Hydromechanical behavior of a deformable rock fracture subject to normal stress

A simple physical model is developed to understand the effect of normal stress on fluid flow through a single fracture. Roughness along the fracture walls plays a definite role in controlling the flow. In the usual parallel plate representation for a fracture, the flow is proportional to the cube of the constant aperture, b . However, when the effect of fracture roughness is taken into account, the flow follows an equivalent ‘cubic’ law where the cube of the single value for the aperture must be replaced by an appropriately weighted average 〈 b 3 〉. To obtain this average value, a physical model was developed wherein the single fracture is represented by a collection of voids and the closure of the fracture results from a deformation of these voids. The model enables one to characterize the fracture roughness from a relationship between the stress‐displacement measurements of intact rock and those of jointed rock. This calculated value of 〈 b 3 〉 leads to flow rate as a function of normal stress. Predicted flow rates using this model are in good agreement with results from laboratory data on granite and basalt. By making several simplifying physical assumptions, we have eliminated the necessity of incorporating fitting parameters to the flow data. In this manner, a basic understanding of the factors controlling the flow of fluids through fractures has been obtained.