Lifetime-Oriented Structural Design Concepts

Friedhelm Stangenberg · Rolf BreitenbücherOtto T. Bruhns · Dietrich HartmannRüdiger Höffer · Detlef KuhlGünther Meschke (Eds.)

Lifetime-OrientedStructural Design Concepts

ABC

Prof. Dr.-Ing. Friedhelm StangenbergRuhr-University BochumInstitute for Reinforced andPrestressed Concrete StructuresUniversitätsstr. 15044780 Bochum, GermanyE-mail: sandra.krimpmann@

ruhr-uni-bochum.de,friedhelm.stangenberg@

ruhr-uni-bochum.de

Prof. Dr.-Ing. Rolf BreitenbücherRuhr-University BochumInstitute for Building MaterialsUniversitätsstr. 15044780 Bochum, Germany

Prof. Dr.-Ing. Otto T. BruhnsRuhr-University BochumInstitute of MechanicsUniversitätsstr. 15044780 Bochum, Germany

Prof. Dr.-Ing. Dietrich HartmannRuhr-University BochumInstitute for Computational EngineeringUniversitätsstr. 15044780 Bochum, Germany

Prof. Dr.-Ing. Rüdiger HöfferRuhr-University BochumBuilding Aerodynamics LaboratoryUniversitätsstr. 15044780 Bochum, Germany

Prof. Dr.-Ing. Detlef KuhlUniversity of KasselInstitute of Mechanics and DynamicsMönchebergstr. 734109 Kassel, Germany

Prof. Dr.-Ing. Günther MeschkeRuhr-University BochumInstitute for Structural MechanicsUniversitätsstr. 15044780 Bochum, Germany

ISBN 978-3-642-01461-1 e-ISBN 978-3-642-01462-8

DOI 10.1007/978-3-642-01462-8

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The Team of SFB 398

Mark Alexander Ahrens • Hussein Alawieh • Matthias Baitsch • FalkoBangert • Yavuz Basar • Christian Becker • Ivanka Bevanda • Jorg Bock-hold • Ndzi Christian Bongmba • Dietrich Braess • Rolf Breitenbucher •Otto T. Bruhns • Christian Duckheim • Andreas Eckstein • Frank Ensslen •Olaf Faber • Mozes Galffy • Volkmar Gornandt • Jaroslaw Gorski • StefanGrasberger • Klaus Hackl • Ulrike Hanskotter • Gerhard Hanswille • Diet-rich Hartmann • Anne Hartmann • Gunnar Heibrock • Martin Heiderich •Jan Helm • Christa Hermichen • Erich Heymer • Rudiger Hoffer • NorbertHolscher • Jan-Hendrik Hommel • Wolfgang Hubert • Hursit Ibuk • MikhailItskov • Hans-Ludwig Jessberger • Daniel Jun • Dirk Kamarys • MichaelKasperski • Christoph Kemblowski •Olaf Kintzel • Andreas S. Kompalka •Diethard Konig • Karsten Konke • Stefan Kopp • Wilfried B. Kratzig • San-dra Krimpmann • Jens Kruschwitz • Detlef Kuhl • Jan Laue • Armin Lenzen• Roland Littwin • Ludger Lohaus • Dimitar Mancevski • Gunther Meschke• Kianoush Molla-Abbassi • Jorn Mosler • Stephan Muller • Thomas Nerzak• Hans-Jurgen Niemann • Andrzej Niemunis • Sam-Young Noh • MarkusPeters • Lasse Petersen • Yuri Petryna • Daniel Pfanner • Tobias Pfister •Gero Pflanz • Igor Plazibat • Rainer Polling • Markus Porsch • ThorstenQuent • Stefanie Reese • Christian Rickelt • Matthias Roik • Jan Saczuk •Jorg Sahlmen • E. Scholz • Henning Schutte • Robert Schwetzke • Max J.Setzer • Bjorn Siebert • Anne Sprunken • Friedhelm Stangenberg • ZoranStankovic • Sascha Stiehler • Mathias Strack • Helmut Stumpf • TheodorosTriantafyllidis • Cenk Ustundag • Heinz Waller • Claudia Walter • HeinerWeber • Gisela Wegener • Andres Wellmann Jelic • Torsten Wichtmann •Xuejin Xu • Natalia Yalovenko

Preface

At the beginning of 1996, the Cooperative Research Center SFB 398 finan-cially supported by the German Science Foundation (DFG) was started atRuhr-University Bochum (RUB). A scientists group representing the fieldsof structural engineering, structural mechanics, soil mechanics, material sci-ence, and numerical mathematics introduced a research program on “lifetime-oriented design concepts on the basis of damage and deterioration aspects”.Two scientists from neighbourhood universities, one from Wuppertal and theother one from Essen, joined the Bochum Research Center, after a few years.The SFB 398 was sponsored for 12 years, until the beginning of 2008 – thisis the maximum possible duration of DFG financial support for an SFB.

Safety and reliability are important for the whole expected service durationof an engineering structure. Therefore, prognostical solutions are needed anduncertainties have to be handled. A differentiation according to building typeswith different service life requirements is necessary. Life-cycle strategies tocontrol future structural degradations by concepts of appropriate design haveto be developed, in case including means of inspection, maintenance, andrepair. Aspects of costs and sustainability also matter.

The importance of structural life-cycle management is well recognized inthe international science community. Therefore, parallel corresponding ac-tivities are proceeding in many countries. In Germany, two other relatedSFBs were established: SFB 524 “Materials and Structures in Revitalisationof Buildings” at Weimar University and the still running SFB 477 “Life-Cycle Assessment of Structures via Innovative Monitoring” at BraunschweigUniversity of Technology. With these two SFBs, a fruitful cooperation wasdeveloped.

The Cooperative Research Center for Lifetime-Oriented Design Concepts(SFB 398) at Ruhr-University has carried out substantial work in many fieldsof structural lifetime management. Lifetime-related fundamentals are pro-vided with respect to structural engineering, structural and soil mechanics,material science as well as computational methods and simulation techniques.Stochastic aspects and interactions between various influences are included.

VIII Preface

Thus, a solid basis is provided for future practical use and, e.g. also for stan-dardization.

The wide range of scientific topics among the specification and determina-tion of external loading and the simulation based lifetime-oriented structuraldesign concepts is presented in an extraordinary format. All scientists of theSFB 398, professors and Ph.D. students, have contributed with a great effortin matchless team work to the present book. As a result of this, the presentwork is not only a collection of project reports, in fact it is almost writtenin the style of a monograph, whereby several authors fruitfully interact in allsections from the highest to the deepest level. Within this philosophy of jointauthorship, authors are denoted in chapters and sections down to the thirdlevel. In special cases, where authors have contributed to a selected deepersection level, they are denoted beside the standard procedure in the regardingtext episode.

All members of SFB 398, with sincere thanks, acknowledge the financialsupport of DFG over more than 12 years. The dedicated research work of allparticipating colleagues and of many guest scientists from diverse countriesalso is gratefully mentioned.

Finally, the great efforts of Springer-Verlag, Heidelberg, to produce thisattractive volume is appreciated very much.

