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

List of Figures XXXIII

3.108 Test setup of test beams VT1 and VT2 . . . . . . . . . . . . . . . . . . . . . 2303.109 Electric circuit to detect complete shear failure of headed

studs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2313.110 Change of initial deflections due to cyclic loading . . . . . . . . . . . . 2343.111 Load-deflection behaviour of test beams VT1 and VT2 in the

static tests after cyclic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2343.112 Experimental determination of the reduced static strength of

the steel section near midspan after high cycle pre-loading . . . . 2353.113 Slip along the interfaces of steel and concrete after first

loading and after cyclic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2363.114 Crack lengths at the stud feet after the cyclic loading phase -

Preparation stages for examination purposes . . . . . . . . . . . . . . . . 2373.115 Representation of different failure surfaces in the principal

strain space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2393.116 Stress-strain diagrams for uniaxial compressive and tensile

loading obtained from the damage model by Mazars . . . . . . . . 2403.117 Anisotropic damage model by [604]: Illustration of the failure

surface in the principal stress space, see eq. (3.29) . . . . . . . . . . . . 2423.118 Definition of a local coordinate system and decomposition

of the traction vector t = into the normal part tn and thetangential part tm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

3.119 Anisotropic elastoplastic damage model by [534]: Influence ofthe scalar coupling parameter β on the stress-strain diagram . . 246

3.120 Yield conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2473.121 Stress-strain relation of concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . 2493.122 Discrete representation of cracks: Traction separation law of

the format t = t([[u]]) across the crack surface . . . . . . . . . . . . . . 253

3.123 Strong Discontinuity Approach: Additive decomposition ofthe displacement field u (equation (3.84)) . . . . . . . . . . . . . . . . . . . 254

3.124 Strong Discontinuity Approach: Strain field resulting fromthe displacement field u(x) = u(x) + u(x) . . . . . . . . . . . . . . . . . . . 254

3.125 Model-based concept for life time assessment of metallicstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

3.126 Numerical and experimental data for (a) material softening and(b) ratcheting effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

3.127 Low Cycle Fatigue in metals: Numerical and experimentalresults for cyclically loaded round notched bar . . . . . . . . . . . . . . . 260

3.128 Low Cycle Fatigue in metals: Damage accumulation andpredicted damage in a cyclically loaded round notched bar . . . . 261

3.129 S-N -approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2633.130 Degradation of compressive strength and sequence effects . . . . . 2633.131 Evaluation of the approach for sequence effects . . . . . . . . . . . . . . 2643.132 Rheological element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2653.133 Fatigue strain evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2673.134 Split of fatigue strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

XXXIV List of Figures

3.135 Evaluation of the split variable βfat . . . . . . . . . . . . . . . . . . . . . . . . 2683.136 Kinked crack and its equivalent elliptical crack . . . . . . . . . . . . . . . 2773.137 Growth of the circular crack and its equivalent elliptical

crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2793.138 Order of the considered sequential loading . . . . . . . . . . . . . . . . . . . 2803.139 Evolution of the geometry and the orientations of the

equivalent elliptical crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2813.140 Evolution of the stiffness components in the principle

directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2823.141 Specimen geometry and different mesh patterns . . . . . . . . . . . . . . 2833.142 Load-cycle curves for different mesh patterns . . . . . . . . . . . . . . . . 2843.143 Chemo-mechanical damage of porous materials within the

Theory of Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2953.144 Conductivity of the pore fluid D0 and macroscopic

conductivity of non-reactive porous media φD0 . . . . . . . . . . . . . . 2993.145 Chemical equilibrium function by Gerard [307, 308] and

