A mathematical treatment of one-dimensional soil consolidation

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 $U\left ( t \right )$ after a time $t$ and ${t^{1/2}}$. By linearizing the equation in a general manner, an expression is obtained for $U\left ( t \right )$ 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.