Loads and Dynamic Effects Background document D4.3

Transcription

1 Loads and Dynamic Effects Background document D Acceleration / m/s Strain /us Time / s Time / s PRIORITY 6 SUSTAINABLE DEVELOPMENT GLOBAL CHANGE & ECOSYSTEMS INTEGRATED PROJECT

2 Sustainable Bridges SB (4) This report is one of the deliverables from the Integrated Research Project Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives funded by the European Commission within 6 th Framework Programme. The Project aims to help European railways to meet increasing transportation demands, which can only be accommodated on the existing railway network by allowing the passage of heavier freight trains and faster passenger trains. This requires that the existing bridges within the network have to be upgraded without causing unnecessary disruption to the carriage of goods and passengers, and without compromising the safety and economy of the railways. A consortium, consisting of 32 partners drawn from railway bridge owners, consultants, contractors, research institutes and universities, has carried out the Project, which has a gross budget of more than 10 million Euros. The European Commission has provided substantial funding, with the balancing funding has been coming from the Project partners. Skanska Sverige AB has provided the overall co-ordination of the Project, whilst Luleå Technical University has undertaken the scientific leadership. The Project has developed improved procedures and methods for inspection, testing, monitoring and condition assessment, of railway bridges. Furthermore, it has developed advanced methodologies for assessing the safe carrying capacity of bridges and better engineering solutions for repair and strengthening of bridges that are found to be in need of attention. The authors of this report have used their best endeavours to ensure that the information presented here is of the highest quality. However, no liability can be accepted by the authors for any loss caused by its use. Copyright Authors Figure on the front page: Photo of a Skidträsk bridge, Sweden, and some plots from the dynamic measurements. Project acronym: Sustainable Bridges Project full title: Sustainable Bridges Assessment for Future Traffic Demands and Longer Lives Contract number: TIP3-CT Project start and end date: Duration 48 months Document number: Deliverable D4.3 Abbreviation SB-4.3 Author/s: R. Karoumi, A. Liljencranz, G. James, KTH, E. Bruwhiler, A. Herwig, EPFL, F. Carlsson, LTH Date of original release: Revision date: Project co-funded by the European Commission within the Sixth Framework Programme ( ) Dissemination Level PU Public X PP RE CO Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)

3 Sustainable Bridges SB (4) SUMMARY This background document deals with dynamic effects of traffic loads on railway bridges and methods for assessment of actual traffic loads. The document presents, in three deliverables D4.3.1, D4.3.2 and D4.3.3, the research work prepared within the WP4 load group. The outcomes of the work reported here is included in Chapter 5 of WP4 s main deliverable Guideline for Load and Resistance Assessment of Existing European Railway Bridges. Based on the outcome from WP1 questionnaires which have been distributed to European Railway Authorities as well as on discussions within the WP4 load group, the following research topics were identified and chosen for detailed study in this project: - Summary of Several European Assessment Codes, - Assessment of actual traffic loads using Bridge Weigh-In-Motion (B-WIM), - Dynamic Railway Traffic Effects on Bridge Elements. It is believed that the work in the above research topics will lead to increased knowledge on railway traffic loads and to better understanding of the dynamics of existing railway bridges. This will result in large savings when existing railway bridges are to be upgraded to carry trains with higher speeds and heavier weights. A lot of effort is spent on research on dynamic effects as it is believed that an accurate evaluation of these effects will bring more understanding of the underlying phenomenon and thus large cost savings. The work is distributed between the following partners: EPFL, KTH, LTH, COWI and DB according to the table below. Research topic Responsible Contributor Reviewer Summary of Several European Assessment Codes Assessment of actual traffic loads using Bridge Weigh-In-Motion (B-WIM) Dynamic Railway Traffic Effects on Bridge Elements KTH EPFL, DB, COWI All KTH LTH EPFL EPFL KTH The present document D.4.3 includes the following three deliverables resulting from the above listed research activities within the WP4 load group: (1) Summary of Several European Assessment Codes (document number D4.3.1) This project is lead by Gerard James (KTH). The aim is: review the Danish, German, Swedish, British, French and Swiss national codes for the assessment of existing railway bridges and in particular to concentrate on the vertical traffic load actions. The manner in which the dynamic amplification factor is treated in the different national standards was to be included in this summary.

4 Sustainable Bridges SB (4) The scope is: only review the standards as they refer to the loads used for the assessment of existing railway bridges. The main emphasis of this review is on the vertical traffic loads and traffic load models. (2) Assessment of actual traffic loads using Bridge Weigh-In-Motion (B-WIM) (document number D4.3.2) This project is lead by Raid Karoumi (KTH). The aim is: - to further develop existing B-WIM method for railway traffic loads assessment, - improve accuracy for calculated axle loads, axle distances and speeds, - present method for developing train loads for probabilistic assessment of bridges - present method for determining probabilistic dynamic amplification factors for probabilistic assessment of bridges. The scope is: Two instrumented railway bridges in Sweden are used in this study for testing of the developed methods. Due to the distribution effect of ballast, the emphasis will be on obtaining accurate static bogie weight rather than individual axle weights. (3) Dynamic Railway Traffic Effects on Bridge Elements (document number D4.3.3) This project is lead by Eugen Brühwiler (EPFL). This background document includes research work on both Dynamic behaviour of bridge elements and Dynamic amplification factors for bridge elements. The aim is: - to improve the knowledge on the dynamic behaviour of bridge elements, - to study dynamic load effects on different bridge elements with respect to span length, stiffness, train characteristics, etc.. Determine factors for the dynamic traffic load effects on bridge elements based on the theoretical analysis and interpretation of results from measurements. Factors will be determined for both fatigue and ultimate limit state. The scope is: Concrete bridges, to a minor extent: steel and masonry bridges. (Emphasis is on short-span bridges.

5 Summary of Several European Assessment Codes Background document D4.3.1 PRIORITY 6 SUSTAINABLE DEVELOPMENT GLOBAL CHANGE & ECOSYSTEMS INTEGRATED PROJECT

6 Sustainable Bridges SB (51) This report is one of the deliverables from the Integrated Research Project Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives funded by the European Commission within 6 th Framework Programme. The Project aims to help European railways to meet increasing transportation demands, which can only be accommodated on the existing railway network by allowing the passage of heavier freight trains and faster passenger trains. This requires that the existing bridges within the network have to be upgraded without causing unnecessary disruption to the carriage of goods and passengers, and without compromising the safety and economy of the railways. A consortium, consisting of 32 partners drawn from railway bridge owners, consultants, contractors, research institutes and universities, has carried out the Project, which has a gross budget of more than 10 million Euros. The European Commission has provided substantial funding, with the balancing funding has been coming from the Project partners. Skanska Sverige AB has provided the overall co-ordination of the Project, whilst Luleå Technical University has undertaken the scientific leadership. The Project has developed improved procedures and methods for inspection, testing, monitoring and condition assessment, of railway bridges. Furthermore, it has developed advanced methodologies for assessing the safe carrying capacity of bridges and better engineering solutions for repair and strengthening of bridges that are found to be in need of attention. The authors of this report have used their best endeavours to ensure that the information presented here is of the highest quality. However, no liability can be accepted by the authors for any loss caused by its use. Copyright Authors Project acronym: Sustainable Bridges Project full title: Sustainable Bridges Assessment for Future Traffic Demands and Longer Lives Contract number: TIP3-CT Project start and end date: Duration 48 months Document number: Deliverable D4.3.1 Abbreviation SB Author/s: G. James, KTH, Date of original release: Revision date: Project co-funded by the European Commission within the Sixth Framework Programme ( ) Dissemination Level PU Public X PP RE CO Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)

7 Sustainable Bridges SB (51) Table of Contents Acknowledgments Introduction Aim Scope Actions General Permanent Actions Ballast and fill material Other permanent actions Variable actions Accidental Actions Variable Actions General Traffic loads Swedish Vertical traffic loads Loads from track laying machines Swedish dynamic factor for traffic load models I, II,IV and V Danish vertical traffic loads Danish dynamic factor φ British vertical traffic loads British dynamic factor φ Swiss and French vertical traffic loads and dynamic factor German vertical traffic loads and dynamic factor Distribution of axle loads Swedish distribution of axle loads Danish distribution of axle loads British distribution of axle loads Horizontal traffic actions Swedish horizontal traffic actions Danish horizontal traffic actions German horizontal traffic actions Swiss and French horizontal traffic actions British horizontal traffic actions Soil pressures from overburdens Fatigue Assessment...43

8 Sustainable Bridges SB (51) 4.1 German approach Swedish and Danish Approach Existing bridges New bridges Dynamic factor for fatigue φ Swiss and French approach British approach (Steel and Wrought Iron) Stage A assessment Partial safety factors for loads Bibliography...51

9 Sustainable Bridges SB (51) Acknowledgments The present document has been prepared, within the work package WP4 of the Sustainable Bridges project, by Gerard James from the Royal Institute of Technology (KTH). The following team of contractors contributed also to the information presented in this document: - COWI A/S, Denmark (Linneberg, M. and Sloth M.) - Deutsche Bahn AG, DB Systemtechnik, Germany (Albert, M. and Bagayoko, L.) - Swiss Federal Institute of Technology EPFL-MCS, Switzerland (Herwig, A.) Furthermore, the reviewing comments from the contractorcowi A/S are very much appreciated.

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11 Sustainable Bridges SB (51) 1 Introduction This document is intended as a background document and is a summary of survey s conducted on existing European guidelines/codes for the assessment of existing railway bridges. Within this load group we have had access to the German, Swiss, French, British, Danish and Swedish guidelines/codes for the assessment of existing railway bridges. With the exception of the British code, these national guidelines/codes have been summarised in earlier background documents produced from this load group, see Linneberg, M. and Sloth M., (2004), Albert, M. and Bagayoko, L., (2004). Herwig, A., (2004). and James, G., (2004). This document summarises these documents and also includes the British assessment code, Railtrack PLC, (2001). The national assessment codes are in constant change and this document relates to the versions detailed in the above references. The document only considers the parts of the code which refer to loads on existing bridges and is to include the treatment of the dynamic amplification factor. In particular, the traffic load and their models will be given most consideration while the other load cases will only be given cursory attention. The French and Swiss codes for assessment appear to closely follow the European codes for new bridges with no real distinction for existing bridges. The British code is by far the most extensive and provides a comprehensive set of rules and guidelines for the assessment of existing railway bridges. The main content of the work treats the material strengths and properties as opposed to the loading. The German code appears to work from the basis of the Eurocode 1 but makes allowances for special circumstances associated with assessment of existing bridges. This is especially noticeable by the use of reduced partial safety factors when extra information is available which supports this reduction. The Swedish and the Danish assessment codes appear to be very similar at least in approach even if the same numbers are not used. They both contain the load models of EC 1 but also contain extra load models for higher allowable axle loads. Also included are load models used for line classification which comply with the line classification of UIC (1987) plus a few extra which are defined by the Danish and Swedish Railway Authorities. 1.1 Aim The aim of this document was to review some of the national codes for the assessment of existing railway bridges and in particular to concentrate on the vertical traffic load actions. The main aim is to review the design philosophy used in the codes rather than yield exact numbers and rules and thereby possibly adopt these methods in the forthcoming guidelines. 1.2 Scope This document has been limited to only reviewing the standards as they refer to the loads used for the assessment of existing railway bridges. While all the loads were to be briefly discussed the main emphasis of this review was to be on the vertical traffic loads and traffic load models. The manner in which the dynamic amplification factor is treated in the different national standards was to be included in this summary.

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13 Sustainable Bridges SB (51) 2 Actions 2.1 General The majority of the codes follow the Eurocode classification of actions on structure namely: Permanent actions, Variable actions, Accidental actions. The British assessment code classifies the loads into the following groups: Dead loads, Superimposed dead loads, Railway live loads, Other live loads, Accidental loads. The British code also includes a serviceability requirement under the heading of a load. This requirement is for the maximum allowable twist of the track considered for a certain load model. The manner in which the national codes define the loads may be different but essentially they all cover the same loads. 2.2 Permanent Actions As the name suggests the permanent actions are the actions on the structure that are constantly present. Related to the British codes this would include the categories Dead load and Superimposed dead load. The majority of the codes provide or refer to standard weights and density tables for different materials when assessing the self-weight of the structure. The material thicknesses and dimensions can be evaluated from drawings or from actual measurements on site. The British code also provides the possibility to assess the density of the materials through testing. The majority of the codes treat ballast and fill material separately, since there can be a variation in the thickness and density of these materials, see below. Both the Danish and the British codes are very specific as regards railway installations and define quite rigorously the different components such as, sleeper, electrical installation, rail, derailment rails, overhead electrical wires and the Danish code even defines loads from signalling posts due wind pressures from passing trains, see Figure Ballast and fill material Ballast Several of the codes recommend that the values of the thickness of the ballast and any extra fill material should be established through site investigation.

14 Sustainable Bridges SB (51) Direction of travel Figure 2.1. Loads from signalling post according to the Danish assessment code. Extra fill material Extra fill material is defined as the fill material besides the ballast that is present on the bridge or pile deck. The definition of the thickness can vary depending on the code, e.g. in Sweden the thickness of the ballast is defined as 600 mm and the rest as fill while in Britain the ballast is defined as 300 mm. In the British code it is possible to reduce the partial safety factor on fill and ballast materials if the thickness of the material is governed or dictated by the form of the construction or through the use of a Plimsole line. The use of reduced partial safety factors is discussed further in Chapter Other permanent actions Other permanent actions that should be considered are listed below: Soil pressure Water pressure Differential column settlement Concrete creep and shrinkage Thermal Prestressing forces The British codes do not specifically mention some of these actions as loads but are considered when discussing certain construction types, e.g. prestressing forces are considered when assessing a prestressed concrete structure. 2.3 Variable actions The variable actions have been deemed the most important to this survey and have therefore been given a separate chapter, see Chapter 3.

15 Sustainable Bridges SB (51) 2.4 Accidental Actions There are a number of accidental actions that should be taken into account when assessing an existing railway bridge and these are simply listed below: Collision forces from a vehicle (this can be a train or a road vehicle depending on the traffic conditions under the bridge). Collision forces from a boat or a ship. The size of the force depends on the type of waterway the bridge crosses and is assessed from case to case. Derailment loading. Severed hanger. Rupture of a cable forming part of a cable stayed bridge Rupture of a tendon in a prestressed concrete bridge

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17 Sustainable Bridges SB (51) 3 Variable Actions General The variable loads that need to be considered for the assessment of existing bridges are listed below. Included in the list below are all the variable loads found in the considered national codes. The majority but not all the actions are mentioned in all the codes. where each and every one of them is to be treated as a load case. For bridges with more than a single track, loads on all tracks are treated as one load case. One of the traffic loads models defined in subsection The track maintenance machine Traction and braking force defined Horizontal mass action Snow load Temperature loading Wind loading Pressure from ice and Actions from waves and flowing water Water pressure Centrifugal forces Nosing forces Actions from soil Frictional forces from bearings Loads on footpaths 3.2 Traffic loads Swedish Vertical traffic loads The effects from trains should be calculated according to the alternative traffic load models I, II, III, IV, V, VI and VII given below. If a bridge is found adequate for one of these load models it is not necessary to check its capacity for a load model of a higher ordered number. I. Iron-ore traffic load model and traffic load model SW/2 including the dynamic coefficient according to subsection This traffic load model is only applicable to routes carrying iron-ore trains. II. Traffic load model BV-2000 including the dynamic factor according to subsection III. Traffic load type BV-4 including the dynamic factor according to subsection IV. Traffic load model UIC 71 and SW/2 including the dynamic factor according to subsection V. Traffic load model UIC 71 including the dynamic factor according to subsection

18 Sustainable Bridges SB (51) VI. The largest of traffic load type BV-2 and BV-3 including the dynamic coefficient according to subsection 0. The highest maximum allowable speed should be calculated, up to a maximum of 120 km/h. VII. The largest of traffic load line class A to D4 including the dynamic coefficient according to subsection 0 together with a corresponding maximum allowable speed 120 km/h which the bridge is capable of allowing. If a bridge is capable of carrying a line class with the highest allowable speed then it is not necessary to check the bridge for the lower classes of line. Otherwise the bridge should be checked to establish at which lower speed it can carry the class of line. In this case, the bridge should also be checked to establish which lower class of line the bridge can carry at full speed. In this context the full speed is the highest allowable speed for the particular part of the line in which the bridge lies. In the cases of alternatives I and IV, a bridge with two tracks should be dimensioned for the case where Iron-ore respectively UIC 71 are on both tracks and for the case where Iron-ore respectively UIC 71 are on one track and the load model SW/2 is on the other. In the cases of alternatives II, III, V, VI and VII, a bridge with two tracks should be dimensioned for the associated traffic load models on each track. For bridges with more than two tracks, the appropriate traffic load models are decided upon from case to case. For ballasted bridges with more than one track, then the distance between tracks should be the actual distance or the one specified by the bridge owner. The traffic load models consist of axle loads and uniformly distributed loads. When checking a structural element the traffic load models should be positioned so as to create the worst loading case for that element and for the type of effect under consideration. This implies that it is possible to reduce the number of axle loads and reduce the length of the UDL and even split it into several components so as to cause the largest possible load effect. Traffic load models I, II, IV and V are to be regarded as equivalent load models while the other load models resemble real freight wagons. It is therefore inherently assumed that, in these latter cases, the locomotives do not produce a larger load effect than the wagons. There is an addition to this text in (Banverket, 2004) to include trains that transport timber (logs) and reads as follows: Besides the traffic load models IV, V, VI and VII, the bridge should also be checked for the traffic load models RV-25 and RV-30, see Table 3.1. The dynamic coefficient should be calculated according to subsection 0. The highest allowable train speed should be calculated up to a maximum, however, of 120 km/h. If the bridge is capable of carrying traffic load models I, II and III, then it will even be capable of carrying RV-25 and RV-30. If the bridge is capable of carrying traffic load models IV, V and VI, then it will even be capable of carrying RV-25, however RV-30 should be check separately. If the bridge is capable of carrying traffic load models VII, then RV-25 and where applicable even RV-30 should be checked. The Iron-ore traffic load model The iron-ore traffic load model is shown in Figure 3.1. For a load bearing system with a span greater than 5 m and sleepers directly attached to it and for structures with at least 0,6 m of ballast, the 4 point loads may be replaced by a UDL of 188 kn/m over the 6.4 metres shown.

19 Sustainable Bridges SB (51) Figure 3.1. The Iron-ore traffic load model. The BV-2000 traffic load model The BV-2000 traffic load model is shown in Figure 3.2. For load bearing system with a span greater than 5 m and sleepers directly attached to it and for structures with at least 0,6 m of ballast, the 4 point loads may be replaced by a UDL of 206 kn/m over the 6.4 metres shown. Figure 3.2. Traffic load model BV-2000 The UIC 71 load model The UIC 71 traffic load model is shown in Figure 3.3. For load bearing system with a span greater than 5 m and sleepers directly attached to it and for structures with at least 0,6 m of ballast, the 4 point loads may be replaced by a UDL of 156 kn/m over the 6.4 metres shown. This is the same load model as LM 71 of Eurocodes 1, (CEN, 2003). Figure 3.3. Traffic load model UIC 71 The SW/2 traffic load model The SW/2 traffic load model is shown in Figure 3.4. This load model is designed to ensure the safe passage of special heavy transports such as electrical transformers etc. This load model can be recognised from Eurocodes 1, (CEN, 2003), where it goes under the same name.

