Anisotropic Poroelastodynamics Solution and Elastic Moduli Dispersion of a Naturally Fractured Rock

In this work, the theory of anisotropic dual-porosity dual-permeability poroelastodynamics is used to simulate the responses of pore pressure, displacement, and stress of a fluid-saturated transversely isotropic naturally fractured cylindrical rock sample. The sample is subjected to a harmonic loading with a constant displacement amplitude at one end. These solutions are then use d to calculate the elastic moduli dispersion of the rock sample. A transversely isotropic water-saturated rock sample is selected as an example to demonstrate the simulation and the mechanisms of the dispersion due to the coupled motions of the rock matrix and fluids in pore spaces and fractures. The effects of material anisotropy on the poromechanical responses and the elastic modulid dispersion of the rock sample are presented. We also show excellent matches between the simulation and laboratory measurements of the dynamic Young's moduli of two shale, one clay, and three sedimentary rock samples.