Effective Stress and Equilibrium Equation for Soil Mechanics 1st Edition by Longtan Shao, Xiaoxia Guo, Shiyi Liu, Guofeng Zheng 1351607414 9781351607414

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ISBN-10 :  1351607414 

ISBN-13 : 9781351607414

Author:  Longtan Shao, Xiaoxia Guo, Shiyi Liu, Guofeng Zheng 

The concept of effective stress and the effective stress equation is fundamental for establishing the theory of strength and the relationship of stress and strain in soil mechanics and poromechanics. However, up till now, the physical meaning of effective stress has not been explained clearly, and the theoretical basis of the effective stress equation has not been proposed. Researchers have not yet reached a common understanding of the feasibility of the concept of effective stress and effective stress equation for unsaturated soils. Effective Stress and Equilibrium Equation for Soil Mechanics discusses the definition of the soil skeleton at first and clarifies that the soil skeleton should include a fraction of pore water. When a free body of soil skeleton is taken to conduct internal force analysis, the stress on the surface of the free body has two parts: one is induced by pore fluid pressure that only includes normal stress; the other is produced by all the other external forces excluding pore fluid pressure. If the effective stress is defined as the soil skeleton stress due to all the external forces excluding pore fluid pressure, the effective stress equation can be easily obtained by the internal force equilibrium analysis. This equation reflects the relationship between the effective stress, total stress and pore fluid pressure, which does not change with the soil property. The effective stress equation of saturated soils and unsaturated soils is unified, i.e., o˜=o˜t –Seuw–(1–Se)ua. For multiphase porous medium, o˜=o˜t –u*,u*=Seiui(i=1,2,…,M). In this book, a theoretical formula of the coefficient of permeability for unsaturated soils is derived. The formula of the seepage force is modified based on the equilibrium differential equation of the pore water. The relationship between the effective stress and the shear strength and deformation of unsaturated soils is preliminarily verified. Finally, some possibly controversial problems are discussed to provide a better understanding of the role of the equilibrium equation and the concept of effective stress.

Effective Stress and Equilibrium Equation for Soil Mechanics 1st Table of contents:

1 Introduction
1.1 Effective stresses
1.1.1 Effective stresses of saturated soils
1.1.2 Main academic perspectives and some comments on effective stress
1.1.3 Effective stress of unsaturated soils
1.2 Equilibrium differential equations
1.2.1 Equilibrium differential equation of foundation soil
1.2.2 Biot consolidation equation
1.2.3 Fredlund’s equilibrium differential equation for unsaturated soils
1.3 Continuous medium matter model for soils
1.3.1 Concept of continuous medium
1.3.2 Continuity of physical quantities of soils
1.3.3 Representative Elementary Volume (REV)
1.3.4 Continuous medium matter model of soils
1.3.5 Pore area and soil skeleton area at cross sections of soils
1.4 Three constitutive phases of soils
1.4.1 Soil skeleton
1.4.2 Water in soils
1.4.3 Gas in soils
1.4.4 Definition of physical indexes for soils’ three phases with the consideration of soil skeleton water
1.5 Soil-water potential and its components
1.6 Soil-water characteristic curves
1.6.1 Physical meaning and basic characteristics of SWCC
1.6.2 Influence factors of SWCC
1.6.3 SWCC and water content distribution in horizontal soil layers
1.7 Main contents of this book
2 Equilibrium differential equations of a soil
2.1 Equilibrium differential equations of soil mass
2.2 Static equilibrium equation of the soil skeleton
2.2.1 Force analysis on the free body of the soil skeleton
2.2.2 Equilibrium differential equations of the independent phase of soil mass
3 Effective stress
3.1 Effective stress equation and physical meaning of effective stress
3.1.1 Effective stress equation
3.1.2 Physical meaning of effective stress
3.2 Relationship between effective stress and shear strength/volumetric strain
3.2.1 Formula of volumetric strain of a soil
3.2.2 Shear strength formula of a soil
3.2.3 Effective stress and the constitutive relationship of a soil
3.3 Primary verification of the correlation between effective stress and shear strength of unsaturated soils
3.4 Effective stress principle for unsaturated soils
3.4.1 Statement of effective stress principle
3.4.2 Simple applications of effective stress principle for unsaturated soils
4 Seepage equation of unsaturated soils
4.1 Seepage equation of saturated soil
4.1.1 Derivation of the formula of Darcy’s law for saturated soil
4.1.2 Seepage equation for saturated soils
4.2 Seepage equation for unsaturated soils
4.2.1 Soil-water interaction force of unsaturated soils
4.2.2 Motion equation and the coefficient of permeability for unsaturated soils
4.2.3 Seepage equation for unsaturated soils
4.3 Formula of seepage force
4.4 The overflow condition of the gas in soils
4.4.1 The overflow condition of the closed air bubbles
4.4.2 The overflow condition for pore air while surface water is infiltrating
5 Discussion on some issues related to effective stress
5.1 Does Terzaghi’s effective stress equation need to be modified?
5.2 Is effective stress pseudo or real stress?
5.3 Effective stress and stress state variables of soils
5.4 Effective stress and soil skeleton stress
5.5 The effective stress of unsaturated soils
5.6 Should contractile skin be the fourth phase?

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Tags: Effective Stress, Equilibrium Equation, Soil Mechanics, Longtan Shao, Xiaoxia Guo, Shiyi Liu, Guofeng Zheng