Aleynikov Spatial Contact Problems in Geotechnics

Boundary-Element Method
1. Auflage 2010
ISBN: 978-3-540-44776-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 648 Seiten

This book presents a systematic approach to numerical solution for a wide range of spatial contact problems of geotechnics. On the basis of the boundary element method new techniques and effective computing algorithms are considered. Special attention is given to the formulation and analysis of the spatial contact models for elastic bases. Besides the classical schemes of contact deformation, new contact models are discussed for spatially nonhomogeneous and nonlinearly elastic media properly describing soil properties.

Autoren/Hrsg.

Aleynikov, Sergey

Inhaltsverzeichnis

1;Obituary;5
2;Foreword;7
3;Preface;9
4;Contents;14
5;1 Spatial Contact Models of Elastic Bases;19
5.1;1.1 Fundamental Solutions of Static Problems of Spatial Theory of Elasticity;19
5.1.1;1.1.1 Concentrated Forces in an Elastic Body;19
5.1.2;1.1.2 Green's Displacement Tensor;20
5.1.3;1.1.3 Kelvin's Tensor of Influence;21
5.2;1.2 Elastic Homogeneous Isotropic Half-Space;23
5.2.1;1.2.1 Mindlin's Solution;23
5.2.2;1.2.2 Boussinesq and Cerruti Solutions;24
5.3;1.3 Coupled Half-Spaces;26
5.4;1.4 Elastic Layered Bases;30
5.4.1;1.4.1 Constant-Width Elastic Layer;30
5.4.2;1.4.2 Variable-Thickness Elastic Layer;35
5.4.3;1.4.3 Multilayer Elastic Half-Space;43
5.5;1.5 Elastic Bases with the Deformation Modulus, Variable with Depth;73
5.5.1;1.5.1 Variation of Deformation Modulus with Depth;73
5.5.2;1.5.2 Normal Concentrated Force Acting on the Half-Space Surface;76
5.5.3;1.5.3 Settlement of a Nonhomogeneous Half-Space Surface;81
5.6;References;101
6;2 Static Analysis of Contact Problems for an Elastic Half-Space;108
6.1;2.1 Boundary Integral Equations of the Contact Problem for an Absolutely Rigid Punch, Deepened into an Elastic Half-Space, Under a Spatial Load System;108
6.2;2.2 Finite-Measure Analogue of the Contact Problem Using Direct Boundary-Element Method;113
6.3;2.3 Numerical-and-Analytical Method of Integration of Fundamental Mindlin's Solutions;118
6.4;2.4 Punch in the Shape of a Rotation Body, Deepened into an Elastic Half-Space;125
6.4.1;2.4.1 Axisymmetric Contact Problem;127
6.4.2;2.4.2 Torsion of an Axisymmetric Punch in an Elastic Half-Space;132
6.5;2.5 Contact Problems for Rigid Punches Located on the Elastic Base Surface;136
6.5.1;2.5.1 Indentation of a Punch with a Flat Smooth Base into an Elastic Half-Space;138
6.5.2;2.5.2 Torsion of an Elastic Half-Space by a Rigid Punch;143
6.6;References;148
7;3 Computer Implementation of Boundary-Element Algorithms;151
7.1;3.1 Software for Solving Spatial Problems of Contact of Foundations with Soil Bases;152
7.2;3.2 Specific Features of Numerical Solutions of Linear Algebraic Equation Systems with Non-symmetrical Matrices, Arising in Boundary-Element Analysis;162
7.3;3.3 Effective Discretization of 2-D Domains of Complex Shape at Numerical Solving of Spatial Contact Problems of Theory of Elasticity;166
7.3.1;3.3.1 Algorithm of Triangulation in the Boundary-Element Method;167
7.3.2;3.3.2 Dual Grids and Their Application in Boundary-Element Method;178
7.4;3.4 Automated Construction of Spatial Grids of Boundary Elements on the Surfaces of Contact of Deepened Foundation Structures with Soil;190
7.5;3.5 Test Examples of Numerical Modeling of Spatial Problems of Contact Interaction;208
7.5.1;3.5.1 Contact Problems for Flat Punches with a Smooth Base;208
7.5.2;3.5.2 Contact Problems with the Account of the Deepening Factor for Axisymmetric Punches, Interacting with an Elastic Half-Space;234
7.6;References;259
