The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

Elastic properties are key parameters during the deformation of rocks. They can be measured statically or dynamically, but the two measurements are often different. In this study, the static and dynamic bulk moduli (K-static and K-dynamic) were measured at varying effective stress for dry and fluid-saturated Westerly granite with controlled fracture densities under isotropic and differential stress states. Isotropic fracturing of different densities was induced in samples by thermal treatment to 250, 450, 650, and 850 degrees C. Results show that fluid saturation does not greatly affect static moduli but increases dynamic moduli. Under isotropic loading, high fracture density and/or low effective pressure results in a low Kstatic/Kdynamic ratio. For dry conditions Kstatic/Kdynamic approaches 1 at low fracture densities when the effective pressure is high, consistent with previous studies. Stress-induced anisotropy exists under differential stress state that greatly affects Kstatic compared to Kdynamic. As a result, the Kstatic/Kdynamic ratio is higher than that for the isotropic stress state and approaches 1 with increasing axial loading. The effect of stress-induced anisotropy increases with increasing fracture density. A key omission in previous studies comparing static and dynamic properties is that anisotropy has not been considered. The standard methods for measuring static elastic properties, such as Poisson's ratio, Young's and shear modulus, involve subjecting the sample to a differential stress state that promotes anisotropy. Our results show that stress-induced anisotropy resulting from differential stress state is a major contributor to the difference between static and dynamic elasticity and is dominant with high fracture density.