Mathematical model for one‐dimensional desiccation and consolidation of sedimented soils

A mathematical model has been developed to represent the physical phenomena that occur during the desiccation and one‐dimensional consolidation of successive layers of hydraulically transported sediments as they are periodically deposited in a containment area. The governing boundary value problem, defined in terms of pore water pressures, consists of two field equations (one for the saturated domain and one for the unsaturated domain), a drainage boundary condition, an evapotranspiration boundary condition and a series of continuity conditions at the interfaces between different layers. A number of simplifying assumptions were made to render the field equations tractable, and a step‐by‐step numerical procedure was used to solve the linearized boundary value problem; at the end of each step, the errors introduced by the simplifying assumptions were corrected. Based on a thorough study of the convergence and stability conditions associated with the numerical approximation employed, a system of automatic corrections was incorporated into the computer program to reduce the time increment if stability problems originate during the solution. Based on the results of a parameter study, it was found that, although drainage conditions at the bottom of the, layer do exert some influence on the consolidation rate during deposition of the dredgings, the evapotranspiration potential renders this effect almost negligible when desiccation takes place at the surface. In contrast, transpiration plays an important, role on the consolidation rate during the early stages of desiccation, but its effect is reduced considerably as the water table approaches an equilibrium position.