Rock Stress-Strain Relationship and Porosity Evolution Model Based on TPHM

In order to investigate the impact of pore and fracture structure on the nonlinear deformation characteristics of rocks during the entire stress-strain process, considering the differences in deformation between pores and the matrix, porous rocks are deconstructed into two components: hard springs and soft springs. The Two-part Hooke’s Model (TPHM) and statistical damage theory are introduced. Based on the TPHM, the complete stress-strain relationship of rocks is established, and the porosity evolution equation for the entire stress-strain process of rocks is derived. This model overcomes the limitation of the traditional Two-part Hooke’s Model, which is unable to represent the plastic deformation of rocks after yielding. It not only accurately characterizes the nonlinear deformation during the pore compaction stage, plastic yielding, stress drop after peak, and residual stress characteristics in the rock compression process, but also effectively represents the porosity variation during the entire stress-strain process of rocks. Extensive experimental data validation has demonstrated that the theoretical curves of this constitutive model align well with the experimental results, with correlation coefficients consistently exceeding 0.9.