Bed thickness-dependent fracturing and inter-bed coupling define the nonlinear fracture spacing-bed thickness relationship in layered rocks: Numerical modeling

Bed-normal fractures or joints are common in sedimentary basins (reservoirs). Fracture spacing S is an important parameter affecting both the mechanical stability and permeability of rock masses. Many studies have focused on predicting this parameter from the bed thickness T. Field measurements do show that S and T are related but frequently in a very nonlinear way so that at T > T0,S stabilizes at a certain value S0. Both T0 and S0 strongly vary in different settings. To understand this S(T) relationship, we conducted 2-D finite-difference modeling of a three-stratigraphic-layer system, where interfaces between competent and incompetent layers have different shear strength values z. The models reproduce not only a general trend of the S(T) dependence in nature but also the observed variability of T0 and S0. These parameters are controlled in the models mostly by z. T0 and S0 rapidly decrease with the z increase, but the ratio T0/S0 approximate to 1.5 remains constant. At small T, the S(T) curves are linear, with slopes kappa, whose reciprocal (1/kappa) is linearly related to z and increases with z increase. The strong nonlinearity of S(T) relationship is explained by the T-dependence of the fracturing process obtained in the models.