Segmented constitutive relationship of weakly cemented sandstone and numerical implementation based on homogeneity

Abstract In this study, we employed triaxial compression tests on weakly cemented sand specimens under varying confining pressures (ranging from 3.5 to 19.5 MPa) to investigate their mechanical properties and deformation characteristics. Utilizing the Two-Parts Hook's Model (TPHM) and statistical damage theory, we constructed a comprehensive model, which was subsequently integrated into the FLAC3D numerical platform. The findings revealed a decrease in the compaction stage as confinement pressure increased, with strains of 0.005 at 3.5 MPa and 0.002 at 19.5 MPa. The TPHM effectively captured the non-linear elastic and elastic deformation before damage onset, while the statistical damage model aptly described post-damage deformation. Incorporating the rock's homogeneity parameter (m) in the model implementation, the simulation results closely matched experimental data, providing a more accurate representation of stress field migration and damage zone evolution during the failure process of weakly cemented sandstone. These findings contribute valuable insights to understanding stability changes in tunnel surroundings, roofs, and floors during coal mining operations in areas with weakly cemented sandstone, thereby offering a reference for practical applications.