two layers of unconsolidated low-velocity sediments. Now, if we assume a minimum-gradient velocity model the third layer would be 18 m deep, which is quite possible in the real condition when the degree of lithification increases gradually with depth and the velocity increases with depth. 100

101 this model has many possible solutions. In addition to the examples cited, a large range of thickness/velocity values for the second layer will result in identical first arrivals. This range can be split subjectively into two ranges: one for the high-velocity and one for the low-velocity case. consider that whenever the seismic energy is delayed in the second layer the same amount of time as is in the case when V1 = V2 Figure (57b), the refraction arrivals from the third layer will remain the same. In addition, as long as V2 is small enough that the refractions from the second layer are never first arrivals, the first arrivals remain the same across the record. The following formula can be used to obtain a rough estimate of the second-layer time: where: = ; = ; i = arcsin ; =. (6) Where: : the raypath time through the second layer; : the raypath length through the second layer; : the velocity of the second layer; : the thickness of the second layer; i : the critical angle between the second and the third layer; : the velocity of the third layer. 101

102 formula (6) that for a certain range of values there are corresponding values that will make equal to the for the second case (Fig. 1b), when =. The exact formula for finding (after changing ) in which arrivals from the underlying layer remain the same is: = ( ) ( ), (7) Where:,,,,, : the thickness, velocity, and the critical angle, respectively, between the second and the third layers before and after the change. Formula (7) can be the hidden-layer nonuniqueness formula, provided that no refractions arrive from the second layer ( ) or that such refractions arrive after the first arrivals. There is a continuous range for, parameters in which the first arrivals remain absolutely the same when formula (7) is applicable. The issue of how different three-layer models can generate the same first arrivals should be taken into consideration from a mathematical standpoint, that is, by applying a given mathematical operator over the model parameters (layer velocities and thicknesses), the resulting data (first arrivals) are calculated. In practice, geophysics must do the opposite, i.e., to define the earth model from the observed data (first arrivals), which from a mathematical standpoint is viewed as solving an inverse problem. A common approach for solving overdetermined, nonlinear inverse problems such as the inverse refraction problem, is to minimize the error function E(x) or misfit functional (ZHDANOV, 2002) in formula (8): E(X) =, (8) Where: : the observed data; : symbolizes the model parameter; A : symbolizes the forward mathematical operators. Therefore, solving the inverse problem requires finding a model for which the error function has a minimum. Using this approach, a solution to the inverse refraction problem can be found for the first arrivals in Figure (57). 102

103 The nonuniqueness problem is most complicated in the case of refraction tomography, in which the number of parameters is equal to the number of cells (M) used for modeling the earth, with each cell potentially having a different velocity. The example in Figure (57) can be considered from a different point of view. If it is assumed that a two-layer model generated the observed first arrivals Figure (57) then the top layer can be split logically into two layers Figure (57b). The velocity ( ) and thickness ( ) of the new second layer can then be changed according to the hiddenlayer nonuniqueness formula (7). A variety of three-layer models can be generated that produce the same first arrivals as the starting two-layer model Figure(57) under the constraint that the possible refractions from the new second layer are not first arrivals. Furthermore, the newly numbered second layer can be split into two layers allowing various four-layer models to be generated with the same first arrivals as the starting two-layer model. Layer-splitting can continue using the same pattern, and various 5, 6, 7, n-layer models can be generated that will produce the same first arrivals as the starting two-layer model. Such models will have (n-2) hidden layers and a corresponding (n-2)*2-parameter hypervalley of nonuniqueness. An extreme (boundary) model would be created when every newly split layer accepts the highest possible velocity ( border as in Figure 58), above which it would start generating first arrivals. In this case the bottom layer (the second layer from the starting two-layer model) would be the deepest. HEALY (1963) computed such an extreme fifty-layer model. Note that inserting just one layer into the starting twolayer model made the estimate of the bottom of the deepest layer vary from 10 to about 18 m, equating to a potential error of about 80% Figure (58). This emphasizes how important a priori information can be in selecting the proper model and in severely limiting the range of nonuniqueness. 103

