Modeling Slope Instability as Shear Rupture Propagation in a Saturated Porous Medium

When a region of intense shear in a slope is much thinner than other relevant geometric lengths, this shear failure may be approximated as localized slip, as in faulting, with strength determined by frictional properties of the sediment and effective stress normal to the failure surface. Peak and residual frictional strengths of submarine sediments indicate critical slope angles well above those of most submarine slopes—in contradiction to abundant failures. Because deformation of sediments is governed by effective stress, processes affecting pore pressures are a means of strength reduction. However, common methods of exami ning slope stability neglect dynamically variable pore pressure during failure. We examine elastic-plastic models of the capped Drucker-Prager type and derive approximate equations governing pore pressure about a slip surface when the adjacent material may deform plastically. In the process we identify an elastic-plastic hydraulic diffusivity with an evolving permeability and plastic storage term analogous to the elastic term of traditional poroelasticity. We also examine their application to a dynamically propagating subsurface rupture and find indications of downslope directivity.Earth and Planetary SciencesEngineering and Applied Science

Some mathematics for the constitutive modelling of soils

The purpose of this paper is to introduce some mathematical techniques which prove to be valuable in the constitutive modelling of soils. All the developments are related to an approach to constitutive modelling called hyperplasticity, in which strong emphasis is placed on the derivation of the entire behaviour of a material from two scalar potentials. Hyperplasticity includes all sufficient conditions to satisfy the laws of thermodynamics, but some conditions are not strictly necessary: they embody a slightly stricter statement than the second law. In this paper this issue is not addressed, but instead some simple models are developed to illustrate the hyperplastic approach. It is left for the reader to judge whether these models are valuable in representing real material behaviour or whether they are too restrictive. The hyperplasticity approach has its roots in the work of Ziegler, and also has much in common with much of the French work in plasticity theory, where the concept of "standard materials" is employed. Much of what is presented here is not new, but represents application of existing mathematical techniques in areas of geotechnics where they are not currently employed. © Springer-Verlag Berlin Heidelberg 2003

A thermomechanical framework for constitutive models for rate-independent dissipative materials

A formulation of elastic-plastic theory for rate independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. Much use is made of Legendre transformations to establish the links between the different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters, and their conjugate variables, which are termed generalized stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation. A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. A systematic presentation is made of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of the two potentials and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous work by Ziegler and other authors, and extends and generalizes work by Collins and Houlsby to include thermal effects

Fundamentals of kinematic hardening hyperplasticity

We present a hyperplastic (thermomechanical) framework for the modelling of kinematic hardening of plastic materials. The advantage of this approach is that it allows a compact development of plasticity theories, which are guaranteed to obey thermodynamic principles. Starting with a model which employs a single kinematically hardening yield surface, we generalize this first to multiple surfaces and then to the case of an infinite number of yield surfaces. At each stage of generalization, the link with conventional plasticity is demonstrated, and examples of one- and multi-dimensional hyperplastic models are presented, together with their interpretation in terms of conventional plasticity theory. © 2001 Elsevier Science Ltd. All rights reserved

Principles of hyperplasticity: An approach to plasticity theory based on thermodynamic principles

Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory. The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis. In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced. Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics. © Springer-Verlag London Limited 2006

A thermomechanical framework for rate-independent dissipative materials with internal functions

This paper builds on previous work by Houlsby and Puzrin (Int. J. Plasticity 16 (2000) 1017) in which a framework was set out for the derivation of rate-independent plasticity theory from thermodynamic considerations. A key feature of the formalism is that the entire constitutive response is determined by knowledge of two scalar functions. The loading history is effectively captured through the use of internal variables. In this paper, we extend the concept of internal variables to that of internal functions, which represent infinite numbers of internal variables. In this case the thermodynamic functions are replaced by functionals. We set out the formalism necessary to derive constitutive behaviour within this approach. The principal advantages of this development is that it can provide realistic modelling of kinematic hardening effects and smooth transitions between elastic and elastic-plastic behaviour. © 2001 Elsevier Science Ltd. All rights reserved

Principles of hyperplasticity: An approach to plasticity theory based on thermodynamic principles

Principles of Hyperplasticity is concerned with the theoretical modelling of the behaviour of solids which undergo nonlinear and irreversible deformation. The approach to plasticity theory developed here is firmly rooted in thermodynamics, so that the models developed are guaranteed to obey the First and Second Laws. Major emphasis is placed on the use of potentials, and the derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown. It is to accentuate this feature that the authors use the term "hyperplasticity", by analogy with the use of "hyperelasticity" in elasticity theory. The use of potentials has several advantages. First it allows models to be very simply defined, classified and, if necessary, developed. Secondly, by employing Legendre Transformations, it permits dependent and independent variables to be interchanged, making possible different forms of the same model for different applications. Emphasis is also placed on the derivation of incremental response, which is necessary for numerical analysis. In the later parts of the book the theory is extended to include treatment of rate-dependent materials. A new and powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is also introduced. Illustrated with many examples of models derived within this framework, and including material particularly relevant to the field of geomechanics, this monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics. © Springer-Verlag London Limited 2006