Delagrave et al. [232] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3023.146 Microstructure, constituents and volume fractions of concrete

as a partially saturated porous media . . . . . . . . . . . . . . . . . . . . . . . 3033.147 Chemical material parameters k and u/ r − 1 and of their

dependence on the liquid saturation sl . . . . . . . . . . . . . . . . . . . . . . 3123.148 Theoretical model for the prediction of the mean value of the

ultimate shear resistance according [684] . . . . . . . . . . . . . . . . . . . . 3173.149 Result of the statistical analysis of the results of 101 statically

loaded push-out tests according to EN 1990 [16] . . . . . . . . . . . . . 3223.150 Comparison of the result of the statistical analysis with the

rules in current German and European standards . . . . . . . . . . . . 3243.151 Preparation stages for examination purposes . . . . . . . . . . . . . . . . 3243.152 Failure modes A and B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3253.153 Weld collar - Close-up view of the crack shown in Figure

3.152 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3263.154 Correlation between reduced static strength and damage at

the stud feet based on the fatigue fracture area . . . . . . . . . . . . . . 3273.155 Correlation between reduced static strength and damage at

the stud feet based on crack lengths . . . . . . . . . . . . . . . . . . . . . . . . 3283.156 Comparison of fatigue test results with the prediction in

Eurocode 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3293.157 Model for the prediction of the fatigue life of a headed shear

stud in a push-out test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3313.158 (a) Reduced static strength over lifetime, (b) Comparison of

the reduced static strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3313.159 Load-slip curve of headed shear studs - load deflection

behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3323.160 Effect of high-cycle loading on the load-slip behaviour . . . . . . . . 3333.161 Elastic stiffness and accumulated plastic slip . . . . . . . . . . . . . . . . . 334

List of Figures XXXV

3.162 Relationship between crack velocity, crack propagation andreduction of static strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

3.163 Fatigue strength and lifetime of cyclic loaded shear studs . . . . . 3363.164 Comparison between the test results with the lifetime

prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3383.165 Damage accumulation considering the load sequence effects . . . . 3393.166 Damage accumulation in the case of multiple block loading

tests with decreasing peak loads . . . . . . . . . . . . . . . . . . . . . . . . . . . 3403.167 Comparison between the test results with the results of the

lifetime prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3403.168 Ductility after high cycle loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 3413.169 Comparison between test results and finite element

calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3423.170 Comparison between test results and finite element

calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3433.171 Test series S9 - Effect of control mode - Effect of low

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3453.172 Failure surface of the improved material model CONCRETE . . 3473.173 Comparison between the results of numerical simulations and

test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3483.174 Test beam VT1 - Effect of high cycle loading on load bearing

capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3483.175 Cyclic behaviour of test beam VT1 . . . . . . . . . . . . . . . . . . . . . . . . . 3503.176 Test beam VT2 - Effect of high cycle loading - Typical crack

formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3513.177 Geometry of a tunnel lining subjected to cyclic hygral and

thermal loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3523.178 Evolution of the crack width w of a tunnel lining subjected

to cyclic hygral and thermal loading . . . . . . . . . . . . . . . . . . . . . . . . 3523.179 Scalar damage measure d at the crown of a tunnel lining

subjected to cyclic hygral and thermal loading . . . . . . . . . . . . . . . 3533.180 Liquid saturation Sl at the crown of a tunnel lining subjected

to cyclic hygral and thermal loading . . . . . . . . . . . . . . . . . . . . . . . . 3543.181 Simulation of a cementitious beam exposed to calcium

leaching and mechanical loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 3553.182 Temporal evolution of the vertical displacement us of the

cementitious beam and prediction of the collapse . . . . . . . . . . . . . 3553.183 Chemo-mechanical analysis of a concrete panel: Conditions . . . . 3563.184 Chemo-mechanical analysis of a concrete panel: Results I . . . . . 3583.185 Chemo-mechanical analysis of a concrete panel: Results II . . . . . 3593.186 Numerical simulation of a concrete beam affected by

alkali-silica reaction: Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3603.187 Numerical simulation of a concrete beam affected by

alkali-silica reaction: Results I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

XXXVI List of Figures

3.188 Numerical simulation of a concrete beam affected byalkali-silica reaction: Results II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

3.189 Numerical simulation of a concrete beam affected byalkali-silica reaction: Results III . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

3.190 Low Cycle Fatigue Model: (a) Spherical pressure vessel, (b)Vertical displacement-time plot of the El Centro earthquake . . . 363