8;4 Contact Interaction of Shallow Foundations with Nonhomogeneous Bases;266
8.1;4.1 Spatial Contact Problems for Rigid Flat-Bottom Punches;268
8.2;4.2 Contact Problems for Rigid Rectangular Punches, Resting on Elastic Nonhomogeneous Bases;293
8.2.1;4.2.1 Contact Interaction at Central Loading;297
8.2.2;4.2.2 Contact Interaction at Off-Centre Loading with the Account of Unilateral Constraints;310
8.3;4.3 Control of the Parameters of Loading and Shape to Provide a Uniform Settlement of Rigid Foundation Plates;315
8.3.1;4.3.1 Formulation of the Problem and Its Numerical Implementation;316
8.3.2;4.3.2 External Load Control;318
8.3.3;4.3.3 Shape Parameter Control;322
8.4;4.4 Spatial Stress-Strained State of the Base of a Rigid Strip Variable-Width Foundation;326
8.4.1;4.4.1 Contact Problem for a Variable-Width Strip Foundation;327
8.4.2;4.4.2 Stress-Strained State of a Strip Foundation Base;330
8.4.3;4.4.3 Contact Pressure Distribution in the Area of the Strip Foundation Width Variation;332
8.5;4.5 Calculation of the Section Kernel Boundary for Rigid Foundation Plates;338
8.6;4.6 Numerical Algorithms of Solving Boundary Integral Equations in Spatial Contact Problems for a Nonlinearly Deformable Base;349
8.6.1;4.6.1 Spatial Contact Model for a Nonlinearly Deformable Base;350
8.6.2;4.6.2 System of Nonlinear Contact Equations of the Contact Problem for Absolutely Rigid Punches of a Complex Shape with a Flat Base;352
8.6.3;4.6.3 Iterative Processes of Solving a Finite-Measure Analogue of the Spatial Contact Problem for a Nonlinearly Deformable Base;354
8.6.4;4.6.4 Contact Problem for a Round Punch on a Nonlinearly Deformable Base;356
8.6.5;4.6.5 Estimation of Nonlinear Deformation Effects from Punch Test Results;363
8.7;4.7 Contact Problem for Orthotropic Foundation Plates with the Account of the Specific Features of Spatially Nonhomogeneous Base Deformation;366
8.7.1;4.7.1 Static Calculations of Foundation Plates on Elastic Bases;367
8.7.2;4.7.2 System of Integro-Differential Equations of Bending of a Plate, Resting on an Elastic Base;373
8.7.3;4.7.3 Calculation of Rectangular Orthotropic Plates Based on Combining Finite-Difference and Boundary-Element Methods;376
8.7.4;4.7.4 Examples of Numerical Modelling of the Contact Interaction of Plates with Elastic Bases;379
8.8;References;387
9;5 Calculation of Bases for Rigid Complex-Shaped Deepened Foundations According to the Second Limiting State in a Three-Dimensional Formulation;400
9.1;5.1 General Information on the Calculation of Bases for Foundation Structures from the Deformations;405
9.2;5.2 Spatial Problems for Calculation of Foundation Bases with the Account of the Depth Factor;411
9.3;5.3 Calculation of Bases for Pyramidal Piles Under Vertical, Horizontal, and Momental Loads;430
9.3.1;5.3.1 Existing Approaches to the Calculation of Piles with a Variable Cross-Section;431
9.3.2;5.3.2 Calculation for the Vertical Load;435
9.3.3;5.3.3 Calculation for the Action of a Horizontal Load;435
9.3.4;5.3.4 Calculation for the Action of an Inclined Load;437
9.3.5;5.3.5 Calculation for the Combined Action of an Inclined Force and a Moment;438
9.4;5.4 Interaction of Bases and Rigid Bored Foundations with Vertical and Inclined Piles;439
9.4.1;5.4.1 Structure, Design, and Specific Features of Calculation of Rigid Pile Foundations with Short Piles and a Pile Raft;440
9.4.2;5.4.2 Vertical Cylindrical Piles Under an Inclined Load;443
9.4.3;5.4.3 Foundations with Inclined Piles and a Rectangular Pile Raft;450
9.5;5.5 Spatial Contact Problem for a Bored Pile Foundation with a Widening;453
9.5.1;5.5.1 Production and Structures of Bored Pile Foundations with a Support Widening;454
9.5.2;5.5.2 Engineering Methods for Calculation of Bored Pile Foundation Bases from the Base Deformation;456
9.5.3;5.5.3 Calculation of Deformations of the Base of a Bored Pile Foundation with a Spheroconical Widening Under a Central Loading (Axisymmetric Contact Problem);458
9.5.4;5.5.4 Calculation of Displacements and Slopes of a Bored Pile Foundation Under an Inclined Load;463
9.6;5.6 Calculation of Contact Interaction of Bases with Slotted Foundations of Industrial and Civil Buildings;469
9.6.1;5.6.1 Slotted Foundations of Various Structural Shapes;469
9.6.2;5.6.2 Calculation of Slotted Foundations Based on the Base Deformation;472
9.6.3;5.6.3 Contact Stress on the Lateral Surface of a Slotted Foundation;491
9.6.4;5.6.4 Slotted Foundations with Lateral Widenings;506
9.7;References;508
10;6 Spatial Contact Problems for Porous Elastic Bases;520
10.1;6.1 Soil Mass Deformation Due to the Pore Pressure Decline;524
10.1.1;6.1.1 Integral Representation of Displacements in a Porous Elastic Medium;524
10.1.2;6.1.2 Dilatation Relations;527
10.2;6.2 Distribution of Pressure in a Layer in Case of Functioning Horizontal Wells;529
10.2.1;6.2.1 Distributed Sources of Predetermined Intensity;529
10.2.2;6.2.2 Account of the Finite Radius of the Well;531
10.3;6.3 Contact Problems for Foundation Structures at a Reduced Pore Pressure in the Soil;532
10.3.1;6.3.1 Integral Equations of a Spatial Contact Problem;532
10.3.2;6.3.2 Finite-Dimensional Algebraic Analogue of the Integral Equation System;534
10.3.3;6.3.3 Numerical Algorithm of Solution of the Contact Problem;535
10.3.4;6.3.4 Contact Problem for Shallow Foundations;537
10.4;6.4 Examples of Numerical Calculations;539
10.4.1;6.4.1 Spatial Deformation of the Land Surface;541
10.4.2;6.4.2 Surface Deformations of the Layer;547
10.4.3;6.4.3 Settlements and Slopes of Rigid Foundation Plates;548
10.5;References;549
11;Conclusions;551
12;Appendix A Fundamental Solutions of Spatial Theory of Elasticity for a Homogeneous Isotropic Half-Space;556
13;Appendix B Numerical Schemes for Surface Integral Calculations;567
13.1; B.1 Parametric Representation of Surface Integrals;567
13.2; B.2 Gauss Cubature Formulae for a Standard Simplex and a Standard Square;571
13.3; B.3 Transformation of Coordinates, Reducing the Order of the Integrand Function Singularities;573
13.4; B.4 Highest Algebraic Order of Accuracy Cubature Formulae of Interpolation-Orthogonal Type Based on Chebyshev Polynomials;576
14;Appendix C Round Punch on an Elastic Layer of Variable Thickness at Central and Off-Centre Load;580
15;Appendix D Foundation Under a Tower-Type Structure on a Wedge Base;591
16;Appendix E Finite-Difference Equations of Cylindrical Bend of Orthotropic Slabs Located on an Elastic Foundation;600
16.1; Patterns for Building up Finite-Difference Equation of Cylindrical Bend of an Orthotropic Slab ;608
17;Appendix F Calculation of the Base for a Pyramidal Pile Under Vertical Load According to the ``Instructions Manual for Design of Foundations Made of Pyramidal Piles'';611
17.1;F.1 General;611
17.2;F.2 Calculation Procedure;614
17.3;F.3 Determination of the Base Settlements S0 Under the Bottom End of the Pile;615
17.4;F.4 Determination of the Base Settlements S1of the Lower Part of the Pile (Partition 1);617
17.5;F.5 Determination of the Base Settlements S2 of the Medium Part of the Pile (Partition 2);618
17.6;F.6 Determination of the Base Settlements S3 of the Upper Part of the Pile (Partition 3);618
18;Appendix G Isolines of Contact Stress on a Lateral Surface of a Slotted Foundation;621
19;Appendix H Numeric Schemes of Volume Integration;637
20;References;642
21;Index;644