Safety of historical stone arch bridges

Contents 1 Introduction...........................................................................................1 1.1 General introduction ........................................................................1 1.2 Advantages and disadvantages of arch bridges .............................12 1.3 Structure of the book .....................................................................14 1.4 Terms .............................................................................................20 1.5 Classification of static bridge types ...............................................29 1.6 Types of arch geometry .................................................................33 1.7 History of stone arch bridges.........................................................36 1.8 Arch bridges from alternative material..........................................47 1.8.1 Steel arch bridges .................................................................47 1.8.2 Wooden arch bridges ...........................................................48 1.8.3 Concrete arch bridges...........................................................49 1.9 Number of arch bridges .................................................................50 References ............................................................................................56 2 Loads....................................................................................................67 2.1 Introduction ...................................................................................67 2.2 Road traffic loads...........................................................................67 2.4 Initial drive forces..........................................................................86 2.5 Breaking forces..............................................................................87 2.6 Wind loading .................................................................................88 2.7 Impact forces .................................................................................89 2.8 Settlements.....................................................................................89 2.9 Temperature loading......................................................................89 2.10 Snow loading ...............................................................................92 2.11 Dead load.....................................................................................92 References ............................................................................................94 3 Computation of historical arch bridges ............................................99 3.1 Introduction ...................................................................................99 3.2 Empirical rules.............................................................................100 3.2.1 Historical rules...................................................................100 3.2.2 Modern rules......................................................................119 2.3 Railroad traffic load.......................................................................82 X Contents 3.3 Beam models ...............................................................................125 3.3.1 Single beam models...........................................................125 3.3.2 Compound beam models ...................................................133 3.4 Finite element method (FEM) .....................................................136 3.5 Discrete element method (DEM).................................................140 3.6 Comparison of testing and modelling..........................................141 3.6.1 Load tests on arches...........................................................141 3.6.2 Comparison results ............................................................144 3.7 Transverse direction (effective width).........................................148 References ..........................................................................................152 4 Masonry strength..............................................................................165 4.1 Introduction .................................................................................165 4.2 Masonry elements........................................................................166 4.2.1 Masonry stones..................................................................166 4.2.2 Mortar................................................................................172 4.3 Maximum centric masonry compression strength .......................176 4.3.1 Model according to DIN 1053-100 ...................................177 4.3.2 Model according to DIN 1053...........................................178 4.3.3 Empirical exponential models ...........................................179 4.3.4 Model according to Hilsdorf .............................................179 4.3.5 Model according to Mann .................................................180 4.3.6 Model according to Berndt................................................181 4.3.7 Model according to Sabha.................................................183 4.3.8 Model according to Ohler..................................................183 4.3.9 Model according to Stiglat ................................................184 4.3.10 Model according to Francis, Horman and Jerrems..........184 4.3.11 Model according to Khoo and Hendry ............................184 4.3.12 Model according to Schnackers.......................................185 4.3.13 Model according to Ebner ...............................................185 4.3.14 Further masonry compression models.............................185 4.5 Moment-Axial force diagrams.....................................................187 4.6 Additional-leaf masonry ..............................................................188 4.6.1 Introduction .......................................................................188 4.6.2 Model according to Warnecke...........................................188 4.6.3 Model according to Egermann ..........................................188 4.7 Shear strength ..............................................................................190 4.8 Proof equations ............................................................................191 References ..........................................................................................192 4.4 Stress-strain relationship .............................................................. 186 Contents XI 5 Investigation techniques ...................................................................199 5.1 Introduction .................................................................................199 5.2 Destructive tests...........................................................................202 5.3 Semi-destructive test methods .....................................................205 5.4 Non-destructive test methods ......................................................205 5.4.2 Impact-echo .......................................................................206 5.4.3 Radar .................................................................................207 5.4.4 Tomography ......................................................................208 5.4.5 Thermography ...................................................................208 5.4.6 Electrical conductivity.......................................................208 5.4.7 Experimental tests on bridges on site ................................208 5.4.8 Photogrammetry and lasercanning ....................................209 References ..........................................................................................210 6 Damages and repair..........................................................................217 6.1 Introduction .................................................................................217 6.2 Damages on historical arch bridges.............................................218 6.2.1 Overview ...........................................................................218 6.2.2 Recent collapses of historical arch bridges........................221 6.2.3 Weathering of the mortar...................................................222 6.2.4 Spalling and contour scaling .............................................223 6.2.5 Salt attack ..........................................................................224 6.2.6 Chemical weathering .........................................................226 6.2.7 Biological weathering........................................................226 6.2.8 Mechanical and physical weathering.................................226 6.2.9 Deformations .....................................................................227 6.2.10 Cracks..............................................................................229 6.3 Repair and strengthening .............................................................235 6.3.1 Introduction .......................................................................235 6.3.2 Strengthening techniques...................................................241 6.3.3 Examples ...........................................................................254 6.4 Arch bridges of the second generation ........................................256 References ..........................................................................................257 7 Safety assessment ..............................................................................265 7.1 Definition of safety and safety concepts......................................265 7.2 Probabilistic safety concept .........................................................269 7.2.1 Introduction .......................................................................269 7.2.4 Hypersphere division method............................................281 7.2.5 Response Surface Method .................................................281 5.4.1 Ultrasound ......................................................................... 205 7.2.2 First-order reliability method (FORM)..............................270 7.2.3 Second-order reliability method (SORM).........................274 XII Contents 7.2.6 Monte Carlo Simulation ....................................................285 7.2.7 Combination of safety indexes ..........................................288 7.2.8 Limitation of the presented methods .................................293 7.2.9 Commercial programs .......................................................295 7.2.10 Goal values of safety indexes ..........................................297 7.3 Semi-probabilistic safety concept................................................301 7.3.1 Introduction .......................................................................301 7.3.2 Partial safety factors ..........................................................303 7.3.3 Characteristic values..........................................................310 References ..........................................................................................323 8 Examples............................................................................................333 8.1 Introduction .................................................................................333 8.2 Examples in literature ..................................................................333 8.3.1 Bridge 1 .............................................................................336 8.3.2 Bridge 2 .............................................................................341 8.3.3 Bridge 3 .............................................................................345 8.3.4 Bridge 4 .............................................................................346 8.3.5 Bridge 5 .............................................................................348 8.3.6 Bridge 6 .............................................................................349 8.3.7 Summary ...........................................................................350 8.4 Further examples .........................................................................351 8.4.1 Historical stone beam bridges ...........................................351 8.4.2 Anchoring chamber of the Blue Wonder Bridge...............352 8.5 Conclusion ...................................................................................354 References ..........................................................................................357 Index .......................................................................................................361