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 ( t ) after a time t t and t 1 / 2 {t1/2} . By linearizing the equation in a general manner, an expression is obtained for U ( t ) U ( t ) 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.
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A. McNabb (1960) studied this question.