Publisher Summary
This chapter focuses on fundamentals of poroelasticity. The presence of a freely moving fluid in a porous rock modifies its mechanical response. Two mechanisms play a key role in the interaction between the interstitial fluid and the porous rock: (i) an increase of pore pressure induces a dilation of the rock; and (ii) compression of the rock causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. These coupled mechanisms bestow an apparent time-dependent character to the mechanical properties of the rock. If excess pore pressure, induced by compression of the rock, is allowed to dissipate through diffusive fluid mass transport, further deformation of the rock progressively takes place. The rock is more compliant under drained conditions than undrained ones. The chapter discusses the formulation and analysis of coupled deformation–diffusion processes, within the framework of the Biot theory of poroelasticity. The Biot model of a fluid-filled porous material is constructed on the conceptual model of a coherent solid skeleton and a freely moving pore fluid.

Fundamentals of Poroelasticity

Incompressible porous media models by use of the theory of mixtures

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

This paper describes recent advances in stability analysis that combine the limit theorems of classical plasticity with finite elements to give rigorous upper and lower bounds on the failure load. These methods, known as finite-element limit analysis, do not require assumptions to be made about the mode of failure, and use only simple strength parameters that are familiar to geotechnical engineers. The bounding properties of the solutions are invaluable in practice, and enable accurate limit loads to be obtained through the use of an exact error estimate and automatic adaptive meshing procedures. The methods are very general, and can deal with heterogeneous soil profiles, anisotropic strength characteristics, fissured soils, discontinuities, complicated boundary conditions, and complex loading in both two and three dimensions. A new development, which incorporates pore water pressures in finite-element limit analysis, is also described. Following a brief outline of the new techniques, stability solutions ...

Geotechnical stability analysis

In situations where a raft foundation alone does not satisfy the design requirements, it may be possible to enhance the performance of the raft by the addition of piles. The use of a limited number of piles, strategically located, may improve both the ultimate load capacity and the settlement and differential settlement performance of the raft. This paper discusses the philosophy of using piles as settlement reducers and the conditions under which such an approach may be successful. Some of the characteristics of piled raft behaviour are described. The design process for a piled raft can be considered as a three-stage process. The first is a preliminary stage in which the effects of the number of piles on load capacity and settlement are assessed via an approximate analysis. The second is a more detailed examination to assess where piles are required and to obtain some indication of the piling requirements. The third is a detailed design phase in which a more refined analysis is employed to confirm the op...

Piled raft foundations: design and applications

An investigation of the stability of numerical solutions of Biot's equations of consolidation

Elasto-plastic consolidation of soil

This paper presents a method of analysis for piled raft systems constructed in layered soils. The method presented takes account of the interactions of the raft, piles and soil without the cost of a full three-dimensional rigorous analysis. This is done by the use of finite layer methods for the analysis of the soil and finite element methods for the raft. Examples are provided in the paper for piled rafts constructed on layered soils, and results are presented for bending moments in the raft and loads in the piles.

Analysis of Piled Raft Systems in Layered Soil

A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier transform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer. (a) for part 2 of the article see TRIS 367147. (TRRL)

Finite layer analysis of consolidation. I

A method is presented for obtaining the consolidation behaviour of a layered soil subjected to strip, circular, or rectangular surface loadings, or subjected to fluid withdrawal due to pumping. The solution method involves applying a Fourier or Hankel transform to the field quantities along with a Laplace transformation. The effect of the Fourier or Hankel transform is to reduce a two- or three-dimensional problem or one involving axial symmetry, to one involving only a single spatial dimension. In cases where the soil is horizontally layered, this has great advantages over conventional methods, such as finite element or finite difference methods, since very little computer storage and data preparation time is required. Solution of the time dependent problem is achieved by applying a Laplace transformation to the field variables, obtaining solutions in Laplace transform space, and then numerically inverting the transformed solutions to obtain the real time behaviour. This eliminates the need for ‘marching type’ schemes where a solution is found from one at a previous time. By direct inversion of the Laplace transform, a solution may be obtained directly at any given time.

John C. Small

Papers

An investigation of the stability of numerical solutions of Biot's equations of consolidation

Elasto-plastic consolidation of soil

Analysis of Piled Raft Systems in Layered Soil

Finite layer analysis of consolidation. I

A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms