One-Dimensional Mathematical Model for Large-Strain Consolidation

A mathematical model is developed to represent the one-dimensional large-strain consolidation of a fully saturated clay. The fluid limit is postulated to be that water content associated with a ‘stress-free’ condition of the soil, and it is taken as the reference state from which strains are measured. Experimental results from a series of permeability tests suggest that the relationship between the logarithm of the coefficient of permeability and the void ratio is not a straight line for the entire range of void ratio considered. In addition, the variation of the constrained modulus as consolidation progresses is taken into account. The resulting boundary value problem involves a nonlinear partial differential equation with void ratio as the dependent variable, and the numerical solution is accomplished by a step-by-step procedure combined with a weighted residual technique which leads to a finite element discretization in the spatial variable and a finite difference discretization in the time variable. The mathematical model is applied to four cases (two involving a salt flocculated kaolinite slurry and two involving a dispersed kaolinite slurry) in the stress range within which a ‘slurry’ is transformed to a ‘soil’. For the particular clay (Hydrite 10) investigated it was found that classical small-strain consolidation theory can adequately describe the deformation-time response for all practical purposes after the effective consolidation stress on the slurry had exceeded a value of about 8 lb/in². (55 kN/m²).