Bochum, Friedhelm Stangenberg, Chairman of SFB 398March 26th, 2009 Otto T. Bruhns, Vice-chairman of SFB 398

Contents

1 Lifetime-Oriented Design Concepts . . . . . . . . . . . . . . . . . . . . . . 11.1 Lifetime-Related Structural Damage Evolution . . . . . . . . . . . . 11.2 Time-Dependent Reliability of Ageing Structures . . . . . . . . . . 31.3 Idea of Working-Life Related Building Classes . . . . . . . . . . . . . 41.4 Economic and Further Aspects of Service-Life Control . . . . . . 51.5 Fundamentals of Lifetime-Oriented Design . . . . . . . . . . . . . . . . 7

2 Damage-Oriented Actions and Environmental Impact . . . . 92.1 Wind Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Wind Buffeting with Relation to Fatigue . . . . . . . . . . . 102.1.1.1 Gust Response Factor . . . . . . . . . . . . . . . . . . . . 112.1.1.2 Number of Gust Effects . . . . . . . . . . . . . . . . . . . 14

2.1.2 Influence of Wind Direction on Cycles of GustResponses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1.2.1 Wind Data in the Sectors of the Wind

Rosette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1.2.2 Structural Safety Considering the

Occurrence Probability of the WindLoading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.1.2.3 Advanced Directional Factors . . . . . . . . . . . . . 232.1.3 Vortex Excitation Including Lock-In . . . . . . . . . . . . . . . 25

2.1.3.1 Relevant Wind Load Models . . . . . . . . . . . . . . 272.1.3.2 Wind Load Model for the Fatigue Analysis

of Bridge Hangers . . . . . . . . . . . . . . . . . . . . . . . . 292.1.4 Micro and Macro Time Domain . . . . . . . . . . . . . . . . . . . 33

2.1.4.1 Renewal Processes and Pulse Processes . . . . . 342.2 Thermal Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.2.1 General Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2.2 Thermal Impacts on Structures . . . . . . . . . . . . . . . . . . . 35

X Contents

2.2.3 Test Stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.4 Modelling of Short Term Thermal Impacts and

Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2.5 Application: Thermal Actions on a Cooling Tower

Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3 Transport and Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.3.1 Traffic Loads on Road Bridges . . . . . . . . . . . . . . . . . . . . 462.3.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.3.1.2 Basic European Traffic Data . . . . . . . . . . . . . . 472.3.1.3 Basic Assumptions of the Load Models for

Ultimate and Serviceability Limit Statesin Eurocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.1.4 Principles for the Development of FatigueLoad Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.3.1.5 Actual Traffic Trends and Required FutureInvestigations . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.3.2 Aerodynamic Loads along High-Speed RailwayLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.3.2.1 Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.3.2.2 Dynamic Load Parameters . . . . . . . . . . . . . . . . 822.3.2.3 Load Pattern for Static and Dynamic

Design Calculations . . . . . . . . . . . . . . . . . . . . . . 872.3.2.4 Dynamic Response . . . . . . . . . . . . . . . . . . . . . . . 90

2.4 Load-Independent Environmental Impact . . . . . . . . . . . . . . . . . 922.4.1 Interactions of External Factors Influencing

Durability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932.4.2 Frost Attack (with and without Deicing Agents) . . . . . 95

2.4.2.1 The ”Frost Environment”: ExternalFactors and Frost Attack . . . . . . . . . . . . . . . . . 96

2.4.2.2 Damage Due to Frost Attack . . . . . . . . . . . . . . 1032.4.3 External Chemical Attack . . . . . . . . . . . . . . . . . . . . . . . . 106

2.4.3.1 Sulfate Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072.4.3.2 Calcium Leaching . . . . . . . . . . . . . . . . . . . . . . . . 107

2.5 Geotechnical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1092.5.1 Settlement Due to Cyclic Loading . . . . . . . . . . . . . . . . . 1092.5.2 Multidimensional Amplitude for Soils under Cyclic

Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

3 Deterioration of Materials and Structures . . . . . . . . . . . . . . . 1233.1 Phenomena of Material Degradation on Various Scales . . . . . 124

3.1.1 Load Induced Degradation. . . . . . . . . . . . . . . . . . . . . . . . 1243.1.1.1 Quasi Static Loading in Cementitious

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Contents XI

3.1.1.1.1 Fracture Mechanism ofConcrete Subjected to UniaxialCompression Loading . . . . . . . . . . . 124

3.1.1.1.2 Fracture Mechanism of ConcreteSubjected to Uniaxial TensionLoadings . . . . . . . . . . . . . . . . . . . . . . 125

3.1.1.1.3 Concrete under MultiaxialLoadings . . . . . . . . . . . . . . . . . . . . . . 126

3.1.1.2 Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 1293.1.1.2.1 Ductile Mode of Degradation in

Metals . . . . . . . . . . . . . . . . . . . . . . . . 1293.1.1.2.2 Quasi-Brittle Damage . . . . . . . . . . . 131

3.1.1.2.2.1 CementitiousMaterials . . . . . . . . . . . . 131

3.1.1.2.2.2 Metallic Materials . . . . 1373.1.2 Non-mechanical Loading . . . . . . . . . . . . . . . . . . . . . . . . . 140

3.1.2.1 Thermal Loading . . . . . . . . . . . . . . . . . . . . . . . . 1403.1.2.1.1 Degradation of Concrete Due to

Thermal Incompatibility of ItsComponents . . . . . . . . . . . . . . . . . . . 140

3.1.2.1.2 Stresses Due to ThermalLoading . . . . . . . . . . . . . . . . . . . . . . . 141

3.1.2.1.3 Temperature and StressDevelopment in Concrete atthe Early Age Due to Heat ofHydration . . . . . . . . . . . . . . . . . . . . . 142

3.1.2.2 Thermo-Hygral Loading . . . . . . . . . . . . . . . . . . 1433.1.2.2.1 Hygral Behaviour of Hardened

Cement Paste . . . . . . . . . . . . . . . . . . 1433.1.2.2.2 Influence of Cracks on the

Moisture Transport . . . . . . . . . . . . . 1473.1.2.2.3 Freeze Thaw . . . . . . . . . . . . . . . . . . . 148

3.1.2.3 Chemical Loading . . . . . . . . . . . . . . . . . . . . . . . 1503.1.2.3.1 Microstructure of Cementitious

Materials . . . . . . . . . . . . . . . . . . . . . . 1503.1.2.3.2 Dissolution . . . . . . . . . . . . . . . . . . . . . 1523.1.2.3.3 Expansion . . . . . . . . . . . . . . . . . . . . . 157

3.1.2.3.3.1 Sulphate Attackon Concrete andMortar . . . . . . . . . . . . . . 157

3.1.2.3.3.2 Alkali-AggregateReaction inConcrete . . . . . . . . . . . . 158

3.1.3 Accumulation in Soils Due to Cyclic Loading: ADeterioration Phenomenon? . . . . . . . . . . . . . . . . . . . . . . 160

XII Contents

3.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1633.2.1 Laboratory Testing of Structural Materials . . . . . . . . . 163

3.2.1.1 Micro-macrocrack Detection in Metals . . . . . . 1633.2.1.1.1 Electric Resistance

Measurements . . . . . . . . . . . . . . . . . . 1633.2.1.1.1.1 Introduction . . . . . . . . . 1633.2.1.1.1.2 Measurement of

the ElectricalResistance . . . . . . . . . . . 165

3.2.1.1.1.3 Calculation of theElectrical Resistance . . 166

3.2.1.1.1.4 Experiments . . . . . . . . . 1663.2.1.1.1.5 Experimental

Results . . . . . . . . . . . . . 1673.2.1.1.2 Acoustic Emission . . . . . . . . . . . . . . 169

3.2.1.1.2.1 Location ofAcoustic EmissionSources . . . . . . . . . . . . . 171

3.2.1.1.2.2 Linear Location ofAcoustic EmissionSources . . . . . . . . . . . . . 171

3.2.1.1.2.3 Location of Sourcesin Two Dimensions . . . 171

3.2.1.1.2.4 Kaiser Effect . . . . . . . . 1723.2.1.1.2.5 Experimental

Procedures . . . . . . . . . . 1723.2.1.1.2.6 Experimental

Results . . . . . . . . . . . . . 1743.2.1.2 Degradation of Concrete Subjected to

Cyclic Compressive Loading . . . . . . . . . . . . . . . 1803.2.1.2.1 Test Series and Experimental

Strategy . . . . . . . . . . . . . . . . . . . . . . . 1803.2.1.2.2 Degradation Determined by

Decrease of Stiffness . . . . . . . . . . . . . 1823.2.1.2.3 Degradation Determined by

Changes in Stress-StrainRelation . . . . . . . . . . . . . . . . . . . . . . . 183