20 Sustainable Bridges SB (51) Figure 3.4. Traffic load model SW/2 This load model should be positioned so as to create the worst loading case for the element and for the type of effect under consideration. Unlike the UDL s of the previous load models, these UDL s should not be shortened or split up. Train load and line class A to D4, BV-2 to BV-4 and RV-30 and RV-25 The axle loads and wagon configurations are detailed in Table 3.1. The wagons should be positioned so as to create the worst load case and should be combined with empty wagons which are represented by a UDL of 10 kn/m but which have the same dimensions as those given in Table 3.1. The UDL s, p, or the axle loads, Q, should be combined so as to create the worst load effect. The first of these typical wagon configurations for line categories A D4 can be recognised from the UIC document (UIC, 1987). The remaining line class trains are the Swedish National Rail Authorities own traffic models for line classification purposes. The last two traffic models RV-30 and RV-25 represent wagons used to transport

21 Sustainable Bridges SB (51) Table 3.1. Traffic load line classes A to D4, BV-2 to BV-4 and RV-30 and RV-25 Line Class/ Load Type Axle Load Q [kn] UDL p [kn/m] A B B C C C D D D BV BV BV RV RV Q Q Q Q 1,5 1,8 6,20 1,8 1,5 12,80 1,5 1,8 7,80 1,8 1,5 14,40 1,5 1,8 4,65 1,8 1,5 11,25 1,5 1,8 5,90 1,8 1,5 12,50 1,5 1,8 4,50 1,8 1,5 11,10 1,5 1,8 3,40 1,8 1,5 10,00 1,5 1,8 7,45 1,8 1,5 14,05 1,5 1,8 5,90 1,8 1,5 12,50 1,5 1,8 4,65 1,8 1,5 11,25 1,5 1,8 7,30 1,8 1,5 13,90 1,5 1,8 5,90 1,8 1,5 12,50 1,5 1,8 5,40 1,8 1,5 12,00 2,0 9,00 2,0 13,00 2,0 9,00 2,0 13,00

22 Sustainable Bridges SB (51) Loads from track laying machines Bridges with a ballasted track should be designed to withstand loading from a machine for changing the track. A load of 900 kn should be evenly distributed between the areas indicated in Figure 3.5. The dynamic coefficient to be used for this loading is 1,2. Figure 3.5. Distribution of the load from a track laying machine Swedish dynamic factor for traffic load models I, II,IV and V a. The vertical loads should be multiplied by a dynamic factor which is a function of the determinant length, according to the following formula: 4 D = 1, L D D is the dynamic coefficient. L D is the determinant length, see Table 3.2. b. Only the vertical effects of the traffic load model should be include the dynamic coefficient. Effects from e.g. braking, acceleration, centrifugal forces etc. are not to include this factor. c. For bridges with extra fill material, in addition to ballast, and which exceeds 0,4 m, the dynamic coefficient may be reduced by a value: ( H 0,4) 0,1 f where H f is the height of the extra fill material, i.e. the distance in metres between the top of the construction and the underside of the ballast. The reduced dynamic coefficient may not be smaller than 1,05.

23 Sustainable Bridges SB (51) d. Footings should be calculated including the dynamic coefficient while effects transmitted into the soil, piling loads and deflections should exclude the dynamic coefficient. e. The dynamic coefficient should not be included if it produces results on the safe side. Determinant Length Table 3.2. Determinant Lengths Case Structural element Determinant Length L D 1 Main and longitudinal beam simply supported continuous Span of beam. The arithmetical mean of the spans multiplied by a factor 1,2 (2 spans), 1,3 (3 spans), 1,4 (4 spans), 1,5 (5 spans or more). 2 Beam and slab frame bridge single span continuous over several supports To be treated as a continuous bridge with three spans. The arithmetical mean of the spans multiplied by a factor 1,3, where the legs (walls) of the frame are each treated as one span. To be treated as a continuous bridge with several spans. The arithmetical mean of the spans multiplied by a factor 1,4 (2 horizontal spans), 1,5 (3 horizontal spans or more). The legs (walls) of the frame are each treated as one span. 3 Arch Twice the span 4 Concrete bridge deck The slabs minimum span (distance between crossbeams or main beams). 5 Steel orthotropic bridge deck steel plate longitudinal stiffener The minimum of the distance between the longitudinal stiffener and the distance between the traverse beams. The distance between the traverse beams. 6 Traverse beam Twice the length of the traverse beam. 7 Hangers Four times the distance between the hangers. 8 Supports, bearings, hinges and anchors The determinant length for the adjoining part of the construction. 9 Run-on slab 80 % of the length of the run-on slab. 10 Cantilever Special table not shown here.

24 Sustainable Bridges SB (51) Dynamic coefficient for traffic load models III, VI, VII, RV-30 and RV-25 The dynamic coefficient used for these traffic loads and classes of line are generally the same as used for the real trains of the Eurocode (CEN, 2003) and comply with the UIC 776-1R leaflet (UIC 1979), i.e. D = 1+ ϕ = 1+ ϕ' + 0,5ϕ '' which implies that the standard of the track complies with that of good track maintenance. Dynamic coefficient for cantilevers affected by traffic loads As regards the dynamic coefficient there are special regulations for the design of cantilevers Danish vertical traffic loads Existing bridges The vertical characteristic train load to be used for a classification of an existing bridge is as specified in Table 3.3. Table 3.3 Resistance classes for existing railway bridges. Uniformly distributed load [kn/m] Axleload [kn] 160 A 180 B1 B2 200 C2 C3 C4 225 D2 D3 D4 250 E4 E5 (LM71) 275 BS-R4 BS-R5 300 BS-S4 BS-S5 BS-S6 330 BS-T5 BS-T6 BS-T7 (BS-2000) The designation of the resistance classes up to 250 kn axle load follows the system given in the RIV system. For axle loads larger than this (below the thick line) the classes follows the Danish Railway Authority's own designation. The axle configuration is according to the design load in the EC1-3 (LM71) code and shown in Figure 3.3. In case an existing bridge has a poor resistance compared to the required class it is possible to apply an alternative axle configuration following the axle configuration of reference goods wagons specified in UIC Code 700-O, c.f. UIC (1987) c in metres Figure 3.6 Alternative axle load configuration for the classification load.

25 Sustainable Bridges SB (51) The axle distance c is given in Table 3.4. Table 3.4 Distance c for alternative axle load configuration (reference goods wagons). Class c [m] A 6.20 B B C C C D D D E4 (LM71) 5.90 E BS-R BS-R BS-S BS-S BS-S BS-T BS-T BS-T7 (BS-2000) 5.50 The reference goods wagons should be coupled in the most unfavourable way and combined in the most unfavourable way with empty wagons with the same configuration and length but with a reduced UDL equal to 10 kn/m. It is assumed that the load from locomotives does not result in larger load effects compared to the load effect from the reference wagon considered. A list of the actual line classes for most Danish railway lines is enclosed as chapter 19.2 in the Danish Assessment Code. New bridges For design the BS-2000 load model is to be applied. This load model BS-2000 represents the static effect of "future" rail traffic. The load model BS-2000 are configured and applied in the same way as LM71, see Figure 3.3. However, the axle load and uniformly distributed load are multiplied by a factor α=1.33 (axle load 330 kn; uniformly distributed load 110 kn/m), which complies exactly with the Swedish load model BV-2000 shown in Figure 3.2. Load reduction for existing bridges For existing bridges with more than one track the characteristic traffic load for the remaining tracks may be reduced depending on the frequency of heavy trains and the probability of two or more heavy trains passing the bridge at the same time. A load reduction may only be determined based on probabilistic calculations or by an agreement with The Danish Railway Authority Danish dynamic factor φ The dynamic factor takes account of the dynamic magnification of stresses and vibration effect in the structure but do not take account of resonance effect and excessive vibrations of the deck. The dynamic factor applies only for speeds less than 220 km/h and where the natural frequency of the structure is within the limits shown in figure 6.9 in EC1-3. If the natural

26 Sustainable Bridges SB (51) frequency of the structure is not within those limits a more detailed dynamic analysis has to be carried out. The vertical loads should be multiplied by a dynamic factor which is a function of the determinant length and maintenance level. In case the axle configuration is according to LM71 the dynamic factor is determined as specified in the EC1-3 section However, if reference goods wagons are used the dynamic factor is determined as specified in the Annex E in EC1-3 where (E.1) is used to determined the dynamic factor for all the lines except the main lines where (E.2) is used. The maintenance level which is input to the determination of the dynamic factor is as indicated in Table 3.5. However, modified maintenance level may be used for existing bridges if the load intensity and/or the speed of the trains are different from the parameters given in Table 3.5. Table 3.5 Design parameters for the railway lines. Railway Speed Load factor α Level of comfort Maintenance level BS 2000 Main line 200 km/h 1,00 very good carefully maintained Regional line 180 km/h 1,00 good standard maintained Suburban line 160 km/h 1,00 good standard maintained Local line 120 km/h 1,00 good standard maintained Goods railway 140 km/h 1,00 acceptable standard maintained British vertical traffic loads Route Availability (RA) Number The assessment of a bridge should be determined in terms of its Route Availability (RA) number, that is its safe traffic load capacity. Route Availability numbers generally range from the lowest capacity RA0 to the highest at RA15 represented by 25 British Standard Units (BSUs) of Type RA1 loading respectively as shown by Table 3.6.

27 Sustainable Bridges SB (51) Table 3.6 Route Availability Classification for Bridges R.A. NUMBER RANGE OF BSUs IN GROUP RANGE OF SINGLE AXLE WEIGHTS IN GROUP RA0 Up to units Under tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA to units to tonnes RA units and over tonnes and over Type RA1 loading excludes dynamic effects which should be added in accordance with Clause and are dependent upon train speed. RA numbers should therefore be determined according to a given train speed. In some cases it may be necessary to determine more than one RA number for a given Bridge, for example RA6 at 100 mph representing passenger trains (normally the permissible speed) and RA10 at 60 mph for freight trains. The number of units of Type RA1 loading that the Bridge can carry should be determined by calculating the live load capacity factor, C, as defined below: Live Load Capacity C = (3.1) Effects of 20 units of Type RA1 loading Capacity in terms of units of Type RA1 loading = 20 C The RA number of the Bridge should be obtained from Table 3.6. Where the assessed RA number is below the RA of the line, the effects under static EUDLs for the real (actual) permitted vehicles and combinations, together with dynamic factors for their respective permitted speeds, may be considered acceptable.

28 Sustainable Bridges SB (51) It should be noted that the RA effect of vehicles on a specific span (loaded length) is often less than the RA classification for the vehicle which has to allow for a full range of Bridge spans. RA1 Loading The static loading used to determine the RA number is shown in Figure 3.7 for 20 units of Type RA1 loading. The Short Lengths configuration should be used when it produces more onerous effects than the axle and uniformly distributed load model. 4x200kN 4x150kN 4x200kN 4x150kN 65kN/m x250kN SHORT LENGTHS 1.8 Figure Units of Type RA 1 Loading Note 1: 20 units of Type RA1 loading is equivalent to Route Availability RA10 without allowance for dynamic effects. It would appear from the British assessment code that only one traffic load model is used for assessment, i.e. the one shown in Figure 3.7. This is quite convenient from a practicing engineer s point-of-view. As far as I can ascertain the load model of RA 1 is applied to the bridge and the capacity of the bridge, C, is calculated in terms of this loading using (3.1). The number of British Standard Units is then calculated using 20 x C. Table 3.6 is then used to yield the RA number of the bridge British dynamic factor φ The dynamic effect in the British assessment code is the same as that derived in UIC (1979) with the exception of the dynamic effect for cross girders. As with other European codes there is a stipulation regarding applicability of this dynamic factor. The stipulations regard train speed and range of natural frequency of the bridge/member. Dynamic Factor for Members other than Transverse Floor Members The dynamic factor ( 1 + ϕ ) should be applied where the speed of trains is 5 mph or greater, up to 125 mph maximum, using the dynamic increment ϕ which should be taken as in Table 3.7.

29 Sustainable Bridges SB (51) Table 3.7 Dynamic Increment ϕ Normal track Permissible speed 100 mph Dynamic Increment ϕ for Bending ( ϕ 1+ ϕ 11 ) Dynamic Increment ϕ for Shear Track maintained for Permissible speed mph Fatigue calculations only Permissible speed 125 mph ϕ 2.3 ϕ 1+ ϕ for Bending ϕ.5 ϕ The factors ϕ 1 and ϕ 11 correspond to the factors ϕ ' and ϕ '' of the UIC leaflet UIC (1979), respectively. Dynamic Factor for Transverse Floor Members The dynamic factor for cross girders and other discrete transverse floor members should be taken as ( 1+ I 4 ), where I 4 is determined from Figure 3.8. For fatigue calculations only the value of I 4 should be taken as 50% of the value shown in Figure 3.8. Reduced Dynamic Effect Where the depth of ballast or non-structural fill exceeds 1.0 metre, the dynamic increment ϕ may be reduced as follows: Reduced dynamic increment h 1 = ϕ (3.2) 10 where h is the depth in metres below underside of sleeper or track to top of arch crown or structural element.

30 Sustainable Bridges SB (51) I Speed mph Figure 3.8 Dynamic Factor I 4 for Transverse Floor Members (British assessment code)

31 Sustainable Bridges SB (51) Swiss and French vertical traffic loads and dynamic factor The Swiss and the French assessment code both adopt the Eurocode approach and therefore use their traffic load models. The French railways include a dynamic analysis where the high-speed traffic models of HSLM-A and HSLM-B are used for lines with allowable speeds greater than 200 km/h. The load models have to be placed in an unfavourable position. Favourable actions have to be neglected. The traffic load models HSLM-A and HSLM-B are the same as those found in Eurocodes and are derived from the research detailed in European Rail Research Institute, (2000). The dynamic effects of the railway traffic have to be considered by the factor Φ, except for the load models HSLM A and HSLM B. It is assumed that factor Φ, refers to the simplified dynamic factor as defined in Eurocodes to be used with load models LM71, SW/0 and SW/2. Table 3.8 The traffic load models of the French and Swiss assessment codes. Static effect - Load model 71 represents the static effect of normal railway traffic - Load model SW/0 represents the static effect of normal railway traffic on continuous girders - Load model SW/2 represents the static effect of heavy railway traffic only in France - Load model empty train represents the static effect of an empty train Dynamic analysis - Load model real trains dynamic analysis can be made using nominal values of specified real trains with a velocity of more than 200 km/h - Load model HSLM-A (International lines) - Load model HSLM-B (International lines) represents the dynamic effect of trains with a velocity of more than 200 km/h for - a span L >= 7m - a span L < 7m in the case of continuous or complex structures (skew structures, structures with significant torsion behaviour, works with lateral beams with significant vibration modes of the deck and the principles girders etc.) represents the dynamic effect of trains with a velocity of more than 200 km/h for - simple beams with a range L smaller than 7m - complex structures in the case of decks with significant vibration modes (works with lateral beams with thin decks for example) Fatigue analysis - Load model 71

32 Sustainable Bridges SB (51) Figure 3.9 Load model HSLM A Table 3.9 Specifications for the HSLM A load traffic model of the French assessment code. Representative train Number of intermediary coaches N Lengths of coaches D [m] Distance between axles within a bogie d [m] Point load P [kn] A A A A A A A A A A Figure 3.10 Load model HSLM B Q k [kn] q k [kn/m] 170 -

33 Sustainable Bridges SB (51) Figure 3.11 Load model empty train: Certain specific verifications justify this particular load. It consists of a constant linear vertical load with a nominal value of 10.0kN/m. Q k [kn] q k [kn/m] - 10

34 Sustainable Bridges SB (51) German vertical traffic loads and dynamic factor (1) Load models given in DS 804 should be applied according to its regulations. Divergent to DS 804, the simplified load model UIC 71 (with line loads) can also be assumed for main girders with a span L < 10 m if a ballast bed exists. For local maintenance or refurbishment the same load model can be applied as given in the latest structural analysis. This only applies if the structure under maintenance or refurbishment is not significant for the stability of the entire building. The exceptional application of service vehicles requires the agreement of the EBA (Federal Railway Office). To avoid the complete recalculation of a building for minor maintainance or refurbishment it is allowed to refer to existing analysis i.e. old load models can be used for the current analysis. Traffic load models (2) The classification of load model UIC 71 is permitted according to section 40 of DS 804. Classification of load model UIC 71 (3) For fatigue assessment the service vehicles should be determined from the date of commission to a stipulated deadline. Approximately, the type standardized service vehicles according to , appendix 6 can be used as service vehicles of the past. For the time span from the deadline to the expected end of service life the type standardized service vehicles according to , appendix 7 should be applied if no specific service loads can be determined. Deadline describes the date of examination (recalculation) of the building. Type standardized service vehicles have been established since the determination of service vehicles of the past is difficult if not impossible due to lack of documentation. They have been developed from the locomotives, wagons and passenger coaches that occurred in the respective time ranges safely covering historical traffic. The so called S3 traffic is a constellation of 6 train types, equivalent to today s mixed traffic. Service vehicles for fatigue assessment (4) Dynamic amplification factors for significant load models should be applied according to DS 804 if no dynamic measurement has been installed. The dynamic amplification factor for the UIC load model also applies for the classified load model UIC 71. Dynamic amplification factor for significant load models

35 Sustainable Bridges SB (51) (5) If no dynamic measurement has been installed, the dynamic amplification factor 1+ ϕ for service vehicles (see paragraph (1)) should be determined for beams as follows: ϕ = a 1 ϕ + a 2 ϕ, ϕ < 1 where ϕ is the proportion for the geometrically intact rail according to appendix 1 ϕ is the proportion taking the imperfection of the rail due to vertical impact into account. The coefficients a 1 and a 2 should be calculated using: Dynamic amplification factor for service vehicles a l = ,1 l for trains with steam engine for the main girders (bridge span l in meters) a 1 = 1,0 for all other trains and components a 2 = 1,0 0,5 0,0 for track condition 3 for track condition 2 for track condition 1 Track condition 3 (minor condition) should be applied for fatigue assessment before This condition should further be applied in case of existing track dents with a maximum depth of 2 mm within a section of 1000 mm or if the maximum speed is limited to 80 km/h within the bridge area. Track condition 2 (normal condition) can be applied for fatigue assessment in the time range between 1930 and 1950 or in case of existing track dents with a maximum depth of 1 mm within a section of 1000 mm or if the maximum speed is limited to 80 km/h < v 140 km/h within the bridge area. Track condition 1 (superior condition) can be applied for tracks without vertical variation if track geometry is always ensured. This can always be assumed if speed limitation v is above 140 km/h. The speed limitation v is the limitation due to vertical variations (dents) of the track, not due to track geometry. 3.3 Distribution of axle loads Swedish distribution of axle loads According to the Swedish code for assessment of existing bridges the manner in which axle loads may be distributed for different types of track and fastener arrangements are shown in Figure Figure As can be seen from Figure 3.14, the Swedish assessment code

36 Sustainable Bridges SB (51) allows for a more generous distribution of the load through ballast when compared with Eurocode, compare a 2:1 distribution with the 4:1 of Eurocodes. Distribution of an axle load when the rail is directly fastened to the steel super- Figure structure. Figure Distribution of an axle load through a rail and sleeper track arrangement. Figure Load distribution through the ballast under a sleeper Danish distribution of axle loads The distribution of axle loads by rails, sleepers and ballast follow the specifications in EC1-3 section British distribution of axle loads Distribution of the axle loads is allowed in the British assessment code according to the rules described below. Dispersal through the track onto Bridge floor elements may be applied as in follows where: F EUDL is a factor by which the unit EUDL loading is multiplied; F A t is a factor which is multiplied by the axle loading; is the depth of ballast between the underside of sleeper and the top of the member in mm;

37 Sustainable Bridges SB (51) L is the effective span in metres of longitudinal members spanning between centres of cross girders or twice the spacing of cross girders in the case of continuous longitudinal members. Longitudinal Members positioned Directly Under the Rails including Rail Bearers, Troughing, Slabs, Plates, Timber Decks etc. For Longitudinal dispersal: To allow for longitudinal dispersal through track: Table 3.10 Live Load Factor For Dispersal Through Track - F EUDL To rail bearers, longitudinal troughing, plate or timber floor etc. L (m) F L (m) EUDL Longitudinal timbers only over cross girders F EUDL < to 3.0 L+ 2.0 up to L > > For Transverse distribution: (i) The effective width of longitudinal troughing, slabs or similar, carrying one track load should be taken as shown in Table 3.11, but not greater than the actual widths. Table 3.11 Effective Widths t (mm) Up to 150 >150 Effective width (m) (ii) For longitudinal timber decks, barlow rails, old rails or similar, an effective width of ( t ) metres with a maximum of 3.0 metres. Transverse Members For Longitudinal dispersal: (i) Cross girder with cross sleepers and ballast. For cross girders spaced at 1.8 metres or more, F A = 1.0. For cross girders spaced at less than 1.8 metres the axle load should be reduced in the ratio:

38 Sustainable Bridges SB (51) Cross girder centres in metres F A = (3.3) 18. (ii) Cross girders with longitudinal timbers. For cross girders spaced 1.5 metres or more, F A = 1.0 For cross girders spaced at less than 1.5 metres with longitudinal timbers equal to or greater than 225 mm deep Cross girder centres in metres F A = (3.4) 18. For cross girders spaced at less than 1.5 metres, with longitudinal timbers less than 225 mm deep Cross girder centres in metres F A = (3.5) 1.5 (iii) Transverse reinforced concrete slabs, effective width = 1.8 metres or actual width if this is less. (iv) The effective width of transverse members should be taken from Table 3.12.

