A Modified Drucker–Prager Model Considering Tensile Strength Reduction and Its Applications in Slope Stability Analysis

The strength reduction method plays a crucial role in the slope stability analysis. Generally, the Mohr–Coulomb (MC) model is commonly used to analyze slope stability. However, the MC model has the computational nonconvergence problem and the overestimated tensile strength. Usually, the Drucker–Prager (DP) model can be used to approximate the MC model on the \({\pi }\) plane utilizing a circle, which can improve the computational nonconvergence problem. However, the DP yield surface still has a corner on the meridian plane, which results in computational instability in extreme circumstances and requires special attention. Additionally, the DP model overestimates the tensile strength. Another work is the modified MC model, which can enhance the computational stability and describe the tensile strength reasonably. However, the implementation of the modified MC model is uneasy due to its complex derivatives. For both the DP model and the MC model, another problem is that the tensile strength does not exist explicitly in the yield function and cannot be reduced directly, which restricts their applications. To address these problems, this paper proposes a modified Drucker–Prager (DP) model, which is easy to implement, numerically stable, and capable of adjusting the tensile strength. Moreover, a strength reduction method considering tensile strength reduction is proposed, which is applicable to the proposed modified DP model and the modified MC model. Finally, the numerical tests demonstrate the effectiveness of the proposed methods. These methods serve as a beneficial supplement to the MC and DP models in slope stability analysis.