3.2.1.2.4 Adequate Description ofDegradation by Fatigue Strain . . . . 185

3.2.1.2.5 Behaviour of High StrengthConcrete and Air-EntrainedConcrete . . . . . . . . . . . . . . . . . . . . . . . 187

3.2.1.2.6 Influence of Various CoarseAggregates and DifferentGrading Curves . . . . . . . . . . . . . . . . 189

Contents XIII

3.2.1.2.7 Cracking in the MicrostructureDue to Cyclic Loading . . . . . . . . . . . 190

3.2.1.2.8 Influence of Single Rest Periods . . . 1913.2.1.2.9 Sequence Effect Determined by

Two-Stage Tests . . . . . . . . . . . . . . . . 1933.2.1.3 Degradation of Concrete Subjected to

Freeze Thaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1943.2.2 High-Cycle Laboratory Tests on Soils . . . . . . . . . . . . . . 1983.2.3 Structural Testing of Composite Structures of Steel

and Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2073.2.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2073.2.3.2 Basic Tests for the Fatigue Resistance of

Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . 2123.2.3.2.1 Test Program . . . . . . . . . . . . . . . . . . 2123.2.3.2.2 Test Specimens . . . . . . . . . . . . . . . . . 2153.2.3.2.3 Test Setup and Loading

Procedure . . . . . . . . . . . . . . . . . . . . . 2163.2.3.2.4 Material Properties . . . . . . . . . . . . . 2173.2.3.2.5 Results of the Push-Out Tests . . . . 219

3.2.3.2.5.1 General . . . . . . . . . . . . . 2193.2.3.2.5.2 Results of the

Constant AmplitudeTests . . . . . . . . . . . . . . . 219

3.2.3.2.6 Results of the Tests withMultiple Blocks of Loading . . . . . . . 222

3.2.3.2.7 Results of the Tests Regardingthe Mode Control and the Effectof Low Temperature . . . . . . . . . . . . 223

3.2.3.2.8 Results of the Tests RegardingCrack Initiation and CrackPropagation . . . . . . . . . . . . . . . . . . . . 225

3.2.3.3 Fatigue Tests of Full-Scale CompositeBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2253.2.3.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . 2253.2.3.3.2 Test Program . . . . . . . . . . . . . . . . . . 226

3.2.3.4 Test Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273.2.3.5 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2273.2.3.6 Material Properties . . . . . . . . . . . . . . . . . . . . . . 2313.2.3.7 Main Results of the Beam Tests . . . . . . . . . . . 232

3.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2363.3.1 Load Induced Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

3.3.1.1 Damage in Cementitious MaterialsSubjected to Quasi Static Loading . . . . . . . . . 2373.3.1.1.1 Continuum-Based Models . . . . . . . . 237

XIV Contents

3.3.1.1.1.1 Damage Mechanics-Based Models . . . . . . . . 238

3.3.1.1.1.2 Elastoplastic Models . . 2443.3.1.1.1.3 Coupled

Elastoplastic-Damage Models . . . . . . 244

3.3.1.1.1.4 MultisurfaceElastoplastic-Damage Model forConcrete . . . . . . . . . . . . 246

3.3.1.1.2 Embedded Crack Models . . . . . . . . 2523.3.1.2 Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 255

3.3.1.2.1 Mechanism-Oriented Simulationof Low Cycle Fatigue of MetallicStructures . . . . . . . . . . . . . . . . . . . . . 2553.3.1.2.1.1 Macroscopic

Elasto-PlasticDamage Model forCyclic Loading . . . . . . . 256

3.3.1.2.1.2 Model Validation . . . . . 2593.3.1.2.2 Quasi-Brittle Damage in

Materials . . . . . . . . . . . . . . . . . . . . . . 2613.3.1.2.2.1 Cementitious

Materials . . . . . . . . . . . . 2613.3.1.2.2.2 Metallic Materials . . . . 270

3.3.2 Non-mechanical Loading and Interactions . . . . . . . . . . 2853.3.2.1 Thermo-Hygro-Mechanical Modelling of

Cementitious Materials - Shrinkage andCreep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2853.3.2.1.1 Introductory Remarks . . . . . . . . . . . 2853.3.2.1.2 State Equations . . . . . . . . . . . . . . . . 2863.3.2.1.3 Identification of Coupling

Coefficients . . . . . . . . . . . . . . . . . . . . 2883.3.2.1.4 Effective Stresses . . . . . . . . . . . . . . . 2893.3.2.1.5 Multisurface Damage-Plasticity

Model for Partially SaturatedConcrete . . . . . . . . . . . . . . . . . . . . . . . 290

3.3.2.1.6 Long-Term Creep . . . . . . . . . . . . . . . 2913.3.2.1.7 Moisture and Heat Transport . . . . 292

3.3.2.1.7.1 Freeze Thaw . . . . . . . . . 2933.3.2.2 Chemo-Mechanical Modelling of

Cementitious Materials . . . . . . . . . . . . . . . . . . . 2943.3.2.2.1 Models for Ion Transport and

Dissolution Processes . . . . . . . . . . . . 295

Contents XV

3.3.2.2.1.1 IntroductoryRemarks . . . . . . . . . . . . 295

3.3.2.2.1.2 Initial BoundaryValue Problem . . . . . . . 296

3.3.2.2.1.3 Constitutive Laws . . . . 2973.3.2.2.1.4 Migration of

Calcium Ionsin Water andElectrolyteSolutions . . . . . . . . . . . . 298

3.3.2.2.1.5 Evolution Laws . . . . . . 3003.3.2.2.2 Models for Expansive Processes . . . 302

3.3.2.2.2.1 IntroductoryRemarks . . . . . . . . . . . . 302

3.3.2.2.2.2 Balance Equations . . . 3053.3.2.2.2.3 Constitutive Laws . . . . 3073.3.2.2.2.4 Model Calibration . . . . 311

3.3.3 A High-Cycle Model for Soils . . . . . . . . . . . . . . . . . . . . . 3133.3.4 Models for the Fatigue Resistance of Composite

Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3163.3.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3163.3.4.2 Modelling of the Local Behaviour of Shear

Connectors in the Case of Cyclic Loading . . . 3173.3.4.2.1 Static Strength of Headed Shear

Studs without Any Pre-damage . . . 3173.3.4.2.2 Failure Modes of Headed Shear

Studs Subjected to High-CycleLoading . . . . . . . . . . . . . . . . . . . . . . . 322

3.3.4.2.3 Correlation between theReduced Static Strength andthe Geometrical Property of theFatigue Fracture Area . . . . . . . . . . . 327

3.3.4.2.4 Lifetime - Number of Cyclesto Failure Based on ForceControlled Fatigue Tests . . . . . . . . . 329

3.3.4.2.5 Reduced Static Strength overLifetime . . . . . . . . . . . . . . . . . . . . . . . 330

3.3.4.2.6 Load-Slip Behaviour . . . . . . . . . . . . 3323.3.4.2.7 Crack Initiation and Crack

Development . . . . . . . . . . . . . . . . . . . 3343.3.4.2.8 Improved Damage Accumulation

Model . . . . . . . . . . . . . . . . . . . . . . . . . 3373.3.4.2.9 Ductility and Crack Formation . . . 341

XVI Contents

3.3.4.2.10 Finite Element Calculations ofthe (Reduced) Static Strengthof Headed Shear Studs inPush-Out Specimens . . . . . . . . . . . . 341

3.3.4.2.11 Effect of the Control Mode -Effect of Low Temperatures . . . . . . 344

3.3.4.3 Modelling of the Global Behaviour ofComposite Beams Subjected to CyclicLoading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3453.3.4.3.1 Material Model for the Concrete

Behaviour . . . . . . . . . . . . . . . . . . . . . 3453.3.4.3.2 Effect of High-Cycle Loading

on Load Bearing Capacity ofComposite Beams . . . . . . . . . . . . . . . 346

3.3.4.3.3 Cyclic Behaviour of CompositeBeams - Development of Slip . . . . . 349

3.3.4.3.4 Effect of Cyclic Loading onBeams with Tension Flanges . . . . . 350

3.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3513.4.1 Durability Analysis of a Concrete Tunnel Shell . . . . . . 3513.4.2 Durability Analysis of a Cementitious Beam

