Finite Elements for Two-Dimensional Consolidation

Abstract

In this chapter the finite element method for the solution of problems of one-dimensional consolidation is presented. The purpose is to develop a method for the analysis of consolidation of a soil consisting of several layers having different properties. 16.1 Basic equation The basic equation of one-dimensional consolidation is (16.1) where pis the excess pore pressure, and where n is the compressibility of the soil, k is the hydraulic conductivity (or permeability), and 'Y is the volumetric weight of the fluid. The initial condition is t = 0 : p =Po, (16.2) and the boundary conditions are supposed to be z = 0 : p = 0, (16.3) ap z = h : az = 0. (16.4) This means that the upper boundary z = 0 is supposed to be fully drained, and the lower boundary z =his impermeable. As an alternative the lower boundary may also be drained, in which case the excess pore pressure p is zero for z = h. In order to eliminate the time derivative the differential equation (16.1) is integrated over a small time intervalll.t. This gives n(p+-p-) = ll.t .!!._(~ dp), dz 'Y dz (16.5) where p-is the value of p at the beginning of the time interval, p+ is the value at the end of the interval, and p is the average value during that interval. It is assumed that this average value can be expressed as (16.6) 280 A. Verruijt, Computational Geomechanics