39 Sustainable Bridges SB (51) Table 3.12 Effective Width of Transverse Members Member Type Effective Width (m) Transverse Troughing Cross sleeper track, sleepers in troughs 1.5 Cross sleeper track up to 150 mm depth of ballast below underside of sleeper to top of troughing Cross sleeper track more than 150 mm depth of ballast below underside of sleeper to top of troughing Longitudinal timber up to 150 mm deep directly on transverse troughing Longitudinal timber more than 150 mm deep directly on transverse troughing Transverse RC slabs 1.8 Transverse Timber decks Chairs directly on the deck 0.6 Cross sleeper track up to 150 mm depth of ballast below underside of sleeper to top of decking Cross sleeper track more than 150 mm depth of ballast below underside of sleeper to top of decking Longitudinal timber up to 150 mm deep directly on decking 1.5 Longitudinal timber more than 150 mm deep directly on decking Dispersal through Ballasted Track For sleepered track 50% of a wheel load may be assumed to be transmitted to the sleeper beneath and 25% distributed to each of the sleepers on each side assuming a sleeper spacing of 800 mm maximum. The load acting on the sleeper may be assumed to be distributed uniformly over the ballast at the underside of the sleeper and over a distance of 800 mm symmetrically about the centre line of the rail (or to twice the distance from the centre of rail to the nearer end of the sleeper if less). A sleeper width of 250 mm may normally be assumed. Dispersal through ballast or similar granular fill may be taken at 15 to the vertical. Where a flexible bridge floor such as flat or buckle plates is stiffened by rigid members such as rail bearers, the relative flexibility of the floor construction may be considered in the distribution of loading. For rail bearers a pressure, under nominal live loading (including dynamic factor) and dead load, of up to a maximum of 1000 kn/m² may be assumed to occur over a

40 Sustainable Bridges SB (51) width of 200 mm (or the stiff bearing width of the rail bearer if greater). This pressure is reduced beneath the remainder of the loaded area, as shown in Figure mm = = 250mm 100% 50% 25% KN/m² Maximum Figure 3.15 Dispersal through Ballasted Track onto a flexible floor with Rail Bearer 3.4 Horizontal traffic actions Swedish horizontal traffic actions Braking and acceleration forces Each load model has an associated braking and acceleration force that is assumed to be evenly distributed along the loaded length of the bridge. Further, the force is assumed to act at the centre line of the track at the same height as the top of the rail (TOR). Lateral force The superstructure of the bridge should be designed to withstand a lateral force of 80 kn working at 90 to the track and at the same height as the TOR. Centrifugal force This force is to take into consideration the effects of the centrifugal forces arising from a train travelling at speed on a bridge that is in a curve. The formulas depend primarily on the actual loading of the train, the speed of the train and the radius of curvature of the track Danish horizontal traffic actions Braking and acceleration forces (traction) The braking and acceleration forces are considered as uniformly distributed along the axis of the track. For existing bridges the load model LM71 (class E4) has an associated braking force at 20 kn/m, limited to 4000 kn for the total length of the bridge. Load model BS 2000 has an associated braking force of 27 kn/m, limited to 5400 kn. For other load models interpolation and extrapolation based on those values may be carried out.

41 Sustainable Bridges SB (51) The traction force is specified in EC1-3 subsection If there is more than one track, the most adverse combination of traction and braking force for two tracks shall be applied. Nosing force In EC1-3 section (2)P the superstructure of the bridge should be designed to withstand a lateral force of 100 kn working at 90 to the track and at the top of the rails. For existing bridges the lateral force may be reduced to 80 kn. For railway bridges with more than one track the most adverse combination of simultaneously applied nosing forces on two tracks shall be considered. Centrifugal force The centrifugal force is specified in EC1-3 section for LM71. The centrifugal force for load model BS-2000, 1.0 LM71 is used German horizontal traffic actions Braking and acceleration forces (traction) Braking and acceleration forces for one-piece and built-up structures should be determined according to DS 804. If a classified load model UIC 71 is used the classifying factor equally applies for the determination of the braking force F X,Br. For buildings in tracks without electrification the acceleration force should be determined as follows: X, = 20 l ξ 600 ξ [ kn] F An with ξ = reduction factor according to DS 804, table 12 l = significant length of acceleration load in m. Nosing force Nosing force should be applied upon every rail at the most unfavourable loction regardless of the existance of a classification of the load model UIC 71. It should be applied horizontally and perpendicular to the track s axis at level with the rail head equalling 60 kn. The nosing force distribution in the ballast bed can be assumed according to DS 804, section 79. Centrifugal force Centrifugal forces should be determined from the significant load models according to the regulations of DS 804, section 55. If the significant load model is a classified load model UIC 71 the classifying factor equally applies for the determination of the centrifugal force Swiss and French horizontal traffic actions The Swiss and French horizontal traffic actions for the assessment of existing railway bridges are in accordance with EC1.

42 Sustainable Bridges SB (51) British horizontal traffic actions Nosing An allowance should be made for lateral loads applied by trains to the track due to nosing which should be taken as two nominal loads spaced at 4.5 metres apart along the track. Each load N should be taken as: For all locomotives, passenger trains, and for freight vehicles where v does not exceed 40 mph: N = 0. 72v (3.6) For freight vehicles where v exceeds 40 mph: ( 40) but not greater than 80 N = v (3.7) where: N is the value of each nosing force in kn; v is defined in Table 3.7. Nosing should be considered as acting in either direction at right angles to the track at rail level and at a location so as to produce the maximum effect in the element under consideration. For elements supporting more than one track nosing should be applied to one track only. Nosing may be assumed applied wholly to one rail corresponding with side contact from the wheel flange. Transverse distribution equally between the rails may be assumed beneath sleepered track. Other than on sleepered track, transverse distribution between members or longitudinal timbers may be considered provided these members are adequately connected. The vertical effects of nosing on elements supporting one rail only should be considered. It may be assumed that 25% of the nosing load will be transmitted longitudinally to each of the sleepers or track fastenings on each side assuming a sleeper or fastening spacing of 800 mm maximum. No addition for dynamic effects should be made to the nosing loads. Centrifugal Load Where the track on a Bridge is curved in plan, allowance for centrifugal action should be made in assessing the elements, all tracks on the structure being considered occupied. The nominal centrifugal load F c in kn, per track acting radially at a height of 1.8 metres above rail Level should be calculated from the following formula:

43 Sustainable Bridges SB (51) ( v + ) P 6 2 F c = f (3.8) 50r where: P is the static axle load or equivalent uniformly distributed load for bending moment as applicable; r is the radius of curvature of the track (in metres); v is the speed in mph as defined in Table 3.7; f is a factor where for L less than 2.88 metres or v less than or equal to 75 mph: f = 1.0 and for L greater than 2.88 metres and vt over 120 km/h: v t f = (3.9) 625 v L where L is the loaded length of the element being considered. The vertical effect of centrifugal load on elements supporting one rail such as railbearers should be considered. This vertical effect may be reduced taking account of any track cant that is present. Centrifugal load may be dispersed using factor F EUDL or F A in section as applicable. No addition for dynamic effects should be made to the centrifugal loads. Longitudinal Loads Allowance should be made for loads due to traction and braking as given in Table 3.13 which are equivalent to 20 BSUs. Loads for a different number of BSUs may be taken pro rata to X these loads, using Longitudinal Load for X BSU s = Value from Table 3.13 (3.10), but not 20 less than that applicable to 10 BSUs. Longitudinal loads should be considered as acting at rail Level in a direction parallel to the tracks. No addition for dynamic effects should be made to the longitudinal loads.

44 Sustainable Bridges SB (51) Table 3.13 Nominal Longitudinal Loads (applicable to 20 BSUs of loading or RA10) Load Arising From Traction (30% of load on Loaded Length L (m) Longitudinal Load (kn) up to driving wheels) from 3 to Braking (25% of load on from 5 to from 7 to (L-7) over up to braked wheels) from 3 to from 5 to over 7 20 (L-7) Longitudinal Load for X BSU s = X Value from Table 3.13 (3.10) 20 For Bridges supporting ballasted track, up to one third of the longitudinal loads may be assumed to be transmitted by the track to resistances outside the bridge structure, provided that no expansion switches or similar rail discontinuities are located on, or within, 18 metres of either end of the bridge. Bridges and elements carrying single tracks should be assessed for the greater of the two loads produced by traction and braking in either direction. Where a Bridge or element carries two tracks, both tracks should be considered as being occupied simultaneously. Where the tracks carry traffic travelling predominantly in opposite directions, the load due to braking should be applied to one track and the load due to traction to the other. Bridges and elements carrying two tracks in the same direction should be subjected to braking or traction on both tracks, whichever gives the greater effect. Consideration should be given to braking and traction acting in opposite directions producing rotational effects. Where elements carry more than two tracks, longitudinal loads should be considered as applied simultaneously to two tracks only. Longitudinal loads may be reduced in for elements carrying more than one track.

45 Sustainable Bridges SB (51) 3.5 Soil pressures from overburdens This load is used for the design of abutments and the legs of slab frame bridges and is the horizontal soil pressure as a result of the vertical train loads being transmitted through the soil on the approach to the bridge.

46 Sustainable Bridges SB (51)

47 Sustainable Bridges SB (51) 4 Fatigue Assessment As is the case with this document as a whole, the fatigue assessment in current codes is only described as they relate to the loading to be considered. How the loads are then used in an analysis relating to specific materials is not described. However, the majority of the codes appear to adopt some form of approach based on S-N curves and Palmgren-Miner cumulative damage hypothesis. 4.1 German approach The German approach to the assessment of the fatigue capacity of an existing bridge appears to be a similar concept to the Eurocode where several typical trains for fatigue assessment are used for analysis purposes. A total of 21 Fatigue trains are shown in the code, however it is not clear from Albert, M. and Bagayoko, L., (2004) how these trains are used in the assessment. One can assume that they are used to produce typical stress cycle whereby some form of fatigue analysis may be performed. How the traffic load history is taken into account is not clear. 4.2 Swedish and Danish Approach The Swedish and Danish approaches appear to be almost identical and the Danish approach is detailed below. The Swedish and Danish Rail Authorities have good records as to the total tonnage passed on different lines. This can either be in terms of gross or net tonnage. This information, together with the simplified traffic model of Figure 4.1 and Table 4.1, may be used to calculate the number of Equivalent Freight Wagons that have passed the bridge in the different periods listed in Table 4.1. Alternatively the equivalent number of individual axles or bogies or the number of Equivalent Freight Train passages may be calculated. In the Swedish code it is assumed that 20 wagons shown in Figure 4.1 constitute a train Existing bridges A check for the structural integrity of an existing bridge for fatigue may be carried out by one of four methods: 1) The maximum and minimum stresses resulting from the possible load arrangements are calculated based on Equivalent Freight Train. The load arrangements include the dynamic factor for fatigue, see subsection ) The number of loading cycles is based on the loading history of the bridge. The stress range is calculated based on loading from Equivalent Freight Trains for existing bridges and the specified axle arrangement according to AD1-3, Danish National Railway Agency, (2003). 3) The stress range is calculated based on a "known" loading history of the bridge modelled by realistic rail traffic through the lifetime of the bridge. 4) The stress range is calculated based on measurements of stresses during a certain period of normal rail traffic and the number of load cycles is determined from a proportioning of the amount of freight during the measuring period compared to that of the loading history of the bridge. The criterion for method 1) is as following: According to the constant stress amplitude, a number of stress cycles which is 10 6 stress cycles for primary carrying elements with a span of Lϕ 6 m and 10 7

48 Sustainable Bridges SB (51) stress cycles for primary carrying elements with a span of Lϕ<6 m and secondary elements where the axle load is the dominating load effect. The correction factor κ=2/3, see explanation below. The criterion for method 2) is as following: The number of stress cycles is based on the length of influence line. If the influence line is short there are a higher number of stress cycles (small stress range) than if the influence line is long (large stress range). The correction factor κ=2/3 The criterion for method 3) and 4) is as following: The stress spectra is determined by "Rain-flow counting" The correction factor κ describes the shape of the stress spectra. κ = 1 would describe a constant stress spectra Δσ, however, in recognition of the fact that the stress spectra is variable for mixed freight traffic and not constant, then the factor has been reduced to 2/3 in the Danish and Swedish codes. The limiting case where κ = 1 corresponds to a case where the train load is actually expected to appear. κ = 2/3 is based on experience and is also applied by the Swedish Rail Authority for mixed traffic. In the Swedish code a value of κ = 5/6 is used on the Iron-Ore Line in recognition of the homogenous traffic situation. An example of a freight wagon of the Equivalent Freight Trains is shown below in Figure 4.1. The characteristic axle loads and the number of axles per wagon for different periods are shown in Table 4.1 for existing bridges. This information can be used to obtain an assessment of the fatigue effects based on the loading history of the bridge. Q Q Q Q 1,5 1, ,8 1,5 11,6-16,6 Figure 4.1. Axle spacing and length over buffers for a freight wagon of the Equivalent Freight Train for all lines.

49 Sustainable Bridges SB (51) Table 4.1. Axle loads (kn) and number of axles per wagon of Equivalent Freight Train" (based on LM71) for different periods. Year Mean Speed P k P m a P o Year is the period for the particular amount of freight. Speed is the speed of the train (km/h) P k is the characteristic value of the axle load (kn) for the calculation of the stress range. P m is the mean value of the axle load (kn) used to calculate the number of train passages. a is the number of axles per freight wagon and is used to calculate the number of train and bogie passages. P o is the axle load (kn) of an empty freight wagon New bridges A check for the structural integrity of a new bridge for fatigue may be carried out by one of two methods: 1) The maximum and minimum stresses resulting from the possible load arrangements are calculated based on BS The load arrangements include the dynamic factor for fatigue, see subsection ) The stress range is calculated based on loading from traffic mix given in AD1-3 in the Danish Assessment Code. The criterion for method 1) is as following: According to the constant stress amplitude is a number of stress cycles which is 10 6 stress cycles for primary carrying elements with a span of Lϕ 6 m and 10 7 stress cycles for primary carrying elements with a span of Lϕ<6 m and secondary elements where the axle load is the dominating load effect. The correction factor κ=2/3 The criterion for method 2) is as following: The stress spectra is determined by "Rain-flow counting"

50 Sustainable Bridges SB (51) Dynamic factor for fatigue φ+1 The static load shall be multiplied with the dynamic factor for fatigue. The dynamic factor applies only for speeds less than 220 km/h and where the natural frequency of the structure is within the limits shown I figure 6.9 in EC1-3. If the natural frequency of the structure is not within those limits a dynamic analyse has to be carried out. In case the axle configuration is according to LM71 the dynamic factor for fatigue is determined according to EC1-3 Annex F. For new bridges the dynamic factor 1+ϕ=1+1.0(ϕ'+½ ϕ'') is used instead of (F.1) for all railways except the main lines where (F.1) is applied. For existing bridges the dynamic fatigue factor is determined by 1+ϕ=1+½(ϕ'+½ ϕ''). For steel bridges with direct rail-fastening the following can be applied: 1+ϕ=1+½(ϕ'+ ϕ'') In the Swedish code the dynamic amplification factor is the same as that used in EC1-2 Annex D, Basis for the fatigue assessment of railway structures. 4.3 Swiss and French approach According to Herwig, A., (2004) the Swiss and French codes for existing railway bridges adopt the method proposed in EC1 for the calculation of fatigue. How historical loading is taken into consideration is not described. It is assumed that the reader is familiar with the approach of the Eurocode EC1, CEN (2003). 4.4 British approach (Steel and Wrought Iron) In the British code for the assessment of steel and wrought iron bridges there are a large number of references to BS 5400: part 10, which unfortunately the author does not possess. This made putting the text into context somewhat difficult. The acceptable reliability may be related to the capability of the bridge to carry railway traffic in the event of failure of an element depending on whether the element is a damage tolerant or a safe life element. The required reliability may be deemed to be achieved by applying factors γ 1 and γ 2 to the relevant stress ranges. Allowance should be made for fatigue damage that has occurred since construction of the bridge to the element considered and for differences between traffic spectra in the past, present and future whenever this is practicable. In the British code it is possible to use up to four different assessment stages. These are: Stage A Fatigue Assessment - Identify Fatigue Criticality by Inspection and Cut-Off Stress Stage B Fatigue Assessment - Damage Calculation to Standard Spectrum Stage C Fatigue Assessment Damage Calculation to Particular Spectrum Stage D Fatigue Assessment Assessment using Measured Strains

51 Sustainable Bridges SB (51) Stage A assessment In this stage A level of assessment the railway live loading is RA railway live loading with the number of units equivalent to that of the route. The dynamic factor follows the recommendations of the UIC leaflet UIC 776-1R, UIC (1979). In the text for this level of assessment it is stated that (i) For all elements which contribute to vertical live load capacity, carry out the following procedure: (a) Apply RA railway live loading with the number of units equivalent to that of the route (which may be in excess of the assessed rating of the bridge) to one or two tracks so as to produce the greatest algebraic maximum and minimum values of stress at the critical locations within the element. Include for dynamic increment evaluated in accordance with Table 3.7 for fatigue for a speed applicable to the applied live loading (NB: this may be less than the line speed); (b) Determine the maximum and minimum values of principal stress, or vector sum stress for weld throat, σ P max and σ Pmin, occurring at the critical locations within the element being assessed; (c) Determine the maximum range of stress σ Rmax equal to the numerical value of σ Pmax minus σ Pmin. For non-welded elements the stress range should be modified in accordance with BS 5400: Part 10 Clause 6.1.3; (d) Multiply the stress range σ Rmax by factors γ 1 and γ 2 to give the factored range of stress σ f max where; σ σ γ γ f max = R max 1 2 (4.1) where γ 1 is obtained from Table 4.2 and γ 2 from Table 4.3. Table 4.2. Values of γ 1 Assessment Stage Method of Analysis Static or Load Distribution Analysis 3D Finite Element A 1.00 NA B, C D (measured strain) 0.80 Table 4.3. Values of γ 2 Inspection Access Damage Tolerant Element Safe Life Element Accessible Inaccessible

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53 Sustainable Bridges SB (51) 5 Partial safety factors for loads One of the key areas where savings can be made within the realms of most of the codes is through the use of reduced values for partial safety factors on loads when more about the loading has been established through e.g. site investigation or measurement. A typical example of this is illustrated by the German code, see the table below. Here we see that large savings can be made especially on the permanent loads through increased knowledge of those loads. Table 5.1. Partial safety factors for actions according to the German assessment code. permanent actions G variable actions Q G1 dead load of members constraint additional actions Action Row Significant criteria γ FG γ FQ γ FA 1 approximate calculation of 1,20 quantities steel structures 2 exact calculation of quantities 1,15 concrete and RC structures G2 dead load of carriageway + road bed ground settlement creep and shrink prestressing traffic loads 3 as 2 with on site control 1,10 4 approximate calculation of 1,30 quantities 5 exact calculation of quantities 1,25 6 as 5 with on site control 1, filling level derived from actual condition, unlimited filling level derived from actual condition, limited by control 1,80 1,50 9 filling level derived from actual 1,20* condition, limited by design 10-1, , ,00 13 load assumptions according to DS 804 apply unconditionally 1,30 load model UIC the applied load model completely covers stresses due 1,20** to possible service loading wind actions 15-1,10 thermal actions 16-1,10 braking and acceleration forces 17-1,10 other variable actions 18-1,10 accidental actions 19-1,00 * This value also applies for carriageways without bedding for all valuation categories ** This value also applies for load models SW and SSW

54 Sustainable Bridges SB (51) Interestingly, in the British code, this type of philosophy is even applied to the traffic live loads, where it is stated that partial safety factors on loads may be reduced, where the loading is of a controlled nature as follows: (a) There is reliable control over the trains that can enter the route in question, and (b) For vehicles which comprise any of the following: Locomotives; Locomotive hauled passenger and/ or mail trains; Other passenger and/ or mail trains; Cranes and track plant not able to carry loads whilst in travelling mode; Freight wagons where loading is physically controlled, for example fluid fuel tank wagons, closed grain or closed cement wagons; Standard coal hopper or similar wagons where the load is weighed before dispatch. Reduced values of fl γ can only be assumed for other vehicles where every vehicle after loading is weighed or is otherwise subject to proper assessment of weight, before details are submitted and accepted for such vehicles to cross the Bridge. These vehicles include freightliner container wagons, open top wagons for aggregates, spoil or waste and wagons for track infrastructure maintenance or renewal.

55 Sustainable Bridges SB (51) 6 Bibliography Albert, M. and Bagayoko, L., (2004). Background Document, Survey of German Code for Existing Railway Bridges. Sustainable Bridges, Technical Report, WP4-17-T D-German Code Survey. Banverket (2000). BVH ; Bärighetsberäkning av järnvägsbroar. Banverket, Borlänge, Sweden. Banverket (2004). BVK ; Ändringar och tillägg till BVH Banverket, Borlänge, Sweden. CEN (2003). EN , EUROCODE 1 - Actions on structures, Part 2 : Traffic loads on bridges. European Committee for Standardization. Danish National Railway Agency, (2003). AD1-3, Application Document for ENV :1995, Traffic loads on bridges, Railway bridges. European Rail Research Institute, (2000). D214, Rail bridges for speeds > 200 km/h, reports 1-9. Herwig, A., (2004). Background Document, Survey of existing French and Swiss Code for load assessment. Sustainable Bridges, Technical Report, WP4-21-T D-French & Swiss Code Survey. James, G., (2004). Background Document, Survey of Swedish Assessment Code. Sustainable Bridges, Technical Report, WP4-31-T D-Swedish Code Survey. Linneberg, M. and Sloth M., (2004). Background Document, Survey of Loads for the Danish Railway Bridge Assessment Code. Sustainable Bridges, Technical Report, P A-WP4-Danish Code Survey. Railtrack PLC, (2001). Railtrack Line Code of Practice: The Structural Assessment of Underbridges. Technical Report, RT/CE/C025. UIC (1979). UIC 776-1R; Loads to be considered in the design of railway bridges. International Union of Railways. UIC (1987). UIC code 700-O; Classification of lines and resulting load limits for wagons. International Union of Railways.

56 Assessment of Actual Traffic Loads Using B-WIM, Site Specific Characteristic Load from Collected Data & Statistical Evaluation of Dynamic Amplification Factors Background document D4.3.2 PRIORITY 6 SUSTAINABLE DEVELOPMENT GLOBAL CHANGE & ECOSYSTEMS INTEGRATED PROJECT

57 Sustainable Bridges SB (62) This report is one of the deliverables from the Integrated Research Project Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives funded by the European Commission within 6 th Framework Programme. The Project aims to help European railways to meet increasing transportation demands, which can only be accommodated on the existing railway network by allowing the passage of heavier freight trains and faster passenger trains. This requires that the existing bridges within the network have to be upgraded without causing unnecessary disruption to the carriage of goods and passengers, and without compromising the safety and economy of the railways. A consortium, consisting of 32 partners drawn from railway bridge owners, consultants, contractors, research institutes and universities, has carried out the Project, which has a gross budget of more than 10 million Euros. The European Commission has provided substantial funding, with the balancing funding has been coming from the Project partners. Skanska Sverige AB has provided the overall co-ordination of the Project, whilst Luleå Technical University has undertaken the scientific leadership. The Project has developed improved procedures and methods for inspection, testing, monitoring and condition assessment, of railway bridges. Furthermore, it has developed advanced methodologies for assessing the safe carrying capacity of bridges and better engineering solutions for repair and strengthening of bridges that are found to be in need of attention. The authors of this report have used their best endeavours to ensure that the information presented here is of the highest quality. However, no liability can be accepted by the authors for any loss caused by its use. Copyright Authors Project acronym: Sustainable Bridges Project full title: Sustainable Bridges Assessment for Future Traffic Demands and Longer Lives Contract number: TIP3-CT Project start and end date: Duration 48 months Document number: Deliverable D4.3.2 Abbreviation SB Author/s: R. Karoumi, A. Liljencranz, KTH, F. Carlsson, LTH Date of original release: Revision date: Project co-funded by the European Commission within the Sixth Framework Programme ( ) Dissemination Level PU Public X PP RE CO Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)

58 Sustainable Bridges SB (62) Table of Contents Summary...5 Acknowledgments Introduction General The importance of accessing actual traffic loads Weigh-in-Motion (WIM) systems WIM for pavement traffic WIM for railways Aim and scope WIM Literature review European WIM research programs Track based Weigh-in-Motion systems WILD GOTCHA Bridge based Weigh-in-Motion systems Bridge Weigh-In-Motion...13 Moses algorithm...14 SiWIM 14 Axle detection methods B-WIM algorithm for railways The algorithm General Determining the speed of the train using the phase difference between signals System calibration Locomotive identification Autocalibration of the system The Twim toolbox Experimental tests The Årstaberg bridge (case study 1) The Skidträsk bridge (case study 2) Conclusions on B-WIM Suggestion for further research Site specific characteristic load from collected data Introduction Measurements and section forces...31

59 Sustainable Bridges SB (62) Measurements Section forces Statistical modelling of loads Introduction Extreme value theory Peaks over threshold Model checking Meeting traffic Model uncertainties Illustrative example Summery Statistical evaluation of the dynamic amplification factor Introduction Analytic model Parametric study Velocity Axle load Bending stiffness First natural frequency Damping Simulations Results and conclusions Bibliography...61

60 Sustainable Bridges SB (62) Summary This background document describes a method for the assessment of actual traffic loads on railway bridges. Furthermore, a method is described on how measured axle loads data can be used as an input to develop a site specific characteristic load. The document also includes a theoretical study on probabilistic dynamic amplification factors. The document describes: - the Bridge Weigh-in-Motion (B-WIM) method for calculating accurate static axle loads from collected data, - methods for determining the train speed from collected data, - method for determining the bridge influence line from collected data, - method for B-WIM auto calibration, - method for developing a site specific characteristic load from collected data, - method for statistical evaluation of the dynamic amplification factors. For the assessment of actual traffic loads, two railway bridges are instrumented and results are presented to highlights the efficiency of the developed algorithms and the effectiveness of this type of instrumentation. Key words: bridge, railway, train, weigh-in-motion, WIM, influence line, calibration, speed measurement, monitoring, characteristic load, axle load, dynamic amplification factors, probabilistic methods.

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62 Sustainable Bridges SB (62) Acknowledgments The present document has been prepared, within the work package WP4 of the Sustainable Bridges project, by the Swedish contractors Royal Institute of Technology (KTH) and Lund University (LTH). The following individuals, from the above listed organisations, have contributed to writing this document: Axel Liljencrantz (KTH, Chapter 1-3), Raid Karoumi (KTH, main editor) and Fredrik Carlsson (LTH, Chapter 4-5). Furthermore, the comments and suggestions of the internal reviewers Eugen Bruehwiler and Andrin Herwig from Swiss Federal Institute of Technology (EPFL) are very much appreciated.

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64 Sustainable Bridges SB (62) 1 Introduction 1.1 General This document is as a background document which presents the research work conducted by KTH and LTH within the WP4 load group. Based on the outcome from WP1 questionnaires which have been distributed to European Railway Authorities as well as on discussions within the WP4 load group, the following research topics were identified: - Summary of Several European Assessment Codes, - Dynamic Railway Traffic Effects on Bridge Elements, - Assessment of actual traffic loads using Bridge Weigh-In-Motion (B-WIM). This research work, i.e. results from the above projects, will be will summarise in Chapter 5 of WP4 s main deliverable Guideline for Load and Resistance Assessment of Existing European Railway Bridges. It is believed that the work in the above research topics will lead to increased knowledge on railway traffic loads and to better understanding of the dynamics of existing railway bridges. This will result in large savings when existing railway bridges are to be upgraded to carry trains with higher speeds and heavier weights. A lot of effort is spent on research on dynamic effects and on developing a method for the assessment of actual traffic loads as it is believed that an accurate evaluation of these effects will bring more understanding of the underlying phenomenon and thus cost savings exceeding 25%. The work is distributed between the following partners: EPFL, KTH, LTH, COWI and DB according to the table below. Activity name Responsible Contributor Reviewer Summary of Several European Assessment Codes Dynamic Railway Traffic Effects on Bridge Elements Assessment of actual traffic loads using Bridge Weigh-In-Motion (B-WIM) & statistical evaluation of dynamic amplification factors KTH EPFL, DB, COWI All EPFL KTH KTH LTH EPFL As can be seen from the above table, the project presented in this document is lead by KTH. KTH is responsible for chapter 1-3, LTH is responsible for chapter 4 and 5 of this document and EPFL is responsible for reviewing the work. The project started in April 2004 and will continue until May The main aim of the first part of this work is to develop, test and improve the accuracy of existing algorithms for assessment of actual static axel load. Consequently, a large amount of measured data/strains will be collected within this project. The second part of this work aims at studying probabilistic methods for the assessment of existing railway bridges. The work in this project will consist of the following: - Description of how data on measured axle loads can be used as an input to develop a site specific characteristic load.

65 Sustainable Bridges SB (62) - Identification of the requirements for instrumentation and data acquisition in order to provide satisfactory data for the analysis of loads. - Description of the B-WIM method for calculating accurate static axle loads etc. from collected data. - Describe methods for determining the train speed from collected data. - Describe methods for determining the bridge influence line. - Describe methods for B-WIM auto calibration. - Describe methods of locomotive identification. - Give two case studies. - Give conclusions and recommendations. - Give references. The work presented and reported in chapter 3 was carried out by Axel Liljencrantz at KTH (see Liljencrantz (2007)). The work presented and reported in chapter 4 and 5 was carried out by Fredrik Carlsson at LTH. 1.2 The importance of accessing actual traffic loads Until recently, most of the research in the area of bridge design has concentrated on the study of the strength of materials and relatively few studies have been performed on assessing actual traffic loads and their effects on bridges. As a result, the correctness of the traffic loads, current safety factors and dynamic amplification factors used today by bridge engineers for design and assessment of bridges can be questioned (James, 2003). The DIVINE project concluded that significant cost reductions are possible in infrastructure maintenance by changing the way the current road and railrod infrastructure is used. Within the bridge engineering community, there is today a considerable interest in the problem of measuring actual traffic loads and their dynamic effects on bridges. In Sweden, several bridges have recently been instrumented by the authors, where strain transducers were placed on the soffit or embedded in the bridge deck. This relatively inexpensive instrumentation makes it possible to: - Determine vehicle characteristics such as speed, axle distances, and static axle loads. This is usually referred to as Bridge Weigh-In-Motion (B-WIM) system, as such an installation converts the bridge into a scale that weighs traffic while moving over the bridge (Quilligan et al., 2002; Quilligan, 2003). - Measure the true dynamic response. The dynamic amplification factors can then be determined using simulations based on measured speeds, static axle loads and distances. 1.3 Weigh-in-Motion (WIM) systems The idea of using B-WIM techniques for performing measurements on railway bridges is relatively new. But WIM techniques have been in use for several decades when measuring pavement traffic and most of the techniques can be transferred to apply to railways in a straightforward way. Therefore, B-WIM for railways has a rich history of pavement based B- WIM research to draw from.

66 Sustainable Bridges SB (62) WIM for pavement traffic Traditionally, traffic monitoring of heavy vehicles was performed by manually counting vehicles and by utilizing static weigh stations. Using this method in a way that produces reasonably unbiased, accurate and statistically relevant data is both expensive and hard. For this reason, different types of semi-automatic or completely automatic weigh-in-motion (WIM) has been of great interest. WIM is the process of measuring the axle load of vehicles in motion. Early WIM methods utilized scales or pressure sensors embedded into the road pavement. Unless the measured vehicles travel at low speed, this type of WIM has proved to be too inaccurate to provide results that are usable for most situations. There has been great interest in increasing the accuracy of WIM methods, and to make it possible to perform WIM on vehicles travelling at full speed. Such a system has many potential benefits, including: - Law enforcement purposes. Studies have shown that approximately 20% of the pavement maintainable costs in the Netherlands are due to overloaded trucks. (Henny, 1998) - Improved road safety. As overweighed trucks have decreased operational performance, they can be a safety hazard. - Improved understanding of pavement damage (Caprez, 1998). There are several problems with the early WIM systems that make them unsuitable for high speed use. These are mostly centered around dynamic effects. A vehicle moving at normal speed has a significant dynamic behavior caused by large number of components, mostly in the vehicle suspension. The road itself is also susceptible to dynamic effects. This situation is made worse by the fact that pavement sensors induce additional dynamic effects, both because they make the road surface less smooth, and because drivers, especially those in overweight vehicles, tend to avoid them. Many improvements to surface WIM systems have been devised. One such method is placing a very large arrays of sensors, spaced at distances designed to maximize the frequency information in the result, leading to a better estimate of vehicle weight. This still has the drawback that the sensors themselves induce more dynamic behavior, making the weighing process more difficult. Another method is to not place the sensors in the pavement, but in the ground below the sensors (Raab, 2005). This has the advantage of not introducing any additional dynamic effects on the vehicle, and also means that measurements are performed over a slightly longer period of time, as the pressure of an axle on the road somewhat is spread out sideways. This second method solves many of the classical pavement WIM problems, but the effects on the weight distribution from temperature changes causes new complications, and it may prove impossible to retrofit an existing road with such sensors WIM for railways The previous discussions on WIM has been centered on WIM for regular pavement traffic. But many of the reasons why WIM is desirable for pavement traffic is also true for railway traffic. Because railways do not have pavements, the pavement-based WIM is not suitable for railway purposes. B-WIM, however, has no such problems. There are however several important differences between B-WIM on railways and B-WIM for regular road traffic. - Trains are much longer, and have many more axles than a road vehicle. This means that the acceleration of the train sometimes needs to be taken into account. - Trains run on tracks. This means that the problems associated with differences in sensor sensitivity based on where in the lane a vehicle is driving do not exist. This can be a large source of inaccuracy in road WIM (Quiligan, 2003).

67 Sustainable Bridges SB (62) - There are no problems with identifying separate trains, since two trains never drive so closely to each other as to be confused with a single entity. - There are only a small number of locomotive types, and electric locomotives usually do not vary in weight, which opens up the potential for autocalibration. 1.4 Aim and scope The main aim is: - to further develop existing B-WIM method for railway traffic loads assessment - improve accuracy for calculated axle loads, axle distances and speeds - present a method for development of site specific characteristic loads - present a method for statistical evaluation of dynamic amplification factors. The scope is: The instrumented concrete railway bridge at Årstaberg in Stockholm and the composite railway bridge near Skidträskån in Norrland will be used for this study and testing. Due to the distribution effect of ballast, the emphasis will be on obtaining accurate static bogie weight rather than individual axle weights.

68 Sustainable Bridges SB (62) 2 WIM Literature review More comprehensive literature review on WIM can be found in Liljencrantz (2007) and Quilligan (2003). 2.1 European WIM research programs Wave (Weighing-in-motion ox Axles and Vehicles for Europe) was a research and development project of the fourth Framework programme (Transport) to further the knowledge on various types of WIM in europe. The two and a half year project ended in The project resulted in new theories, models, algorithms and procedures, as well as several field tests to evaluate these developments. Possibly the most significant result of WAVE was the development of B-WIM methods used commercially by the Slovenian ZAG corporation. 2.2 Track based Weigh-in-Motion systems WILD The WILD (Wheel Impact Load Detector) system is a track-based wheel defect detection system designed for railways using rail-mounted strain gauges. WILD can be used to: Check for wheel impacts Perform Weigh-in-Motion Test rail stress Check for skewed tracks Measure ambient conditions, like temperature, wind direction, etc. As can be seen, the WILD system has many potential uses, but while it is useful for detecting wheel- and track defects, it is generally not accurate enough for WIM purposes. A more detailed analysis of the WILD system can be found in James (2003) and at GOTCHA Graaf et. Al. (2005) have developed a system for railway WIM based on glass fibre sensors that measure the vertical deflection of the rails themselves. This system, known as GOT- CHA, has been used to instrument several train tracks in the Netherlands. The accuracy of GOTCHA seems to be higher than the accuracy for the WILD system, a test run using 600 passes of a single electrical locomotive had a standard deviation of 1.16% on the locomotive weight. GOTCHA has been equipped with an automatic calibration system. This system uses locomotives for calibration, as well as pattern recognition to detect empty passenger cars for calibration. GOTCHA has also been used to detect wheel defects. Further information about GOTCHA can be found at Bridge based Weigh-in-Motion systems Bridge Weigh-In-Motion Bridge Weigh-In-Motion (B-WIM) is a type of WIM that utilizes a bridge to perform the measurements. This can be compared to the use of sensors embedded further down into the track described in the previously. This method has several advantages:

69 Sustainable Bridges SB (62) - The main problem in WIM that can be lessened in B-WIM is that of dynamic effects. As described above, WIM systems are notoriously sensitive to dynamic effects because the measurements are performed over a very short period of time. A B-WIM configuration usually is constructed to measure a vehicle over at least one bridge span, which is enough to average out dynamic effects for nearly any type of vehicle. - Instrumenting a bridge also allows you to collect data on the bridge itself. Such measurements can provide valuable information on bridges, which, depending on the situation, can mean decreased maintenance costs, improved safety and longer bridge lifetime. - A bridge can often be retrofitted with B-WIM sensors without halting traffic. Pavement and track based WIM requires one to halt traffic during installation, which can be prohibitively costly, especially when using multiple sensors or deeply embedded sensors. Moses algorithm All proposed B-WIM algorithms rely on variations of an observation know as Moses algorithm (Moses, 1979), which is the observation that a load moving over a structure such as a bridge will stress a sensor placed on the bridge in proportion to the product of the value of the influence line at the loads momentary position and the axle load magnitude. This implies that if the locations of a vehicles axles, and the sensors influence line of the bridge is known, the axle load can be readily estimated. Because of dynamic effects, these estimates will vary with each sample, but because a B-WIM system allows one to perform many measurements over a relatively long period of time, these dynamic effects can be minimized. The system used by (Moses, 1979) consisted of a button box, tape switches, strain gauges and an instrumented van. It produced results with standard errors of less than 10%. Further improvements to the system reduced this error to roughly 6%, but the algorithm proved unsuccessful at detecting tandem axles. CULWAY During the 1980 s, a large amount of B-WIM related work was performed in Australia. The AXWAY and CULWAY systems did not use Moses algorithm, instead they used the assumption that the area under the influence line is proportional to the gross vehicle weight. The system was hampered by the slow computers of the time, which did not allow for real-time processing, and instead required manned operation. SiWIM Within the WAVE program (see above) a commercial B-WIM system called SiWIM was developed at ZAG in Ljubljana (Znidaric, 2005). While some early tests (Quilligan, 2003) showed many miss-matches caused by the lack of temperature correction, later studies featuring temperature compensation have been found to give very accurate results. The SiWIM program has also been extended to handle many different types of bridges, different types of influence lines and instrumentation without axle detectors. Further B-WIM improvements (Quilligan, 2003) has proposed several improvements to existing B-WIM algorithms. These include: - The use of a 2D influence line, i.e. an influence surface. This is beneficial since the influence line for many bridge types varies depending on the transverse position of the vehicle on the bridge. According to Quilligans tests, these variations are on the order of 5% for many bridges.

70 Sustainable Bridges SB (62) - An accurate method for calculating the influence line of a bridge through a small set of measured test runs. - Improved handling of multi-vehicle events. It was shown that using a 2D model gave a large increase in the robustness of the detection code. Using these techniques, Quilligan was able to attain the A(5) accuracy class for one of his trial WIM setups, which is the highest accuracy class available. Axle detection methods One of the problems WIM-algorithms face is that of axle detection. In traditional pavement- WIM systems, at least two sensors, usually in the form of pneumatic tubes, are placed on the road surface. This is of course not possible for railway traffic. However, one possible solution is to install two sensors at known distance on the rail. This method has a drawback. The installation of the sensor requires one to halt traffic. For these reasons, it has been suggested that a system for axle detection without any road surface sensors is desirable. Originally such systems where referred to as 'Free-of-Axle- Detector' (FAD), but because of initial confusion on the meaning of the name, they are now usually referred to or 'Nothing-On-Road' (NOR). For B-WIM applications, several such algorithms have been suggested, using the sensor output from the bridge to detect the individual axles of a vehicle. This is not a trivial process, since the very long measurement periods in B-WIM means that multiple axles will influence the sensor at the same time, giving a 'smeared' result, as seen in Figure 1. (Znidaric, 2005) has designed a NOR system for bridges, which uses advanced filtering techniques to give sharper peaks that result in separate axles. (Dunne, 2005) use wavelet signal analysis to achieve the same type of results. This thesis will propose a third such algorithm, based on pattern matching. All these techniques exploit the same knowledge about the system, namely that one knows roughly what the signal from a single axle should be. Performing axle detection them becomes the process of finding the distribution of axles that most closely matches the original input. Voltage /V Time / s Figure 1 Shows how multiple closely spaced axles are difficult to separate.

