Unsaturated Soil Mechanics with Probability and Statistics  book cover
1st Edition

Unsaturated Soil Mechanics with Probability and Statistics

ISBN 9781138553682
Published August 27, 2019 by CRC Press
188 Pages 105 B/W Illustrations

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Book Description

Soil is fundamentally a multi-phase material – consisting of solid particles, water and air. In soil mechanics and geotechnical engineering it is widely treated as an elastic, elastoplastic or visco-elastoplastic material, and consequently regarded as a continuum body.

However, this book explores an alternative approach, considering soil as a multi-phase and discrete material and applying basic Newtonian mechanics rather than analytical mechanics. It applies microscopic models to the solid phase and fluid phases, and then introduces probability theory and statistics to derive average physical quantities which correspond to the soil‘s macroscopic physical properties such as void ratio and water content.

This book is particularly focused on the mechanical behaviour of dry, partially saturated and full saturated sandy soil, as much of the physicochemical microscopic characteristic of clayey soil is still not clear. It explores the inter-particle forces at the point of contact of soil particles and the resultant inter-particle stresses, instead of the total stress and effective stress which are studied in mainstream soil mechanics. Deformation and strength behaviour, soil-water characteristic curves, and permeability coefficients of water and air are then derived simply from grain size distribution, soil particle density, void ratio and water content.

A useful reference for consultants, professional engineers, researchers and public sector organisations involved in unsaturated soil tests. Advanced undergraduate and postgraduate students on Unsaturated Soil Mechanics courses will also find it a valuable text to study.

Table of Contents

1. Introduction

1.1 Brief history of mechanics leading to path of current soil mechanics

1.2 Scope of this boook

2. Review of Probability Theory and Statistics

2.1 Hierarchy of population, sample population and sample

2.2 Sample points in sample space

2.3 Random variables and probability distribution

2.4 Parameters of probability distribution

2.5 Normal distribution and Logarithmic normal distribution

2.6 Regression analysis

2.7 Markov chain

3. Microscopic Models of Soil using Probability Distributions

3.1 Macroscopic physical quantities of saturated-unsaturated soil and their phase diagram

3.2 Microscopic probabilistic models of solid, gas and liquid phases

4. Microscopic Physical Quantities Derived from Void Ratio and Probability Distributions

4.1 Number of Soil Particles per Unit Volume

4.2 Characteristic length

4.3 Number of Contact Points per Unit Volume and Unit Area

4.4 Calculation of N prt, D cht, N cv and N ca for simple cubic packing of uniform spheres

5. Inter-particle Force Vector and Inter-particle Stress Vector

5.1 Notation of inter-particle force vector and inter-particle stress vector

5.2 Inter-particle force vector at a contact point and inter-particle stress vector on a plnae

5.3 Inter-particle force vector and inter-particle stress vector due to gravitational force

5.4 Inter-particle force vector and inter-particle stress vector due to seepage force

5.5 Inter-particle force vector and inter-particle stress vector due to surface tension

5.6 Inter-particle force vector and inter-particle stress vector due to external force

5.7 Summary for normal and tangential components of inter-particle stress vectors

6. Modeling of Pore Water Retention Using Elementary Particulate Model (EPM)

6.1 Soil suction

6.2 Modeling of soil-water characteristic curve

6.3 Modeling of hysteresis of soil-water characteristic curve

6.4 Correction of pore size distribution for soil-water characteristic curve

7. Modeling of Pore Water and Pore Air Flows Using Elementary Particulate Model (EPM)

7.1 Permeability of fluid phases through coarse-grained soil

7.2 Correction of pore size distribution for coefficient of water permeability

7.3 Governing equation for saturated-unsaturated seepage flow in soil

8. Stability Analysis using proposed models

8.1 Average coefficient of friction and potential slip plane

8.2 Potential slip plane

8.3 Apparent cohesion due to surface tension

8.4 Self-weight retaining height

8.5 Typical stability analyses in geotechnical engineering problems

9. Deformation Analysis using proposed Models

9.1 Microscopic motion of soil particles corresponding to macroscopic deformation

9.2 Derivation of strain increments

9.3 Evaluation of continuous and discontinuous motions of soil particles

10. Numerical Experiment of soil tests for saturated-unsaturated soil

10.1 Microscopic physical quantities for numerical experiment

10.2 Soil-water characteristic curve

10.3 Saturated-unsaturated permeability coefficient with respect to pore water

10.4 Stability analysis

10.5 Deformation analysis

11. Issues to be solved in future

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Ryosuke Kitamura is an emeritus professor at Kagoshima University, Japan. He is a recipient of the 1983 Outstanding Paper Award for Young Researchers of the Japanese Geotechnical Society, the 2003 Outstanding Paper Award of Japan Society of Civil Engineers and JGS Medal for Merit for 2004; and has served as a chairman or member of several technical committees of JSCE and JGS.

Kazunari Sako is currently an associate professor of Kagoshima University, Japan. He is a recipient of the 2009 Outstanding Paper Award for Young Researchers of JGE. He serves an editorial member of Japanese Geotechnical Journal, Soils and Foundations, and the Journal of the Japanese Society of Civil Engineering.