Dual-Porosity Strain Energy Function Model Based on Stiff and Compliant Porosities

Abstract A novel dual-porosity strain energy function model based on the dual-porosity framework was proposed and applied to delineate the rock into stiff (the rock matrix and stiff pores) and compliant (predominantly penny-shaped cracks) components. By deriving each component’s contribution to strain energy, a nonlinear seismic wave equation that evolves with porosity was formulated by integrating the kinetic energy equation with Lagrangian equations. Furthermore, it was analyzed how the stiff rock frame and compliant pores, separately and coupled, influence the seismic wave velocity, revealing a nonlinear relationship with pore compressibility. Unlike conventional effective medium approaches that solely account for the stiff rock frame, the proposed coupled dual-component model overcomes the limitations of univariate analyses, shedding light on the microstructural mechanisms by which crack closure enhances the effective rock frame’s stiffness, thereby providing a more comprehensive interpretation of the pressure-dependent behavior of elastic seismic wave velocities.