Effective Stress and Equilibrium Equation for Soil Mechanics

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.

1 Introduction 1.1 Effective stresses 1.2 Equilibrium differential equations 1.3 Continuous medium matter model for soils 1.4 Three constitutive phases of soils 1.5 Soil-water potential and its components 1.6 Soil-water characteristic curves 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 3 Effective stress 3.1 Effective stress equation and physical meaning of effective stress 3.2 Relationship between effective stress and shear strength/volumetric strain 3.3 Primary verification of the correlation between effective stress and shear strength of unsaturated soils 3.4 Effective stress principle for unsaturated soils 4 Seepage equation of unsaturated soils 4.1 Seepage equation of saturated soil 4.2 Seepage equation for unsaturated soils 4.3 Formula of seepage force 4.4 The overflow condition of the gas in soils 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?

Dr. Longtan Shaois a professor in the Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning, China. He was born in China, where he obtained his bachelor degree, master degree and Ph.D. from Dalian University of Technology. He has been engaged in the research on the theory of soil mechanics, geotechnical testing technology and equipment development, and stability analysis of soil structures. Dr. Xiaoxia Guo is a Senior Engineer in the Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning, China. She was born in China, and obtained bachelor, master and doctoral degrees from Dalian University of Technology. She has been engaged in the research on soil constitutive model, geotechnical testing technology and equipment, and stability analysis of soil structures. Dr. Shiyi Liu obtained B.S. degree from Jilin University and Ph.D. degree from Dalian University of Technology. He joined the School of Resources and Civil Engineering at Northeastern University (Shenyang, China) as a Lecturer in 2016. His major research interests are slope stability analysis, lateral earth support structures and underground excavation. Guofeng Zheng is a Ph.D. student in the Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning, China. His major research interest is the properties of unsaturated soils.