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72 Sustainable Bridges SB (62) 3 B-WIM algorithm for railways 3.1 The algorithm General B-WIM or bridge weigh-in-motion is the process of converting an instrumented bridge into a scale for weighing passing vehicles. This section describes the implemented railway B-WIM algorithm which is partly based on previous research by Quilligan (2003). The B-WIM algorithm, which has been implemented in the MATLAB language, produces the following results: - Axle distances. - Static axle loads. - The speed and acceleration of the train. - The direction of the train. - The track on which the train is crossing. As the resolution of the B-WIM algorithm depends on the bridge type and if the track is ballasted or not. For most bridges, the individual axles of a bogie can not be separated. Consequently, for such bridges the B-WIM algorithm incorrectly identifies bogies as axles. This has not been found to decrease the algorithm's efficiency. The algorithm works using the above listed values to calculate a simulated strain curve. The square difference between this curve and the actual measured load curve is then minimized. The algorithm consists of the following steps: 1. Load the calibration data, including the influence line for each sensor. 2. Calculate the speed of the train using the phase difference method. 3. Detect the number of axles and make a rough estimate of their position, speed and load. 4. Adjust the axle positions, axle load and the speed and acceleration of the train to minimize the difference between the calculated and the actual strain curve A thorough description of the important steps in the algorithm is available in Liljencrantz (2007) which can be downloaded from Determining the speed of the train using the phase difference between signals The B-WIM algorithm outlined in the previous chapter relies on a good initial guess of the train speed. Because this calculation needs to be performed before the actual B-WIM calculation, it must not depend on knowing anything about axle positions etc. One way of doing this is to identify a peak on the strain curve on two sensors placed a few meters away from each other, and measure the time difference between the two peaks. This time is the time it takes for the train to travel the distance between the two sensors, from which the speed can be easily calculated. Determining the speed of a train using the method described above relies on identifying a peak which represents the same axle on both sensor U1 and sensor U4. Though this method provides a reasonable first guess it is difficult to accurately computerize the operation of identifying peaks, since noise may shift the maximum strain measured away from the actual peak. A simpler and much more accurate method consists of finding

73 Sustainable Bridges SB (62) the phase difference between the signal for the two sensors which minimize the difference between the two signals. This can be expressed mathematically as trying to find the value p which maximizes the following equation: S S N p 1, n 4, n+ p n= 1 N p where S a,b is the strain recorded by sensor a at time step b and N is the number of samples. Figure 2 shows how the difference between the signals varies when a phase difference is introduced. Figure 2 shows the result of calculating the above equation for varying p. The highest peak is clearly identifiable, and the p for which it occurs is inversely proportional to the train speed. This method is fast, robust and accurate; furthermore, it does not require any knowledge about the train passing by. The only additional information beside the strain curves which needs to be supplied is a constant which should theoretically be the distance between the sensors U1 and U4. In practice the influence line for sensors which are not placed at the centre of the bridge will be asymmetrical, which results in a systematic error. Because of this, a calibration run using a train travelling at a known speed is recommended for maximum precision System calibration System calibration can be performed using locomotives from random crossing traffic without requiring user interference. The true speed of the train as well as the mass of at least one wagon or locomotive needs to be known to complete the calibration process. It is usually relatively easy to attain the mass of the locomotives in a train set, so this should not present a problem. If the speed of the calibration train is not known, it can be approximated using the phase difference and the distance between the sensors, but this will usually lead to large systematic errors (roughly 30%) due to the fact that the influence line of the bridge at the two sensor positions will usually not be symmetrical and completely centered above the sensor. The calibaration process consists of the following steps:

74 Sustainable Bridges SB (62) 1. Make an initial guess on the appearance of the influence line. Several guesses can be made using different functions to generate the influence line. 2. Perform a regular axle detection using the guessed influence line. 3. Find the influence line that minimizes the least squares difference between the actual strain curve and the strain curve generated using the train data. 4. Calculate the proportionality constants between static axle load and strain sensor voltage, c j. For this step, it is obviously necessary to know the axle loads of the locomotive. The algorithm will fail if none of the influence lines chosen in the first step resemble the actual influence line. A Gauss bell shaped influence line has proven to work very well. The last step of the calibration deserves some elaboration. Moses algorithm was originally used to calculate the axle weight given an influence line. But Quilligan (2003) used the algorithm in reverse to calculate the influence line given a known set of axle weights and a strain curve. If all axles of the system are separated, this is a trivial problem. In the real world bridges spans are longer than the axle distance of a wagon, meaningthat it can not be expected that axles are separated from each other in the strain curve. The problem of calculating the influence line i of a bridge given a strain curve recording r of multiple axles traversing the bridge at known times with known speeds using Moses algorithm can be expressed as a sparse linear equation of T variables, where T is the number of samples in the strain curve. This is done by constructing a matrix A, which is of size TxL, where L is the number of elements in the desired influence line. The element on the n:th row and the m:th column of A corresponds to the strain at time step n generated by any axle at point m on the influence line. This means that A is a sparse matrix consisting of one diagonal line for each axle of the train. If A is multiplied by a vector representing an influence line i, this will result in a strain curve. Since we want this strain curve to approximate the measured strain curve r, we want to find an influence line i, which will satisfy the relationship Ai=r. Since we can determine the number of samples in our generated influence line, it might seem like a good idea to use L=T. This is not the case, since it will usually result in a singular A. Instead one should choose L much smaller than T and use the least squares minimization of the above system. This will result in an accurate estimate of i Locomotive identification The B-WIM algorithm produces estimates of the static axle load and axle distances of all locomotives and wagons passing over the bridge. Given a database of locomotives, this information can be used to identify the locomotive type. If we assume that the errors in mass and speed calculations are independent, and given the standard deviation of the speed and mass calculations (Which will be presented later in this article), it is possible to calculate the probability that a given locomotive would give rise to the given output. Given calculated axle distance d c and mass m c, known locomotive data from the database d l and m l, as well as the standard deviation of the calculation σ d and σ m, the probability of the given train giving rise to the calculated output is p(d c -d l, σ d)p(m c -m l, σ m), where p(x, σ)=e -(x/σ) Autocalibration of the system An algorithm for automatically calibrating the B-WIM system has been developed. After initially calibrating the system using the method described in the above section, each passing train is identified using the method described in section If a locomotive is identified with a high confidence, the new train can be used for autocalibration. The autocalibration procedure takes the old calibration data and merges it with the new data, in order to produce a

75 Sustainable Bridges SB (62) calibration curve which is the running average of multiple train passes, which should further minimize errors. 3.2 The Twim toolbox This section describes Twim, a toolbox designed to make it easy to perform B-WIM calculations. The toolbox contains a small number of functions written in the MATLAB programming language, designed to perform B-WIM calculations on any suitably instrumented bridge. Twim is designed to provide users who are vaguely familiar with MATLAB with a powerful set of WIM-tools that allows them to perform advanced calculations without special training. To that end, the toolbox has a small number of functions that perform well defined tasks. These tasks include calibration, WIM detection, result visualization and locomotive identification. The case studies described in this chapter have all been performed using the Twim toolkit. A thorough description of Twim is available in Liljencrantz (2007) which can be downloaded from Experimental tests The Årstaberg bridge (case study 1) At the new Årstaberg railway station, three railway bridges have been built during the year The bridge carrying two ballasted railway tracks for traffic heading towards the city of Stockholm was instrumented and opened for traffic in July 2003 (Figure 3). The bridge has a span of 14.4 m, is made of reinforced self compacting concrete and is of the integral type, i.e. the construction is continuous as it is constructed without movement joints at the junction of the deck with abutments. The deck supporting the tracks is 0.8 m to 1.3 m thick and the sidewalls are 0.9 m thick. The sidewalls are also continuously connected to a 1.0 m thick bottom slab. For the verification of the measurements and as a basis for analysis and numerical simulations, FE-models of the bridge have been developed. Some Simulations of the dynamic response of the passing train are made using a program developed by the second author and described in Karoumi (1998). The results of these simulations are not presented here due to space limitation however they can be found in Karoumi et al. (2004), and future reports. Description of the instrumentation and data acquisition system at the Årstaberg bridge Four special resistance strain transducers (Figure 4), produced at The Royal Institute of Technology (KTH) in Stockholm, were embedded in the concrete section of the deck supporting the two railway tracks. The total length of each transducer is 300 mm. Between the two anchor plates, 50 mm in diameter, there is a strain element made of a steel tube, 10 mm in diameter, to which four strain gauges are attached. The strain gauges were connected as a full Wheatstone bridge. The cables are routed inside the steel tube, which was later encapsulated with several coatings for protection and to ensure that the deformations are only introduced to the anchor plates. The data acquisition system MGCplus from Hottinger Baldwin Messtechnik (HBM) was chosen for this instrumentation, connecting each strain transducer to a ML55B amplifier. As the main interest is to measure/calculate actual traffic loads and load effects on the high speed line, three of the transducers were placed under that track (Figure 5). Only one transducer, U3, was placed under the second track which is for commuter trains that are of less interest in this project. Since multiple sensors are located at the centre of the bridge, but be-

76 Sustainable Bridges SB (62) neath the different tracks, it can be easily determined in which of the two lanes a train is running. In the case of multiple trains passing the bridge simultaneously, a low resolution splitting of the signal into one signal for each track can also be accomplished. Figure 3 shows the instrumented integral bridge during construction at Årstaberg. Figure 4 shows the resistance strain transducer produced at (KTH) in Stockholm.

77 Sustainable Bridges SB (62) Figure 5 shows the location of sensors U1-U4, embedded in the bridge deck. B-WIM results from the Årstaberg bridge The axle detection algorithm above successfully detected every axle of every train passing that was recorded during the course of half a day. The trains that are used for calibration purposes are of course excluded from the analysis. 140 Calculated speed / km/h Phase difference Influence line width Real speed / km/h Figure 6 shows the measured "real" speed of thirteen commuter train sets and five regular train sets along the x-axis and the B-WIM calculated speed on the y-axis. Two different methods for calculating the speed were used, these are shown separately.

78 Sustainable Bridges SB (62) There are, as described above, several means of calculating the speed of the train from the collected data. Figure 6 shows how the trains speed, calculated using the two different algorithms described above, varies with its speed as measured by the speed laser pistol (Considered here to be the real speed). The average difference between calculated and measured speed is very small and varies depending on which trains are used for calibration. This is not surprising, since the calibration process should remove any systematic error. The standard deviation of the difference between calculated and measured speed is about 5% for both calculation methods. It should be noted that the speed calculations are co-variant which implies that a significant portion of the error comes from the laser pistol. Such errors originate from various sources, including train acceleration (speed measurements where done about 100 meters before the bridge), the pistol not being completely parallel to the train tracks at the time of measuring and other sources of error in the speed pistol. Calculated weight / Tonnes Relative gross weight error Real weight / Tonnes Speed / km/h Figure 7 shows the variation of calculated gross weight estimate with real gross weight and the variation of gross weight estimate error with speed for 13 locomotives. Figure 7 shows how the locomotives calculated gross weight varies with its real gross weight. The average error is small and varies between different runs. This is not surprising since the calibration process should remove any systematic errors. The standard deviation of the error in estimated gross weight is approximately 2%. The error in estimated bogie load is approximately 2.5%. Figure 7 also shows how the error in the locomotives calculated gross weight varies with the speed of the locomotive. There is no obvious tendency towards speed dependency. It should be noted that the variation in speed between the different locomotives is small, such tendencies might well be noticeable at higher or lower speeds. The speed values used to produce Figure 7 is the calculated speed, not the speed as measured by the laser pistol. This is because the laser pistol was not used on all of the trains used to produce the figure. It should also be noted that several of the trains used to produce Figure 7 had more than one locomotive. It is interesting to note that there appears to be a slight co-variation in the error of multiple locomotives in the same train.

79 Sustainable Bridges SB (62) Voltage /V Voltage /V U Time / s U Time / s Voltage /V Voltage /V U Time / s U Time / s Figure 8 shows the actual strain curve (in blue) and the simulated one (in red). The green crosses represent detected axles. Voltage /V Voltage /V U Time / s U Time / s Figure 9 shows the actual strain curve (in blue) and the simulated one (in red) when using a bell shaped influence line on sensor one and four. The green crosses represent detected axles. Figure 8 and Figure 9 show how closely the simulated strain curve matches the actual strain curve. Figure 8 uses the calculated influence line of the bridge, while Figure 9 uses a simple bell-shaped influence line. After system calibration, the B-WIM system had very small systematic errors in speed and weight measurements. The standard deviation of the error in speed using the two calculation methods is about 5%. The standard deviation in locomotive gross weight error is about 2% and the standard deviation of the error in bogie weight is about 2.5%.

80 Sustainable Bridges SB (62) The Skidträsk bridge (case study 2) The Skidträsk Bridge in Norrland (Northern part of Sweden) is a 36 m long simply supported composite bridge (Figure 10) carrying one ballasted track. The track is subjected to normal maintenance but the quality of track was not verified. For more information, see the Licentiate thesis by Axel Liljencrantz (Liljencrantz, 2007). Figure 10 shows the Skidträsk bridge. Description of the instrumentation and data acquisition system at the Skidträsk bridge The Skidträsk bridge is instrumented (at mid-span and one quarter point) with 4 strain gauges mounted on the two main steel beams to monitor longitudinal strains, 3 accelerometers on the two main steel beams to monitor vertical deck accelerations, 2 B-WIM strain transducers mounted on the soffit of the track slab to monitor transverse strain and one air temperature sensor. The data acquisition system is connected to a portable computer at site. This computer is connected to the telephone network using the Swedish wireless MobiSIR system which is a GSM based communication system owned by Banverket (the authority responsible for rail traffic in Sweden). All data logging, data processing and data storage is made on this computer at site and only interesting data and result files are transferred to KTH. To connect, remotely manage and for operational control of these site computers and of the data acquisition systems, the software pcanywhere from Symantec is used. B-WIM results from the Skidträsk bridge The Skidträsk bridge has been continually monitored for a period of several days, and all train passages have been stored. During this time 113 train passages were recorded. Some

81 Sustainable Bridges SB (62) of these were false positives, broken recordings or discarded for other reasons, leaving 85 passages on which the B-WIM algorithm was used. The three trains which resulted in the highest detected bogie loads recorded during these passages had bogie loads of 57, 56 and 54 tonnes. The highest train speeds were 161, 154 and 147 km/h. The highest vertical bridge deck accelerations were 9.9, 9.6 and 9.2 m/s 2. Figure 11 and Figure 12 show the train that had the highest detected vertical bridge deck acceleration. This train is the Swedish ``Steel arrow'' iron ore train pulled by three RC4 engines Acceleration / m/s Time / s Figure 11 shows a plot of the highest vertical bridge deck acceleration measured at the midspan of the eastern steel beam on the Skidträsk bridge Strain /us Time / s Figure 12 shows the strain curve for the train giving the maximum vertical bridge deck acceleration on the Skidträsk bridge (Same as in Figure 11). The blue line is the measured strain, the red line is calculated strain and the green crosses are detected bogie positions.

82 Sustainable Bridges SB (62) Figure 13 and Figure 14 show that there is no obvious correlation between maximum bogie load and vertical bridge deck acceleration as well as between speed and vertical bridge deck acceleration Figure 13 No obvious correlation between the maximum bogie load and maximum vertical bridge deck acceleration measured at the mid-span of the eastern steel beam during 85 train passages at the Skidträsk bridge Correlation factor = Acceleration / m/s Train speed / km/h Figure 14 No obvious correlation between train speed and maximum vertical bridge deck acceleration measured at the mid-span of the eastern steel beam during 85 train passages at the Skidträsk bridge.

83 Sustainable Bridges SB (62) 3.4 Conclusions on B-WIM The phase differences of the signals can be used to quickly calculate the speed of a passing train. Using the width of the influence line was found to give a slightly more accurate results. The bridge instrumentation on the Årstaberg bridge and the Skidträs kridge are not sensitive enough to separate the axles of a single bogie. This will probably be the case for most railway bridges used for B-WIM instrumentation. This might cause a problem when wagons using different bogie distance pass over the bridge. In practice, it was found that compensating for this actually decreased the precision of the system, though further research into this might increase the systems precision. It is unknown how large part of the speed calculation error comes from the direct speed measurements using the speed laser pistol. It is noteworthy that the speed calculations performed very well for trains on the commuter track of the Årstaberg bridge, even though this track only had one sensor underneath it. The information from the sensors placed under the neighbouring high speed track provided enough information to accurately complete the phase calculations described in section The locomotive identification algorithm that was used on the recorded train passages from the Årstaberg bridge correctly identified all locomotives with a high degree of certainty. This was not a very difficult task since only 3 types of locomotives where measured, with significant differences in both mass and axle distance. The results from the Skidträsk bridge indicate that for the registered speed interval, the train mass is more critical than the train speed for the maximum vertical acceleration of the bridge deck. It should be remembered that cargo trains with high load usually travel at slower speeds than lightly loaded passenger trains. In conclusion, the B-WIM system described above is accurate enough to correctly weigh the bogies of the train sets and identify the locomotives that passed over the Årstaberg and Skidträsk bridges during measurements Suggestion for further research Future work should focus on evaluating dynamic effects, implementing the system in a realtime environment as well as studying accelerating trains in order to make the axle detection algorithm more robust. Future topics for research include: - Investigate if the accuracy of the system can be increased by combining sensors measuring local behaviour and sensors measuring global behaviour, in order to better compensate for dynamic effects. - Investigate how much the accuracy of the system decreases when measuring wagons with only two axles, and if they can be separated from regular bogies. - Investigate long term changes in the dynamic properties of the instrumented bridges.

84 Sustainable Bridges SB (62) - Investigate how the properties of the bridge change between seasons. Specifically, how does the damping properties of the bridge change when the ballast is frozen. - Investigate how well the autocalibration system handles variations in sensor sensitivity due to temperature changes. - Investigate what types of bridges can be used to give accurate B-WIM results.

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86 Sustainable Bridges SB (62) 4 Site specific characteristic load from collected data 4.1 Introduction This chapter describes a method by which one is able to determine site specific characteristic train loads from measurements. The methods described should be seen as guidelines and any number or value of say characteristic value or reliability indices should be seen as examples. The actual values to be used should be approved by the relevant authority. 4.2 Measurements and section forces To be able to perform a reliability analysis statistical information about all the basic variables in the limit state function must be available. From WIM measurements statistic information about train characteristics are determined. The most important characteristics to determine static section forces in train bridges are the axle loads and axle positions. From these characteristics and use of different types of influence lines it is possible to get the desired section forces. This section give a presentation of how to determine statistical distribution functions for section forces in bridges based on WIM measurements Measurements WIM measurement systems have two advantages. One, the measured trains do not have to stop to being weighed and two, the measurements can go on for a long time. The train data are collected continuously at the measuring station by a logger and prepared by the system so the measured data can be presented properly. The outputs from a measurement are e.g.: Date and time for passing Lane of passing Velocity Number of axles Position of each axle Weight of each axle The two most important data when to determine static section forces in rail way bridges are the position of the axles and their weight. With such data it is possible to determine static section forces in bridges very accurately. WIM methods are described previous in this document and will therefore not be described further here. How to use the measured WIM data to develop section forces will be described in the following section Section forces WIM measurements give information about the location and the weight of each axle of the measured train. WIM measurements of real trains are not available to the author and therefore to explain the methodology train load model A6 in Eurocode 1 (2002) will be used. A6 consists of two power coaches, two end coaches and 23 intermediate coaches. The total length of the train is approximately 380 m and each axle load F is 180 kn. Figure 15 is an illustration of train load model A6, for further information see Eurocode 1 (2002).

87 Sustainable Bridges SB (62) F d D d D d Figure 15 Illustration of type train A6 Eurocode 1 (2002). To be able to determine section forces in different types of bridges and bridge elements, influence lines has to be utilized. To illustrate how the section forces are determined the influence line for the mid span moment in a simply supported bridge is used, see Figure 16. 0,25 0,20 0,15 MAB 0,10 0,05 0,00 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Position of the concentrated load, x Figure 16 Influence line for the mid span moment in a simply supported beam. To determine the maximum moment by type train A6 the train is stepped over the influence line and in each step the mid span moment is determined, see Figure 17. In this case the span of the bridge is 10 m, the span is then shorter than the distance between two bogies, D see Figure 15 and that is the reason why the static moment under some time interval is zero. Moment [knm] Time [s] Figure 17 Mid span moment generated by train type A6, Eurocode (2002) The maximum load effect in the bridge is generated by one of the last coaches of the train. In this case where the distances and the axle loads are deterministic one do not have to step the train over the influence line to determine the maximum load effect. As mentioned in the beginning of this section real WIM measurements of train loads were not available, instead a simulation is preformed to simulate the out put from a real measurement. In this case the axle load is assumed normal distributed with a mean value of 180 kn and a standard deviation of 18 kn. The locations of the axles are also assumed normal distributed, the mean value is set to the nominal according to train type A6 and the standard deviation is set to 0,25 m. Figure 18 shows an example of a simulation.