3.191 Low Cycle Fatigue Model: (a) Damage accumulation(El Centro earthquake), (b) Temporal evolution of themaximal void volume fraction f . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

4.1 Overview of the methodological implementation of lifetimeoriented design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

4.2 Numerical modeling and general multiphysics problem . . . . . . . . 3754.3 Modeling and numerical analysis of multiphysics problems . . . . 3764.4 Illustration of isotropic Lagrange shape functions . . . . . . . . . . . 3814.5 Illustration of anisotropic Lagrange shape functions . . . . . . . . 3824.6 Computation of generalized element tensors of multiphysics

p-finite elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3874.7 Sinusoidial loading of a truss member and rel. error of

internal energy plotted over the number of dof . . . . . . . . . . . . . . . 3884.8 Modified Legendre-polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 3904.9 Comparison of high order shape function concepts . . . . . . . . . . . . 3914.10 Comparison of the structure of element vectors and matrices

for the Legendre- and Lagrange-concept . . . . . . . . . . . . . . . . . 3924.11 3D-p-element: definition and numbering of element vertices

(Ni), edges (Ei) and faces (Fi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3934.12 3D-p-shape functions: nodal, edge, face and internal modes

for different polynomial degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3954.13 Structure types, corresponding classical finite element models

and 3D-p finite element models with spatially anisotropicapproximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

4.14 Hygro-thermo-mechanical loading of a structural segment,Fieldwise anisotropic discretization using the p-FEM . . . . . . . . . 398

4.15 Discretization of the standard structures (truss, slab, shell)into an infinite numbers of elements . . . . . . . . . . . . . . . . . . . . . . . . 399

4.16 Relative reduction of system nodes/dof for differentstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

4.17 Strategy for solving non-linear vector equation ri(u) = r . . . . . . 4044.18 Control of load factor and Newton-Raphson iteration . . . . . . 4044.19 Algorithmic set-up of the load controlled Newton-Raphson

scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4064.20 Illustration of arc-length methods and predictor step

calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4074.21 Algorithmic set-up of the arc-length controlled

Newton-Raphson scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

List of Figures XXXVII

4.22 Design of Newmark type time integration schemes . . . . . . . . . . 4134.23 Illustration of Newmark and generalized mid-point

approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4144.24 Algorithmic set-up of Newmark-α schemes including error

controlled adaptive time stepping . . . . . . . . . . . . . . . . . . . . . . . . . . 4174.25 Galerkin time integration schemes . . . . . . . . . . . . . . . . . . . . . . . . 4184.26 Algorithmic set-up of discontinuous and continuous

Galerkin time integration schemes . . . . . . . . . . . . . . . . . . . . . . . . 4234.27 Modular concept for multiphysics finite element programs . . . . . 4254.28 Example geometry and warping-based error criterion . . . . . . . . . 4324.29 Two-element example with two hanging nodes . . . . . . . . . . . . . . . 4344.30 Beam 1: Geometry and boundary conditions . . . . . . . . . . . . . . . . . 4354.31 Beam 1: Load-displacement curve for tolerr = 10−5 and crit1

(various nGP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4354.32 Beam 1: Different states of mesh refinement (Q1SPs/o, 16El.),

contours: accumulated plastic strain . . . . . . . . . . . . . . . . . . . . . . . . 4364.33 Beam 1: Load-displacement curve and number of elements

for tolerr = 10−7 and crit1 (various nGP0) . . . . . . . . . . . . . . . . . . . 4374.34 Beam 1: Load-displacement curve and number of elements

for different tolerances and crit2 (Q1SPs/o, nGP0 = 16) . . . . . . . 4384.35 Beam 2: Load-displacement curve and number of elements

for different tolerances and crit2 (Q1SPs/o, nGP = 16) . . . . . . . . 4384.36 Beam 2: Different states of mesh refinement (Q1SPs/o,

