QUANTITATIVE SOLUTIONS IN THE MECHANICS OF UNSATURATED POROUS-MEDIA

Porous materials are made of a solid matrix, which usually has a compl icated inner structure, and contain open and close pores. They are con sidered as unsaturated if at least one gas phase is present. For insta nce geomaterials may contain water, water vapour and dry air. The soli d and fluids usually have different motions. Because of them and the d ifferent material properties, there is interaction between the constit uents. We have hence coupling between the fields, e.g. displacements, water pressure, capillary pressure and temperature. The quantitative s olution of realistic problems involving multiphase materials is theref ore rather complicated and time consuming ([1]). A considerable amount of effort has been and is being put into the search for appropriate s olution algorithms. One way to speed up the solution is matrix partiti oning ([2]), where we solve for one block of the field variables by ke eping the other blocks frozen. Then we solve for the second block etc. Hence each time smaller problems are to be solved, and their coupled nature is preserved. This procedure has been used extensively in the p ast in the form of the so called standard staggered procedure of Gauss -Seidel type ([3]): e.g. for non-isothermal consolidation of fully sat urated porous media ([4]) and for isothermal behaviour of fully and pa rtially saturated porous media ([5]). However this approach was usuall y limited to a sequential form of solution. The development of compute r architecture points strongly toward parallelism: either massively pa rallel processors (MPP), which are rather expensive, or clusters of wo rkstations connected by a network ([6-8]). This enables the implementa tion of a parallel solution of the problem. Among the different possib ilities the following two seemed particularly attractive: the standard staggered procedures ([3]), which can be implemented in parallel fash ion and where the numerical properties are known, or the domain decomp osition method (DD) ([9-11]), where the equations for the different fi elds are kept together, but the domain is split into two or more subdo mains. Drawbacks of the first method is the proper balancing of the fi elds between the different processors: each field may have a different number of variables, three per node for vectors (e.g. displacement ve ctor) and one per node for scalars (e.g. gas or capillary pressure), o r else elements with different node number for the fields may be used (e.g. 9-node elements for displacements and 4-node elements for pressu res). Further the speed (in terms of eigenvalues) of convergence for t he different fields may also differ. In case of domain decomposition t he balancing would be easier, but there is not much experience in non- linear coupled problems. In the paper some of these problems will be b riefly discussed.