104 Chapter 5 Tomographic approach to refraction travel-time inversion 1) Fundamentals of seismic tomography: The main objective of the tomographic method is to find the interior distribution of values inside the object by means of projections (sums of some interior values) measured outside it. The observations used in tomography are line integrals of some function of the medium. In the seismic case, the travel time or amplitude of seismic waves is measured and the function can be the slowness (reciprocal of velocity) or the attenuation factor. For a two-dimentional medium, the tomographic problem is to determine the function f(x,y) given a set of its projections, or line integrals: P(,α) = For a range of projection angles α = ( ), where,,, and α are as shown in Figure (59). The integration is performed from the transmitter to the receiver. A complete set of ray sums at a given angle is called a projection or a profile. f(x,y) is a continuous two-dimentional function and an infinite number of projections are required from a reconstruction. In practice, f(x,y) is calculated at a finite number of points from a finite number of projections. Seismic tomography can be divided into two main principles: 1) wave equation tomography (WET or diffraction-tomography), which is based on the Born or Rytov approximation for the inverse scatter problem (Devaney, 1984; Wu and Toksoz, 1987). 2) Ray tomography, which is based on rays and the high frequency solution of the ray equation. In spite of advances in waveform inversion, traveltime tomography can be the primary tool for analyzing seismic data. Arrival times associated with the first pulse can be easily observed and their uncertainties reliably estimated. The waveforms are usually complicated due to the later arriving phases like tube waves. 104

105 Figure (59). The geometry of tomography where the - axes are rotated around the x-y axes by an angle α (Bodo Lehmann). The wave propagation method used in ray tomography is an approximation of geometrical optics and describes the propagation in terms of rays. The spatial variations of the investigated structure should be small on the scale of a wavelength and diffraction effects are neglected. According to the most simple model it is assumed that ray paths are straight lines (no refraction) and all rays have the minimum propagation time. A disadvantage of this method is the reconstruction of an unknown function from its path integrals over straight lines. Wave equation tomography is better than ray tomography as WET uses both the dynamic (amplitude, waveform) and kinematic (phase or traveltime) information in the wave field. The waveform is also affected by the following factors: - Kind of source signal; - Radiation characterization of the source; - Absorption of the wave energy; - Coupling between geophone and soil. It can be mentioned that just when all the above mentioned effects are assessed correctly, a satisfactory result can be obtained with wave equation tomography. In seismic ray tomography the medium to be imaged is discretised into a grid of rectangular elements, in each of the elements the slowness value is considered to 105

106 be constant Figure (60), and the calculated travel time the cells can be defined as below: of a ray passing through = : calculated traveltime of ray; : length of ray path in the cell; : slowness of the cell; N : number of grid elements. Traveltimes for all rays can be written in the following matrix form: T = D. S (1) T : vector with length M (traveltimes); S : vector with length N (cells); D : vector (M N) with ray length in each cell. The problem of reconstructing a function from its integrals has a non-unique solution unless an infinite number of integrals can be measured. As a rule of thumb it is assumed that if the difference in velocity distribution in the area under investigation does not exceed 15% a straight-ray approximation is accepted and rays do not need to be traced. If the difference in velocity distribution exceeds 15% straight-ray inversion cannot be used and the real ray paths must be calculated (Worthington, 1984). 106

107 Figure (60). Net describing the parameters for three exemplary ray paths and for the cells by assumption of straight ray propagation (Bodo Lehmann). Some of the main mathematical approaches used for the solution of the image reconstruction problem can be described as following: 1) Back-projection (BP): The advantage of this approach is the low computation time, but it produces reconstructions with substantial artefacts. It is better to apply this method to estimate the first value for the slowness distribution and can be considered as a starting model for applying more complicated reconstruction techniques. The slowness distribution of the j th cell is calculated like below: = Where: : the total distance between the source and the receiver; : the length of the th ray path in the th cell. 107

108 It can be considered that, if a ray does not travel through a cell then for that cell is zero. If the value of is taken approximately, it can be equal to 1 for the case in which the ray crosses the cell and equal to 0 otherwise. BP does not produce good reconstructions because each ray sum is applied not only to the points of changed velocity, but also to all points along the ray path. Due to this, there is darkness for the reconstructions with BP. The disadvantages of BP are the poor reconstructions, the impossibility of integration of prior information also the impossibility of using curved ray reconstruction. 2) Matrix inversion (conjugate gradient method, CG; least square method, LSQR): If in equation (1), matrix D is square, the unknown slowness distribution can be obtained through inverting it. Hestenes and Stiefel (1952), Scales (1987), Paige and Saunders (1982), and Golub and Kahan (1965) described these methods. The main disadvantage of matrix inversion methods which are applied to tomography is the large computational effort. Equation (3) represents an array of M traveltimes and N cells which in principle can be solved by inverting the matrix D: S =. T Where: : the matrix inverse of D The following problems are considered concerning matrix inversion for tomographic purposes: 1) the projection data can be inconsistent because of noise or other artefacts. In this case the solution is ambiguous. This problem can be solved by finding values for, which minimize the square projection error: min = 2) if the size of the image is very large, the reconstruction matrix requires too many elements without practical use, this problem can be solved by using a coarser grid. 3) the matrix D cannot be directly inverted if the matrix is not square (M ). In this case generalized matrix inversion and singular value decomposition (SVD) should treat it. 108

