Consolidation of Clay by Sand Drain under Time-Dependent Loading

Abstract

The mathematical theory and physical laws of one-dimensional consolidation of clayey soils are well-known. Sand drains accelerate the consolidation process. Several analytical and experimental studies have already reported on sand drain consolidation of clayey soils. However, the literature does not contain a nonlinear theory of sand drain consolidation under time-dependent loading that can take into account any effective stress! void ratio/permeability variations. A generalized governing equation, capable of yielding a large class of ana­ lytical solutions for these variations is derived in this paper. Closed-form solutions are presented for the variation of pore water pressure with a time factor and load increment ratio under time-dependent loading. The analytical formulation is validated by comparing the solution with the standard results available in the literature for in­ stantaneous loading, constant permeability, and constant compressibility. Following the equal strain approach, this paper presents a particular form of generalized governing equation, capable of yielding a large class of analytical solutions for time-depen­ dent loading, which can handle any effective stress!void ratio/ permeability variations. The use of this governing equation is illustrated by presenting the closed-form solution for the case where the effective stress/void ratio/permeability response takes the form U) a~~r) =1 :leo (~;) In the equal strain approach, e is a function of t only. Therefore