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Our first text on this subject Computational Geomechanics with Special Reference to Earthquake Engineering was published 23 years ago and has been out of print for much of the past decade. It was the first book of its kind having as the main topic Computational Dynamic Aspects of Geomechanics which obviously comprise statics also. In the intervening period, there was a rapid expansion in the research and practical applications of these types of problems, which has prompted us to write this new and thoroughly updated version.

It contains not only the results of research carried out at our four institutions but also reports on the work done elsewhere. The chapters from the previous edition have been extensively updated and new chapters have been added to give a much broader coverage of recent research interests. The Preface to the first edition was written by the Late Professor Oleg Cecil Zienkiewicz. Its validity is still fully conserved today. So, we reprinted large parts of it.

Although the concept of effective stress in soils is accepted by all soil mechanicians, practical predictions and engineering calculations are traditionally based on total stress approaches. When the senior author began, in the early seventies, the application of numerical approaches to the field of soil mechanics in general and to soil dynamics in particular, it became clear to him that a realistic prediction of the behavior of soil masses could only be achieved if the total stress approaches were abandoned. The essential model should consider the coupled interaction of the soil skeleton and of the pore fluid. Indeed, the phenomena of weakening and of “liquefaction” in soil, when subjected to repeated loading such as that which occurs in earthquakes, can only be explained by considering this “two‐phase” action and the quantitative analysis and prediction of real behaviour can only be achieved by sophisticated computation. The simple limit methods often applied in statics are no longer useful. It, therefore, seems necessary at the present time to present, in a single volume, the basis of such computational approaches because a wider audience of practitioners and engineering students will require the knowledge which hitherto has only been available through scientific publications scattered throughout many journals and conferences. The present book is an attempt to provide a rapid answer to this need. Since 1975, a large number of research workers, both students and colleagues, have participated both at Swansea and elsewhere in laying the foundations of numerical predictions which were based largely on concepts introduced in the early forties by Biot. However, the total stress calculation continues to be used by some engineers for earthquake response analysis, often introduced with linear approximations. Such simplifications are generally not useful and can lead to erroneous predictions. In recent years, centrifuge experiments have permitted the study of some soil problems involving both statics and dynamics. These provide a useful set of benchmark predictions. Here a validation of the two‐phase approach was available and a close agreement between computation and experiment was found. A very important landmark was a workshop held at the University of California, Davis, in 1993, which reported results of the VELACS project (Verification of Liquefaction Analysis by Centrifuge Studies) sponsored by the National Science Foundation of the USA.

At this workshop, a full vindication of the effective stress, two‐phase approaches was clearly available and it is evident that these will be the bases of future engineering computations and prediction of behavior for important soil problems. The book shows some examples of this validation and also indicates examples of the practical application of the procedures described. During numerical studies, it became clear that the geomaterial – soil would often be present in a state of incomplete saturation when part of the void was filled with air. Such partial saturation is responsible for the presence of negative pressures which allow some “apparent” cohesion to be developed in noncohesive soils. This phenomenon may be present at the outset of loading or may indeed develop during the dynamic process. We have therefore incorporated its presence in the treatment presented in this book and thus achieved wider applicability for the methods described.

Despite a large number of authors, we have endeavored to present a unified approach and have used the same notation, style, and spirit throughout. The first three chapters present the theory of porous media in the saturated and unsaturated states and thus establish general backbone to the problem of soil mechanics.

Even though the fundamental nature of the basic theory remains unchanged as shown in Chapters 2 and 3, many of the other chapters have been substantially updated. The following part of the book has been extensively restructured, reworked, and updated, and new chapters have been added such as to cover essentially all the important aspects of computational soil mechanics.

Chapter 4, essential before numerical approximation, deals with the very important matter of the quantitative description of soil behavior which is necessary for realistic computations. This chapter has been substantially rewritten such as to introduce new developments. It is necessarily long and devotes a large part to generalized plasticity and critical‐state soil mechanics and also includes a simple plasticity model. The generalized plasticity model is then extended to partially saturated soil mechanics. Presentation of alternative advanced models such as bounding surface models and hypoplasticity concludes the chapter.

Chapter 5 addresses some special aspects of analysis and formulation such as far‐field solutions in quasi‐static problems, input for earthquake analysis and radiation damping, adaptive finite element requirements, the capture of localized phenomena, regularization aspects and stabilization for nearly incompressible soil behavior both in dynamics and consolidation permitting to use equal order interpolation for displacements and pressures.

Chapter 6 presents applications to static problems, seepage, soil consolidation, hydraulic fracturing, and also examples of dynamic fracturing in saturated porous media. Validation of the predictions by dynamic experiments in a centrifuge is dealt with in Chapter 7.

Chapter 8 is entirely devoted to application in unsaturated soils, including the dynamic analysis with a full two‐phase fluid flow solution, analysis of land subsidence related to exploitation of gas reservoirs, and initiation of landslides.

Chapter 9 addresses practical prediction, application, and back analysis of earthquake engineering examples. Finally, Chapter 10 pushes the limits of the analysis beyond failure showing the modeling of fluidized geomaterials with application to fast catastrophic landslides.

We are indebted to many of our coworkers and colleagues and, in particular, we thank the following people who over the years have contributed to the work (in alphabetical order of their surnames):

 T. Blanc,

 G. Bugno,

 T.D. Cao,

 P. Cuéllar,

 S. Cuomo (MP),

 P. Dutto,

 E. González,

 B. Haddad,

 M.I. Herreros,

 Maosong Huang,

 E. Kakogiannou,

 M. Lazari,

 Chuan Lin,

 Hongen Li,

 Li Tongchun,

 Liu Xiaoqing,

 D. Manzanal,

 M. Martín Stickle

 A. Menin,

 J.A. Fernández Merodo,

 E. Milanese,

 P. Mira,

 M. Molinos,

 S. Moussavi,

 R. Ngaradoumbe Nanhornguè,

 P. Navas,

 T. Ni,

 Jianhua Ou,

 M. Passarotto,

 M.J. Pastor,

 C. Peruzzo,

 F. Pisanò,

 M. Quecedo,

 V. Salomoni,

 L. Sanavia,

 M. Sánchez‐Morles,

 R. Santagiuliana,

 R. Scotta,

 S. Secchi,

 Y. Shigeno,

 L. Simoni,

 C. Song,

 A. Yagüe,

 Jianhong Ye,

 M. Yoshizawa,

 H.W. Zhang.

Finally, we would like to dedicate this edition to the memory of the Late Oleg Cecil Zienkiewicz. Without his inspiration and enthusiasm, we would not have undertaken the research work reported here. We would also like to thank our beloved Late Helen Zienkiewicz, wife of Professor Zienkiewicz, who kindly allowed us to celebrate Oleg’s decades of pioneering and research field defining achievements in computational geomechanics.

Andrew H. C. Chan

Manuel Pastor

Bernhard A. Schrefler

Tadahiko Shiomi

Hobart, Madrid, Padua, Tokyo, January 2022