Exposed to Calcium Leaching and ExternalLoading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

3.4.3 Durability Analysis of a Sealed Panel with aLeakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

3.4.4 Numerical Simulation of a Concrete Beam Affectedby Alkali-Silica Reaction . . . . . . . . . . . . . . . . . . . . . . . . . 359

3.4.5 Lifetime Assessment of a Spherical MetallicContainer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

4 Methodological Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 3654.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

4.1.1 Classification of Deterioration Problems . . . . . . . . . . . . 3664.1.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3684.1.3 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3694.1.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

4.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3724.2.1 Generalization of Single- and Multi-field Models . . . . . 372

4.2.1.1 Integral Format of Balance Equations . . . . . . 3734.2.1.2 Strong Form of Individual Balance

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3744.2.2 Strategy of Numerical Solution . . . . . . . . . . . . . . . . . . . . 3764.2.3 Weak Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

4.2.3.1 Weak Form of Coupled Balance Equations . . 377

Contents XVII

4.2.3.2 Linearized Weak Form of Coupled BalanceEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

4.2.4 Spatial Discretization Methods . . . . . . . . . . . . . . . . . . . . 3794.2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3794.2.4.2 Generalized Finite Element Discretization

of Multifield Problems . . . . . . . . . . . . . . . . . . . . 3804.2.4.2.1 Approximations . . . . . . . . . . . . . . . . 3804.2.4.2.2 Non-Linear Semidiscrete

Balance . . . . . . . . . . . . . . . . . . . . . . . 3834.2.4.2.3 Linearized Semidiscrete Balance . . 3854.2.4.2.4 Generation of Element and

Structural Quantities . . . . . . . . . . . . 3864.2.4.3 p-Finite Element Method . . . . . . . . . . . . . . . . . 387

4.2.4.3.1 Onedimensional Higher-OrderShape Function Concepts . . . . . . . . 3894.2.4.3.1.1 Shape Functions of

the Legendre-Type . . . 3894.2.4.3.1.2 Comparison of Both

Shape FunctionConcepts . . . . . . . . . . . . 390

4.2.4.3.2 3D-p-Finite Element MethodBased on Hierarchical LegendrePolynomials . . . . . . . . . . . . . . . . . . . . 3924.2.4.3.2.1 Generation of

3D-p-ShapeFunctions . . . . . . . . . . . 392

4.2.4.3.2.2 SpatiallyAnisotropicApproximationOrders . . . . . . . . . . . . . . 394

4.2.4.3.2.3 Field-wise Choice ofthe ApproximationOrder . . . . . . . . . . . . . . . 397

4.2.4.3.2.4 GeometryApproximation . . . . . . . 402

4.2.5 Solution of Stationary Problems . . . . . . . . . . . . . . . . . . . 4034.2.5.1 Numerical Solution Technique . . . . . . . . . . . . . 4034.2.5.2 Iteration Methods . . . . . . . . . . . . . . . . . . . . . . . 4034.2.5.3 Arc-Length Controlled Analysis . . . . . . . . . . . 407

4.2.6 Temporal Discretization Methods . . . . . . . . . . . . . . . . . . 4084.2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

4.2.6.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . 4104.2.6.1.2 Newmark-α Time Integration

Schemes . . . . . . . . . . . . . . . . . . . . . . . 411

XVIII Contents

4.2.6.1.3 Galerkin Time IntegrationSchemes . . . . . . . . . . . . . . . . . . . . . . . 411

4.2.6.2 Newmark-α Time Integration Schemes . . . . . 4124.2.6.2.1 Non-linear Semidiscrete Initial

Value Problem . . . . . . . . . . . . . . . . . 4124.2.6.2.2 Numerical Concept of

Newmark-α Time IntegrationSchemes . . . . . . . . . . . . . . . . . . . . . . . 413

4.2.6.2.3 Time Discretization . . . . . . . . . . . . . 4144.2.6.2.4 Approximation of State

Variables . . . . . . . . . . . . . . . . . . . . . . 4144.2.6.2.5 Algorithmic Semidiscrete

Balance Equation . . . . . . . . . . . . . . . 4154.2.6.2.6 Effective Balance Equation . . . . . . . 4154.2.6.2.7 Newmark-α Algorithm . . . . . . . . . . 416

4.2.6.3 Discontinuous and Continuous GalerkinTime Integration Schemes . . . . . . . . . . . . . . . . 4164.2.6.3.1 Time Discretization . . . . . . . . . . . . . 4184.2.6.3.2 Continuity Condition . . . . . . . . . . . . 4184.2.6.3.3 Temporal Weak Form . . . . . . . . . . . 4194.2.6.3.4 Linearization . . . . . . . . . . . . . . . . . . . 4194.2.6.3.5 Temporal Galerkin

Approximation . . . . . . . . . . . . . . . . . 4194.2.6.3.6 Discontinuous Bubnov-Galerkin

Schemes dG(p) . . . . . . . . . . . . . . . . . 4214.2.6.3.7 Continuous Petrov-Galerkin

Schemes cG(p) . . . . . . . . . . . . . . . . . 4224.2.6.3.8 Newton-Raphson Iteration . . . . . . . 4224.2.6.3.9 Algorithmic Set-Up of Galerkin

Schemes . . . . . . . . . . . . . . . . . . . . . . . 4224.2.7 Generalized Computational Durabilty Mechanics . . . . 4244.2.8 Adaptivity in Space and Time . . . . . . . . . . . . . . . . . . . . 425

4.2.8.1 Error-Controlled Spatial Adaptivity . . . . . . . . 4254.2.8.1.1 Variational Functional . . . . . . . . . . . 4274.2.8.1.2 Interpolation . . . . . . . . . . . . . . . . . . . 4284.2.8.1.3 Stress Computation . . . . . . . . . . . . . 4284.2.8.1.4 Discretized Weak Form . . . . . . . . . . 4294.2.8.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . 4304.2.8.1.6 Hanging Node Concept . . . . . . . . . . 4314.2.8.1.7 Error Criteria . . . . . . . . . . . . . . . . . . 431

4.2.8.1.7.1 Warping-BasedError Criterion . . . . . . 431

4.2.8.1.7.2 Residual-BasedError Criterion . . . . . . 432

4.2.8.1.8 Program Flow . . . . . . . . . . . . . . . . . . 433

Contents XIX

4.2.8.1.9 Transfer of History Variables . . . . . 4344.2.8.1.10 Examples . . . . . . . . . . . . . . . . . . . . . . 434

4.2.8.1.10.1 Uniaxial Bending(Beam of UniformThickness) . . . . . . . . . . 434

4.2.8.1.10.2 Uniaxial Bending(Beam of VariableThickness) . . . . . . . . . . 437

4.2.8.1.10.3 Biaxial Bending(Thick Plate ofUniform Thickness) . . 439

4.2.8.2 Error-Controlled Temporal Adaptivity . . . . . . 4434.2.8.2.1 Local a Posteriori h- and

p-Method Error Estimates . . . . . . . 4434.2.8.2.2 Local a Posteriori h- and

p-Method Error Indicators . . . . . . . 4444.2.8.2.3 Local Zienkiewicz a Posteriori

Error Indicators . . . . . . . . . . . . . . . . 4444.2.8.2.4 Adaptive Time Stepping

Procedure . . . . . . . . . . . . . . . . . . . . . 4464.2.8.2.5 Algorithmic Set-Up . . . . . . . . . . . . . 447

4.2.9 Discontinuous Finite Elements . . . . . . . . . . . . . . . . . . . . 4484.2.9.1 Overview and Motivation . . . . . . . . . . . . . . . . . 4484.2.9.2 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

4.2.9.2.1 Extended Finite ElementMethod (XFEM) . . . . . . . . . . . . . . . 4494.2.9.2.1.1 Partition of Unity . . . . 4494.2.9.2.1.2 XFEM