109 4) if there are not enough projections to provide N independent equations there will be infinite possible solutions. This problem can be solved by picking a solution which minimizes certain quantities such as the total amount of slowness fluctuation (i.e. min = ). Where: : the average cell slowness. The main disadvantage of matrix inversion methods used for tomography is the large computational effort in comparison with other methods. The number of operations involved is of the order of M.N (typically for several thousands of traveltimes (M) and grid elements (N)). It can be mentioned that, CG methods converge in at most iterations. However even considering round-off errors and data errors, it usually takes many fewer iterations to obtain an acceptable approximation to S. for singular problems, both CG and LSQR converge to an acceptable solution, but then diverge if the iterations are continued. Reconstruction using ray tracing techniques is feasible with matrix inversion. And it is performed by inverting the matrix D to find the unknown slowness distribution, tracing the rays having this slowness field and re-inverting the matrix with the updated ray paths. Prior information such as an initial model can be helpful. There is an advantage for matrix inversion method, which is the easy implementation of different types of source-receiver configuration. 3) iterative reconstruction (ART, SIRT): This method is an iterative improvement process to reach to an optimum solution. Among the different iterative reconstruction procedures, two most prominent methods are the algebraic reconstruction technique (ART) by Gordon, Bender and Herman (1970), Gordon (1974) and the simultaneous iterative reconstruction technique (SIRT) by Gilbert (1972). The iterative techniques have been proved to be the most advantageous in geophysical image reconstruction (Worthington, 1984). The advantages are the relatively low computation time for reconstruction, the fact that all types of source-receiver configuration can be accommodated easily, the opportunity to introduce prior information into the system and the opportunity to use curved ray reconstructions. The ART variation can be considered as the most efficient one since a large amount of updating is performed during each iteration without any increase in computing time. 109

110 One disadvantage for this method is that the method is not able to properly handle the noisy data. One important issue when applying the Art algorithm concerns the sequence in which projections are chosen during the correction process, because the slowness distribution at the end of an iteration reflects the last projection more than those used early in the iteration. Another disadvantage of these iterative numerical techniques is the possibility of no convergence at all or convergence to a mathematically acceptable model but with a physically unrealistic set of values for the slowness constants. To prevent it, some constraints should be considered, but the problem is that the values are unknown in advance of the reconstruction and overconstraining S may prevent the user from obtaining the true value. Usually no upper bound is set but a lower limit must be defined to keep the S values from reaching physically impossible negative values. Comparison of the different tomographic inversion methods: A comparison of the different tomographic inversion methods was performed by Miranda (1989). From this comparison it can be conclude that the ART has to be applied for the synthetic data examples. SIRT should be applied for the field and synthetic data examples with added noise, because the technique is robust with noisy data. Using SIRT the smoother appearance for the pictures is obtained compared to others and noise does not critically deteriorate the reconstructed images. Backprojection shows mainly the outlines of anomalies. The LSQR algorithm is suitable for noiseless data, but with noise contamination the results are critically deteriorated, the same can be considered also to the Conjugate gradient method. Considering the SIRT, this method is not dependent on the order of ray paths and is more stable and robust compared to the ART. SIRT can be applied even when the picked traveltimes are affected by experimental errors and some mispicks. Mathematical background of the SIRT method: SIRT algorithm is the most suitable inversion method and commonly used for practical applications. This method uses a modified Kaczmarz method (Kaczmarz, 1937) in seismic ray tomography. The matrix form equation (1) consists of the following vectors: 110

