Unsaturated soil mechanics with probability and statistics

The book, Unsaturated Soil Mechanics with Probability and Statistics, is a crisp distillation of Prof. Kitamura’s lifelong research on unsaturated soils. Co-authored with his former doctoral student, Kazunari Sako, they managed to condense more than 40 years of research work into a book of about 170 pages. The book is divided into 11 chapters. A brief background on the development of classical and unsaturated soil mechanics, and a summary of the book are given in the introduction. The authors pointed out that the approach adopted in the book is an extension of the approaches of Mogami (1965, 1967) and Murayama (1964, 1990). More specifically, probability theory was used to deal with the change in particulate soil structure of coarse-grained soil instead of the usual continuum mechanics. Having set the book in perspective, a review of probability theory and statistics is provided in Chapter 2. This is a very useful chapter as the relevant probability theory and statistics are introduced to ease the reader into the mathematics that are found throughout the rest of the book. Chapter 3 gives a brief account of the macroscopic physical quantities of soils and then starts to build microscopic models using probability distribution to give the particulate soil structure and pore structure in soil. Chapter 4 then looks at how the microscopic physical quantities of number of particles per unit volume, characteristic length, number of contact points per unit volume and unit area, and demonstrates how these microscopic quantities are calculated for simple cubic packing of spheres. The forces and stresses at the contact point between soil particles are described in Chapter 5. Seepage and capillary rise are also described in Chapter 5. Chapter 6 introduces the concept of elementary particulate model (EPM) to model the pore water retention. The explanation of the ink-bottle model schematically and mathematically provides an interesting alternate view of hysteresis in the soil-water retention curve. Chapter 7 derives the unsaturated and saturated coefficients of permeability using the EPM and pore size distribution. Chapter 8 provides some guidance for obtaining friction angle, shear stress on the potential slip plane, apparent cohesion due to suction and a self-weight retaining height using the concepts presented in the earlier chapters. This is then followed by some brief description of their applications to bearing capacity, earth pressure and slope stability. Chapter 9 looks at the deformation behaviour from the microscopic model’s view. This chapter proves challenging to read as it suggests that during deformation the angles at the contact points may change, appear, and disappear. This is then extended to the potential slip plane to estimate the change in contact angle with the change in stress state during deformation using probability theory (Markov process). Chapter 10 illustrates how soil-water characteristic curves, self-weight retaining height and permeability function can be numerically modelled using the microscopic physical quantities. Finally, in Chapter 11, the limitations of the proposed model are summarized and provides suggestions of how they may be overcome in future. Overall, the book is useful to postgraduate students and researchers who like to learn or apply the particle mechanics approach to soil mechanics. The book is not cluttered with too much mathematical details and provides sufficient guidance for the reader to start working on it. Particularly useful is the illustration of how the microscopic physical quantities can be related to the macroscopic physical quantities and to common problems in geotechnical engineering so that a quantum leap is not needed to apply the approach. There are some parts of the book that I found less satisfying. One is the assumption that the inter-particle forces consist of that due to self-weight, capillary, seepage, external, osmotic pressure and physicochemical action, and the elimination of the interparticle forces due to osmotic pressure and physicochemical action. The authors could have provided a more complete explanation of the interparticle forces and the basis for elimination of the interparticle forces due to osmotic pressure and physicochemical action. Second is on the concept of self-weight retaining height where there is no equivalent counterpart in classical soil mechanics. The significance of this concept is unclear. Lastly, the numerical simulations for saturated and unsaturated soil tests in Chapter 10 only show comparison of the numerical results and experimental data for Shirasu’s soil-water characteristic curve and permeability function. It would have been more convincing if other common sands and other tests with similarly good agreement are also illustrated. However, it must be emphasized that Unsaturated Soil Mechanics with Probability and Statistics is a theoretical book that presents an approach to model the behaviour of unsaturated coarse-grained soil. There are several aspects that are left for the readers to explore as explained by the authors in the last chapter of the book.