Measurement of the shear to normal compliance ratio is one of the few remote sensing techniques available for estimating the in situ properties of fractures. We present an accurate yet efficient method for predicting the normal and shear compliance of fractures using an asperity-based approach. The resultant capabilities provide an efficient, versatile tool for predicting the normal and shear compliance of fractures with arbitrary roughness under a given level of closure stress. We apply the method to the prediction of evolving shear compliance under closure stress. We also calculate the corresponding anisotropic conductivity of the deformed fractures and find that the direction of highest shear compliance correlates well with the direction of highest fracture conductivity. This suggests that the degree of shear compliance anisotropy may be an indicator of conductivity anisotropy in natural fractures over a range of stresses.
Seismic and acoustic measurements are the most readily available methods for inferring the mechanical properties of fractures and faults in the field. As a consequence, many authors have sought to develop approaches that can relate the geometric properties of a fracture to its seismic or acoustic signature. In particular, the ratio of shear compliance to the normal compliance has been pursued as an indicator of the microstructure within a fracture or as an indicator of fluid content . Kachanov et al.  studied the similarities and difference between treating fractures as surfaces with discrete points of contact versus traction-free cracks. They found that although the resulting formulas for the fracture compliances have similar form, the microstructural parameters controlling the magnitude of the results were different. Sayers et al.  pointed out that such approximations obtain very different results because fundamentally distinct assumptions are made regarding the way the fracture surface interact. Sayers et al.  concluded that such discrepancies can be avoided if more realistic geometries and deformation models are utilized for the asperities or cemententation within the fracture. Sayers et al.  went on to demonstrate that 2-D finite element calculation can address asperity deformation directly and provide more reliable insight into the shear and normal compliance of fractures. In theory, more representative results could be inferred through the use of 3-D finite elements, however, it is currently impractical to use such an approach for large fractures or within extensive parameter studies