DisplacementField . . . . . . . . . . . . . . . 452

4.2.9.2.1.3 IntegratingDiscontinuousFunctions . . . . . . . . . . . 458

4.2.9.2.1.4 p-Version of theXFEM . . . . . . . . . . . . . . 469

4.2.9.2.1.5 3D XFEM . . . . . . . . . . 4734.2.9.2.1.6 XFEM for Cohesive

Cracks . . . . . . . . . . . . . . 4764.2.9.2.2 Strong Discontinuity Approach

and Enhanced Assumed Strain . . . 4794.2.9.2.2.1 Kinematics:

ModelingEmbedded StrongDiscontinuities . . . . . . . 479

XX Contents

4.2.9.2.2.2 NumericalImplementation . . . . . . 482

4.2.9.2.2.3 Numerical Example:3-Point BendingProblem . . . . . . . . . . . . 486

4.2.9.3 Crackgrowth Criteria . . . . . . . . . . . . . . . . . . . . . 4884.2.9.3.1 Hoop Stresses . . . . . . . . . . . . . . . . . . 4894.2.9.3.2 Mode-I-Crack Extension . . . . . . . . . 4904.2.9.3.3 Minimum Energy . . . . . . . . . . . . . . . 492

4.2.9.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4934.2.9.4.1 Double Notched Slab . . . . . . . . . . . . 4934.2.9.4.2 Anchor Pull-Out . . . . . . . . . . . . . . . . 494

4.2.10 Substructuring and Model Reduction of PartiallyDamaged Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4984.2.10.1 Motivation and Overview . . . . . . . . . . . . . . . . . 4994.2.10.2 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5014.2.10.3 Derivation of a Substructure Technique for

Nonlinear Dynamics . . . . . . . . . . . . . . . . . . . . . . 5024.2.10.3.1 Craig-Bampton Method . . . . . . . . . 5024.2.10.3.2 Model Reduction of Linear

Dynamic Structures . . . . . . . . . . . . . 5034.2.10.3.2.1 Modal Reduction . . . . . 5034.2.10.3.2.2 Proper Orthogonal

Decomposition . . . . . . . 5044.2.10.3.2.3 Pade-Via-Lanczos

Algorithm . . . . . . . . . . . 5044.2.10.3.2.4 Load-Dependent

Ritz Vectors . . . . . . . . . 5064.2.10.3.3 Substructuring in the

Framework of NonlinearDynamics . . . . . . . . . . . . . . . . . . . . . . 5064.2.10.3.3.1 Discretisation and

Linearisation . . . . . . . . 5064.2.10.3.3.2 Primal Assembly . . . . . 5094.2.10.3.3.3 Solution of the

DecomposedStructure . . . . . . . . . . . 511

4.2.10.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5124.2.11 Strategy for Polycyclic Loading of Soil . . . . . . . . . . . . . 517

4.3 System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5194.3.1 Covariance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5204.3.2 Subspace Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

4.3.2.1 State Space Model . . . . . . . . . . . . . . . . . . . . . . . 5204.3.2.2 Subspace Identification . . . . . . . . . . . . . . . . . . . 5224.3.2.3 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 527

Contents XXI

4.4 Reliability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5284.4.1 General Problem Definition . . . . . . . . . . . . . . . . . . . . . . 5294.4.2 Time-Invariant Problems . . . . . . . . . . . . . . . . . . . . . . . . . 531

4.4.2.1 Approximation Methods . . . . . . . . . . . . . . . . . . 5314.4.2.2 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . 533

4.4.2.2.1 Importance Sampling . . . . . . . . . . . . 5344.4.2.2.2 Latin Hypercube Sampling . . . . . . . 5354.4.2.2.3 Subset Methods . . . . . . . . . . . . . . . . 536

4.4.2.3 Response Surface Methods . . . . . . . . . . . . . . . . 5374.4.2.4 Evaluation of Uncertainties and Choice of

Random Variables . . . . . . . . . . . . . . . . . . . . . . . 5394.4.3 Time-Variant Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 540

4.4.3.1 Time-Integrated Approach . . . . . . . . . . . . . . . . 5404.4.3.2 Time Discretization Approach . . . . . . . . . . . . . 5404.4.3.3 Outcrossing Methods . . . . . . . . . . . . . . . . . . . . . 541

4.4.4 Parallelization of Reliability Analyses . . . . . . . . . . . . . . 5424.4.4.1 Reliability Analysis of Fatigue Processes . . . . 5434.4.4.2 Parallelization Example . . . . . . . . . . . . . . . . . . 544

4.5 Optimization and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5454.5.1 Classification of Optimization Problems . . . . . . . . . . . . 5464.5.2 Design as an Optimization Problem . . . . . . . . . . . . . . . . 5474.5.3 Numerical Optimization Methods . . . . . . . . . . . . . . . . . 551

4.5.3.1 Derivative-Based Methods . . . . . . . . . . . . . . . . 5524.5.3.2 Derivative-Free Strategies . . . . . . . . . . . . . . . . . 555

4.5.4 Parallelization of Optimization Strategies . . . . . . . . . . . 5594.5.4.1 Parallelization with Gradient-Based

Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5604.5.4.2 Parallelization Using Evolution Strategies . . . 5604.5.4.3 Distributed and Parallel Software

Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5614.6 Application of Lifetime-Oriented Analysis and Design . . . . . . 561

4.6.1 Testing of Beam-Like Structures . . . . . . . . . . . . . . . . . . . 5624.6.1.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 5634.6.1.2 Identification of Modal Data . . . . . . . . . . . . . . 5634.6.1.3 Updating of the Finite Element Model . . . . . . 566

4.6.2 Lifetime Analysis for Dynamically LoadedStructures at BMW AG . . . . . . . . . . . . . . . . . . . . . . . . . . 5724.6.2.1 Works for the New 3-Series Convertible . . . . . 5724.6.2.2 The Shaker Test . . . . . . . . . . . . . . . . . . . . . . . . . 5744.6.2.3 Approach 1: Time History Calculation and

Amplitude Counting . . . . . . . . . . . . . . . . . . . . . 5744.6.2.3.1 Structural Analysis Using Time

Integration . . . . . . . . . . . . . . . . . . . . 5754.6.2.3.2 Cycle Counting Using the

Rainflow Method . . . . . . . . . . . . . . . 575

XXII Contents

4.6.2.3.3 Damage Calculation . . . . . . . . . . . . . 5764.6.2.4 Approach 2: Power Spectral Density

Functions and Calculation of SpectralMoments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5774.6.2.4.1 Structural Analysis Using

Power Spectral Density (PSD)Functions . . . . . . . . . . . . . . . . . . . . . 577

4.6.2.4.2 Analytical Counting Method . . . . . 5784.6.2.4.3 Damage Accumulation for the

Analytical Case . . . . . . . . . . . . . . . . . 5794.6.2.5 Comparison of the Results . . . . . . . . . . . . . . . . 5804.6.2.6 Summary and Outlook . . . . . . . . . . . . . . . . . . . 582

4.6.3 Lifetime-Oriented Analysis of Concrete StructuresSubjected to Environmental Attack . . . . . . . . . . . . . . . . 5834.6.3.1 Hygro-Mechanical Analysis of a Concrete

Shell Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 5834.6.3.1.1 Conclusive Remarks on the

Hygro-Mechanical Analysis . . . . . . 5904.6.3.2 Calcium Leaching of Cementitious

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5914.6.3.2.1 Calcium Leaching of a

