A computational model for seismically induced liquefaction [Elektronische Ressource] / von Vera Struckmeier
155 Pages
English
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A computational model for seismically induced liquefaction [Elektronische Ressource] / von Vera Struckmeier

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155 Pages
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Braunschweiger Schriften zur Mechanik Nr. 62 2007AcomputationalmodelforseismicallyinducedliquefactionvonVera StruckmeierInstitut für Angewandte MechanikTechnische Universität BraunschweigHerausgegeben vom Mechanik Zentrum derTechnischen Universität BraunschweigSchriftleiter: Prof. Dr. rer. nat. H. AntesInstitut für Angewandte MechanikPostfach 332938023 BraunschweigVon der Fakultät Architektur, Bauingenieurwesen und Umweltwissenschaftender Technischen Universität Carolo Wilhelmina zu Braunschweigzur Erlangung des Grades eines Doktor Ingenieur (Dr. Ing.)genehmigte DissertationEingereicht am 30. März 2007Mündliche Prüfung am 7. Mai 2007BerichterstatterProf. Dr. rer. nat. H. AntesProf. Dr. Ing. T. CrespellaniEur. Ing. Prof. A.H.C. Chan Copyright 2007 V. Struckmeier, BraunschweigBSM 62 2007ISBN 9783 920395 61 6Alle Rechte, insbesondere der Übersetzung in fremde Sprachen, vorbehalten.Mit Genehmigung des Autors ist es gestattet, dieses Heft ganz oder teilweisezu vervielfältigen.AcomputationalmodelforseismicallyinducedliquefactionDissertationsubmitted to and approved by theFaculty of Architecture, Civil Engineering and Environmental SciencesUniversity of Braunschweig - Institute of Technologyand theFaculty of EngineeringUniversity of Florencein candidacy for the degree of aDoktor Ingenieur (Dr. Ing.) /?

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Published 01 January 2007
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Braunschweiger Schriften zur Mechanik Nr. 62 2007
Acomputationalmodelforseismically
inducedliquefaction
von
Vera Struckmeier
Institut für Angewandte Mechanik
Technische Universität BraunschweigHerausgegeben vom Mechanik Zentrum der
Technischen Universität Braunschweig
Schriftleiter: Prof. Dr. rer. nat. H. Antes
Institut für Angewandte Mechanik
Postfach 3329
38023 Braunschweig
Von der Fakultät Architektur, Bauingenieurwesen und Umweltwissenschaften
der Technischen Universität Carolo Wilhelmina zu Braunschweig
zur Erlangung des Grades eines Doktor Ingenieur (Dr. Ing.)
genehmigte Dissertation
Eingereicht am 30. März 2007
Mündliche Prüfung am 7. Mai 2007
Berichterstatter
Prof. Dr. rer. nat. H. Antes
Prof. Dr. Ing. T. Crespellani
Eur. Ing. Prof. A.H.C. Chan
 Copyright 2007 V. Struckmeier, Braunschweig
BSM 62 2007
ISBN 9783 920395 61 6
Alle Rechte, insbesondere der Übersetzung in fremde Sprachen, vorbehalten.
Mit Genehmigung des Autors ist es gestattet, dieses Heft ganz oder teilweise
zu vervielfältigen.Acomputationalmodelforseismicallyinduced
liquefaction
Dissertation
submitted to and approved by the
Faculty of Architecture, Civil Engineering and Environmental Sciences
University of Braunschweig - Institute of Technology
and the
Faculty of Engineering
University of Florence
in candidacy for the degree of a
Doktor Ingenieur (Dr. Ing.) /
?)Dottore di Ricerca in Risk Management on the Built Environment
by
Vera Struckmeier
from Hamburg, Germany
Submitted on 30 March 2007
Oral examination on 7 May 2007
Professoral advisors Prof. Dr. rer. nat. H. Antes
Prof. Dr. Ing. T. Crespellani
Eur. Ing. Prof. A.H.C. Chan
2007
?)Either the German or the Italian form of the title may be usedThe dissertation is published in an electronic form by
the Braunschweig university library at the address
http://www.biblio.tu bs.de/ediss/data/Acknowledgments
First of all, I wish to express my deep gratitude to my supervisor Prof. Heinz Antes for the
support and the encouragement provided during the period of my research work. I would like
also to thank him for the opportunity he gave me to work together with the Computational
Engineering group of the department of Civil Engineering, University of Birmingham.
I sincerely wish to express my deep appreciation to Prof. Andrew H.C. Chan from the
University of Birmingham together with Prof. Martin Schanz from the University of Graz for their
useful suggestions, comments and revisions of this thesis.
I would like to thank Prof. Teresa Crespellani for her interest in my research and her valuable
advice on writing the thesis.
To all my colleagues in the Institute of Applied Mechanics at the Technical University Braun
schweig I would like to express my thanks for their support.
The work is financially supported by the Deutsche Forschungsgemeinschaft within the
international graduate research program »Risk Management of Natural and Civilisation Hazards on
Buildings and Infrastructure«. I thank Prof. Udo Peil and Prof. Claudio Borri for conceiving
and coordinating this international doctoral course.
Toallmyfriends,myfamilyandespeciallytoStephanCapellaroIwouldliketothankfortheir
patience with me during the final stages of writing this work.Iwishtodedicatethisthesistomyparents
LisaandHeinrichStruckmeier.Contents
Introduction 1
1 Biot’sTheoryofPoroelasticity 9
1.1 Constitutive Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 FiniteElementSolutionoftheBiotEquation 12
2.1 Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 u p Discretization of the Biot equation . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 in space . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Choice of Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Discretization in time/Integration in time . . . . . . . . . . . . . . . . 17
3 BEMFormulation 20
3.1 Fundamental Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Boundary Element Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Validation by Comparison to a 1 d Analytical Solution . . . . . . . . . . . . . 30
3.3.1 Poroelastic Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Wave propagation in a Poroelastic Half Space . . . . . . . . . . . . . . 35
4 ConstitutiveRelationsinSoilMechanics 42
4.1 Classical Theory of Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.1 Incremental Stress and Strain relationship . . . . . . . . . . . . . . . . 45
4.1.2 Elasto plastic material models for soil . . . . . . . . . . . . . . . . . . 52
4.2 Critical State Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Bounding Surface Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Cyclic Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.2 Pastor Zienkiewicz mark III (1986) Model (PZ3 model) . . . . . . . . 63
5 IterativeCouplingofBEMandFEM 76
5.1 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1.1 Linear elastic 2 d column . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1.2 Poroelastic 1 d column . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1.3 2 d halfspace . . . . . . . . . . . . . . . . . . . . . . . . . 84
III CONTENTS
5.2 Influence of the spatial and time discretization . . . . . . . . . . . . . . . . . . 90
5.2.1 Spatial discretization and time discretization under different frequency
input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Coupled poroplastic poroelastic 2d halfspace . . . . . . . . . . . . . . . . . . 99
5.3.1 Seismic excitation of the coupled 2d halfspace . . . . . . . . . . . . . 110
Conclusions 113
A ExplicitExpressionsfortheFundamentalSolutions 116
A.1 Fundamental solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.1.1 Solutions in 3 d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.1.2 in 2 d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
B MathematicalPreliminaries 120
B.1 Matrix of Cofactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
B.2 Distributions or Generalized Functions . . . . . . . . . . . . . . . . . . . . . . 120
B.3 Convolution Quadrature Method . . . . . . . . . . . . . . . . . . . . . . . . . 123
NotationIndex 125