16 El.), contours: accumulated plastic strain . . . . . . . . . . . . . . . . . 4394.37 Plate 1: Geometry and boundary conditions . . . . . . . . . . . . . . . . . 4404.38 Plate 1: Load-displacement curve and number of elements for

different tolerances and crit2 (Q1SPs, nGP = 8) . . . . . . . . . . . . . . 4404.39 Plate 1: Load-displacement curve for different tolerances and

crit2 (Q1SPs, nGP = 8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4414.40 Plate 1: Different states of mesh refinement (Q1SPs/o,

16 El.), contours: accumulated plastic strain . . . . . . . . . . . . . . . . . 4414.41 Plate 1: Load-displacement curve and number of elements

for different load steps and crit2 (Q1SPs/o, nGP = 8,tolerr = 0.01) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

4.42 Plate 1: Load-displacement curve and number of elementsfor different load steps and crit2 (Q1SPs, nGP = 8,tolerr = 0.0001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

4.43 Illustration of h- and p-method error estimates andindicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

4.44 Algorithmic set-up for the error controlled adaptive timeintegration by Newmark-α schemes . . . . . . . . . . . . . . . . . . . . . . . 447

4.45 Algorithmic set-up for the error controlled adaptive timeintegration by Newmark-α or p-Galerkin methods andh-method error estimates/indicators . . . . . . . . . . . . . . . . . . . . . . . . 447

XXXVIII List of Figures

4.46 Algorithmic set-up for the error controlled adaptive timeintegration by p-Galerkin methods and p-method errorestimates/indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

4.47 Function to be approximated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4504.48 Approximation of equation (4.147) . . . . . . . . . . . . . . . . . . . . . . . . . 4514.49 Normal and tangential vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4524.50 Four crack tip functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4534.51 Crack with one kink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4544.52 Crack after mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4564.53 Multiple kinked crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4564.54 Multiple kinked crack after the first mapping . . . . . . . . . . . . . . . . 4574.55 Point x and mirrored point x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4584.56 Strain ε from equation (4.173) for the integral (4.175) . . . . . . . . 4624.57 Number of integration points used in the numerical

integration of (4.174) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4624.58 Strain ε from equation (4.173) for the integral (4.177) . . . . . . . . 4634.59 Number of integration points used in the numerical

integration of (4.176) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4634.60 Strain ε from equation (4.173) for the integral (4.179) . . . . . . . . 4654.61 Number of integration points used in the numerical

integration of (4.178) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4654.62 Strain ε from equation (4.173) for the integral (4.181) . . . . . . . . 4664.63 Number of integration points used in the numerical

integration of (4.180) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4664.64 Strain ε from equation (4.173) for the integral (4.183) . . . . . . . . 4674.65 Number of integration points used in the numerical

integration of (4.182) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4674.66 Strain ε from equation (4.173) for the integral (4.185) . . . . . . . . 4684.67 Number of integration points used in the numerical

integration of (4.184) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4684.68 Tension test configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4694.69 Displacements ux for the deformed system using bilinear

shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4704.70 Displacements ux for the deformed system, left: using

bi-quadratic shape functions, right: using quadratichierarchical shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

4.71 Differences of displacements inside the 1st blending element . . . 4714.72 Differences of displacements inside the 2nd blending element . . 4714.73 Differences of displacements inside the 3rd blending element . . . 4724.74 Differences of displacements inside the 4th blending element . . . 4724.75 Differences of displacements inside the 5th blending element . . . 4734.76 Numerical integration in the context of X-FEM: Subdivision

of the continuum element into six sub-tetrahedrons . . . . . . . . . . . 4754.77 Separation of a sub-tetrahedron by a plane crack segment . . . . . 4754.78 C0-crack plane evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

List of Figures XXXIX

4.79 Definition of the crack plane by point P and normal vector n . . 4774.80 Constant strain triangular element cut by means of a planar

internal boundary ∂sΩ; see [745] . . . . . . . . . . . . . . . . . . . . . . . . . . . 4814.81 Enhanced discontinuous displacement field ru (Hs − ϕ): (a)

bi-linear approximation (2 nodes in Ω+); (b) bi-quadraticapproximation (1 node in Ω+) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

4.82 Numerical study of a notched concrete beam: dimensions (in[cm]) and material parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

