A hybrid boundary element‐finite element analysis procedure for fluid flow simulation in fractured rock masses

Abstract

Extension of numerical techniques to the analysis of fissure flow in three‐dimensional rock masses of realistic complexity and extent constitutes an important facility in civil engineering and resource exploitation practice. Migration velocities of contaminants and fluid discharge will always be higher for a true three‐dimensional network over a two‐dimensional representation in that the effect of critical, out‐of‐plane intersections may be correctly accommodated. Revised direct boundary element formulations are developed that are capable of discretizing individual fissure discs and their intersections with adjacent fissures. Discretization coverage, by definition, is limited to the fissure edges and internal intersections, with this factor alone being a major advantage of the technique over the more conventionally utilized domain methods. Appropriate manipulation of the resulting set of equations is shown to yield a fully populated, positive definite, symmetric tensor representing the geometric conductivity of a single fissure disc. The retained degrees‐of‐freedom for the ‘super element’ are purely in terms of the fissure intersections with a minimum of 1 degree‐of‐freedom required per intersection. Global matrix assembly and solution is accomplished by standard finite element techniques, the global matrix being, in general, sparsely populated. The procedure is ideally suited to micro‐computer solution in that a reduced degree‐of‐freedom system is obtained from a much larger and computationally, intractable system. The advantages of boundary solution procedures are realized with minimal data input requirements and effective representation of high potential gradients. The sparsely populated and symmetric from of the global matrix retains one of the more favourable assets of the secondary finite element formulation.