1st Edition

The SMP Concept-Based 3D Constitutive Models for Geomaterials

By Hajime Matsuoka, De'an Sun Copyright 2006
    160 Pages 112 B/W Illustrations
    by CRC Press

    The Cam-Clay model is a fundamental constitutive model in soil mechanics, but is only suitable for normally consolidated clay under triaxial compression stress states. The SMP failure criterion is the most reasonable three-dimensional extension of the Mohr-Coulomb failure criterion from the point of view of its physical meaning, mathematical expression and geometrical presentation. To integrate the Cam-Clay model with the SMP criterion and extend it to sand and other geomaterials is one of the fundamental tasks in geotechnical engineering. This book introduces the SMP criterion, the integration of the SMP criterion with the well-known Cam-clay model, and the application of the SMP criterion to the general elastoplastic constitutive models for geomaterials like clay, sand and unsaturated soil. In addition to the theoretical development of constitutive models, the book is full of high-quality experimental data obtained from conventional and true triaxial tests on various soils. The scope and the level of the book ensure that it will be a valuable resource for postgraduate students, academics and geotechnical engineering professionals alike



    Chapter 1 Spatially Mobilized Plane (SMP) and SMP criterion

    1.1 Origin of SMP

    1.2 Stress-strain relation based on Compositely Mobilized Plane (CMP)

    1.3 Stress-strain relation based on Spatially Mobilized Plane (SMP)

    1.4 Failure criteria for metals and granular materials

    1.5 Failure criterion for cohesive-frictional materials


    Chapter 2 Introduction to Cam-clay model

    2.1 Introduction

    2.2 Original Cam-clay model

    2.2.1 Principal direction of plastic strain increment and adopted stress and strain variables

    2.2.2 Determination of plastic potential and yield functions

    2.2.3 Determination of strain-hardening rule

    2.2.4 Determination of

    2.2.5 Detailed derivation of

    2.3 Modified Cam-clay model

    2.3.1 Principal direction of plastic strain increment and adopted stress and strain variables

    2.3.2 Determination of plastic potential and yield functions

    2.3.3 Determination of strain-hardening rule

    2.3.4 Determination of

    2.3.5 Detailed derivation of


    Chapter 3 The Cam-clay model revised by the SMP criterion

    3.1 Introduction

    3.2 The SMP criterion and a transformed stress tensor

    3.3 The Cam-clay model revised by the SMP criterion

    3.4 Comparison of model predictions with experimental data

    3.5 Concluding remarks

    Appendix 1 Derivation of

    Appendix 2 Derivation of elastoplastic constitutive tensor Dijkl


    Chapter 4 Elastoplastic constitutive models for geomaterials using transformed stress

    4.1 An elastoplastic model for sands and clays

    4.1.1 Introduction

    4.1.2 A unified hardening parameter for both clays and sands

    4.1.3 A unified elastoplastic model for both clays and sands

    4.1.4 Prediction versus experiment

    4.1.5 Modelling confining pressure dependence of strength and deformation

    4.1.6 Conclusions

    4.2 An elastoplastic model for K0-consolidated soils

    4.2.1 Introduction

    4.2.2 The Sekiguchi-Ohta model and its stress-dilatancy relation

    4.2.3 An anisotropic hardening elastoplastic model for K0-consolidated clays and sands

    4.2.4 Comparison of model predictions with experimental results Modelling triaxial behaviour Modelling plane strain behaviour

    4.2.5 Elastoplastic constitutive tensor

    4.2.6 Conclusions

    4.3 An elastoplastic model for unsaturated soils

    4.3.1 Introduction

    4.3.2 Effective stress for unsaturated soils

    4.3.3 Transformed stress tensor based on Extended SMP criterion

    4.3.4 Formulation of model for unsaturated soils Strength of unsaturated soil Formulation of model in isotropic stress state Formulation of model in general stress

    4.3.5 Triaxial tests on unsaturated soils Triaxial test apparatus for unsaturated soils Unsaturated soil specimen Stress paths

    4.3.6 Comparison of model predictions with experimental results Model parameters and their determination Model predictions versus experimental results

    4.3.7 Concluding remarks


    Chapter 5 Concluding remarks


    Hajime Matsuoka is Professor of Civil Engineering at the Nagoya Institute of Technology in Japan and the author of a number of books. His research interests include Earth Reinforcement and Vibration Reduction by Soilbags, in-situ Direct Shear Test and Constitutive Models for Soils.

    De'an Sun is Professor of  Engineering at the Department of Civil Engineering, Shanghai University.  His current research interests include Unsaturated Soil Mechanics and Soil Constitutive Modelling.

    Professors Matsuoka and Sun were awarded the Technical Development Prize from The Japanese Civil Engineering Society in 2004.