Numerical simulation of nonlinear consolidation problems by models based on the network method

Abstract

• Nonlinear consolidation models for any type of constitutive dependences and eliminating the most restrictive hypotheses. • Tabulated models are also designed and solved by the network method. • The network models are built from very simple rules, providing the almost exact solution of the problem. The nonlinear consolidation problem in saturated soils, for any type of constitutive dependences of the hydraulic permeability and the void ratio on the effective pressure, has been numerically simulated by the network method. Three different network models, based on logarithmic and/or potential constitutive dependences, called the Davis and Raymond, Juárez-Badillo and Cornetti and Battaglio models, as well as a fourth one with dependences in tabulated form, are solved. In addition, new network models that delete the two restrictive hypotheses assumed by these authors are presented. These hypotheses are the influence of the void ratio changes in the term of contraction of the governing equation and the influence of the thickness change of the volume element as consolidation progresses. Only a few rules based on elementary theory of circuits are required for the design of the models, whose solution is reliable with relatively small grids and computational times. After verifying the results of the network method with the solutions of the classic authors, the extended models have been used to address a real case of consolidation.