On Mathematical Analysis of Soil Structure using Consolidation Equations

I. O. Abiala; J. A. Olayemi

I. O. Abiala
J. A. Olayemi

Keywords: consolidation, finite difference, mathematical, soil structure, two-dimensional

Abstract

This paper deals with an explicit finite difference solution for the one- and two-dimensional consolidation of a homogeneous clay layer. The finite difference method approximates the solution of a continuous problem by representing it in terms of a discrete set of elements such that there is an integer number of points in depth and an integer number of times at which we calculate the field variables; in this case, just the excess pore water pressure. The calculation of the average degree of consolidation is used as a medium for comparison between the numerical analysis and the empirical analysis. Here, we have solved two-dimensional consolidation equations numerically by using Alternating Direction Implicit (ADI) Method. Moreover, tridiagonal methods are used here alongside the ADI method. The main idea behind this technique is to avoid the complexities which usually occur while solving higher order partial differential equations. Finally, numerical examples are presented to show the relationship between the Pore Water Pressure (PWP) and Depth Time Grids (DTG). It was also discovered that the Average Degree of Consolidation (U_ave) directly varies with respect to the Time factor (T_v) as the time step increases.

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