Landslides frequently occur in several mountainous areas because of their unique engineering–geological conditions and other external factors (earthquakes, rainfall, etc.). In this paper, the landslide in Southwest China is used as the research objective to examine the landslide’s stability under different working conditions. The influencing factors and the formation mechanism of the landslide are analyzed based on the geological environment and essential characteristics of the landslide. In addition, the transfer coefficient method and the GeoStudio software were used to assess the landslide stability. The analysis results demonstrate that the joint action of landforms, geological structures, rainfall, and other factors caused the landslide. Furthermore, the slipped tension fracture induced the failure mode. The transfer coefficient method results showed that the landslide was stable under natural conditions and unstable under rainstorm conditions, which is consistent with the numerical simulation result. The shear strength sensitivity analysis results depicted an apparent linear relationship among cohesion c, internal friction angle φ, and stability coefficient. Moreover, the stability of the unstable slope is more sensitive to φ than to c.

The three-parameter Weibull distribution has a strong ability to fit many kinds of experimental data, which provides a solution for using a unified expression to characterize the elastic-brittle, strain softening, elastic-plasticity, and other constitutive behaviors of rocks. Therefore, a statistical damage constitutive model based on three-parameter Weibull distribution was constructed through theoretical analysis and derivation. Its expression ability was verified by combining with the conventional triaxial compression test data of marble. Meanwhile, the application effect of this statistical damage constitutive model on granite and sandstone was analyzed. The results show that the statistical damage constitutive model of rock based on three-parameter Weibull distribution can well express elastic-brittle, elastic-plastic, strain softening behaviors of rock by setting reasonable constitutive parameters, which lays a theoretical foundation for constructing a unified rock constitutive model. Conventional triaxial tests of marble show that with the increasing of confining pressure (⁠ $σ3$= 5, 15, 25, 35 MPa), the plastic deformation increases and the failure mode gradually changes from brittle tensile failure to shear failure, showing brittle-ductile and brittle-plastic transition characteristics. And its constitutive behaviors are characterized by elastic-brittleness, strain softening, and elastic-plasticity, which can be well expressed by the statistical damage constitutive model. When $σ3$ is 25 and 35 MPa, sandstone samples show elastic-brittle behavior. And for granite samples, they show strain softening behavior when $σ3$ is 5 MPa. The statistical damage constitutive model is also suitable for describing both sandstone elastic-brittle behavior and granite strain softening behavior. It is concluded that the three-parameter Weibull distribution provides a useful approach to characterize various constitutive behaviors of rock, and the model has a wide potential in numerical simulation for mining engineering, geoengineering, and other rock engineering.