Un método numérico para la obtención de relaciones constitutivas en rocas fracturadas

Abstract

In this study constitutive relations for unsaturated fractured rocks using a numerical procedure that mimics the laboratory technique of measurement are determined. Three-dimensional rock samples with random vertical and horizontal fractures are computationally constructed. Each fracture is conceptualized as a three-dimensional plate whose hydraulic properties are described by the van Genuchten model. The procedure is based on the numerical solution of the steady-state unsaturated flow equation in a three-dimensional cubic domain, on a regular mesh of one million elements, using a hybridized mixed finite element method. The saturation and hydraulic conductivity values are numerically computed from the simulation results, for several values of pressure head. The simulated relations are fitted using two recently proposed analytical expressions for unsaturated fractured rocks. Numerical examples show that both models can match reasonably the simulated saturation relations.