4.83 Numerical study of a notched concrete beam using theproposed multiple crack concept and the rotating crackapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

4.84 Sketch for the computation of the SIF for a kinking crackwith r → 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

4.85 Schematic figure for the calculation of the SIF with constantradius for kinking cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

4.86 Sketch of KII (left) and |KII | (right) depending on the angleθ for a three point bending test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

4.87 Energy function Πtot for a three point bending test . . . . . . . . . . 4934.88 Crack simulation of a double notched slab: System, material

data and finite element mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4944.89 Crack simulation of a double notched slab: Visualization of

the crack topology by the φ = 0-level set . . . . . . . . . . . . . . . . . . . . 4954.90 Crack simulation of a double notched slab: Comparison of

crack topology and of load-displacement curves . . . . . . . . . . . . . . 4954.91 Bumerical investigation of crack propagation of an anchor

pull-out test: System and finite element mesh (NE = 996) . . . . 4964.92 Numerical investigation of crack propagation of an anchor

pull-out test: Crack topology and displacement u3 in pull-outdirection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

4.93 Numerical investigation of crack propagation of an anchorpull-out test: Stress σ33 at the beginning and the end of thecrack process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

4.94 Numerical investigation of crack propagation of an anchorpull-out test: Load-displacement curve . . . . . . . . . . . . . . . . . . . . . . 498

4.95 Concept for the efficient simulation of dynamic, partiallydamaged structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

4.96 Decomposition of the structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5074.97 Geometry and loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5134.98 Exploded view of the bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5144.99 Damage evolution in the largest two hangers . . . . . . . . . . . . . . . . 5154.100 Displacement in X2-direction in point B . . . . . . . . . . . . . . . . . . . . 5164.101 Mean relative displacement-based error in point B . . . . . . . . . . . 5164.102 Comparison of a pure implicit and an explicit calculation of

accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

XL List of Figures

4.103 General definition of the failure domain depending onscattering resistance (R) and stress (S) values . . . . . . . . . . . . . . . 529

4.104 Standardization of an exemplary 2D joint distributionfunction for a subsequent FORM/SORM analysis . . . . . . . . . . . . 532

4.105 Comparison of Latin Hypercube Sampling and Monte-CarloSimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

4.106 Parallel execution of stochastically independent DC-MCS offatigue analyses on a distributed memory architecture [824] . . . 545

4.107 Parallel software framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5614.108 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5624.109 Damage equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5634.110 Singular values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5644.111 1’st eigenfrequency and mode shape . . . . . . . . . . . . . . . . . . . . . . . . 5644.112 2’nd eigenfrequency and mode shape . . . . . . . . . . . . . . . . . . . . . . . 5654.113 3’rd eigenfrequency and mode shape . . . . . . . . . . . . . . . . . . . . . . . . 5654.114 4’th eigenfrequency and mode shape . . . . . . . . . . . . . . . . . . . . . . . . 5664.115 Cut modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5664.116 Optimization topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5704.117 The new 3-series convertible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5734.118 3-series convertible with battery . . . . . . . . . . . . . . . . . . . . . . . . . . . 5744.119 Battery as vibration absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5744.120 FE model of the shaker test arrangement . . . . . . . . . . . . . . . . . . . 5754.121 Measured acceleration data for the y-direction . . . . . . . . . . . . . . . 5764.122 Power spectral density function of the resulting von Mises

stress for the elements of Figure 4.119, load direction y . . . . . . . 5774.123 Dirlik distribution function of the stress amplitudes . . . . . . . . 5794.124 Typical stress picture for load in y-direction (Time History

Analysis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5814.125 Expected life time in arbitrary time units for the Time

History calculation (acceleration load in y-direction) . . . . . . . . . . 5824.126 Hygro-mechanically loaded concrete shell structure: System

geometry and material data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5844.127 Hygro-mechanically loaded concrete shell structure: Hygral

boundary conditions of the inner and outer surface of theshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

4.128 Hygro-mechanically loaded concrete shell structure: Finiteelement mesh of the numerical analysis . . . . . . . . . . . . . . . . . . . . . 585

