Applications in Geomechanics

ISBN-13: 9783642830143 / Angielski / Miękka / 2012 / 173 str.

Carlos A. Brebbia

Opis

The first volume of this series dealt with the Basic Principles of Boundary Elements, while the second concentrated on time dependent problems and Volume three on the Computational Aspects of the method. This volume studies the applications of the method to a wide variety of geomechanics problems, most of which are ideally suited for boundary elements demonstrating the potentiality of the technique. Chapter 1 deals with the application of BEM to three dimensional elastody namics soil-structure interaction problems. It presents detailed formulations for rigid, massless foundations of arbitrary shape both in the frequency and time domains. The foundations are assumed to be resting on a linearly elastic, homogeneous, isotropic half-space and be subjected to externally applied loads on obliquely incident body. The chapter reviews the major advances in soil foundation interaction presents a series of numerical results and stresses the practical application of BEM, pointing out the high accuracy and efficiency of the technique, even when using coarse mesh discretizations."

Spis treści

1 Three-Dimensional Soil-Structure Interaction By Boundary Element Methods.- Abstract.- 1.1 Introduction.- 1.2 Field Equations.- 1.2.1 Time Domain Integral Representation.- 1.2.2 Frequency Domain Integral Representation.- 1.3 Numerical Implementation.- 1.3.1 Time Domain Approach.- 1.3.2 Frequency Domain Approach.- 1.4 Massless Foundations.- 1.4.1 Externally Applied Dynamic Loads.- 1.4.2 Obliquely Incident Seismic Waves.- 1.5 Massive Foundations - Superstructure.- 1.6 Numerical Results.- 1.7 Conclusions.- References.- 2 Dynamics Of Foundations.- Abstract.- 2.1 Introduction.- 2.2 Integral Representation of the Displacements of the General Elastodynamic Problem.- 2.2.1 Fundamental Solution.- 2.2.2 Reciprocal Theorem.- 2.2.3 Direct Integral Representation.- 2.3 Integral Representations of the Displacements of the Steady-state Problem.- 2.3.1 Fundamental Solution.- 2.3.2 Reciprocal Theorem.- 2.3.3 Direct Integral Representation.- 2.3.4 Indirect Integral Representation.- 2.4 Time Domain Boundary Element Method.- 2.4.1 Two-Dimensional Problems.- 2.5 Frequency Domain Boundary Element Method.- 2.5.1 Direct Formulation.- 2.5.2 Indirect Formulation.- 2.6 Dynamic Stiffness of Foundations.- 2.7 Three-Dimensional Foundations.- 2.7.1 Effect of the Number of Elements Under the Foundation.- 2.7.2 Effect of the Extension of the Soil Free-surface Discretization.- 2.7.3 Static Stiffnesses.- 2.7.4 Dynamic Stiffness Coefficients.- 2.8 Two-Dimensional Foundations.- 2.8.1 Viscoelastic Half-plane.- 2.8.2 Layered Soil. Effect of a Compliant Bedrock.- 2.8.3 Elliptical Soil Deposit on Viscoelastic Bedrock.- 2.9 Axisymmetric Foundations.- 2.10 Seismic Response of Foundations.- 2.10.1 Three-Dimensional Foundations.- 2.10.2 Two-Dimensional Foundations.- 2.11 Dynamics of Foundations by the Time Domain BEM.- References.- 3 Boundary Integral Equation Methods For Consolidation Problems.- 3.1 Introduction.- 3.2 Statement of the Problem.- 3.3 Potential Representation of Solution.- 3.4 Analytical Applications.- 3.5 Numerical Method.- 3.6 Numerical Examples.- 3.6.1 Circular Disc.- 3.6.2 Circular Hole in an Infinite Plane.- 3.6.3 Loaded Halfplane.- 3.7 Other Formulations.- 3.8 Concluding Remarks.- Acknowledgement.- References.- 4 A Review Of Boundary Element Models Of Saltwater Intrusion.- Abstract.- 4.1 Introduction.- 4.2 Cross Sectional Flow Models.- 4.2.1 Mathematical Statement of the Problem.- 4.2.2 Boundary Element Formulation.- 4.2.3 Steady-state Sea-Water Intrusion.- 4.2.4 Horizontal Motion of the Interface - Explicit Solution.- 4.2.5 Vertical Motion of the Interface - Implicit Solution.- 4.3 Horizontal Flow Models.- 4.3.1 Mathematical Statement of the Problem.- 4.3.2 Boundary Element Formulation.- 4.4 Discussion and Conclusions.- Acknowledgements.- References.- 5 Boundary Element Modelling Of Interface Phenomena.- Abstract.- 5.1 Introduction.- 5.2 Basic Equations.- 5.3 Frictional Interface.- 5.4 Plastic Interface.- 5.5 Numerical Results.- 5.6 Conclusions.- 5.7 Appendix.- 5.8 Notations.- References.- 6 Heterogeneities In Flows Through Porous Media By The Boundary Element Method.- 6.1 Introduction.- 6.2 Governing Equations for Darcy’s Flow.- 6.3 Heterogeneous Porous Media.- 6.3.1 Constant Hydraulic Conductivity.- 6.3.2 Piecewise Homogeneous Media.- 6.3.2.1 Multizone Formulation.- 6.3.2.2 Single Potential Formulation.- 6.3.3 Variable Hydraulic Conductivity.- 6.3.3.1 Iterative Scheme.- 6.3.3.2 Domain Scheme.- 6.3.3.3 Direct Green’s Function Scheme.- 6.4 Heterogeneous Fluid.- 6.4.1 Steady-state Miscible Fluid Flow.- 6.4.2 Transient Interface of Immiscible Fluid.- 6.4.2.1 Multizone Approach.- 6.4.2.2 Single Potential Approach.- 6.5 Embedded Heterogeneity.- 6.5.1 Multizone Approach.- 6.5.2 Singularity Distribution.- 6.6 Concluding Remarks.- References.- 7 Time Dependent Group Flow Analysis.- Abstract.- 7.1 Introduction.- 7.2 Mathematical Formulation.- 7.3 Free Surface Calculations.- 7.4 Discretization.- 7.5 Numerical Results.- 7.6 Experimental Investigation.- 7.7 Summary and Conclusions.- References.- 8 Unconfined Groundwater Flow.- 8.1 Introduction.- 8.2 Theoretical Formulation.- 8.2.1 Governing Equations in Domain.- 8.2.2 Free Surface Boundary Condition.- 8.2.3 Other Boundary Conditions.- 8.3 Numerical Formulation.- 8.3.1 The Integral Equation in Three Dimensions.- 8.3.3 Three-Dimensional Problems.- 8.3.4 Axisymmetric Problems.- 8.3.5 Two-Dimensional Problems.- 8.3.6 Treatment of the Free Surface Boundary Condition.- 8.4 Recharge Problems.- 8.5 Well Problems.- 8.6 Seepage from a Lagoon.- Acknowledgements.- References.