111 T = (2) With M traveltimes and the model function, here the slowness of the grid elements (cells), S = (3) With N grid elements, and the ray path lengths for M rays and N cells in D: D = (4) Considering that D in equation (1) can be thought as a linear operator that operates on the estimated model vector S producing the measured data vector T. equation (3) can be formulated for tomographic purposes as: = D. (5) Although equation (5) cannot be directly solved, the true model vector should be determined as with given and D. the problem becomes one of finding a generalized inverse operator. Practically, it is very difficult to determine the generalized inverse operator for two reasons: First, D is usually quite large and sparse. Second, D is usually ill conditioned due to the ray distribution, which makes computation of the inverse of D very unstable. Kaczmarz s method solves the problems associated with the inversion of a large and sparse matrix and provides an efficient means for determining an approximate solution to equation (5) using an iterative procedure. 111

112 Instead of updating the model after tracing each ray in the forward modeling step as is done in the ART algorithm, all rays are traced through the current estimated model and a model correction is found for each ray. The basic strategy of the iterative methods is the application of corrections to arbitrary initial cell slowness in an attempt to match the measured ray projections. The former match is lost as new corrections are applied, the procedure is repeated until the calculated projections agree with the measured ones within the desired accuracy. The accuracy is only limited by the number of iterations. The procedure is like this: a starting set of values is chosen for the slowness vector ; for example a constant slowness or the result of a back-projection can be used. Step 1: The projections are calculated from the starting values. Conduct forward modeling (ray tracing) : = For all rays k=1,, M and the iteration step. Step 2: Calculation of the correction for each cell by examining the rays cutting through that cell and averaging the corrections recommended for each ray. There are two different methods to apply the corrections which are the addition and the multiplication correction. In the case of an addition type each cell gets a weighted correction. The weighting coefficients of the correction are a function of the path length through each cell in proportion to the difference between and for the path (Dines and Lytle, 1979). = Where: = - 112

113 In the multiplication type the new value of slowness present assigned value : is in proportion to its = Regardless of which type of correction method is chosen, the ART algorithm operates by applying that correction to the values in a path as soon as the correction is calculated. For example as soon as is calculated for the path, all the cells through which the path passes are updated. But the SIRT method does not apply any correction until all correction terms for all paths through all cells are computed. Then all correction terms of all the paths passing through a given cell are averaged, and the cell slowness is updated by this average correction. Step 3: The correction is added to the slowness of the cell in order to generate its new value for use in the next iteration (q+1): Addition case: = + Multiplication case: =. Thus if a calculated ray sum (traveltime) is too small compared with the measured value, then each cell that contributes to this ray is increased in slowness by an appropriate amount. After performing it for all cells and all rays, the first iteration is completed. During the iteration the value of computed through: = Is compared with the true value of for each path. All differences between these values should be used to correct, so that in the next iteration the will be closer to the true values. The procedure is repeated until the desired accuracy is obtained. The difference between iterative methods and back-projection is due to the fact that the quantities being backprojected are correction terms derived from the projections, instead of the projections themselves, and they are added to the previous values. If the starting 113

114 point is a blank screen (S = 0) then the first iteration is identical to back-projection. A single iteration could not be exact because the back-projection is not exact. Finding a suitable stopping criterion for this iterative reconstruction technique is not simple. It can be stopped after an optimum number of iterations which is defined by trial and error by some users. Another approach is to continue iterating until a certain criterion is satisfied, e.g. a threshold for the residual error, or the rate of decrease of error. Detailed discussion of main topic of this thesis (tomographic approach for fire damaged material): Considering a layered material with unknown properties of each layer, the matter is to study the wave propagation through different layers through tomographic approach with focus on the iterative SIRT method in case when the member or the layered material is exposed to damage especially a fire and to investigate how the velocities or slownesses distribution from the top layer to the deepest one changes because of the deteriorating of the top layers, it is clear that as the temperature rises the velocity in the member decreases or the slowness (reciprocal of the velocity) increases. After developing some theoretical issues which will be discussed below, some numerical calculations have been performed in order to prove the theory and to understand how it works. As the first step, a two-layerd material is taken into account with the thickness (th), and the slownesses as shown in the Figure(61), and a trapezoidal path for wave propagation is considered: Figure (61). Two-layered material with trapezoidal assumed wave propagation. According to the Snell s law, the aim is to find the path which minimizes the time, 114