4.129 Hygro-mechanically loaded concrete shell structure:Deformation and stresses due to dead load . . . . . . . . . . . . . . . . . . 586

4.130 Hygro-mechanically loaded concrete shell structure:Distribution of the saturation Sl . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

4.131 Hygro-mechanically loaded concrete shell structure: Damageevolution at the support area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

4.132 Hygro-mechanically loaded concrete shell structure: Damagezone and accelerated transport process in the area of cracks . . . 588

List of Figures XLI

4.133 Hygro-mechanically loaded concrete shell structure:Distribution of saturation Sl and damage variable d acrossthe shell thickness (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

4.134 Hygro-mechanically loaded concrete shell structure:Distribution of saturation Sl and damage variable d acrossthe shell thickness (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

4.135 Calcium leaching of a cementitious bar and a cementitiousbeam: Geometry, FE mesh and chemical loading history . . . . . . 591

4.136 Calcium leaching of a cementitious bar: Numerical resultsobtained from the cG(1) method . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

4.137 Calcium leaching of a cementitious bar: Numerical resultsand time integration error obtained from adaptive Newmarkintegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

4.138 Calcium leaching of a cementitious bar: Time historiesc(t, X1)/c0 obtained from dG(p)-integration (t [108s],X1 [mm]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596

4.139 Calcium leaching of a cementitious bar: Time historiesc(t, X1)/c0 obtained from cG(p)-integration (t [108s],X1 [mm]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597

4.140 Calcium leaching of a cementitious bar: Spatial local andglobal error estimates for Newmark time integrations . . . . . . . . 598

4.141 Calcium leaching of a cementitious bar: Logarithm of errorestimates eΔt/5 for dG-methods with different time steps Δt . . . 599

4.142 Calcium leaching of a cementitious bar: Logarithm of errorestimates ep/p+1 for dG-methods with different time steps Δt . . 600

4.143 Calcium leaching of a cementitious bar: Logarithm of errorestimates ep/p+1 and eΔt/5 for cG-methods with differenttime steps Δt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601

4.144 Calcium leaching of a cementitious bar: Average relativeerrors of the Newmark method and Galerkin methods . . . . . 603

4.145 Calcium leaching of a cementitious beam: Numerical resultsobtained from cG(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604

4.146 Calcium leaching of a cementitious beam: Investigation ofthe oscillations in the results of cG(1)- and cG(2)-solutions . . . . 605

4.147 Calcium leaching of a cementitious beam: Investigation ofthe robustness of the cG(1)-solution for small Tc� . . . . . . . . . . . . 606

4.148 Pictures of damaged road bridge in Munster (Germany) andcorrespondent FE models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

4.149 Refined FE models of a connecting plate and thecorrespondent welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608

4.150 Effective stress values of a connecting plate under a constantrod deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

4.151 Representative surface of partial damage values for varyingwind and initial displacements at the critical tie rod . . . . . . . . . . 611

XLII List of Figures

4.152 Time-dependent evolution of the failure probability of criticalmaterial points in the welding region and the bulk material . . . 612

4.153 Optimization model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6134.154 Optimization results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6144.155 The road bridge at Hunxe (Germany) shortly before its

deconstruction in 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6164.156 Location of prestressing tendons and crack pattern observed

on the bridges main girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6174.157 Location of drilling cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6184.158 Comparison of stress-strain curves between bridge concrete

and laboratory concretes with different strengths [193] . . . . . . . . 6204.159 LM-micrograph of in-situ concrete . . . . . . . . . . . . . . . . . . . . . . . . . 6214.160 Total longitudinal (left) and fatigue strain (right) at Smax . . . . . 6224.161 Correlation between fatigue strain and the residual stiffness

for Smax/Smin = 0.675/0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6234.162 Three dimensional Finite Element model of the road bridge

at Hunxe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6244.163 Applied corrosion model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6264.164 Modified S-N curves for steel and fatigue damage evolution

function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6274.165 Higher order statistical moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 6284.166 Validation of input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6284.167 Evolution of compressive strength and histogram of concrete

strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6294.168 Random field dependency on correlation length and

eigenvalues used for reconstruction of correlation matrix . . . . . . 6324.169 Load deflection diagram and time deflection diagram 3D . . . . . . 6334.170 Load deflection curves and lifetime distribution and

estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6334.171 State space model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6364.172 Impulse excitation in laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . 6394.173 Comparison between measured signals and signals from

identified model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6394.174 Cantilever bending beam used for experiments in laboratory . . . 6414.175 Drawing from the cantilever bending beam with the location

of saw cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6414.176 Markov parameters for damage detection . . . . . . . . . . . . . . . . . . . 6424.177 Bridge near Hunxe / Germany (span: 62.5m) . . . . . . . . . . . . . . . . 6434.178 System modification: hanger cut through . . . . . . . . . . . . . . . . . . . . 6434.179 Torsional mode from reference system and after cut hanger . . . . 6444.180 Recalculation of a centrifuge model test of Helm et al. [365] . . . 6464.181 Parametric studies of shallow strip foundations under cyclic

loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6474.182 FE calculations with stochastically fluctuating void ratio . . . . . . 648

List of Figures XLIII

4.183 FE calculation of vibratory compaction and bridgesettlements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649

4.184 Calculation of pore water pressure accumulation due toearthquake loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

4.185 FE calculation of a geogrid-reinforced embankment . . . . . . . . . . . 6514.186 FE calculation of a monopile foundation of an offshore wind

power plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

5.1 Reinforced concrete column under fatigue loading . . . . . . . . . . . . 6545.2 Load-carrying-capacity and response surface method . . . . . . . . . 6545.3 Time-dependent hazard function and time-dependent

reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6555.4 Multi-level system approach followed during the lifetime

analysis of the arched steel bridge [826] . . . . . . . . . . . . . . . . . . . . . 6565.5 Multi-scale modeling and analysis of fatigue-related

structural problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6575.6 Comparison of resulting time-dependent failure probabilities

of the researched connection plate . . . . . . . . . . . . . . . . . . . . . . . . . . 658

List of Tables

2.1 Conversion of the wind data of the observation station at theairport of Hannover into data for the building location . . . . . . . . 20

2.2 Determination of a reduced characteristic suction force onthe facade element after Figure 2.8 . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Statistical parameters of the traffic records of Auxerre (1986) . . 492.4 Relation between gross weight of the heavy vehicles and the

axle weights of the lorries of types 1 to 4 in % (mean valuesand standard deviation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.5 Distance of axles in [m] of the different types of vehicles(mean values and standard deviation) . . . . . . . . . . . . . . . . . . . . . . 50

2.6 Statistical parameters of the corrected static traffic recordsof Auxerre (1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.7 Different cross-sections and traffic types for the randomgenerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.8 Traffic data of different locations and characteristic values ofgross and axle weight [720] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.9 Different design situations and corresponding return periodsand fractiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.10 Factors Ψ for the determination of the representative valuesfor serviceability limit states acc. to [9] . . . . . . . . . . . . . . . . . . . . . 63

2.11 Traffic categories acc. to Eurocode 1-2 . . . . . . . . . . . . . . . . . . . . . . 662.12 Statistical parameters of the traffic records at highway A61

(2004) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.13 Relation between gross weight of the heavy vehicles and the

axle weights of the lorries of types 1 to 5 (mean values) . . . . . . . 762.14 Readings: winter 05/06 and winter 06/07; field station

Meißen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.1 Classification of pore sizes in concrete according to [724] . . . . . . 1513.2 Influences on the degree of chemical attack . . . . . . . . . . . . . . . . . . 1523.3 Changes of concrete properties due to cyclic loading . . . . . . . . . . 185

XLVI List of Tables

3.4 Crack characteristics at certain number of cyclesSmax/Smin = 0.675/0.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

3.5 Correlation between frost suction and internal damage dueto freeze-thaw testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

3.6 Summary of the single level tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 2133.7 Summary of the tests with multiple blocks of loading . . . . . . . . . 2143.8 Mean values of material properties of concrete according to

