Mechanical damage evolution and a statistical damage constitutive model for water-weak sandstone and mudstone

The weakening effect of water on rocks is one of the main factors inducing deformation and failure in rock engineering. To clarify this weakening effect, immersion tests and post-immersion triaxial compression tests were conducted on sandstone and mudstone. The results showed that the strength of water-immersed sandstone decreases with increasing immersion time, exhibiting an exponential relationship. Similarly, the strength of water-immersed mudstone decreases with increasing environmental humidity, also following an exponential relationship. Subsequently, a statistical damage model for water-weakened rocks was proposed, changes in elastic modulus to describe the weakening effect of water. The model effectively simulated the stress-strain relationships of water-affected sandstone and mudstone under compression. The R2 values between the theoretical and experimental peak values ranged from 0.962 to 0.996, and the MAPE values fell between 3.589% and 9.166%, demonstrating the model's effectiveness and reliability. The damage process of water-saturated rocks corresponds to five stages: compaction stage - no damage, elastic stage - minor damage, crack development stage - rapid damage increase, post-peak residual stage - continuous damage increase, and sliding stage - damage completion. This study provides a foundational reference for researching the fracture characteristics of overlying strata during coal mining under complex hydrogeological conditions.