A mathematical treatment of one-dimensional soil consolidation

Abstract

Terzaghi’s conception of the nature of one-dimensional soil consolidation [1] is shown to lead to a non-linear differential equation. A dimensional analysis of this equation and the boundary conditions of the standard consolidation test [2] gives a more general explanation of a well known linear relationship between the total consolidation U ( t ) U\left ( t \right ) after a time t t and t 1 / 2 {t^{1/2}} . By linearizing the equation in a general manner, an expression is obtained for U ( t ) U\left ( t \right ) which includes secondary consolidation terms. Two solutions of the linearized equation are obtained; the first for the standard consolidation test and the second for consolidation under a boundary load increasing uniformly with time.