115 Considering different arrangements for transmitter and receiver probes it can be mention that from a certain distance between the probes to higher distances the wave which travels through deeper layer determines the propagation time. It can be explained in this way, as the surface layers are damaged and the velocity propagation in these layers is slow compare to the deeper layers, the path which goes to lower layers is faster than shallow ones. From the Figure (61), the following formulation can be developed:. D = 2. + (D 2d). According to the above formula, the inclined parts which are developed in first layer are multiplied to the slowness of the first layer and the horizontal part is multiplied by the slowness of the second layer. Now if every term is divided by thickness the problem goes to be dimensionless, here two additional parameters are defined for this reason: D =. th a = α. th. = 2. + ( 2α).. = 2. = -1 According to the Snell s law:. sin (Ɵ) =. sin (π/2) Sin (Ɵ) = Tang (Ɵ) = α = 115

116 . = ( ) = ( ) = = 2 When the values are calculated, the break points of the X-T plot are found similar to the Figure (62), and the path is determined Figure (62). X-t curve or a two-layered medium and the breaking point. Now, numerical analysis through developing the formulas in EXCEL and MATHCAD are performed in order to be able to model the materials containing different number of layers (a 12-layer medium in this case study), by assuming a sort of slownesses, building the D matrix and calculating the numerical travel-times and comparing with measured times, then finding the errors and updating the slownesses then following it performing the second iteration to go one further step which reduces the errors. 116

117 If the parameter (a) which is the horizontal projection of the inclined stretch in Figure (61) is considered as ( ) and having the thickness (th), the following formulas are developed in an Excel sheet: (1) Where deepest is the index of the deepest layer involves in that path and the thickness of layer i, its slowness. is = =. (2) Where: : inclined distance of the i stretch. Now the total travel time in a the generic path is calculated as below: = +. Where: : the one half of the length of the horizontal path between the layers deepest and deepest-1. Now the critical distance between the probes is calculated which makes equal the traveltime directly at the surface ( at ) and along the complex path described by the refraction in several layers (based on the Snell s law). +. =. = + Then the can be obtained: + [ - ]. =. -. =. ( - ) 117

118 .. -. = =.. =.. Finally we have: = (3) Now there is two alternatives for waves to propagate: (1) running directly from emitter to receiver, (2) going deep as inclined through the layers, then running in a horizontal path with the velocity higher than the surface layer and finally emerge to the surface layer again. Considering the second option, if just taking the curved branch until the wave reaches to the deepest layer, it takes some time for the first part also the symmetric part, now if the time consumed in this path is less than the propagation time on the surface, it means that there is no need to involve any horizontal stretch, and just going deep in an inclined path and suddenly reflect up to the surface is saving time. Now an equation can be developed somehow, the time to go straight is equal to the time to go deep and the emerge, sometimes it seems that the horizontal branch should be negative, because to have the same time ( it is faster to go deep), the wave should go deep than a backward wave path for a while to waste time, then going forward and finally emerging to the surface, just in this way two traveltimes are the same and this does not make sense. It can be mentioned that there are two possibilities for reaching from the source to the target, first, the way that allows the same time on the surface according to the formula (3) which should be doubled, second, twice of the formula (1) to go along inclined branches and finally picking the maximum distance between two cases. As a point it can be considered that if the distance between the probes is small the wave tends to go directly on the surface because the propagated wave from the source is strong enough to reach the target directly, but when the distance is getting larger as the aim is to find the fastest wave which is the first arriving to the target, the wave which goes in inclined paths through deep layers is the first arrival, and it can be mentioned that in most of the cases there is also a horizontal path in the interfaces of the deep layers which wave propagates through it because of the high velocity in deeper layer and as the distance between the probes is larger, this horizontal part is more helping the propagation comparing the surface path. 118

119 Now in the spread sheet the inclined distances in each layer are calculated applying the formula (2). As the main aim of the excel sheet is to finally compare the numerical times calculated with the experimental times, it can be a good way to make some synthetic data as the experimental data using a suitable software like mathcad through linear interpolation and inputting the obtained x-t plot to the excel sheet, then assuming a column of slownesses for layers, start iterating (multiplying matrix of distances to the vector of slownesses) and investigating the trend of convergence to real data. To assume the first series of slownesses, as the layered material under the study is considered to be damaged on top layers due to a fire exposure, it should be considered that the slowness of top layer should be a relatively large value and going deeper and deeper this value goes to be smaller because of approaching to the condition of pristine material. Another point, after doing each iteration and finding a column of numerical times, the error of each measurement should be calculated which is the difference of the numerical and experimental times. Error = numerical time experimental time In this step the matrix of corrections should be built considering the two methods of correction. 1) Addition method: According to the below formula the correction matrix is defined: = (4) Then the average of the values related to all the performed tests for each layer is calculated and the below formula is developed: = + (5) Applying the formula (5), the slowness values for the next iteration are updated which should converge gradually to the experimental values. Now having the experimental slownesses from the mathcad sheet, the difference between the experimental and numerical values is calculated for all the layers. 119