Cementitious Bar . . . . . . . . . . . . . . . 5924.6.3.2.1.1 Analysis of the

Numerical Results . . . . 5924.6.3.2.1.2 Adaptive Newmark

Solution . . . . . . . . . . . . 5944.6.3.2.1.3 Robustness of

Galerkin Solutions . . . . 5944.6.3.2.1.4 Error Estimates for

Newmark Solutions . . . 5944.6.3.2.1.5 Error Estimates for

Galerkin Solutions . . . . 5984.6.3.2.1.6 Order of Accuracy

of Galerkin Schemes . . 6004.6.3.2.2 Calcium Leaching of a

Cementitious Beam . . . . . . . . . . . . . 6014.6.3.2.2.1 Analysis of the

Numerical Results . . . . 6024.6.3.2.2.2 Robustness of

ContinuousGalerkin Solutions . . . . 603

4.6.4 Arched Steel Bridge Under Wind Loading . . . . . . . . . . 6074.6.4.1 Definition of Structural Problem . . . . . . . . . . . 6074.6.4.2 Probabilistic Lifetime Assessment . . . . . . . . . . 610

4.6.4.2.1 Micro Time Scale . . . . . . . . . . . . . . . 610

Contents XXIII

4.6.4.2.2 Macro Time Scale . . . . . . . . . . . . . . 6114.6.4.3 Results of Structural Optimization . . . . . . . . . 6134.6.4.4 Parallelization of Analyses . . . . . . . . . . . . . . . . 6144.6.4.5 Final Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 615

4.6.5 Arched Reinforced Concrete Bridge . . . . . . . . . . . . . . . . 6164.6.5.1 Numerical Simulation . . . . . . . . . . . . . . . . . . . . 617

4.6.5.1.1 Experimental Investigation onMechanical Concrete Properties . . 6184.6.5.1.1.1 Non-destructive

Tests . . . . . . . . . . . . . . . 6184.6.5.1.1.2 Destructive Tests . . . . . 6194.6.5.1.1.3 Microscopic

Analysis . . . . . . . . . . . . 6214.6.5.1.1.4 Cyclic Tests . . . . . . . . . 621

4.6.5.1.2 Finite Element Model . . . . . . . . . . . 6244.6.5.1.3 Material Model . . . . . . . . . . . . . . . . . 6254.6.5.1.4 Damage Mechanisms . . . . . . . . . . . . 625

4.6.5.1.4.1 Corrosion of theReinforcement SteelBars . . . . . . . . . . . . . . . . 625

4.6.5.1.4.2 Fatigue of thePrestressingTendons . . . . . . . . . . . . 626

4.6.5.1.5 Modelling of Uncertainties . . . . . . . 6274.6.5.1.5.1 Long-Term

Developement ofConcrete Strength . . . . 628

4.6.5.1.5.2 Determination ofMaterial Properties . . . 630

4.6.5.1.5.3 Modelling of SpatialScatter by RandomFields . . . . . . . . . . . . . . 631

4.6.5.1.6 Lifetime Simulation . . . . . . . . . . . . . 6324.6.5.1.7 Conclusions . . . . . . . . . . . . . . . . . . . . 634

4.6.5.2 Experimental Verification . . . . . . . . . . . . . . . . . 6344.6.5.2.1 State Space Model for

Mechanical Structures . . . . . . . . . . . 6354.6.5.2.2 White Box Model - Physical

Interpretable Parameters . . . . . . . . 6364.6.5.2.3 Identification of Measured

Mechanical Structures . . . . . . . . . . . 6374.6.5.2.3.1 Black Box Model -

DeterministicSystemIdentification . . . . . . . . 637

XXIV Contents

4.6.5.2.3.2 Differences betweenTheory andExperiment . . . . . . . . . 638

4.6.5.2.4 Experiments . . . . . . . . . . . . . . . . . . . 6414.6.5.2.4.1 Cantilever Bending

Beam . . . . . . . . . . . . . . . 6414.6.5.2.4.2 Tied-Arch

Bridge nearHunxe - Germany . . . . 642

4.6.5.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . 6454.6.6 Examples for the Prediction of Settlement Due to

Polycyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

5 Future Life Time Oriented Design Concepts . . . . . . . . . . . . . 6535.1 Exemplary Realization of Lifetime Control Using Concepts

as Presented Here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6535.1.1 Reinforced Concrete Column under Fatigue Load . . . . 6535.1.2 Connection Plates of an Arched Steel Bridge . . . . . . . . 6555.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658

5.2 Lifetime-Control Provisions in Current Standardization. . . . . 6585.3 Incorporation into Structural Engineering Standards . . . . . . . 659

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

List of Figures

1.1 Lifetime-related aspects of structural concrete . . . . . . . . . . . . . . . 21.2 Evolution of degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Time-dependent reliability of structures . . . . . . . . . . . . . . . . . . . . . 31.4 Time-dependent reliability of structures with upgrading by

repairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Working-life related building classes . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Service Life control and economic aspects . . . . . . . . . . . . . . . . . . . 61.7 Related Collaborative Research Centers . . . . . . . . . . . . . . . . . . . . . 6

2.1 Typical wind load process (a), and related low frequency (b)and high frequency (c) response of a structure [572] . . . . . . . . . . 10

2.2 Curve of the total variance of the base bending moment of acantilever due to buffeting excitation plotted over frequencies[572] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Comparison of the occurence of repeated wind effects atdifferent locations in Germany and a codified representation . . . 15

2.4 Distribution of absolute frequencies of normalized gustresponses into subsequent classes of different levels of effect . . . . 17

2.5 Comparison of the distribution of cyclic stress amplitudeswith the S-N curve (Wohler curve) of stress concentrationcategory 36* after [30] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.6 Rosettes of wind quantities at Hannover (12 sectors, 50 yearsreturn period) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.7 Roughness lengths of the terrain in the farther vicinity of thebuilding location [771] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.8 Sketch of a building contour and facade element exposed to apressure coefficient cp = −1.4 [32] . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.9 Von Karman vortex trail formed by vortex shedding . . . . . . . . 262.10 Dependence of the vortex shedding frequency fv on the wind

velocity u. fn is the natural frequency of the structure . . . . . . . . 27

XXVI List of Figures

2.11 Wind velocity, measured and simulated deflection vs. timefor the bridge hanger 1 (left) and 2 (right) . . . . . . . . . . . . . . . . . . 30

2.12 Width of the lock-in range for bridge tie rods . . . . . . . . . . . . . . . . 322.13 Measured and simulated amplitude of the displacement

within and outside of the lock-in range . . . . . . . . . . . . . . . . . . . . . 332.14 Sample realizations of a renewal process (left) and of a

pulse-process (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.15 Wavelength of the visible light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.16 Climatic load on a structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.17 Test stand for the analysis of thermal actions on concrete

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.18 Measured temperature profile during a summer day . . . . . . . . . . 412.19 Rainflow analysis of the macroscopic temperature behaviour . . . 422.20 Temperature behaviour due to a sudden change in solar

radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.21 Temperature distributions determined at 16 layers within a

cooling tower shell under constant external load actions . . . . . . . 442.22 Effect of the mean wind speed on the development of the

temperature difference of a cooling tower shell . . . . . . . . . . . . . . . 452.23 Frequency distribution of the total weight G of the

representative lorries per 24 hours based on traffic data ofAuxerre in France (1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.24 Gross vehicle and axle weight distribution of recorded trafficdata from England, France and Germany . . . . . . . . . . . . . . . . . . . 48

2.25 Histogram of vehicle Type 3 and approximation by twoseparate distribution functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.26 Comparison of measured and theoretical values for thedensity function of intervehicle distances . . . . . . . . . . . . . . . . . . . . 51

2.27 Model for the vehicles and local irregularities and powerspectral density of the pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.28 Eigenvalues of the first mode of steel and concrete Bridges[169] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.29 Cumulative frequency of the action effects for differentvehicle speeds [530] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.30 Influence of the quality of the pavement on the dynamicamplification factor ϕ [530] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.31 Influence of the span length and the number of loaded laneson the dynamic amplification factor ϕ . . . . . . . . . . . . . . . . . . . . . . 56

2.32 Additional dynamic factor Δϕ taking into accountirregularities of the pavement [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.33 Determination of the characteristic values of the actioneffects from the random generations of loads . . . . . . . . . . . . . . . . . 58