EN 206-1 [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2183.9 Mean values of material properties of steel members . . . . . . . . . . 2193.10 Average test results per stud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2193.11 Loading parameters and results of the tests with two blocks

of loading (series S5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2223.12 Loading parameters and results of the tests with four blocks

of loading (series S6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2223.13 Average test results per stud in series S9 . . . . . . . . . . . . . . . . . . . . 2233.14 Measured mean values of the peak load and the load range

at discrete number of load cycles in tests S9 4 . . . . . . . . . . . . . . . 2233.15 Loading parameters and block lengths in tests S9 5 . . . . . . . . . . . 2243.16 Average test results per stud in series S11 and S13 . . . . . . . . . . . 2253.17 Mean values of material properties of concrete according to

EN 206-1 [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2313.18 Mean values of material properties of steel members . . . . . . . . . . 2323.19 Main test results of beams VT1 and VT2 . . . . . . . . . . . . . . . . . . . 2333.20 Parameter of the elasto-plastic micropore damage model for

20MnMoNi55 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2603.21 Low Cycle Fatigue in metals: Number of load cycles until

failure obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2613.22 Characteristics of the applied sequential loading . . . . . . . . . . . . . 2813.23 Summary of the functions, material constants and reference

quantities of the high-cycle model . . . . . . . . . . . . . . . . . . . . . . . . . . 3143.24 Summary of the statically loaded push-out tests with decisive

criterion “failure of the concrete” (tests 1 - 27) . . . . . . . . . . . . . . 3193.25 Summary of the statically loaded push-out tests with decisive

criterion “failure of the concrete” (tests 28 - 58) . . . . . . . . . . . . . 3203.26 Summary of the statically loaded push-out tests with decisive

criterion “shear failure of the stud” . . . . . . . . . . . . . . . . . . . . . . . . . 3213.27 Result of the statistical analysis according EN 1990, Annex

D [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3233.28 Mean values of the crack length ah(see Figure 3.155) in test

series S11 and S13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

4.1 Multi-dimensional Lagrange shape functions . . . . . . . . . . . . . . . 3824.2 Total number of geometric entities (vertices, edges, faces) of

the discretizations with an infinite number of elements . . . . . . . . 3994.3 Convergence criteria of iterative solution methods . . . . . . . . . . . . 405

List of Tables XLVII

4.4 Comparison of iteration methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 4064.5 Constraints and load factor increments of selected arc-length

methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4094.6 Error indicators for Newmark type time integration schemes

for non-linear second order initial value problems . . . . . . . . . . . . 4454.7 Error indicators for Newmark type time integration schemes

for non-linear first order initial value problems . . . . . . . . . . . . . . . 4464.8 Equivalent square sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5144.9 Modal Assurance Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5694.10 Gauss-Newton (cp/cd=800/1smm) . . . . . . . . . . . . . . . . . . . . . . . 5714.11 Gauss-Newton iteration (cp/cd=1400/1mm) . . . . . . . . . . . . . . . 5714.12 Results for an early design proposal . . . . . . . . . . . . . . . . . . . . . . . . 5824.13 Standard parameter set [307, 454, 457] . . . . . . . . . . . . . . . . . . . . . . 5924.14 Calcium leaching of a cementitious bar: Average relative

errors of the Newmark method, discontinuous Galerkinmethods and continuous Galerkin methods . . . . . . . . . . . . . . . . 602

4.15 Type of random variables (RV) included in the reliabilityproblem used to describe the scatter of wind load parametersas well as material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

4.16 Comparison of resulting runtime values analyzing theconnecting plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

4.17 Dynamic elastic moduli Edyn (mean) and their standarddeviations (SD) of the concrete after a service life of 50years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

4.18 Relevant mechanical concrete properties Estat, εu and fc(mean values) as well as their standard deviations (SD) aftera service life of 50 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

4.19 Number of elements of structural members . . . . . . . . . . . . . . . . . . 6244.20 Determination of compressive strength at time of

construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6294.21 Concrete strength grades according to German standards . . . . . 6304.22 Summary of the results of the FE calculations of strip

foundations under cyclic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 647