Stresses between 3D fractures in infinite and layered elastic solids

Periodically distributed opening mode fractures are often found in layered sedimentary rocks. The stress analysis related to opening mode fractures in layered solids is solved by a new numerical approach combining (3D) fast Fourier transform with the theory of periodic eigenstrain and the conjugate gradient method. Results show that the fracture spacing to layer thickness ratio for embedded opening mode fractures, using a three-dimensional (3D) model, is in good comparison with that of the plane strain case (two-dimensional model). The critical value of the fracture spacing to layer thickness ratio increases for a stiff layer case and decreases for a stiff surrounding solid case. Out-of-plane fracture length is also studied as a parameter in the 3D modeling. Opening mode surface fractures in a layered half-space were also studied. The results show that a critical fracture saturation ratio exists for this case and occurs when the normal surface stress transitions from tensile to compressive. This stress state is shown to be caused by a bending effect in the layer.