88 Sustainable Bridges SB (62) Moment [knm] Time [s] Figure 18 Mid span moment in a bridge with a span of 10 m generated by a simulated train. As can be seen in Figure 18 the maximum moment in the mid span of the beam arise when one of the first coaches enter the beam. To determine the maximum load effect from measured trains it is necessary to step all the measured trains over the influence line and determine for each train the wanted maximum load effect. In this example 200 simulated trains had been stepped over the influence line and Figure 19 shows the empirical distribution for the mid span moment together with a fitted normal distribution. 1 0,9 0,8 0,7 FX 0,6 0,5 0,4 Fitted dist. Events 0,3 0,2 0, Moment [knm] Figure 19 Empirical and fitted distributions for the mid span moment. The distribution in Figure 19 describes the natural distribution for the moment at this specific lane. One must assume that the traffic loads on the bridge and even their effects are time invariant, i.e. there is no systematic change in the type of railway traffic on the bridge or of the traffic load effects. Examples of divergence from this assumption are time variant traffic loads such as an increase in allowable axle load or a change in the type of traffic from say predominantly freight to passenger or a systematic increase in the intensity of the traffic. The above assumption that the traffic loads are time invariant also places a strict criterion upon the measurements of traffic loads. The assumption implies that the measurements should be carried out so that they well represent the typical traffic situation on the bridge and are able to capture significant events such as the passing of particularly heavy traffic. In the case of railways this may mean that measurements should be conducted throughout the entire day as freight traffic has a tendency to run at nights and measurements limited to office hours would potentially miss these events. Any possible seasonal changes in the railway traffic should also be represented in the measurements. The distribution shown in Figure 19 represents the natural variation of the load effect in a simply supported bridge with a span of 10 m. Such types of distributions can be used in reliability analyses in the service limit state, but in the ultimate limit state it is the extreme value distributions which are of interest. To get the extreme value distributions for section forces some kind of extrapolation methods have to be utilized since it is not possible of economical

89 Sustainable Bridges SB (62) and time reasons to measure train load under such a long time. Methods to get the extreme value distribution are accounted for in section Statistical modelling of loads Introduction Extreme values are an important concept when assessing structural reliability in the ultimate limit state. In this section, focus is on the maximum values because it is the loads that are of interest in this study. The nature of variable loads are that they fluctuate in time, and it is maximum values which are of interest. To be able to perform a reliability based assessment of a structure, all the variables in the limit state function must be described by theirs statistical distribution. Variable loads are as earlier mentioned time dependent and are therefore best described by random processes. Such processes are not easy to handle in reliability analyses. An often used way to circumvent the difficulties is to make the process stationery. This can be done if the load is described as its maximum value during a specified period, reference period. The reference period is generally set to one year, which has the advantage that e.g. climate related loads in different reference periods can be considered uncorrelated. Another important concept in structural design is the safety index, β. β is directly dependent on the length of the reference period. In this subsection a short introduction of extreme values and the Peaks Over Thresholds (POT) method will be given. It is always necessary to check the validity of the chosen statistic model, the last subsection give a presentation of some useful goodness of fit test methods Extreme value theory The classical extreme value theory descends from a distribution, { X, X } M n such that M n = max X n (4.1) where X 1, X 2... X n are independent identically distributed random variables from a distribution X. X is called the parent distribution. If X is the distribution for variable load, e.g. the train load in a bridge, the maximum distribution M n is related to the time period and the intensity of trains that are trafficking the bridge. As an example, let X N(0,1) and M n = max{ X n }, Figure 20 show the probability density functions of M 10, M 100, M 1000 and M together with the parent distribution ,6 1,4 n=1000 n= ,2 1 n=100 fx(x) n 0,8 0,6 0,4 N(0,1) n=10 0, x

90 Sustainable Bridges SB (62) Figure 20 Maximum of standard normal distributed independent random variables. Figure 20 shows that the mean value increases and the standard deviation decreases when n increases. It can be shown, see Coles (2001) that the distribution of M n can be determined from the parent distribution according to: n M ( x) = [ FX ( x (4.2) F n )] Equation 4.2 is the exact probability function for maxima, but is not always useful in practice because it doesn t follow any standard distribution and it is often very difficult to use analytically. Two exceptions are the cases when F X is exponential or normal distributed. In both cases F M becomes Gumbel distributed with cumulative distribution function given as x b a e F ( x) = e (4.3) X F X is exponen- where a and b are parameters of the Gumbel distribution. For the case that tial distributed with cumulative distribution function F X x m ( x) = 1 e (4.4) where m is the parameter in the exponential distribution. Maximum of n independent identically exponential distributed random variables is Gumbel distributed with parameters according to: a = m b = m ln(n) For the other case when become b = F a = X n 1 f ( b)n X (4.5) F X is normal distributed the parameters of the Gumbel distribution (4.6) where f X is the probability density function for the normal distributed random variable X. Finally, the parent distribution influences both the convergence and the variation of the extreme value distribution, e.g. an exponential distributed variable converges faster than a normal distributed variable, n 5 and n 20 respectively. It was found that equation 4.2 converge against an asymptotic distribution when n. There is a family of three types of such maximum distribution types I, II and III also called the Gumble, Fréchet and Weibull distribution respectively. The cumulative distribution functions for maximum Type I, II and III are given below: The cumulative distribution function of a Gumbel distribution, Type I is given by G X x b ( x) = exp exp x a (4.7)

91 Sustainable Bridges SB (62) The cumulative distribution function of a Fréchet distribution, Type II is given by G X GX ( x) = 0 x b ( x) = exp a k x b x > b The cumulative distribution function of a Weibull distribution, Type III is given by G X ( x ) = exp x b a G ( x ) = 0 X k x > b x b where a, b and k are the scale, location and shape parameter respectively. It is postulated in equations that the parameters a and b are > 0 and that parameter k in equations 4.6 and 4.7 is 0. The three extreme value distributions, type I, II and III described above can be compounded into one distribution called the General Extreme Value distribution, (GEV) see WAFO and Coles (2001) with cumulative distribution function given by 1 x b k FX ( x) = exp 1 k a x b F x = X ( ) exp exp a if k 0 if k = 0 (4.8) (4.9) (4.10) where a, b and k are the scale, location and shape parameter respectively. Equation 4.10 is valid for k ( x b) < a, a > 0 and k, b arbitrary. The shape parameter k is often called the Extreme Value Index (EVI), because, if k > 0 the GEV is a Weibull distribution, if k = 0 the GEV is Gumbel distributed and finally if k < 0 the GEV is Fréchet distributed. Figure 21 shows three GEV distributions with different shape parameter. 0,25 0,2 k=0,5 fx(x) 0,15 0,1 k=-0,5 k=0 0, x Figure 21 Probability distribution functions for GEV distributions with different shape parameters, with equal scale and location parameters, a = 2 and b = 7 respectively. The case when k > 0 is called Weibull tail. In this case the distribution is bounded at the right tail, i.e. it can not take values lager than b + ( a k). If k < 0, called the Fréchet tail or heavy tail, the distribution is not bounded and slowly approaches zero. The Gumbel tail, when k = 0 is as the Fréchet tail not bounded, but approaches zero faster than the Fréchet distribution. A

92 Sustainable Bridges SB (62) great advantage of using the GEV distribution is that the type of extreme value distribution, I, II or III need not be predefined when fitting data to the distribution. Another feature with the GEV distribution is that the distribution is stabile under maximum formation, i.e. if X 1, X 2... X n are independent GEV distributed random variables and M n = max{ X 1, X 2... X n }, then M n is also GEV distributed. For the case when k 0 the parameters of M are given by: n b n k n = k an = a n a = b + k k k ( 1 n ) For the case when k = 0, the parameters of M n are given by: b n a n = a = b + a ln(n) (4.11) (4.12) Finally, in codes the characteristic value of a load is often described in terms of percentile values. For variable loads the characteristic value is often defined as the 98 th percentile from its annual maximum distribution. This implies the characteristic load will be exceeded by a probability of 2 % each year. This also implies that the characteristic value of the load will be exceeded in average once every fifty year, the return period of the variable load. If the variable load is approximated by a GEV distribution the characteristic value, x k is given by: x k x = k k ( 1 ( ln( F ( x) )) ) a b + k = b a ln( ln( F X X ( x))) if k 0 if k = 0 (4.13) Peaks over threshold The Peaks Over Threshold (POT) method is used to estimate quantiles outside the range of observed data. The idea with the method is to only use the extreme tails of the distribution of the observed data. A distribution which fits the tail data well is chosen. This is done by choosing a suitable, relatively high threshold, u and only uses the events, x that exceed u in the future analysis. The differences between x and u are fitted to a standard distribution and from that distribution the extreme quantiles are estimated. To illustrate the potential of the POT method an example is shown. The example is taken from Carlsson (2006) and is valid for traffic loads on road bridges, but the methodology is the same for train loads on railway bridges. Figure 22 show the empirical distribution for the mid span moment in a simply supported bridge with a span of 30 m. The distribution is built up by WIM measured heavy vehicles in Sweden.

93 Sustainable Bridges SB (62) FX 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Moment [knm] Figure 22 Empirical distribution for the mid span moment. Figure reproduced from Carlsson (2006). The distribution shown in Figure 22 seems to be built up by a couple of different distributions. This is of course the case due to the moment arisen from different types of vehicles. This would also be the case if the measurements had been done on a railway bridge as there are different types of trains, e.g. passenger trains and freight trains on the same lane. When assessing section forces in bridges in the ultimate limit state, only the highest section forces are of interest, i.e. the upper tail of the distribution. The POT method implies that one has to choose a suitable threshold and try to fit a standard distribution to the differences between the event and the threshold. In this case the threshold is set to 2985 knm and Figure 23 shows the differences together with a fitted exponential distribution. 1 0,9 0,8 Events Fitted dist. FX 0,7 0,6 0,5 0,4 0,3 0,2 0, Moment-u [knm] Figure 23 Empirical and fitted exponential distribution for the differences between the moment and the threshold. Figure reproduced from Carlsson (2006). Figure 23 shows that the differences can be approximated with an exponential distribution. In this case the parameter m in the exponential distribution is determined to 112 knm. The total number of heavy vehicles is as earlier mentioned 31800, the fitted distribution in Figure 23 is based on the 318 largest moments which implies that the shares of vehicles, λ u that exceed the threshold is 1 %. λ u should be interpreted as the intensity of vehicles that exceed the threshold. Let us assume that the number of exceedances under a given reference period is Poisson distributed. It can be shown that the maximum of a Poisson distributed number of exceedances over a threshold u is a Gumbel distributed variable and the parameters of the distribution are given by:

94 Sustainable Bridges SB (62) a = m b = b + m ln( λ u ) (4.14) Equation 4.14 is very useful; by using this equation it is possible to determine the distribution for any section force as a function of the traffic intensity on the bridge. Of course the parameter m and the threshold u are dependent on the boundary conditions, span and the type of section force of interest. If the exceedances over the threshold can not be approximated with an exponential distribution one should try to use the Generalized Pareto Distribution (GPD) which is more flexible than the exponential distribution since it has three parameters. Information about this distribution can be found in e.g. Embrechts et. al. (1999). Maximum of a Poisson distributed number of GPD distributed exceedances is a GEV distributed variable. One should be careful when choosing a threshold and it is important to have in mind that: The chosen distribution for exceedances, exponential or GPD distribution, is a good approximation of the data. A large threshold will improve the Poisson approximation of the number of exceedances, but gives less data to estimate the parameters of the exponential or GPD distribution. The agreement of the distribution that approximate the exceedances can be checked by some tests which will be described in the next section Model checking Whenever a mathematical model is adopted from measured data it is necessary to check the validity of the model against the original data. In order to check the assumed statistical distributions against the original measured data it is common to use so-called goodness-of fit tests. Some examples of such tests are the chi-square ( 2 ), the Anderson-Darling and the Kolmogorov-Smirnov (K-S) tests. Descriptions of these tests are available in several standard text books on statistics, e.g. Johnson (1994). The disadvantage of these tests on the extreme value distributions is that they test the compliance of the data mostly towards the centre of the distributions rather than highlighting their compliance in the all important upper tail behaviour. The probability plot which will be discussed later in this sub-section is also weak in illustrating any differences between the model and the measured data in the upper tail area. A simple plot Another diagnostic tool is to use probability papers, such as the Gumbel or Normal probability papers. These involve a transformation of the data such that a plot of the data under the transformation creates a straight line on the plotting paper if the data complies with the model; see e.g. (Castillo, 1987; Schneider, 1997; Johnson, 1994). Empirical Distribution Function If we have a sample x 1... x n which are identical independent observations from an unknown distribution function F. Usually one does not know the actual distribution F and this must be estimated. This is usually done by means of the empirical distribution function, F ~,. First, by ordering the sample into ascending values such that x (1) x (2)... x (i)... x (n) Note that the use of the brackets in the index indicates the ordered sample. Also common in the ordered sample notation is the use of x i:n, denoting the i-th largest sample in sample of size n. The empirical distribution function used may be defined as

95 Sustainable Bridges SB (62) i F ~ 0.5 ( x) = for x ( i) x x( i+ 1) (4.15) n There are several estimations of the empirical distribution function to be found in literature. Another commonly used estimation is i/(n + 1). In (Schneider, 1997; Castillo, 1987) the advantages and disadvantages of the different estimations are discussed. Castillo recommends the above estimation for use in extreme value analysis; however for large samples the choice of estimation has little effect. From the sample x 1... x n it is then possible to fit an assumed distribution to this sample so that the estimated distribution function of F is given by Fˆ, this is usually done under the assumption that the sample comes from a certain distribution or family of distributions. There are then several diagnostic tools available to see if theoretical model represented by Fˆ is a good fit to F, estimated by F ~. Two such tools are the probability plot and the quantile plot, also known as the QQ plot, which are described below. The quantile plot and the probability plot essentially show the same information but use different scales. However, what appears to be a good fit on the one plot is not necessarily so on the other. Probability Plot The probability plot is used to compare the empirical cdf, F ~., with the fitted mathematical model s cdf, estimated by Fˆ, see the above subsection. The plotting positions of the ordered independent observations given by (4.16) are i 0.5, Fˆ ( n x (i) ) for i = 1, 2, K, n (4.16) The resulting plot should produce a straight line at 45 degrees if the fitted mathematical model is a good representation of the sample. The weakness of the probability plot for extreme value applications is that both F ( x (i) ~ ) and F ˆ ( x (i) ) tend to 1 as ( x (i)) increases. Thus they will tend to show agreement in the upper end of the tail although this is area is of most interest. This problem is avoided in the quantile plot discussed below. Quantile Plot The quantile plot is created by plotting the estimated quantiles against the ordered sample. The plotting points consist of: ˆ 1 i 0.5 F, x( i ) for i = 1, 2, K, n (4.17) n The inverse of the estimated distribution is used to evaluate the quantiles, where the estimated parameters are part of the estimated distribution. Figure 24 below illustrates the advantage of the quantile plot in extreme value applications over other similar plots often used. In Figure 24 (b) a histogram together with the estimated pdf s are shown these can be hard to interpret. Figure 24 (c) shows the probability plot and as mentioned previously this tends to produce agreement at the upper right tail of the distributions since both the empirical and the theoretical cdf tend to 1. Figure 24 (d) shows the

96 Sustainable Bridges SB (62) QQ-plot for the same data and as can be seen from this diagram any discrepancies in the upper tail area between the model and the data are clearly highlighted in this plot. Figure 24 Shows an example of different types of plots. (a) is a histogram of the maximum moment per train. (b) shows a histogram of the maximum normalised moment per 50 trains together with the probability density functions for two estimated distributions. (c) Shows a probability plot for the two estimated distribution functions while (d) shows a similar plot but for a quantile plot. Figure reproduced from James (2003). 4.4 Meeting traffic For bridges with two or more tracks there is a possibility of a meeting between two trains on the bridge. The number of meetings on the bridge depends on the train intensity, the velocity of the train, length of the bridge and length of the train. The number of meetings, n, between trains on the bridge within a certain reference period affects the size of the maximum section forces in the bridge. If F X (x) is the distribution function that describe the section forces generated by a meeting between two trains, the appearance of F X (x) depends on the characteristics of the two meeting trains. The distribution of the maximum section forces during a certain time period is given by equation 4.2.

97 Sustainable Bridges SB (62) For traffic loads on road bridges it is widely accepted that the numbers of meetings during the reference period is Poisson distributed. For trains that s not the case, since trains generally follows some kind of time schedule. That implied that the trains do not randomly arrive to the bridge. To determine the numbers of meetings on the actual bridge instead one has to analyze the time schedule and try to determine how many meetings that can be expected during the reference period. 4.5 Model uncertainties The model uncertainties on the load side of the failure equation take care of uncertainties in the: load calculation model load effect calculation model The model uncertainties θ are often modeled as normal- or lognormal distributed variables. If the model uncertainty is normal distributed, it has a mean value about zero and is commonly introduced into the calculation model as follows. Y = θ + f ( X1... X n) (4.18) Or if the variable is lognormal distributed, it has a mean value about one and is introduced into the calculation models as Y = θ f ( X1... X n) (4.19) where Y is the response of the structure and f ( X1... X n) is the model with the inherent basic variables that describes the load effect. The choice of the variation of the model uncertainties affects the result of the reliability analysis to a large extent, see Carlsson (2006). If the variation is set to low one could jeopardize the safety of the structure, but on the other hand if they are set to high they will totally dominate the result of the analysis. It is not an easy task to give an exact answer of how to chose the parameters to model uncertainties. To give some guide lines, the authors, the cov for model uncertainties related to load models should be in the range between The higher values should be chosen for more complexes bridge types, e.g. long bridges with many spans and the lower for short span bridges where only one or a few axles generate section forces. 4.6 Illustrative example From measurements and use of influence lines it is possible to determine the natural variation of a section force and determine its distribution functions as earlier described. In the ultimate limit states one is interested of how the maximum section forces are distributed during a period of time, the reference period. It is as earlier mentioned not of time and economical reasons possible to measure the train loads during such a long time as required to get reliable data to establish extreme value distributions for section forces. The intention with this section is to illustrate how one can use different statistical tools to determine the extreme value distributions. Again the author has not access to real measurements instead the data comes from simulations and also in this case type load A6 in Eurocode 1 (2002) has been used. In load type A6 the axle load is set to 180 kn, in the simulations the load is assumed normal distributed with a mean value of 180 kn and a cov of 15%. The distances between the axle loads is assumed deterministic and the values given in Eurocode 1 (2002) has been used trains have been simulated and for each train the maximum mid span moment in a simply supported bridge with a span of 10 m have been determined. Figure 25 show the empirical distribution and the fitted normal distribution function for the mid span moment.

98 Sustainable Bridges SB (62) 1 0,8 0,6 FX(x) 0,4 Emp. dist. Fitted dist. 0, Moment [knm] Figure 25 Fitted normal distribution and empirical distribution function for the mid span moment in a simply supported bridge with a span of 10 m. For the fitted normal distribution function the parameters, mean and standard deviation, where determined to 879,1 and 36,1 knm respectively. The simulated values seem to be well represented by a normal distribution and the quantile plot Figure 26 confines the statement. 1 0,8 Theoretical quantiles 0,6 0,4 0, ,2 0,4 0,6 0,8 1 Empirical quantiles Figure 26 Quintile plot for the ongoing example. The quantile plot shown in Figure 26 shows that the moment can be modelled by a normal distribution. The quantile plot is a visual test there are numerical tests that can be applied also. Two examples of such tests are the mean square error (MSE) and the Kolmogorovs- Smirnoff (KS) test. For the MSE test a test value close to 0 and for the KS test close to 1 represent a good fit. The test values in this case where for the MSE and the KS tests determined to 0,0012 and 0,76 respectively. In this case it seems sufficient to assume that moment in the mid span of a simply supported bridge can be modelled by a normal distribution. This normal distribution describes the natural variation of the moment and as earlier mentioned it is the extreme value distributions which are of interest. Let s say that on this specific lane the train intensity is trains per year and the question is how the maximum moment generated by the trains is distributed? Maximum of independent, equal, normal distributed variables are Gumbel distributed. The parameters of the Gumbel distribution are given by equation 4.6. For this example the parameters a and b are determined according to

99 Sustainable Bridges SB (62) b = F a = f 1 X X ( x, u, σ ) = F 1 X 1 = ( b, μ, σ ) n f X ( 1, μ, σ ) = FX ( 1, 879.1, 36.1) = 1013,43 knm n 1 = 9,13 knm (1013.4, 879.1, 36.1) where μ and σ are the mean value and standard deviation of the normal distribution earlier determined to 879,1 and 36,1 knm respectively. n is the number of trains during the reference period, in this case per year. f X and F X is the probability function and the in- 1 verse distribution function respectively for the normal distribution. Another possibility to determine the Gumbel parameters is to do a simulation; the base in the simulation would be the normal distribution. In Matlab it possible to simulate normal distributed variables and from these data select the largest moment. This procedure is repeated a hundred times and the data are fitted to a extreme value distribution. The fitted extreme value distributions together with the empirical distribution are show in Figure ,9 1 Emp. Dist. 0,8 0,7 0,6 0,95 GEV dist. FX(x) 0,5 FX(x) 0,9 0,4 Gumb dist. 0,3 0,2 0,85 0, Moment [knm] 0, Moment [knm] Figure 27 Cumulative distribution functions for the extreme mid span moment in a simply supported bridge. The right figure is a close up of the left figure. According to theory, maximum of normal distributed variables is a Gumbel distributed variable. In the case according to the previous page the parameters a and b were determined to 1013,4 and 9,1 knm respectively. The simulation gives the same values for the correspondent parameters. That is of course at satisfaction, but the right figure in Figure 27 it seem as a general extreme value distribution with parameters k, a and b equal to 0,1, 9,3 and 1013,9 knm respectively is a better choice. The reason that a general extreme value distribution is better than a Gumbel distribution depends on that the number of simulations is too small, with a higher number of simulations the extreme value distribution should be Gumbel distributed. Another way to determine extreme value distributions is to use the POT-method. That implies that a threshold is set and only values higher than the threshold are used in the further analyse. This is an advantage, since for section forces the highest values are the important ones. For the ongoing example the threshold is set to 895 knm, and that implies that 317 out of 1000 moments exceed the threshold. Figure 26 show the quantile plot for the normal assumption and it looks sufficient. Figure 28 is an enlargement of the same quantile plot, only values that exceed the threshold are shown.

