Stiffening of Bulk Modulus in Poroelastic Medium with Rising Pore Pressure: A Comprehensive Sensitivity Study using a Closed-Form Solution Method

This study presents high-resolution stress models of synthetic porous media consisting of regularly arranged cylindrical pores, with and without internal pressure. The stress distribution within the elastic solid matrix surrounding fluid-filled pores under uniaxial compressive stress is analyzed for: (1) drained conditions (negligible pore pressure) and (2) undrained conditions (with various pore pressures). A Linear Superposition Method (LSM) is applied to quantify elastic displacements and solve for the stress tensor field throughout the porous medium. Resolving for the pore-scale stresses in a poroelastic medium is relevant for diverse engineering disciplines. Oversimplified assumptions about the geometry and stress distribution can result in inaccurate predictions of mechanical behavior under different loading conditions. The study systematically investigates the effects of internal pressure, pore size, and porosity on the effective bulk modulus. Results reveal a non-linear, pressure-dependent relationship between bulk modulus and porosity. Notably, we identify a critical pressure state (P_CRIT) where the bulk modulus becomes nearly independent of porosity. Beyond this point, a counterintuitive phenomenon of pressure-induced stiffening emerges under high pore pressure. Analysis of stress-strain distributions elucidates the mechanisms underlying this behavior. The new approach in this study for estimating macroscopic properties from microstructural parameters is highly applicable in designing durable engineering structures, optimizing geothermal and petroleum reservoir practices, and enhancing underground storage operations.