2.34 Load Model 1 according to Eurocode 1-2 . . . . . . . . . . . . . . . . . . . . 592.35 Comparison of the Load Model 1 in Eurocode -2 with the

characteristic values obtained from real traffic simulations . . . . . 59

List of Figures XXVII

2.36 Determination of the representative values and thecorresponding dynamic factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.37 Factors ψTR for frequent design situations acc. to [37] foraverage pavement quality with Φ(Ωh) = 16 . . . . . . . . . . . . . . . . . . 61

2.38 Influence of the pavement quality on the factor ΨTR forfrequent design situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.39 Determination of stress spectra and damage accumulationdue to fatigue loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.40 Fatigue strength curves for structural steel and reinforcement . . 642.41 Typical examples for fatigue strength categories . . . . . . . . . . . . . . 652.42 Set of lorries of Fatigue Load Model 4 in Eurocode -2 and

contact surfaces of the wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.43 Distribution of transverse location of centre line of vehicles

and dynamic load amplification factor near expansion joints . . . 672.44 Linear damage accumulation and damage equivalent dynamic

amplification factor ϕfat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.45 Influence of the pavement quality on the damage equivalent

dynamic amplification factor [530] . . . . . . . . . . . . . . . . . . . . . . . . . . 682.46 Fatigue Load model 3 in Eurocode 1-2 and fatigue verification

for steel structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.47 Example for the damage equivalent factor λe [530] . . . . . . . . . . . 702.48 Determination of the damage equivalent factor λ1 . . . . . . . . . . . . 702.49 Factors λ1 for steel bridges given in Eurocode 3-2 . . . . . . . . . . . . 712.50 Assumptions for the factor λ4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.51 Damage equivalent factor λmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.52 Development of the freight traffic on roads, railways and

ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742.53 Development of the number of heavy vehicles per day and

relative frequency of the gross weight for articulated vehicles . . 752.54 Development of the number of permits of heavy transports

in Bavaria and North-Rhine Westphalia and examples forvehicles for heavy transports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.55 Traffic records from the Netherlands recorded in 2006 . . . . . . . . 772.56 Heavy vehicles on the basis of the modular concept

(Giga-Liners) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782.57 Axle spacing and allowable axle weights of ”Giga-Liners” . . . . . 782.58 Pressure time history at the track-side face of a 8 m high

wall; at a fixed position; V = 234.3 km/h, [573] . . . . . . . . . . . . . . 802.59 Pressure distribution along the track-side face of a wall at

two different train speeds [573] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.60 Full scale tests performed along the high speed line

Cologne-Rhine/Main . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.61 3 Effect of train speed stagnation pressure on the head pulse

acting at the track-side face of a wall . . . . . . . . . . . . . . . . . . . . . . . 83

XXVIII List of Figures

2.62 Pressure coefficients of the head pulse from 34 passages(at the track-side wall face) at 1.65 m above track level . . . . . . . 84

2.63 Distance between the pulse peaks and the zero crossing (ΔL1= pressure maximum, ΔL2 = pressure minimum) . . . . . . . . . . . . 84

2.64 Head pulse in a free flow at various distances from the trackaxis [98] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

2.65 Head pulse in the presence of a wall . . . . . . . . . . . . . . . . . . . . . . . . 852.66 Load pattern over the height of the wall . . . . . . . . . . . . . . . . . . . . 872.67 Variation of the time lag between maxima and minima of the

head pulse over the wall height transformed to V = 300 m/s . . . 882.68 Load factor for the load distribution over the height of the

wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882.69 Pattern of pressure coefficients cp for the ICE-3 train . . . . . . . . . 892.70 Noise protection wall and mode shape of the 1st mode . . . . . . . . 902.71 Time history of post top displacement calculated for a post

in the middle of the wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 912.72 Resonant amplification of the displacement maximum vs. the

natural frequency at train speeds between 200 and 300 km/h . . 922.73 Resonant amplification of the displacement minimum vs. the

natural frequency at train speeds between 200 and 300 km/h . . 922.74 Schematic diagram - Interaction of climate, environmental

attack and damage process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932.75 Examples of reinforcement corrosion and concrete corrosion . . . 942.76 Attacks on concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952.77 Surface of frost damaged concrete in situ . . . . . . . . . . . . . . . . . . . . 962.78 Microcracking of cement paste(left); ESEM image of frost

damaged concrete (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 972.79 Field exposure (left); Modified multi-ring electrode (right) . . . . 972.80 Effects at specific depths of water

penetration(left); Dependence of Arrhenius factor b onmoisture content (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

2.81 Air temperature and rainfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 992.82 Freeze-thaw cycle illustrated by example (left); Temperature

curve during thaw phase on November 26 (right) . . . . . . . . . . . . . 1002.83 Exemplary illustration of the change in resistance at depth

level 6.6 cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012.84 Frequency of freeze-thaw cycles depending on minimum

temperature (left) and maximum cooling and thawing rates(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

2.85 External damage of concrete specimens after one winter . . . . . . 1032.86 Correlation between surface scaling and degree of visual

damage on field exposed specimens . . . . . . . . . . . . . . . . . . . . . . . . . 1042.87 Development of external damage . . . . . . . . . . . . . . . . . . . . . . . . . . . 1052.88 Comparison of the surface scaling obtained in laboratory and

in field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

List of Figures XXIX

2.89 Concrete damage caused by thaumasite . . . . . . . . . . . . . . . . . . . . . 1082.90 Corrosion on mortar coatings in two drinking water

reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1082.91 Sources of cyclic loading of soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1102.92 Cyclic stresses in a soil element a) due to a passing wheel

load and b) due to an earthquake loading . . . . . . . . . . . . . . . . . . . 1112.93 Accumulation of settlement due to cyclic loading . . . . . . . . . . . . . 1112.94 Decomposition of a signal with varying amplitudes into

packages of cycles with constant amplitude . . . . . . . . . . . . . . . . . . 1132.95 Distinction between uniaxial IP-, multiaxial IP- and

OOP-cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1152.96 Hodograph for detrending of a strain path . . . . . . . . . . . . . . . . . . 1162.97 Multiaxial amplitude definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172.98 Complex strain loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

3.1 Schematic stress-strain diagram of cementitous materialssubjected to uniaxial compression [867] . . . . . . . . . . . . . . . . . . . . . 125

3.2 Schematic stress-strain diagram of cementitous respectivelygeological materials due to tension [538] . . . . . . . . . . . . . . . . . . . . 127

3.3 Stress-displacement diagram of a concrete specimen subjectedto cyclic tensile loading [381] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

3.4 Biaxial failure envelope for concrete [467, 567] . . . . . . . . . . . . . . . 1283.5 Stress-displacement diagrams obtained from triaxial

compression tests for three levels of confining pressure σ2 . . . . . 1283.6 Failure surface of concrete in principal stress space and crack

patterns corresponding to different triaxial loading conditions . . 1293.7 Ductile fracture surfaces of a round notched bar after 30

cycles with notch radius 2mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1303.8 (a) Void nucleation due to fracture of inclusions, (b) partition

of inclusion-matrix-area, (c) void coalescence . . . . . . . . . . . . . . . . 1303.9 Schematic S-N curves for concrete (Wohler curves) . . . . . . . . . . . 1313.10 Fatigue fracture of concrete specimens due to cyclic

compression load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323.11 Number of cycles to failure Nf for different load levels and

their variation [627] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323.12 Stress-strain relation of concrete measured after different

number of cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1333.13 Development of total longitudinal strain with the cycle ratio

(N/Nf ) [383] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1343.14 Change of secant modulus of elasticity [383] . . . . . . . . . . . . . . . . . 1353.15 Development of the value of the residual strength [70] . . . . . . . . 1353.16 Wohler curves for tensile loads [207] . . . . . . . . . . . . . . . . . . . . . . . . 1363.17 Wohler curves for flexural loads [865] . . . . . . . . . . . . . . . . . . . . . . . 1373.18 Development of strains in tensile loading [207] . . . . . . . . . . . . . . . 1373.19 Development of strains in bending [662] . . . . . . . . . . . . . . . . . . . . . 138