120 Summing the differences proportional to all layers, finally a diagram can be drawn which is illustrating the rate of convergence. 2) Multiplication method: Having the below formula: = The correction values of involved measurements for each of the layers is averaged and applying the below formula the new slownesses for using in the next iteration are calculated. In this step similar to the addition method the difference between the slownesses of experimental and numerical slownesses are calculated for each layer, then the summation of them is taken and the diagram showing the rate of convergence is drawn. The case study is a 12-layered material, the thickness of each layer is equal to 5 mm, and 20 measurements are performed. In order to check the consistency of the method, some noises can be applied to the experimental time data which can be because of any heterogeneous effect in the material. Results of the whole procedure: The results of the analysis can be the following diagrams: 1) x-t plot of the experimental and numerical data and the condition of convergence; 2) Slowness-depth plot of the current and real data; 3) distance-depth plot and investigation of being monotonically changing; 4) rate of convergence plot. Inputting the x-t data of a series of UPV tests on a sample which can be also synthetically produced by using mathcad software into the excel sheet and assuming the values of slownesses equal to one at first iteration for all the layers the following plot and results are obtained for four different cases to be under consideration: a) multiplication method without noisy data; 120

121 time T (us) b) multiplication method with some noise in experimental time values; c) addition method without noisy data; d) Addition method with some noise in experimental time values. Considering the two software applied in this work, there is an important point for selecting the velocity and slownesses values, in another word, there are two possibilities to pick the values, first, using the relative values for the velocities and slownesses which in this case for example the velocity at 20 c of the pristine material is considered to be one and following it for damaged concrete a portion of one, second, using the real values, i.e, knowing the velocity of compression wave in pristine concrete is about 4, this value is considered as the maximum value for velocity. the tests have been performed for both of the cases. As a point, because there is not any specific defined criteria for continuing the iterations, the iterations are developed by somewhere that the convergence rate does not progress any more or the trend changes to divergence. 1) x-t plot (real slownesses): The slownesses are the first estimation values for each of the layers experimental numerical distance X (mm) a1) multiplication method without noisy data (real slownesses = 0.25) 121

122 time T (us) time T (us) time T (us) experimental numerical distance X (mm) b1) multiplication method with noisy data (real slownesses = 0.25) experimental numerical distance X (mm) c1) addition method without noisy data (real slownesses = 0.25) experimental numerical distance X (mm) d1) addition method with noisy data (real slownesses = 0.25) 122

123 time T (us) time T (us) time T (us) 2) x-t plot (relative slownesses): experimental numerical distance X (mm) a2) multiplication method without noisy data (slownesses = 1) experimental numerical distance X (mm) b2) multiplication method with noisy data (slownesses = 1) experimental numerical distance X (mm) c2) addition method without noisy data (slownesses = 1) 123

124 depth (mm) time T (us) experimental numerical distance X (mm) d2) addition method with noisy data (slownesses = 1) 3) slowness-depth plot (real slownesses): The red diagrams are the reference slownesses (synthetic values ). slowness (us/mm) current S a3) multiplication method without noisy data (real slownesses = 0.25) real S 124

125 depth (mm) depth (mm) depth (mm) slowness (us/mm) b3) multiplication method with noisy data (real slownesses = 0.25) c3) addition method without noisy data (real slownesses = 0.25) d3) addition method with noisy data (real slownesses = 0.25) current S real S slowness (us/mm) current S real S slowness (us/mm) current S real S 125

126 depth (mm) depth (mm) depth (mm) 4) slowness-depth plot (relative slownesses): slowness (us/mm) current S a4) multiplication method without noisy data (slownesses = 1) b4) multiplication method with noisy data (slownesses = 1) real S slowness (us/mm) slowness (us/mm) current S real S current S c4) addition method without noisy data (slownesses = 1) 126 real S

127 depth (mm) depth (mm) depth (mm) slowness (us/mm) d4) addition method with noisy data (slownesses = 1) current S real S 5) distance-depth plot (real slownesses): 0 distance X (mm) a5) multiplication method without noisy data (real slownesses = 0.25) 0 distance X (mm) b5) multiplication method with noisy data (real slownesses = 0.25) 127

