Modelization of dynamic soil-structure interaction using integral transform-finite element coupling [Elektronische Ressource] / Josia Irwan Rastandi

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2003
• Nombre de lectures: 42
• Langue: Deutsch
• Poids de l'ouvrage: 3 Mo

Extrait

Lehrstuhl für Baumechanik der Technischen Universität München


Modelization of Dynamic Soil-Structure Interaction
Using Integral Transform-Finite Element Coupling



Josia Irwan Rastandi


Vollständiger Abdruck der von der Fakultät für Bauingenieur- und Vermessungswesen der
Technischen Universität München zur Erlangung des akademischen Grades eines
Doktor-Ingenieurs
genehmigten Dissertation.

Vorsitzender : Univ.-Prof. Dr.-Ing. K.-U. Bletzinger
Prüfer der Dissertation :
1. Univ.-Prof. Dr.-Ing. H. Grundmann
2. Univ.-Prof. Dr.-Ing. H. Kreuzinger



Die Dissertation wurde am 09.10.2003 bei der Technischen Universität München eingereicht und
durch die Fakultät für Bauingenieur- und Vermessungswesen am 14.11.2003 angenommen.















To my wife Stella and our little daughter, Jessica
Zusammenfassung

Das Ziel dieser Arbeit ist eine zuverlässige Modellierung der Wellenausbreitung bei der Bauwerk-
Bodenwechselwirkung in der Strukturdynamik. Dazu gehört sowohl die ausreichende Erfassung
der Verhältnisse in unmittelbarer Bauwerksumgebung (Nahbereich), als auch die zutreffende
Beschreibung der Ausbreitungsvorgänge in die weitere Bauwerksumgebung (Fernbereich). Für den
Fernbereich (Halbraum) werden Integraltransformations-methoden benutzt. Eine flexible
Beschreibung der Verhältnisse in unmittelbarer Bauwerks-umgebung wird am besten durch die
Behandlung mit der Finite-Element-Methode erzielt. So sind fast keine Einschränkungen
hinsichtlich der Geometrie und der Lastannahmen hinzunehmen.









Abstract

The aim of this work is a reliable modelling of the wave propagation in dynamic soil-structure in-
teraction. A small FEM domain will be introduced to model the structure and its surrounding area,
while The Integral Transform Method (ITM) is used to model the Half-space. With this Coupling
Method (ITM-FEM) there is no more limitation in case of local irregularities. Acknowledgements


This research was done during my work as a Ph.D. candidate at the Lehrstuhl für Baumechanik
der Technischen Universität München from 1999 until 2003.
I wish to express my sincere gratitude to Univ.-Prof. Dr.-Ing. Harry Grundmann for giving me
the opportunity to work at the institute and for his excellent supervision of my work. And I
gratefully appreciate his willingness to discuss and readiness to help.

I thank also Univ.-Prof. Dr.-Ing. Heinrich Kreuzinger who always gave me his recommendations
for DAAD and for being the second examiner of my dissertation, and to Univ.-Prof. Dr.-Ing.
Kai-Uwe Bletzinger as the chairman of my oral Ph.D. examination.

Special thanks Dr.-Ing. Markus Schneider for his useful comments and suggestions for this work.
And I want to thank also all of my colleagues who helped me not only as colleagues but also as
friends.

My studies were carried out under the Deutscher Akademischer Austauschsdienst (DAAD) pro-
gram and my thanks go to them for the financial support they gave me during the whole period
of my stay in Germany.

My sincere thanks to my father, mother, sisters and brother for their prayers, love and encour-
agement.

Very special thanks go to my beloved wife Stella, for her support and patience during the hard
times of finishing this dissertation, and not forget to our little daughter Jessica, thank you for
being my inspiration.

Contents

Contents ......................................................................................................................................................... i

List of Symbols............................................................................................................................................ iii
Mathematical symbols ............................................................................................................................ v

1 Introduction ............................................................................................................................................. 1
1.1 General Remarks ....................................................................................................................... 1
1.2 Overview..................................................................................................................................... 1
1.3 Subjects Covered ....................................................................................................................... 3

2 Modelling of Soil ..................................................................................................................................... 4
2.1 Propagation of Waves in Continuum ..................................................................................... 4
2.2 Damping ..................................................................................................................................... 7
2.3 Equation of Motion and Wave Equation in Elastic Half-space ......................................... 8
2.4 Layered Half-space.................................................................................................................. 12
2.5 Forced Vibration of The Layered Half-space...................................................................... 14
2.5.1 Particular Solution for Upper Layer................................................................................. 16
2.5.2 Homogeneous Solution...................................................................................................... 19
2.6 Examples for Forced Vibration of The Layered Half-space............................................. 23
2.6.1 Special Cases, h = 0............................................................................................................. 23
2.6.2 Examples for Volume Forces in The Half-space........................................................... 33

i ii Contents
_______________________________________________________________________________________________________

3 Dynamic Matrix of Excavated Half-space.........................................................................................39
3.1 Model and Substitute Model.................................................................................................. 39
∞[]D3.2 Substructure Matrix 41
3.3 Special Case, h = 0................................................................................................................... 44
3.3.1 Point Unit Load................................................................................................................... 44
3.3.2 Uniform Block Load........................................................................................................... 51
3.4 Excavated Half-space... 57

4 Dynamic Soil-Structure Interaction with ITM-FEM Approach .................................................... 62
FE4.1 Substructure Matrix []D ................................................................................................... 62
4.2 Coupling Between FEM and ITM ........................................................................................ 63
4.3 Full Half-space as ITM-FEM Couple Structure ................................................................. 65

5 Application Example ............................................................................................................................ 70
5.1 Problem Description and Modelization............................................................................... 70
5.2 Results and Discussions.......................................................................................................... 72

6 Summary ................................................................................................................................................. 80

References................................................................................................................................................... 81

List of Figures............................................................................................................................................. 86

_____________________________________________________________________________________________________ List of Symbols
The following list defines the principal symbols used in this work. Other symbols are defined in
context. Rectangular matrices are indicated by brackets [ ], and column vectors by braces { }.
Overdots indicate differentiation with respect to the time, and primes usually denote differentiation
with respect to the space variable. An overbar indicates complex number.

a , a Opening widths of the excavated half-space x y
b ,b Bottom widths of-space x y
c Viscous damping of SDOF system
c Velocity of P-wave p
c Velocity of S-wave s
h Depth of the excavated half-space
k Stiffness of SDOF system
k , k Wave numbers x y
k Wave number of P-wave p
k Wave number of S-wave s
k Radial wave number r
m Mass of S