XXX List of Figures

3.20 Degradation process of relevant concrete properties due totensile loadings [429] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

3.21 Degradation process of relevant concrete properties due toflexural loadings [866] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

3.22 Stiffness reduction by high cycle fatigue . . . . . . . . . . . . . . . . . . . . . 1393.23 Model for brittle damage by microcrack growth . . . . . . . . . . . . . . 1403.24 Stresses in a concrete slab at one-sided, non-linear cooling

from the top [145] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1413.25 Temperature and stress development during the

first hydration phase in restrained concrete elements[763, 145, 466] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

3.26 Hygric strains vs. relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . 1443.27 Hygric strains vs. relative humidity & vs. water content . . . . . . . 1443.28 Hygric strains vs. surface free energy change . . . . . . . . . . . . . . . . . 1453.29 Hygric strains vs. surface free energy change & comparison

between measured and calculated hygric strains . . . . . . . . . . . . . . 1463.30 Sorption isotherms vs. relative humidity . . . . . . . . . . . . . . . . . . . . 1463.31 Solid density vs. relative humidity . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.32 Schematic diagram of hygric mechanisms and properties of

hardened cement paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1483.33 Comparison of macroscopic and microscopic situation of the

micro-ice-lens model during the heating and cooling phase . . . . 1493.34 Volume fractions of constituents of hardened cement paste as

a function of the water cement ratio [448] . . . . . . . . . . . . . . . . . . . 1513.35 Schematic illustration of the dissolution- and loading induced

long-term deterioration of concrete . . . . . . . . . . . . . . . . . . . . . . . . . 1533.36 Equilibrium states between the calcium concentration s

and the ratio c/s: experimental [114, 115] and analytical[307, 308] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

3.37 Decrease of compressive strength as a function of the increasein porosity resulting from calcium leaching [172] . . . . . . . . . . . . . 155

3.38 Expansion behaviour of flat mortar prisms with Portlandcement during storage in sodium sulfate solution [502] . . . . . . . . 158

3.39 Alkali-silica reaction damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1593.40 Accumulation of stress or strain, illustrated for the

two-dimensional case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1613.41 Evolution of the electrical resistance vs. number of cycles

during fatigue - plain and circular specimen . . . . . . . . . . . . . . . . . 1673.42 Evolution of the electrical resistance during fatigue - plain

specimen block-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1673.43 Electrical potential - plane specimen. . . . . . . . . . . . . . . . . . . . . . . . 1683.44 Electrical potential - circular specimen . . . . . . . . . . . . . . . . . . . . . . 1683.45 Evolution of electrical resistance vs. crack length during

fatigue - plain and circular specimen . . . . . . . . . . . . . . . . . . . . . . . 1693.46 Waveform parameters for a burst-signal . . . . . . . . . . . . . . . . . . . . . 170

List of Figures XXXI

3.47 Location of the source in two dimensions . . . . . . . . . . . . . . . . . . . . 1723.48 Geometry of the plain specimen. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1733.49 Geometry of the circular specimen . . . . . . . . . . . . . . . . . . . . . . . . . 1733.50 The position of AE-transducers on the plain specimen . . . . . . . . 1743.51 The position of AE-transducers on the circular specimen . . . . . . 1743.52 Rate of event counts during fatigue - plain specimen . . . . . . . . . . 1753.53 Rate of event counts during fatigue - circular specimen . . . . . . . 1753.54 Total event counts during fatigue - plain specimen . . . . . . . . . . . 1763.55 Total event counts during fatigue - circular specimen . . . . . . . . . 1763.56 Origin of acoustic emission - plain specimen . . . . . . . . . . . . . . . . . 1773.57 Origin of acoustic emission - circular specimen . . . . . . . . . . . . . . . 1773.58 Acoustic emission event counts vs. amplitude - plain

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1783.59 Acoustic emission event counts vs. amplitude - circular

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1783.60 Acoustic emission event counts vs. frequency - plain

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1793.61 Acoustic emission event counts vs. frequency - circular

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1793.62 Execution of the single-stage and two-stage test . . . . . . . . . . . . . 1813.63 Decrease and scatter of Estat at Smax/Smin = 0.675/0.10

(single-state-tests) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1823.64 Decrease and scatter of Edyn at Smax/Smin = 0.675/0.10

(single-state-tests) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1833.65 Variation of maximal bearable number of load cycles to

failure Nf [627] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1833.66 Measured longitudinal strain at Smax (Smax/Smin =

0.60/0.10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1843.67 Stress-strain curves at different number of cycles

(Smax/Smin = 0.60/0.10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1843.68 Total strain at Smax/Smin = 0.675/0.10 . . . . . . . . . . . . . . . . . . . . 1863.69 Calculation of fatigue strain at Smax . . . . . . . . . . . . . . . . . . . . . . . 1863.70 Formation of fatigue strain (schematically) . . . . . . . . . . . . . . . . . . 1873.71 Fatigue strain at Smax/Smin = 0.675/0.10 . . . . . . . . . . . . . . . . . . . 1873.72 Correlation between the fatigue strain and the residual

stiffness for different load levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1883.73 Correlation between the fatigue strain and the residual

stiffness of normal and high strength concrete . . . . . . . . . . . . . . . 1883.74 Correlation between the fatigue strain and the residual

stiffness of normal and air-entrained concrete . . . . . . . . . . . . . . . . 1893.75 Correlation between the fatigue strain and the residual

stiffness subjected to different aggregates in concrete . . . . . . . . . 1893.76 Correlation between the fatigue strain and the residual

stiffness subjected to different grading curves in concrete . . . . . . 1903.77 Light microscopy micrographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

XXXII List of Figures

3.78 Load history with various rest periods [150] . . . . . . . . . . . . . . . . . 1923.79 Behaviour of the longitudinal strain at

Smax/Smin = 0.675/0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1923.80 Related longitudinal strain at Smax/Smin = 0.675/0.10 . . . . . . . 1933.81 Correlation between the fatigue strain and the residual

stiffness subjected to different sequences of cyclic loading . . . . . 1943.82 Steps of exposure and measuring during CDF/CIF test [731] . . 1953.83 Example relationship between RDM and relative moisture

uptake - concrete type 2 [610] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953.84 Internal damage due to freeze-thaw cycles at several depths

of the specimen (left), Moisture uptake vs. number offreeze-thaw cycles (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

3.85 Test devices and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1993.86 Cyclic flow rule (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2003.87 Cyclic flow rule (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2013.88 Intensity of accumulation in drained cyclic element tests on

soils (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2023.89 Intensity of accumulation in drained cyclic element tests on

soils (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2043.90 Influence of the grain size distribution curve on Dacc . . . . . . . . . . 2053.91 Undrained cyclic tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2063.92 Effect of cycles at σ = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2073.93 Application of headed shear studs in composite bridges . . . . . . . 2083.94 Load-deflection behaviour of headed shear studs embedded

in solid concrete slabs under static loading . . . . . . . . . . . . . . . . . . 2093.95 Fatigue strength curve for cyclic loaded headed shear studs

according [685] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2103.96 Safety concept to determine the lifetime of composite

structures subjected to high cycle loading . . . . . . . . . . . . . . . . . . . 2113.97 Tests with multiple blocks of loading . . . . . . . . . . . . . . . . . . . . . . . 2133.98 Tests to compare the effect of the mode control - force control

vs. displacement control - and the effect of low temperature . . . 2153.99 Duration of the crack initiation phase and crack growth

velocity due to very low cyclic loads [685] . . . . . . . . . . . . . . . . . . . 2163.100 Details of the push-out test specimen . . . . . . . . . . . . . . . . . . . . . . . 2163.101 Servo hydraulic actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2173.102 Position of transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2183.103 Development of plastic slip over the fatigue life in series

S1 - S4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2203.104 Decrease of static strength vs. lifetime due to high cycle

loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2213.105 Test programme and loading parameters of the composite

beam tests VT1 and VT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2263.106 Details of test beam VT1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2283.107 Details of test beam VT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229