128 depth (mm) depth (mm) depth (mm) 0 distance X (mm) C5) addition method without noisy data (real slownesses = 0.25) distance X (mm) d5) addition method with noisy data (real slownesses = 0.25) 6) distance-depth plot (relative slownesses): 0 distance X (mm) a6) multiplication method without noisy data (slownesses = 1) 128

129 depth (mm) depth (mm) depth (mm) 0 distance X (mm) b6) multiplication method with noisy data (slownesses = 1) 0 distance X (mm) C6) addition method without noisy data (slownesses = 1) 0 distance X (mm) d6) addition method with noisy data (slownesses = 1) 129

130 Sum of the differences between slownesses Sum of the differences between slownesses Sum of the differences between slownesses 7) rate of convergence, Sum of the differences between slownessesiteration number (real slownesses): Rate of Convergence multiplication iteration number a7) multiplication method without noisy data (real slownesses = 0.25) Rate of Convergence multiplication iteration number b7) multiplication method with noisy data (real slownesses = 0.25) Rate of Convergence iteration number C7) addition method without noisy data (real slownesses = 0.25) addition 130

131 Sum of the differences between slownesses Sum of the differences between slownesses Sum of the differences between slownesses Rate of Convergence addition iteration number d7) addition method with noisy data (real slownesses = 0.25) 8) rate of convergence, Sum of the differences between slownessesiteration number (relative slownesses): Rate of Convergence iteration number a8) multiplication method without noisy data (slownesses = 1) Rate of Convergence multiplication multiplication iteration number b8) multiplication method with noisy data (slownesses = 1) 131

132 Sum of the differences between slownesses Sum of the differences between slownesses Rate of Convergence addition iteration number c8) addition method without noisy data (slownesses = 1) Rate of Convergence addition iteration number d8) addition method with noisy data (slownesses = 1) Considering the above plots which are the results of the iterative process for finding the solution of the travel times and to control the rate of convergence for slownesses, the following comments can be written: 1) The x-t plots obtained by applying each of the addition and multiplication correction methods are showing good results (good match between the experimental and numerical values). 2) about the slownesses convergence some of the plots show some jumps, this can be justified as the problem of cracks, heterogeneous or not homogeneous properties for each layer, or a high difference between the velocities of two layers which causes 132

133 sudden jumps in depth-slowness plot. This problem is obviously visible in addition method. 3) the next problem is relating to the distance-depth plots, it means, in some cases the trend of these plots is not monotonic which can be engaged to the matter of selecting the best path, i.e. to go along the shallower layers or going along an inclined path to deeper layers. The problem is obvious in addition method. Performing a series of indirect UPV measurements in order to have a sort of real data values for x-t diagram to be compared with the numerical ones: Considering a fire damaged concrete block, a series of indirect UPV tests have been performed on it after calibrating the probes using a calibration block, the first location for the receiver probe is considered to be in the distance of 70 mm from the emitter location. To make a better connection between the probes and the surface of the concrete sample, some gel was used Figure(63). The transmitter excitation was supplied through a pulse maker, the receiver probe was connected to a wide band conditioning amplifier that was connected to the input of digital oscilloscope. Data transfer has been performed via an USB cable interface to an IMB compatible laptop for saving data. Figure (63), UPV measurement arrangement for indirect testing. Having the output data from the performed measurements on the undamaged and damaged blocks and developing some calculations in an excel sheet, the offset length and the x-t plot are obtained which can be as the real experimental input data to the 133

134 time (µs) previous excel sheet in order to develop the iterations and investigate the convergence rate. Having the time and distances from indirect UPV measurements, knowing the value for offset length which is obtained by dividing the intercept over the slope of x-t curve, the following results and x-t plots for the undamaged and damaged blocks are obtained: 1) Undamaged block: test N.O distance (mm) recorded transmit time (µs) offset length (mm) actual length (mm) Table (9). X-t results obtained from performing the UPV tests on undamaged block distances (mm) Figure (64). X-t plot as the result of the UPV testing on undamaged block. 134

135 2) Damaged block: test N.O distance (mm) recorded transmit time (µs) offset length (mm) actual length (mm) Table (10). X-t results obtained from performing the UPV tests on damaged block. Figure (65). X-t plot as the result of the UPV testing on damaged block. 135

