This book discusses the numerical simulation of the various static and transient phenomena that occur in soil media.
Chapter 2 introduces the various field equations governing the response of multiphase soil media. Emphasis is given to coupled formulations (Biot's type) in which the soil system is viewed as consisting of an assemblage of particles that form a skeleton whose voids are filled with water and air or gas. The soil system is thus viewed as a two- (saturated soil) or multi-phase material whose state is described by the stresses (or pressures) and kinematics within each phase. It is shown how these equations reduce to those that govern:
fully static situations
quasi-static consolidation phenomena
fully transient dynamic situations such as those that prevail under impact and/or earthquake loading conditions.
The constitutive equations for the soil skeleton are postulated in terms of ‘effective stresses’. Various constitutive descriptions for the ‘fluid’ phases in the case of partially saturated soil systems are also discussed.
Chapter 3 discusses the numerical implementation. A finite-element discretisation is used for the spatial description. The resulting coupled semi-discrete (time continuous) finite-element equations are integrated in time by using a variety of finite-difference time-stepping algorithms. It is shown what trade-offs are available depending upon which field description is adopted (u-w-p, U-V or u-p description), and which situation (short-term, intermediate or long-range) is to be dealt with.
Chapter 4 provides a description of various non-linear constitutive models for the soil skeleton. Emphasis is given to elasto-plastic constitutive descriptions, and various theories are mentioned, including kinematic hardening, bounding surface and hypoplasticity. Most of the attention is given to the ‘generalised plasticity’ formulation that has been favoured at Swansea. In this formulation the concept of a yield function, fundamental to classical elasto-plastic descriptions, is abandoned and replaced by the reduced notion of ‘directions’ in stress space. Such a formulation is therefore very much akin to hypoplasticity, and suffers from the same limitations. In particular, the central notion of ‘consistency’ of classical plasticity is lost, which renders the accurate and consistent numerical integration of the non-linear rate equations next to impossible. The numerical treatment of the generalised plasticity equations provided by the authors is limited to an explicit integration. This is illustrated in Chapter 9, in which the source code (Fortran) for the integration of a ‘generalised von Mises’ model is provided. A subcycling procedure together with a forward tangent integration is used. It is well known that such an integration procedure results in gross inaccuracies, as the stress point drifts away from the yield function since no corrections are made for consistency (see e.g. Computational inelasticity by J. C. Simo and T. J. R. Hughes, Springer, 1998).
The remaining chapters mostly deal with benchmark or validation exercises using the computer code DIANA-SWANDYNE developed at Swansea. In Chapter 5, various examples are given for static, consolidation and dynamic problems. In Chapter 6, the VELACS centrifuge program is discussed, and various numerical simulations of the tests are presented. It is not clear whether the numerical results presented pertain to class A predictions or back-analyses. In any case, the comparison between computation and observation is said to be ‘good or excellent’. In Chapter 7, back-analyses are presented for major earthquake events such as Kobe and Niigata (Japan) and the lower San Fernando dam in California (USA).
Chapter 8 is short, and considers radiation boundary conditions in dynamic situations (a simple viscous dashpot is used), adaptive refinement procedures, and stabilisation procedures to remove the ‘wiggles’ in computed responses in near-incompressible systems. Chapter 9 provides a short description of the DIANA-SWANDYNE computer program developed at Swansea.
The authors are the originator and products of the Swansea school, and the book is clearly written for the Swansea school audience. In particular, it ignores other important works and contributions from ‘outsiders’, and therefore provides a somewhat slanted description of the ‘state of the art’ in this important area of computational geomechanics.