100 Sustainable Bridges SB (62) 1 0,95 Theoretical quantiles 0,9 0,85 0,8 0,75 0,7 0,7 0,75 0,8 0,85 0,9 0,95 1 Empirical quantiles Figure 28 Quantile plot for the normal assumption, only values larger than the threshold. Figure 28 shows a good agreement for the right tail between simulated values and fitted normal distribution. But it can maybe be better, let s try to fit an exponential distribution for the differences between the moments and the chosen threshold. Figure 29 shows the empirical distribution together with a fitted exponential distribution and belonging quantile plot. 1 1 FX(x) 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Moment-threshold [knm] Evernt Exp Theoretical quantiles 0,8 0,6 0,4 0, ,2 0,4 0,6 0,8 1 Empirical quantiles Figure 29 To the left, empirical and fitted exponential distribution with m=25,4 knm for the mid span moment and to the right the correspondent quantile plot. Comparing Figures 28 and 29 shows that the normal assumption is better than the exponential assumption. Another way is to try to fit a Generalized Pareto Distribution (GPD) to the differences between the simulated moment and the chosen threshold, again the threshold is set to 895 knm. Figure 30 shows the empirical distribution together with a fitted GPD for the differences between moment and threshold. The Figure 30 also shows belonging quantile plot.

101 Sustainable Bridges SB (62) 1 1 FX(x) 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Moment-threshold [knm] Emp. GPD Theoretical quantiles 0,8 0,6 0,4 0, ,2 0,4 0,6 0,8 1 Empirical quantiles Figure 30 To the left, empirical and fitted GPD with k and α equal to 0,1957 and 30,4395 knm respectively for the mid span moment. To the right the correspondent quantile plot. Figure 30 shows that the differences between the simulated moments and the threshold are well approximated by a Generalized Pareto Distribution. Even numerical goodness of fit tests such as the KS and MSE tests show that the right tail of the distribution is best described by a GPD. The cumulative distribution function for a GPD with the parameter k 0 is given by F X ( x k, ) 1 k kx, σ = 1 1 (4.20) σ where k and σ are parameters of the distribution. There is a nice relationship between the GPD and the GEV distribution, maximum of a Poisson distributed number of independent GPD variables is GEV distributed. The parameters of the GEV distribution is given by k a b GEV GEV GEV = k GPD a = GPD λ a = u GPD k GEV a k GPD GPD (4.21) where indexes GPD an GEV refer to respective distribution. u and λ are the threshold and the expected number of events that exceed the threshold during the reference period. For the ongoing example with trains during the reference period the GEV parameters are determined according to: k a b GEV GEV GEV = 0,2 30,4395 = (0, ) 0,1957 = 6,3 24, ,4395 = 895 = 1018,4 0,1957 These values of the parameters are in the same magnitude as the previously evaluated according to maximum of normal distributed variables which is satisfying. This method is a bit more complicated than the first one and it is adequate to ask the question why use the POTmethod? There are two answers to that question, 1 if the parent distribution is not of common type e.g. normal or exponential which is very common in many cases. The POT method is effective in these cases since the method do not take notice of the parent distribution. 2 the most important part of the parent distribution is the right tail and the GPD is very easy to fit with high accuracy to that part of the distribution since it has three parameters.

102 Sustainable Bridges SB (62) To use the method described above, one assumption is that the number of exceedances is Poison distributed. This fact could be a problem since trains are running according to time schedules, i.e. not fully randomly. But on the other hand if the threshold is set relatively high the number of exceedances is low and that improves the Poison approximation. 4.7 Summary This section describes how to determine statistical distributions for section forces generated by real train in bridges. The real train loads are measured and analysed by a WIM measurement system. Such systems are able to measure and collect train characteristics continuously for a long time. From that data and use of influence line it is possible to determine the statistical distributions for different section forces. Design in the ultimate limit state requires the extreme value distributions for the section forces. It is of course of time and economical reasons not possible to measure the train loads during such a long time. Instead one has to use some kind of extrapolation method to get the extreme value distributions. Tools to determine such distributions are given in this chapter. One very important question is, for how long time must the measurements go on to make it possible to establish reliable extreme value distributions for section forces in bridges. It is not easy to answer that question. A general answer to that question is that the measurements must go on during such a long time that it is possible to determine the natural variation of the train characteristics. To be able to determine static load effects such, characteristics are axle loads and axel positions.

103 Sustainable Bridges SB (62)

104 Sustainable Bridges SB (62) 5 Statistical evaluation of the dynamic amplification factor 5.1 Introduction The load effect generated by trains in bridges is composed by two parts, one static and one dynamic. The static part is due to the gravity effect of the train at rest. The dynamic effect will occur when the train moves and comes in vertical vibration. In this chapter the magnitude of the dynamic effect is investigated and a statistical description of dynamic effect is given. 5.2 Analytic model The elastic moment in a bridge is in this report determined by a numerical model taken from Frýba and Náprstek (1998). The model describes the moment (static and dynamic) in a simply supported bridge in section x and time t, given by j [ f ( t tn ) h( t tn ) ( ) f ( t Tn ) h( t Tn )] N Fn 3 2 M ( x, t) = = 1 M = 1 0 j ωω 1 1 j n (5.1) F where M 0 is the static moment in section x and F n is a sequence of N axle loads moving with constant speed c. d n is the distance between the first axle and axle n with d 1 = 0, see Figure 31. N is the total number of axles and j is the mode. t n and T n are the times when th the n axle enters and leaves the bridge respectively. d n d 2 F n F 2 F 1 x ct l Figure 31 Illustration of variables related to equation 5.1. h (t) is the Heaviside unit function given by: h( t) = 0 h( t) = 1 for for t < 0 t 0 (5.2) The excitation frequency, ω is given by πc ω = (5.3) l where l is the span of the bridge and c is the velocity of the train. The natural frequency of the bridge ω for mode j is given by j ω = j 4 4 j π EI 4 l μ (5.4)

105 Sustainable Bridges SB (62) where EI is the elastic bending stiffness for the constant cross section of the beam. μ is the constant mass per unit length of the beam. The function f (t) is given by f ω' ω' j D jω 1 j ω d t () t = sin( jωt + λ) + exp sin( ω' t + γ ) where ω ' j is given by j (5.5) ω' j 2 j 2 d = ω ω (5.6) ω d, the circular frequency of damping is given by ω d = ϑ f 1 (5.7) where ϑ and f 1 are the logarithmic decrement of damping and first natural frequency. D is given by: D ( ω j ω ) + j ω ω = j 4 d (5.8) λ and γ are given by jωω λ = arctan ω j ω 2 j d 2 2 (5.9) and γ = arctan ω 2 d 2ω ω' ω d 2 ' j j 2 + j ω 2 (5.10) respectively. In this study the interesting section in the beam is in the middle, x = l 2 and for 2 this section M 0 = 2Fl π. Equation 5.1 can then be rewritten as: M ( l 2, t) = N j = 1 n= 1 2F l π j [ f ( t t ) h( t t ) ( ) f ( t T ) h( t T )] n 3 2 j ωω 2 1 n n 1 n n (5.11) The dynamic amplification factor (DAF) in this report is the ratio between the total moment and the static. Another possibility is to define the DAF as the relation between deflections. The analytic model to determine the total deflection (static and dynamic) is similar to the one used for the moment. The deflection υ at location x at time t is given by j [ f ( t t ) h( t t ) ( ) f ( t T ) h( t T )] N Fn 3 2 v( l 2, t) = = 1 υ = 1 0 j ωω1 1 j n n n n n (5.12) F where υ 0 is the deflection at location x. Equation 5.12 is as equation 5.1 only useful for simply supported bridges. The deflection υ 0 generated by a force F at x = l 2 is given by: 3 2Fl ν 0 = 4 (5.13) π EI

106 Sustainable Bridges SB (62) 5.3 Parametric study The purpose with the parametric study in this section is to identify parameters which have large effect on the result of a dynamic analyse. The inputs to the model given in the previous section are: Number of axle loads, N Axle loads, F F,... FN 1, 2 Positions of axles, d d,... d N Velocity of the train, c Span of the bridge, l 1, 2 Self weight of the bridge, μ Bending stiffness, EI First natural frequency, f 1 Damping of the bridge, ϑ The parameters related to the train, number of axles, axle loads and positions of axles are taken from Eurocode 1 (2002), load model HSLM-A6. The load model consists of 13 coaches, 2 power cars and 2 end coaches. The total length of the load model is approximately 380 m and consists of 40 axles. The train model is shown in Figure 32 and numerical values for axle loads and axle positions are given in Table 1. NxD 4F 3F 2F 2F 2F 3F 4F d d d d d d d D D D D D ,525 3, Figure 32 Load model HSLM-A6 according to Eurocode 1 (2002). Table 1 Numerical values for parameters related to load model HSLM-A6. Number of coaches ( N ) Coach length ( D ) [m] Bogie axle spacing ( d ) [m] Point loads ( F ) [kn] The velocity of the train is set to 200 km/h as a reference value. According to Eurocode 1 (2002) for lanes where the allowed velocity is greater than 200 km/h a dynamic analysis of the bridge is required.

107 Sustainable Bridges SB (62) The Swedish Rail Administration has presented standard designs for short span railway bridges. Characteristics for one of the standard bridges, bending stiffness, first natural frequency and damping are used in this parametric study. The span of the bridge is 10 m and the cross section of the bridge is shown in Figure Figure 33 Cross section of a standard trough bridge with a free span of 8 to 11 m. Further data for the standard bridge with span 10 m are given in Table 2. Table 2 Characteristics for a standard railway bridge with a span of 10 m according to the Swedish Rail Administration. Span ( l ) Mass ( μ ) Train velocity ( c ) Bending stiffness ( EI ) First natural frequency ( f 1 ) Damping (ϑ ) [m] [kg/m] [m/s] [Nm 2 ] [Hz] ,6 11,8* ,09 0,34 The purpose with this research is to get better knowledge of the statistical description of the DAF. The DAF can be defined in different ways. In this report three different DAF:s are analysed, DAF 1, DAF 2 and DAF 3. DAF 1 is the ratio between the maximum dynamic moment, M d,max and the simultaneous static moment, M s, sim. DAF 2, is the ratio between the dynamic moment M d, sim simultaneous with the maximum static moment M s, max and the last one DAF 3 which is the relation between the maximum dynamic and the maximum static moments generated any time during the passage of the train. An illustration of the different definitions of the DAF:s is shown in Figure 34.

108 Sustainable Bridges SB (62) M d,sim M s,max M d,max M s,sim Moment [knm] Stat. Dyn Time [s] Figure 34 Dynamic and static mid span moment in a simply supported bridge with a span of 10 m. In the parametric study five parameters were selected, velocity, axle load, bending stiffness, first natural frequency and damping. One of these variables is varied while the others are kept constant with base values accounted for above. The results of the parametric study will be discussed in the next five subsections. A general conclusion, not unexpected is that DAF2 DAF3 DAF1. For the discussion about the DAF:s in the following subsections focus is on DAF 3, since this definition of the DAF is most useful for engineers. The first studied parameter is the velocity Velocity The base value for this parameter is set to 200 km/h as mentioned above. Figure 35 shows the static moment, the maximum dynamic moment and the DAF:s as a function of velocity ,0 Moment [knm] Stat. Dyn. Dynamic amplification factor 1,8 1,6 1,4 1,2 1,0 DAF1 DAF2 DAF , Velocity [km/h] Velocity [km/h] Figure 35 Static and maximum dynamic mid span moment left and DAF:s right as a function of the velocity.

109 Sustainable Bridges SB (62) Figure 35 shows that for velocities up to 100 km/h the dynamic effect can be neglected. In the interval 100 to 225 km/h the DAF increases slowly and almost linearly from 1 to 1,2. For velocities greater than 225 km/h the DAF increases fast with velocity. It is obvious that velocity of the train is an important parameter in dynamic analyses of railway bridges. DAF 2 gives always the lowest dynamic amplification of the three different DAF:s,sometimes values less than one. This definition of the DAF is not interesting for engineering applications and will therefore not be studied in the further analyses. DAF 1 is the true interpretation of the dynamic amplification, since the static and the dynamic moment is present simultaneously. DAF 1 gives the highest amplification factors. A disadvantage with this definition is that in that point in time where DAF 1 determined is not always the highest total moment present. DAF 3 is the most useful way to define the dynamic amplification factor from a bridge designers point of view. With this definition of the DAF one can determine the maximum total moment in the bridge by multiplying the maximum static moment with the DAF Axle load This parameter is the only one that affects the magnitude of the static moment. Figure 36 to the left shows that the lines for the static and dynamic moments are almost parallel, which implies that the DAF is almost independent of the magnitude of the axle load ,0 Moment [knm] Stat. Dyn. Dynamic amplification factor 1,8 1,6 1,4 1,2 DAF1 DAF , Axle load [kn] Axel load [kn] Figure 36 Maximum static and dynamic mid span moments (left) and to the right DAF:s (right) as a function of the axle load Bending stiffness Figure 37 shows that the DAF depends on the bending stiffness. Increasing bending stiffness leads to decreasing dynamic effects.

110 Sustainable Bridges SB (62) ,0 Moment [knm] Stat. Dyn. Dynamic amplification factor 1,8 1,6 1,4 1,2 DAF1 DAF ,0E+09 9,0E+09 1,3E+10 1,7E+10 1,0 5,0E+09 9,0E+09 1,3E+10 1,7E+10 EI [Nm 2 ] EI [Nm2] Figure 37 Maximum static and dynamic mid span moments (left) and to the right DAF:s (right) as a function of the bending stiffness First natural frequency Figure 38 shows that the DAF is almost independent of the first natural frequency. The DAF decreases slightly when the first natural frequency increases. The first natural frequency is of course dependent on the stiffness and mass of the bridge. Here the mass is kept constant, this implies that if the first natural frequency increases the bending stiffness also increases ,0 Moment [knm] Stat. Dyn. Dynamic amplification factor 1,8 1,6 1,4 1,2 DAF1 DAF , First natrural frequency [Hz] First natrural frequency [Hz] Figure 38 Maximum static and dynamic mid span moments (left) and to the right DAF:s (right) as a function of the first natural frequency.

111 Sustainable Bridges SB (62) Damping The damping υ is defined as 2πξ 100, where ξ is the damping ratio in %. Figure 39 shows that if the damping is low υ < 0, 15 this parameter can affect the result of a dynamic analysis to a great extent. Otherwise, increasing damping leads to slightly decreasing DAF ,0 Moment [knm] Stat. Dyn. Dynamic amplification factor 1,8 1,6 1,4 1,2 DAF1 DAF ,0 0,2 0,4 0,6 0,8 1,0 Damping 1,0 0,0 0,2 0,4 0,6 0,8 1,0 Damping Figure 39 Maximum static and dynamic mid span moments (left) and to the right DAF:s (right) as a function of the damping. There are a lot of old bridges in Europe still in use. The trains are getting faster and heavier to keep up with user demands. This could be a problem since the velocity of the train is the parameter that has the largest influence on dynamic effects. The second most important parameter is the bending stiffness. In assessment of existing railway bridges, probabilistic analysis may be employed. For this purpose a statistical description of all the random variables in the limit state function is needed. One of these random variables is the DAF. The statistical description of this variable will be further investigated in the following section. 5.4 Simulations Simulations are used to determine statistical properties for different DAF:s. The base in the simulations is equation 5.1 and most of the variables involved in the equation are treated as random variables. Statistical distributions for DAF:s are determined for simply supported bridges of two materials, steel and reinforced concrete. The investigation is made for spans of 5, 10 and 15 m and the velocities of the trains are 150, 200 and 250 km/h. This implies that in total 18 different DAF:s are investigated. In each simulation a train is stepped over the bridge and for each step the dynamic and static moments are determined. The length of the step is 0,05 m. The simulation process is repeated 500 times and in each process a DAF (relation between maximum dynamic moment and maximum static moment) is calculated. The 500 determined DAF:s are then fitted to a standard distribution. To get a reliable statistical description of the DAF it is necessary to have reliable statistical descriptions of the random variables in equation 5.1. Statistical distributions related to the train load are given in Table 3.

112 Sustainable Bridges SB (62) Table 3 Random variables related to the train. Variable Symbol Distribution Mean value Standard dev Axle load F Normal 150 kn 15 kn Axle position d Normal Nominal A6 0,10 m Velocity v Normal 150, 200and 15 km/h 250 km/h Empirical data for trains are not accessible to the author; instead load model HSLM-A6 in Eurocode 1 (2002) is used as a base to model the train load. Each axle of the train is assumed normal distributed with a mean value of 150 kn and a standard deviation of 15 kn. Measurements of real trains are made in Sweden and presented in a thesis by James (2003). According to James (2003) the cov for a single axle load is approximately 10 % and according to histograms shown in the thesis it seems sufficient to assume that a normal distribution is a good approximation for the axle load. The axle loads given in Eurocode 1 (2002) are characteristic values and from these values the mean value of the normal distributed variable is determined. The distance between axles is assumed normal distributed with a mean value according the nominal distance in load model HSLM-A6. The standard deviation for this random variable is set to 0,10 m. There are no measurement known by the author that can confirm this assumption. But is seems reasonable to have a low standard deviation since there must be good knowledge of how wagons and trains are constructed. The velocity of the train is also assumed normal distributed with mean values of 150, 200 and 250 km/h. The standard deviation is set to 15 km/h. The characteristics of the concrete bridge with a span of 10 m in Table 4 are taken from the standard drawings made by the Swedish Rail Administration. Characteristics for the other bridges In Table 4 and 5 are taken from Frýba (1996) and James (2003). Table 4 Statistical description of variables related to concrete bridges. Span Bending stiffness 1:st natural frequency Damping Self weight [m] Mean [GNm 2 ] cov. [%] Mean [Hz] cov. [%] Mean [-] cov. [%] [tons/m] 5 1,5 5 32,4 5 0,63 5 4, ,8 5 15,1 5 0, , ,0 5 9,7 5 0, ,2 Table 5 Statistical description of variables related to steel bridges. Span Bending stiffness 1:st natural frequency Damping Self weight [m] Mean [GNm 2 ] cov. [%] Mean [Hz] cov. [%] Mean [-] cov. [%] [tons/m] 5 1,5 5 19,1 5 0,64 5 2, ,8 5 11,8 5 0,23 5 5, ,0 5 8,9 5 0, ,1

113 Sustainable Bridges SB (62) In the simulations the self weight and the span of the bridges are treated as constants. The bending stiffness is in accordance with JCSS (2001) modelled as a log-normal distributed variable. Statistical models for the damping and first natural frequency is hard to find in the literature. The chosen distributions and cov:s for these random variables is chosen by the author with guidance to James (2003) and ERRI D 214 The results from the simulations will be accounted for in the next section. 5.5 Results and conclusions In the parametric study five parameters were studied, velocity of the train, magnitude of axle loads, damping, bending stiffness, and first natural frequency of the bridge. It was found that increasing velocity and increasing axle loads increase the dynamic effects while an increase in the other parameters decrease dynamic effects. It was also found that the parameters that have the largest influence on dynamic effects are the velocity and the bending stiffness. To determine the statistical distributions for the DAF:s simulations were used. In total, 18 different DAF:s were determined, 9 for concrete bridges and 9 for steel bridges. 3 different spans and 3 different train velocities for each material were investigated. In the simulations the parameters investigated in the parametric study were modelled as random variables. In each simulation 500 DAF:s are determined, and fitted to standard distributions. In this case the normal and log-normal distributions are used. Figure 40 is an example from a simulation of a concrete bridge with a span of 10 m and the mean value for train velocity is set to 150 km/h. 1 0,9 0,8 0,7 FX 0,6 0,5 0,4 0,3 0,2 0,1 0 0,9 1,1 1,3 1,5 1,7 DAF Empirical Normal Log-normal Figure 40 Empirical CDF together with fitted normal and lognormal distributions for DAF. The mean value and standard deviation for the DAF in Figure 40 were determined to 1.13 and 0.12 respectively. By study of Figure 40 it is not easy to determine which of the two distributions which is the best approximation of the DAF. A quantile plot of the data is shown in Figure 41.

