Study on Mechanical Properties and Damage Statistical Constitutive Model of Hard Sandstone in Central Yunnan Under Temperature-Humidity Cycles

Previous systematic studies on the mechanical properties of hard rock in Central Yunnan have been relatively limited. To investigate the effects of alternating temperature and humidity variations in different seasons on the mechanical properties of rocks, the hard sandstone from the Chuxiong section of the Central Yunnan Water Diversion Project was selected as the research object. Based on laboratory physical property tests, ultrasonic tests, deformation tests, uniaxial compressive strength tests, and splitting tensile strength tests, triaxial compression tests were conducted on hard sandstone in Central Yunnan under different temperature-humidity cycles. The variation characteristics of stress–strain behavior and shear strength indexes were systematically analyzed. By introducing the theory of continuous damage mechanics and based on the Weibull distribution of rock micro-element strength and the Drucker–Prager criterion, a statistical damage constitutive model of hard sandstone in Central Yunnan was established, with the secant modulus used to characterize the pre-peak damage characteristics under temperature-humidity cycles. The results showed that the peak principal stress of hard sandstone in Central Yunnan decreased according to a power function with increasing numbers of temperature-humidity cycles, whereas the peak strain exhibits a power-law increasing trend. The sensitivity coefficient of the pre-peak secant modulus to the number of cycles exhibited a pattern of slow increase at low strain levels followed by a sharp increase and gradual stabilization as the strain point increased. Temperature-humidity cycling has a significant weakening effect on the shear strength parameters of hard sandstone in Central Yunnan. After three cycles, the cohesion and internal friction angle decreased by 19.84% and 2.70%, respectively, when compared with those before cycling. After six cycles, they decreased by 23.25% and 2.99%, respectively. The shear strength parameters exhibited a decreasing trend characterized by a rapid initial decline followed by a slower decline and gradual stabilization as the number of cycles increased. Compared with the conventional model that defines the damage variable based on the elastic modulus, the proposed damage constitutive model, which uses the secant modulus to characterize the pre-peak damage characteristics of hard sandstone under temperature-humidity cycles, can better describe the nonlinear variation characteristics before the peak of the stress–strain curve. The errors of the predicted peak principal stress and peak strain are both within 6%. Further research could investigate the advantages of using the secant modulus to characterize the damage constitutive model of rock under temperature-humidity cycling by expanding the sampling area, increasing the number of cycles, and employing other approaches.