A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Abstract

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses. This study conducts uniaxial compression tests on layered sandstone with various bedding angles (0°, 15°, 30°, 45°, 60°, 75° and 90°) to explore the impact of bedding angle on the deformational mechanical response, failure mode, and damage evolution processes of rocks. It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load. This model is employed to study the damage accumulation state and its evolution within the layered rock mass. This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression. The results revealed that as the bedding angle increases from 0° to 90°, the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease, slightly increase, and then decline again. The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure. As indicated by the modulus’s degradation, the damage characteristics can be categorized into four stages: initial no damage, damage initiation, damage acceleration, and damage deceleration termination. The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process. Moreover, the theoretical constitutive model curves closely align with the actual stress – strain curves of layered sandstone under uniaxial compression. The introduced constitutive model is concise, with fewer parameters, a straightforward parameter determination process, and a clear physical interpretation. This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.