136 time T (us) time T (us) the obtained distance-time results from the UPV measurements on the fire damaged block were considered as the real experimental data for making the comparison with the numerical data by applying the previous iterative procedure in excel sheet. And the x-t plots and the condition of convergence are as the following diagrams: 180 experimental 160 numerical distance X (mm) Figure (66). addition method (slownesses: up to down) experimental numerical distance X (mm) Figure (67). multiplication method (slownesses: up to down). According to the Figures (66) and (67), the convergence problem is seen for both of the addition and multiplication methods, a point which can be considered in this figure is that the x-t data extracted from the UPV tests are not smoothly changing and there are sharp jumpings for them which can be due to the heterogeneous condition, cracks and spalling of the damaged concrete, and the iterative convergence method was not properly able to converge to the experimental data. 136

137 Chapter 6 Conclusion and recommendations: Nowadays, for the matter of time and economical issues, the aim is to repair and reuse the damaged buildings instead of demolishing them, but it depends on the type and intensity of the damage, the effects of it on the structure, then to decide if the building should be totally demolished and built again or can be repaired and used again. The aim of this thesis is on the fire damages to the concrete members and investigation of strength reduction of it by applying NDTs especially ultrasonic pulse velocity measurements and comparing them with the developed SIRT method results through tomography, finding the errors and iterating to obtain the best convergence between the experimental and numerical data. The problem is that, the properties of different parts of a concrete member or a layered material is unknown after exposing to an intensive fire scenario due to the spalling, cracks and strength reduction of it. To find a better view about a damaged member, the tomography approach was applied by using the SIRT method, the synthetic and real distance-time results were compared with the theoretical values in an iterative operation and the consistency of the SIRT method, addition and multiplicative correction methods was investigated. From the results the below comments can be noted: 1) In order to check the consistency of the applied methods, some noises were applied to the experimental traveltime values by adding random values, but there was not an obvious change in the results. 2) The distance-time data obtained from the real UPV measurements on a severely damaged concrete block are very unstable results with large fluctuations in the x-t plot, which neither of the iterative methods was able to properly converge to these unstable data. 3) Main differences between the addition and multiplication methods are obvious in: A) slowness-depth plots, where the convergence results between the reference and numerical slowness values is good by multiplication method but there are some jumps in the plot relating to the numerical values in the addition method. This issue can be analyzed from the point of view that the addition method is not properly able to converge to the real data especially when the member is severely damaged and there are a lot of microcracks also the variation of slownesses from surface layer to the deepest one. B) distance-depth plots, where the multiplication method is showing 137

138 a monotonic trend as the distances increase, but the trend is not monotonically progressing for the addition method. At the end it is worthwhile to mention that, having the improvements of the UPV nondestructive testing with a huge number of researches and papers available on this topic, this method of investigation can be considered as the best ND technique to obtain more improvements in the field of concrete members investigations especially when suffering a damage. One consideration can be the application of UPV measurements on a damaged concrete sample in laboratory and then extracting a core of this sample and investigating the property changes of it through visual inspection and drilling in order to control the consistency of the non-destructive UPV testing. Another issue which can be taken into consideration in the field of damaged layeredmaterial inspection may be the combination of different NDTs, somehow that the obtained results can be as reliable as the destructive techniques. 138

139 Appendix (Excel and Mathcad sheets): The Figure (68) is showing the initial slowness values for all the layers from surface to the deepest one which in this case is considered to be one, the thickness of each layer, the central depth and the summation of the differences between the reference and calculated slowness values. Figure (68). Figures (69), (70) are showing the procedure to build the formula for finding the value of the half part of the critical distance. Figure (69). 139

140 Figure (70). Choosing the maximum value between the horizontal projection of the inclined branch and the half of the critical distance. Figure (71). Figure (72). 140

141 Figure (73). Base on the addition correction method, the matrix of correction is built: Figure (74). 141

142 The following Figure is showing the travel-time results of an experimental test, the numerical values and the differences between the numerical and experimental ones which are the errors. Figure (75). The following Figure is showing the values of central depths and the velocity of each layer which are considered in Mathcad sheet, and then using linear interpolation and integration, the x-t plot is released which is then the input of the excel sheet as a series of experimental values. Figure (76). 142

143 Figure (77). Figure (78). 143

144 Figure (79). Figure (80). 144

145 Figure (81). 145