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.
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.
This book provides an in-depth overview of current knowledge about Osteogenesis, including molecular mechanisms, transcriptional regulators, scaffolds, cell biology, mechanical stimuli, vascularization and osteogenesis related diseases. Hopefully, the publication of this book will help researchers in this field to decide where to focus their future efforts, and provide an overview for surgeons and clinicians who wish to be directed in the developments related to this fascinating subject.
Terahertz biomedical imaging has become an area of interest due to its ability to simultaneously acquire both image and spectral information. Terahertz imaging systems are being commercialized, with increasing trials performed in a biomedical setting. As a result, advanced digital image processing algorithms are needed to assist screening, diagnosis, and treatment. "Pattern Recognition and Tomographic Reconstruction" presents these necessary algorithms, which will play a critical role in the accurate detection of abnormalities present in biomedical imaging. Terhazertz tomographic imaging and detection technology contributes to the ability to identify opaque objects with clear boundaries, and would be useful to both in vivo and ex vivo environments, making this book a must-read for anyone in the field of biomedical engineering and digital imaging.
The most salient feature of security returns is uncertainty. The purpose of the book is to provide systematically a quantitative method for analyzing return and risk of a portfolio investment in di?erent kinds of uncertainty and present the ways for striking a balance between investment return and risk such that an optimal portfolio can be obtained. In classical portfolio theory, security returns were assumed to be random variables, and probability theory was the main mathematical tool for h- dling uncertainty in the past. However,the world is complex and uncertainty is varied. Randomnessis nottheonly typeofuncertaintyinreality,especially when human factors are included. Security market, one of the most complex marketsintheworld,containsalmostallkindsofuncertainty. Thesecurity- turns are sensitive to various factors including economic, social, political and very importantly, people’s psychological factors. Therefore, other than strict probability method, scholars have proposed some other approaches including imprecise probability, possibility, and interval set methods, etc. , to deal with uncertaintyinportfolioselectionsince1990’s. Inthisbook,wewantto addto thetools existingin sciencesomenewandunorthodoxapproachesforanal- ing uncertainty of portfolio returns. When security returns are fuzzy, we use credibility which has self-duality property as the basic measure and employ credibilitytheorytohelpmakeselectiondecisionsuchthatthedecisionresult will be consistent with the laws of contradiction and excluded middle. Being awarethat one tool is not enough for solving complex practical problems, we further employ uncertain measure and uncertainty theory to help select an optimal portfolio when security returns behave neither randomly nor fuzzily. One core of portfolio selection is to ?nd a quantitative risk de?nition of a portfolio investment.
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