Effective Stresses in Soil and Rock and Consolidation in Three Dimensions

In the following, the continuum model for a fully saturated porous material is presented. The theory is mainly due to M.A. Biot [3, 4]. We shall only consider a twophase system consisting of a solid skeleton and a single pore fluid, e.g. water. The theory for three-dimensional consolidation is developed. Anisotropic permeability of the material is allowed, but for simplicity the analysis is restricted to isotropic linear elastic material behaviour. However, the theory is easily extended to elastoplasticity. Finally, it will be shown that the effective stresses in a porous material may in general not be calculated as proposed by Terzaghi. Whereas highly accurate results are achieved for residual soils, i.e. sand, silt and clay, poor results are obtained for cemented materials such as concrete and rock. Here it is recommended to follow the stress approach proposed by Biot. 1. BASIC DEFINITIONS A porous material, or matrix, with the total volume V is considered. The material is fully saturated, and the pores are assumed to be distributed randomly in space so that the material on a macroscopic level may be described as a continuum. The volume is divided into two parts, V = Vs + Vf , (1) where Vs is the volume of the solid phase, i.e. the grain skeleton, and Vf is the volume of fluid. In geotechnical engineering, the subscript f is generally substituted by the subscript w, since the pore fluid is usually water. In saturated porous materials, e.g. soil, a part of the pore fluid is constrained. For example, a part of the water in clay is chemically bound to the clay mineral, and in rock or granular soil some of the water may be trapped in cracks that are not connected to the primary system of pores. This part of the fluid belongs to the solid phase, i.e. to Vs, since it cannot move relatively to the solid matrix. Hence, only the volume of interconnected voids is included in the definition of Vf , cf. Fig. 1. Unfortunately, in real soil or concrete etc. it may be difficult to determine which part of the pore fluid is free to move relatively to the solid skeleton. Solid Fixed fluid Free fluid 1-n n Vf