Spatial Contact Problems in Geotechnics (eBook)

Boundary-Element Method

Sergey Aleynikov (Autor)

eBook Download: PDF

2010 | 2010
XIX, 648 Seiten
Springer Berlin (Verlag)
978-3-540-44776-4 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 10.11.2010
• Reihe/Serie: Foundations of Engineering Mechanics
• Reihe/Serie: Foundations of Engineering Mechanics
• Zusatzinfo: XIX, 648 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: algorithm • algorithms • Analysis • Boundary-Integral Equations • Contact Mechanics • Geomechanics • Geotechnical Engineering • Soil Mechanics • Soil-Structure Interaction
• ISBN-10: 3-540-44776-8 / 3540447768
• ISBN-13: 978-3-540-44776-4 / 9783540447764