Mechanical prediction of fracture aperture in layered rocks

Two types of opening-mode fractures (joints) are commonly found in layered rocks. One is called unconfined because fracture heights are much less than the layer thickness and they behave like fractures in massive rocks. The other is called confined because the fractures terminate at the layer boundaries. We investigate the mechanical control on apertures in these systems using the theory of elasticity. An analytical solution demonstrates that the ratio of aperture to height (aspect ratio) of an unconfined fracture in a homogeneous, isotropic medium is linearly related to the average strain, the overburden stress, and the internal fluid pressure within the fracture. Numerical results based on of the finite element method (FEM) for an unconfined fracture in the central layer of a three-layer model agree with the analytical result when the fractured layer and neighboring layers have the same elastic constants. The aspect ratio of the unconfined fracture is insensitive to the ratio of Young's modulus of the fractured layer to that of the neighboring layers and to the differences in Poisson's ratios. The FEM results for confined fractures show that their aspect ratio is linearly related to the average strain, the overburden stress, and the internal fluid pressure. However, the aspect ratio increases nonlinearly with increasing fracture spacing to layer thickness ratio because of the mechanical interaction between adjacent fractures. The interaction becomes insignificant when the spacing to layer thickness ratio is >similar to 6.0. The aspect ratio of confined fractures depends on the ratio of Young's modulus of the fractured layer to that of the neighboring layers. This dependence is significant when the fracture spacing to layer thickness ratio is < 1.3; otherwise, it is negligible. In all of these cases the aspect ratio of confined fractures is insensitive to variations in Poisson's ratios. Furthermore, the FEM results predict that fracture accommodated strain measured by the traditional scan line method may slightly overestimate the average normal strain when the spacing to layer thickness ratio is <similar to 1.0, and may slightly underestimate this strain for greater ratios.