114 Sustainable Bridges SB (62) 1,0 0,8 Theoretical quantiles 0,6 0,4 Normal Log-normal Serie3 0,2 0,0 0 0,2 0,4 0,6 0,8 1 Empirical quantiles Figure 41 Quantile plot for the DAF for the concrete bridge with a span of 10 m and the velocity of the train is 150 km/h. By studying Figure 41, the log-normal distribution seems to gives the best fit for the DAF. Numerical goodness of fit tests such as the MSE (Mean Square Error) and the Kolmogorov-Smirnof tests give the same result. The DAF:s investigated for other combinations of material, spans and train velocities are similar to the shown example. Figure 42 shows the simulated mean values of the DAF as a function of the train velocity. 1,5 1,5 1,4 1,4 1,3 L=5m 1,3 L=5m DAF 1,2 L=10m L=15m DAF 1,2 L=10m L=15m 1,1 1,1 1,0 1, Velocity [km/h] Velocity [km/h] Figure 42 Mean value of the DAF as a function of the velocity at different spans. Left, concrete bridges and right steel bridges. Figure 43 shows the standard deviation of the DAF as a function of velocity for different spans.

115 Sustainable Bridges SB (62) 0,30 0,30 0,25 0,25 0,20 L=5m L=10m L=15m 0,20 L=5m L=10m L=15m DAF 0,15 0,10 DAF 0,15 0,10 0,05 0,05 0, Velocity [km/h] 0, Velocity [km/h] Figure 43 Standard deviation of the DAF as a function of the velocity at different spans. To the left the material of the bridge is concrete and to the right the material is steel. Figure 42 shows, as expected, that the mean value of the DAF increases when the velocity of the train increases. The figure also shows that the DAF is higher for bridges with spans of 5 m than for bridges with spans of 10 and 15 m. This is a bit strange since the bending stiffness in relation to the span is the same for all bridges. A possible explanation is that for longer bridges there is most of the time more than one axle simultaneously on the bridge as the train passes. This fact can imply that the dynamics of the two axles cancel out each other. This is not the case for the bridges with a span of 5 m. Figure 43 shows that the standard deviation of the DAF is independent on material, span and velocity of the train. In conclusion; the velocity of the train and the bending stiffness of the bridge have the largest influence on the result of a dynamic analyse. The DAF can be modelled by a log-normal distribution. The mean value is strongly dependent on train velocity. The standard deviation is about 0.15 and is independent on train velocity. The determined statistical distributions of the DAF are determined from simulations. There are of course uncertainties in the choice of distribution functions for some of the random variables, especially the damping and the first natural frequency. But on the other hand the parametric study showed that these variables do not have large effect on the result of a dynamic analysis.

116 Sustainable Bridges SB (62) 6 Bibliography Caprez, M., WIM applications to pavements. Preproceedings of 2:nd European conference on Weigh-In-Motion of road vehicles. Lisbon, Portugal. Carlsson, F., Modelling of traffic loads on bridges, based on measurements of real traffic loads in Sweden. Ph.D. thesis, Lund Institute of Technology, Lund, Sweden. Castillo, E., Extreme value theory in engineering. Academic press, Inc. ISBN Coles, S., An introduction to statistical modelling of extreme values. Springer-Verlag, ISBN De Graaf, H-J., De Jong, E.J.J., Van Der Hoek, M., GOTCHA: Compact system for measuring train weight and wheel defects. In: Fourth International Conference on Weigh-In- Motion. Taipei, Taiwan. Embrechts, P., Klüppelberg, C., Mikosch, T., Modelling extremal events for insurance and influence. Springer-Verlag, ISBN Eurocode Actions on structures Part 2: Traffic loads on bridges. pren :2002, E CEN Brussels. ERRI D Rail bridges for higher speed than 200 km/h, Research report of the European rail research institute, Utrecht. Frýba, L., Náprstek, J., Aperance of resonance vibration on railway bridges. Advances in civil and structural engineering computing practice, B.H.V. Topping (editor), Civil-Comp Press, Edinburgh, , Henny, R.J., Experimental use of WIM with Video for Overloading. Preproceedings of 2:nd European conference on Weigh-In-Motion of road vehicles. Lisbon, Portugal. James, G., Analysis of traffic load effects on railway bridges. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden. Johnson. R., Miller and Freund s probability and statistics for engineers. Prentice Hall, New Jersey, fifth edition. Karoumi, R., Respons of cable-stayed and suspension bridges to moving vehicles - analysis methods and practical. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden. Karoumi, R., Wiberg, J., Olofsson, P., July Monitoring traffic loads and traffic load effects on the new Årstaberg railway bridge. In: Second international conference on structural engieneering, mechanics and computation. Cape Town, South Africa. Liljencrantz, A., Monitoring railway traffic loads using Bridge Weight-in-Motion. Licentiate thesis, TRITA-BKN. Bulletin 90, Royal Institute of Technology, Stockholm, Sweden. Download from: Moses, F., May/June Weigh-in-motion system using instrumented bridges. ASCE Transportation Engineering Journal 105, Quilligan, M., Bridge weigh-in-motion, development of a 2-d multivehicle algorithm. Licentiate thesis. Royal Institute of Technology. Quilligan, M., Karoumi, R., O Brien, E. J., May Development and testing of a 2- dimensional multi-vehicle. In: Second international conference on structural engieneering, mechanics and computation. Orlando, USA.

117 Sustainable Bridges SB (62) Schneider, J., Introduction to safety reliability of structures. Structural engineering documents. IABSE Pub. ISBN WAFO a Matlab toolbowfor analysis of random waves and loads. Brodtkorb P., Johannesson, P., Lindgren G., Rychlik, I., Rydén J. (2000). Lund Institute of Technology, Department of mathematical statistics.,lund, Sweden. Znidaric, A., Lavric, I., Kalin, J., Nothing-On-the-Road axle detection with threshold analysis. In: Fourth International Conference on Weigh-In-Motion. Taipei, Taiwan.

118 Dynamic Railway Traffic Effects on Bridge Elements Background document D4.3.3 PRIORITY 6 SUSTAINABLE DEVELOPMENT GLOBAL CHANGE & ECOSYSTEMS INTEGRATED PROJECT

119 Sustainable Bridges SB (33) This report is one of the deliverables from the Integrated Research Project Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives funded by the European Commission within 6 th Framework Programme. The Project aims to help European railways to meet increasing transportation demands, which can only be accommodated on the existing railway network by allowing the passage of heavier freight trains and faster passenger trains. This requires that the existing bridges within the network have to be upgraded without causing unnecessary disruption to the carriage of goods and passengers, and without compromising the safety and economy of the railways. A consortium, consisting of 32 partners drawn from railway bridge owners, consultants, contractors, research institutes and universities, has carried out the Project, which has a gross budget of more than 10 million Euros. The European Commission has provided substantial funding, with the balancing funding has been coming from the Project partners. Skanska Sverige AB has provided the overall co-ordination of the Project, whilst Luleå Technical University has undertaken the scientific leadership. The Project has developed improved procedures and methods for inspection, testing, monitoring and condition assessment, of railway bridges. Furthermore, it has developed advanced methodologies for assessing the safe carrying capacity of bridges and better engineering solutions for repair and strengthening of bridges that are found to be in need of attention. The authors of this report have used their best endeavours to ensure that the information presented here is of the highest quality. However, no liability can be accepted by the authors for any loss caused by its use. Copyright Authors Project acronym: Sustainable Bridges Project full title: Sustainable Bridges Assessment for Future Traffic Demands and Longer Lives Contract number: TIP3-CT Project start and end date: Duration 48 months Document number: Deliverable D4.3.3 Abbreviation SB Author/s: E. Bruwhiler, A. Herwig, EPFL, Date of original release: Revision date: Project co-funded by the European Commission within the Sixth Framework Programme ( ) Dissemination Level PU Public X PP RE CO Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)

120 Sustainable Bridges SB (33) Table of Contents Summary... 4 Acknowledgments Introduction Aim and scope Dynamic factors for the examination of a railway bridge Effect of dynamic traffic action at ultimate limit state Introduction The vehicle-bridge system and its excitation The gravity effect Influence of strain-rate Assumptions on failure behaviour Scenario impact-like excitation Origin of impact-like excitation Single oscillator model and energy dissipation Double oscillator for vehicle bridge interaction Conclusions on the effects of dynamic traffic action at ULS Dynamic factors for the structural safety verification at ultimate limit state Effect of dynamic traffic action due to track irregularities under service conditions Introduction Wheel force amplifications due to track irregularities Modelling of carriages Modelling of track irregularities Car weight influence on the wheel force amplification Amplification of bridge action effects due to moving trains Carriage behaviour for the modelling of carriage-bridge interaction Bridge behaviour Modelling of the system carriage + bridge Analysis in the time domain, influence of carriage mass Excitation by an impulse The 2 nd natural mode of the carriage is dominant Conclusions on dynamic effects under service conditions Dynamic factors for the serviceability and fatigue safety verification References... 33

121 Sustainable Bridges SB (33) Summary This background document 1 describes the dynamic traffic action effects on bridge elements at ultimate and serviceability limit state. According to this, the differentiation is made between the dynamic interaction at ultimate limit state, acting on the assumption that material behaviour is inelastic and the interaction at serviceability state, limiting on pure elastic behaviour. The significance of several dynamic phenomena for the respective limit state is discussed. The influence of decisive parameters is demonstrated using simple dynamic models. Appropriate amplification factors are proposed for each limit state. 1 This document is based on research work under the supervision of Prof. Eugen Brühwiler conducted by Dr Hannes Ludescher [Ludescher 2003] that has been extended for rail traffic action by Andrin Herwig.

122 Sustainable Bridges SB (33) Acknowledgments The present document has been prepared by the Swiss contractor École Polytechnique Fédérale de Lausanne (EPFL) within the work package WP4 of the Sustainable Bridges project. The following individuals from the above-mentioned organisation have contributed to writing this document: Eugen Brühwiler and Andrin Herwig. Furthermore, the comments and suggestions of the internal reviewer Raid Karoumi from Royal Institute of Technology (KTH) are very much appreciated.

123 Sustainable Bridges SB (33) 1 Introduction In the examination of the structural safety, fatigue safety and serviceability of railway bridges, dynamic effects of railway traffic action are usually considered by so called dynamic amplification factors or impact factors. Dynamic amplification of rail traffic action can be caused by: - Rail surface irregularities, - Wheel defects, - Train (vehicle) braking and acceleration, - Curved trajectories (centrifugal forces), - Trains with equal axle spacings running at critical speed, - the effect of moving axles. Amplification factors do not only cover the dynamic amplification of wheel forces but also the amplification of action effects due to bridge oscillations. If the bridge is susceptible to the dominant frequencies of the dynamic wheel forces, vehicle and bridge oscillations are closely linked, which results in relatively complex bridge-vehicle interaction. Although bridge-vehicle interaction has been the subject of numerous theoretical studies, there are no results that cover dynamic traffic action at ultimate limit state of structural elements. All studies and tests have been carried out for elastic bridge behaviour. The objective of this Background Document is to show in Section 4, whether dynamic action due to railway traffic can be dissipated due to plastic deformations at ultimate limit state and under which conditions this is admissible. In Section 5, elastic bridge behaviour under dynamic service loading is investigated and dynamic factors relevant for the fatigue and serviceability checks are deduced. 2 Aim and scope This document targets the dynamic effect of relevant loading scenarios. For ultimate limit state (Section 3), the description of the dynamic behaviour is limited on ULS relevant hazard scenarios for the loading (resonance effects of high-speed passenger trains on lines with mixed traffic are not ULS relevant). The resonance effect of freight trains is not investigated here as there is a low probability of the occurrence of resonance for ULS relevant loads (the coincidence of overloading, regular axle spacing and resonance speed). The focus is made on the effect of (single) overloaded freight carriages moving over track irregularities. For fatigue and serviceability limit state (Section 4), the focus is made on the effect of wellloaded carriages moving over track irregularities. The resonance effect due to trains with regular axle spacing is not considered as it is assumed that resonance is very seldom nor even avoided by speed restrictions or other measures.

124 Sustainable Bridges SB (33) 3 Dynamic factors for the examination of a railway bridge The objective of the examination of a railway bridge is to show that for given traffic loads the three following requirements are fulfilled regarding: - the ultimate limit state (involving ultimate resistance and stability of the structure) through verification of the structural safety, - the ultimate fatigue limit state through the verification of the fatigue safety, - the serviceability limit state (involving functionality, comfort of persons, appearance) through the verification of the serviceability. Regarding dynamic factors for the examination of a railway bridge, two cases need to be distinguished, and consequently, two different kinds of dynamic factors need to be established: - Ultimate limit state (structural safety): Bridge structures made of reinforced concrete and steel show distinctly inelastic, ductile behaviour at ultimate limit state which allows for internal redistribution of action effects and to have insufficient resistance announced by excessive deformations. In the verification of the structural safety, plastic deformation of the structure is commonly assumed. As a consequence, a dynamic factor relevant for the ultimate limit state of the structure needs to be considered. (Thus, a dynamic factor based on elastic bridge behaviour is strictly not applicable.) Also, occasional (or maximum) values of dynamic factor need to be considered in the structural safety verification. - Fatigue and serviceability limit states: Dynamic factor based on elastic bridge behaviour is appropriate in the case of both fatigue and serviceability limit states. In both cases, the bridge structure is subjected to traffic loads under service conditions and remains in the elastic state. As a consequence, a dynamic factor based on elastic bridge behaviour needs to be considered. In this case, a frequent value of dynamic factor may be considered since occasional events may be easily accepted. Each case will be discussed in the following and corresponding values for the dynamic factor will be deduced.

125 Sustainable Bridges SB (33) 4 Effect of dynamic traffic action at ultimate limit state 4.1 Introduction Bridge structures made of reinforced concrete and steel are designed to show distinctly inelastic, ductile behaviour when attaining ultimate limit state, in order to allow for internal redistribution of action effects and to have insufficient resistance announced by excessive deformations. At ultimate limit state, an amplification factor based on elastic bridge behaviour is strictly not applicable. In structural engineering, various methods have been developed in order to design a structure for dynamic action, e.g. for earthquake or impact loading. Only allowing the structure working beyond the elastic domain leads to economic solutions. By considering the deformation characteristics of reinforcing and structural steels beyond their yield point, their high plastic deformability can be exploited. This is especially interesting in the case of dynamic action, where plastic deformation has the effect of a powerful damper and results in a very efficient dissipation of kinetic energy. But also with static loads, plastic deformations ( ductility ) considerably increase the load carrying capacity of statically indeterminate systems due to internal redistribution of action effects. Elastic behaviour is characterised by very low structural damping (typically less than 1%), which is an important condition for bridge oscillations to attain a relevant level. 4.2 The vehicle-bridge system and its excitation This chapter focuses on the dynamic behaviour with freight trains, as they are relevant for ultimate limit state with lines of mixed traffic. As freight carriages contain rather stiff suspensions (compared to passenger coaches), the passage over track irregularities is the most important cause for the transfer of dynamic energy to the bridge structure, which may occur at a relative wide range of velocities, compared to the excitation due to a train with regular axle spacing at critical speed for resonance. Already a single axle group of two overloaded carriages may suffice to cause maximum dynamic effect. In order to analyse the effect of dynamic traffic action at ultimate limit state, simple models are appropriate and useful. However, it is essential to understand the behaviour of the whole system in order to establish and evaluate the models correctly. The model has to represent three major components: - the vehicle, - the bridge and - the excitation. In reality, each of these components is rather complex and requires sophisticated models for a precise representation. However, for a given problem (e.g. the investigation of the dissipation of a given (kinetic) energy in the bridge element due to plastic deformation), the complexity of each component may be reduced considerably as a lot of phenomena and dynamic properties of some sub components do no significantly influence the result. The advantages of simpler models are that they are easy to build and to analyse, which allows to concentrate on the actual problem. Theoretically, a bridge is a system with an infinite number of degrees of freedom and eigenmodes. It reacts differently for different vehicle positions and changes its dynamic properties as it starts to interact with the vehicle. The vehicle has more the character of a multi-body system, with the vehicle body and the axles moving as rigid bodies. The tyres (the track superstructure) and suspensions, with the latter displaying non-linear behaviour in

126 Sustainable Bridges SB (33) the case of steel suspensions, determine the deformation capacity. For oscillations induced by track irregularities, the excitation is a relatively complex function of the rail profile, the vehicle speed and the axle spacing. Traditionally, two major phenomena are considered in the analysis of dynamic traffic action: resonance and impact. Especially in the safety verification of bridge deck slabs, two other reasons for dynamic traffic action must not be neglected: braking and centrifugal forces due to curved trajectories which cause horizontal acceleration and the amplification of wheel or axle loads. Scenario resonance due to train velocity : Resonance due to moving loads may occur with bridges that are crossed by trains of equal axle spacing at certain speeds, even without the effect due to track irregularities. The magnitude of these speeds is in a narrow domain, which may be estimated by simple formulas. However, this phenomenon is predominantly a serviceability problem as it may occur also with trains of small axle loads. Theoretically, cannot be entirely excluded that resonance vibrations lead to deformations beyond the elastic domain. High-speed passenger trains with regular axle spacing are not ULS relevant due to their relative low weight compared to freight trains. Scenario resonance-like excitation due to track irregularities : If the rail surface irregularities on a bridge contain distinct periodicities, axle groups travelling at a critical speed can excite the vehicle-bridge system at its fundamental frequency, which is usually the frequency most prone to resonance. Due to the transient nature of the excitation by moving vehicles, true resonance due to track irregularities is not possible. Scenario impact-like excitation : Specific irregularities like deformed wheels, rail joints, rail defects and unforeseen obstacles on the rail can cause a strong, sudden excitation of the vehicle-bridge system. In contrary to normal rail surface and wheel irregularities, abnormal or accidental irregularities are usually of a much higher magnitude. As the vehicle passes the irregularity, each axle provokes a kind of an impact, which is attenuated by the flexibility of the rail sleeper system and wheel suspensions. Depending on the axle spacing and the vehicle speed, the effect of subsequent axles is increased or diminished.

127 Sustainable Bridges SB (33) impact resonance In Figure 1, both scenarios of pronounced dynamic bridge loading are illustrated with field test measurements from a road bridge [Cantieni 1983]. Impact-like excitation is provoked with an artificial obstacle at the centre of the first span, whereas the resonance-like excitation is the result of usual road surface irregularities. It is important to note that major dynamic amplification is likely to happen only if the bridge reaction is dominated by one frequency, which is in interaction with oscillations of the vehicle body. Scenario strong horizontal acceleration : Braking, acceleration and centrifugal effects cause also an amplification of wheel forces. The dynamic amplification results from a redistribution of wheel forces, whereas the total vehicle load remains unchanged. Amplification factors can be easily expressed in function of the vehicle geometry, the braking deceleration, the acceleration or centrifugal acceleration. Although braking can excite noticeable bridge oscillations, this scenario primarily increases the maximum dynamic wheel force. A fundamental difference to the other two scenarios is that dynamic amplification due to horizontal acceleration cannot be dissipated by plastic deformations. [Consequently, this scenario will not be dealt with more in detail.] This preliminary evaluation of relevant scenarios shows that impact-like excitation is by far the most relevant case. Impact-like excitation causes not only very high dynamic wheel forces, but also important bridge oscillations. Field tests (on road bridges) with artificial obstacles often result in amplification factors beyond 2.0, whereas the tests without these obstacles rarely yield values beyond 1.5 [Paultre et al. 1992]. For all three scenarios, ultimate limit state is only attained if the vehicles are extremely heavy and the bridge is rather weak or deficient. Subsequently it is shown that the bridge needs to be already heavily loaded before dynamic amplification takes place. 4.3 The gravity effect Figure 1: Illustration of impact-like and resonance-like excitation (measurements on a road bridge by [Cantieni 1983]) Although the (static) effect of gravity loads is very well known, the effect of gravity in connection with the dissipation of dynamic traffic action is somewhat unusual and not adequately considered. The effect can be illustrated by means of a linear elastic spring (constant k [N/m]) that is subsequently loaded by two weights of mass m (Figure 2). Due to the action of the first mass,