Finite element for Richards’ equation in porous rocks

Abstract

The interaction processes of water movement and environment have several aspects important to engineering and geology, which motivate a large amount of research all over the world. As computers with larger capacity become available and affordable, several simplifications used in the past have become meaningless, and nonlinear complex phenomena like unsaturated flow can be processed in affordable machines. The reduction of water flow capacity of filters and drains in embankments due to unsaturated zones, and the environmental problems of remediation of contaminated zones in porous rock masses at the vadose zone are examples of special problems in which advanced modeling should be applied to avoid misleading conclusions or dreadful consequences. The unsaturated flux can also be important in understanding the influence of humidity in the bowing phenomenon in calcitic marbles, since laboratory tests have shown different evolutions of this pathology in partially saturated samples and in completely wet or dry samples. Moreover, this formulation also has important application in building envelope modeling, like in evaporative roofs which enhance thermal comfort in hot weather. To increase the understanding of unsaturated problems, this paper presents a finite element formulation for applications in unsaturated flow in stiff porous media, like sedimentary rocks or concrete. The formulation is based on Richards’ equation for one-dimensional flows and it includes a linear interpolation of suction, as well as an arbitrary implicit parameter.