Limit Analysis and Soil Plasticity

by Chen, Wai-Fah

• ISBN13: 9781932159738
• ISBN10: 1932159738
• Format: Paperback
• Copyright: 2007-12-01
• Publisher: J. Ross Publishing

Summary

Devoted to the theory and applications of limit analysis as applied to soil mechanics, this text also contains information on soil plasticity and rock-like material such as concrete. The first part of the book describes the techniques of limit analysis in detail and are illustrated by many examples. The second part deals with the applications of limit analysis to "classical soil mechanics problems" and in the third part the author presents advances on bearing capacity problems of concrete blocks or rock. The fourth part discusses the modern development of the theory of soil plasticity.

Author Biography

Dr. Wai-Fah Chen is a member of the U.S. National Academy of Engineering and an Honorary member of the American Society of Civil Engineers

Table of Contents

Foreword	p. VII
Preface	p. IX
Introduction	p. 1
Introduction	p. 1
Slip-line method and limit equilibrium method	p. 5
Limit analysis method	p. 8
A brief historical account of soil plasticity	p. 12
The assumptions and theorems used in limit analysis	p. 15
Introduction	p. 15
Perfectly plastic assumption and Coulomb yield criterion	p. 16
The kinematic assumption on soil deformations and the concept of flow rule	p. 25
The assumption of small change in geometry and the equation of virtual work	p. 33
Theorems of limit analysis	p. 35
Limit theorems for materials with non-associated flow rules	p. 40
Limit analysis by the upper-bound method	p. 47
Introduction	p. 47
Rigid block sliding separated by narrow transition layer	p. 49
Intermixing of homogeneous deforming regions and rigid block sliding	p. 63
Intermixing of inhomogeneous deforming regions and rigid block sliding	p. 73
Evaluation of the minimum solution for an assumed mechanism	p. 89
The dissipation functions	p. 99
Limit analysis by the lower-bound method	p. 107
Introduction	p. 107
Mohr's diagram and basic relations	p. 109
Discontinuities in the stresses	p. 114
Jump conditions at a discontinuity surface of Tresca material	p. 121
Jump conditions at a discontinuity surface of Coulomb material	p. 125
Discontinuous fields of stress viewed as pin-connected trusses - Tresca material	p. 131
Discontinuous fields of stress viewed as pin-connected trusses - Coulomb materials	p. 140
Graphical construction of discontinuous stress fields	p. 152
Combined method for solving the problems involving overlapping of discontinuous stress fields	p. 156
Progressive failure of footings	p. 169
Introduction	p. 169
Plane strain notched tensile specimen (Von Mises material)	p. 170
Plain strain punch indentation of rectangular blocks (Von Mises material)	p. 174
Uniform strip load on a shallow stratum of undrained clay (Von Mises material)	p. 179
Rigid strip footing on an elastic stratum	p. 181
Rigid strip footing on an overconsolidated stratum of insensitive clay (extended Von Mises material)	p. 184
Rigid strip footing on a stratum of undrained clay (Von Mises material)	p. 195
Rigid circular punch on an elastic-plastic strain hardening layer (isotropic hardening Von Mises material)	p. 202
A brief historical sketch	p. 206
Summary and conclusions	p. 208
Bearing capacity of strip footings	p. 211
Introduction	p. 211
Limit analysis, slip-line and limit equilibrium methods	p. 212
Soil governing parameters	p. 220
Bearing capacity of a strip footing on a general c-[phis]-[gamma] soil	p. 222
Bearing capacity of a strip footing on cohesionless soils (N[subscript gamma] factor)	p. 245
Bearing capacity of a strip footing on a c-[phis] weightless soil (N[subscript c] and N[subscript q] factors)	p. 267
Bearing capacity determination by slip-line method	p. 279
Bearing capacity of footings on nonhomogeneous anisotropic soils	p. 286
Summary and conclusions	p. 294
Bearing capacity of square, rectangular and circular footings	p. 295
Introduction	p. 295
Square, rectangular and circular footings on a semi-infinite medium - lower bounds	p. 295
Square and rectangular footings on a semi-infinite medium - upper bounds	p. 297
Square and circular footings on a finite block - lower bounds	p. 302
Square and circular footings on a finite block - upper bounds	p. 307
Square and circular footings on a semi-infinite layer - lower bounds	p. 312
Square and circular footings on a semi-infinite layer - upper bounds	p. 320
Bearing capacity of circular footings by slip-line method	p. 327
Active and passive earth pressures	p. 341
Introduction	p. 341
Coulomb's solution of vertical retaining wall problems	p. 344
Coulomb's solution of general retaining wall problems (Fig. 8.7a)	p. 351
Two-triangle mechanism (Fig. 8.8)	p. 354
Logsandwich mechanism (Figs. 8.9 and 8.10)	p. 359
Arc-sandwich mechanism (Fig. 8.12)	p. 364
Discussion of results	p. 370
Comparison with known solutions	p. 377
Earth pressure tables	p. 385
Summary and conclusions	p. 398
Stability of slopes	p. 399
Introduction	p. 399
Logspiral mechanism passing through the toe	p. 403
Logspiral mechanism passing below the toe	p. 409
Stability of slopes in anisotropic, non-homogeneous soils	p. 416
Shape of critical slip surface and its associated normal stress distribution	p. 435
Summary and conclusions	p. 445
Bearing capacity of concrete blocks or rock	p. 447
Introduction	p. 447
A simplified material model	p. 450
A modified Coulomb stress criterion with zero tension cut-off (Fig. 10.8a)	p. 455
A modified Coulomb criterion with a small but not zero tension cut-off (Fig. 10.8b)	p. 457
Bearing capacity under a strip loading - upper bound	p. 458
Bearing capacity under a strip loading - lower bound	p. 462
Three-dimensional square and circular punches-upper bound	p. 467
Three-dimensional square and circular punches - lower bounds	p. 470
Friction effects on the bearing capacity of blocks	p. 476
Concrete blocks with a concentric cable duct (Fig. 10.4a)	p. 477
Concrete blocks with an eccentric cable duct - small eccentricity (Fig. 10.4b)	p. 482
Concrete blocks with an eccentric cable duct - large eccentricity (Fig. 10.4b)	p. 485
Experimental study of the strain field	p. 490
Comparison of test results with calculated strengths	p. 494
Approximate solution	p. 497
Summary and conclusions	p. 499
Double-punch test for tensile strength of concrete, rock and soils	p. 501
Introduction	p. 501
Elastic stress distribution in splitting tests	p. 503
Limit analysis of splitting tensile tests	p. 507
Plastic stress distribution in splitting tests by slip-line method	p. 513
Plastic stress distribution in splitting tests by finite element method	p. 516
Plastic stress distribution in double-punch test and limit analysis solution	p. 519
Experimental results of double-punch test for concrete materials	p. 528
Experimental results of double-punch test for rocks	p. 537
Experimental results of double-punch test for soils	p. 540
Soil plasticity - Theory and application	p. 543
Introduction	p. 543
Extended Von Mises perfectly plastic model for soil	p. 544
An elastic-plastic strain hardening model for soil	p. 553
An elastic-plastic strain hardening-fracture model for concrete	p. 564
Finite element formulation	p. 584
Integration of the displacement rate equilibrium equations	p. 587
Example 1 - Rigid strip footing on a soil stratum	p. 590
Example 2 - Plane strain punch-indentation of concrete blocks	p. 597
Summary and conclusions	p. 603
References	p. 607
Author index	p. 631
Subject index	p. 634
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