Anisotropy is a critical characteristic of rock and profoundly affects the mechanical behavior of layered formations, particularly under true triaxial stress. To capture this behavior, this study proposes a modified failure criterion incorporating a novel anisotropy modulation function f ( β, σ 2 ), which incorporates both bedding inclination β and the diminishing contribution of intermediate principal stress σ 2 to anisotropic characteristics (especially for rocks with a high strike angle). Based on this function, a failure criterion for layered rock is constructed by multiplying f ( β , σ 2 ) with an existing intact-rock criterion. The proposed formulation satisfies key limiting conditions: f ( β , σ 2 ) degenerates to f(β) under conventional triaxial loading, and when β = 0°, f ( β , σ 2 ) = 1, so that the criterion reduces to the intact-rock form. To validate the modified criterion, 1133 sets of experimental and simulated data from conventional and true triaxial tests for layered rocks were analyzed. The fitting results demonstrate that the proposed modulation function accurately captures the strength behavior of layered rocks under both conventional and true triaxial stress states. In addition, the physical significance of the model parameters is discussed, offering a robust theoretical basis for predicting anisotropic rock strength. Highlights A new failure criterion is proposed considering β , ω , and σ 2 effects. For β = 0°, the modified criterion will reduce to an intact criterion, with f ( β , σ 2 ) = 1. The function may reduce to 2D version f(β) from 3D version f(β , σ 2 ) when σ 3 = σ 2 . The model is validated against an extensive data set confirming its high predictive accuracy.
Gao et al. (Mon,) studied this question.