Exploring Two-Point Liquid Loading Effects on Transversely Isotropic Poroelastic Media Through Green’s Functions Analysis

Green’s functions for two-point liquid sources analyze anisotropic mechanical-fluid interactions, providing insights for real-world applications and enabling precision in design optimization across geomechanics and biomechanics. In this paper, we uniquely derive the expression for a two-point fluid source influenced by poroelasticity in an infinite transversely isotropic material, providing a novel contribution to the literature. Initially, we obtain the general solution for the governing equations using the potential theory method with Almansi’s theorem. Subsequently, building on the general solution, we derive a fundamental solution for a two-point fluid source using harmonic functions with undetermined constants. These constants are determined through continuous and equilibrium conditions. The resulting exact solutions serve as benchmarks for numerical codes and approximate solutions, offering crucial support for a wide range of project problems. To provide further insight, we present complex numerical examples illustrating the physical mechanisms through contours. Results show symmetry around two-point fluid sources, with higher magnitudes and sign changes indicating compression and expansion zones. Zero contours and inflection points are identified, while coupling effects diminish in the far field and become singular at the sources, providing valuable insights into their spatial extent and intensity. To validate our results, we compare them with existing literature, enhancing the credibility of our approach and contributing to the ongoing dialog in the field.