Unsaturated Soil Mechanics with Probability and Statistics

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

Biography

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.