The novel strength criterion and the associated constitutive model based on the finite deformation behavior for the rock under the disturbance stress paths

Abstract

To develop a novel 3D Hoek–Brown strength criterion and an associated constitutive model based on the finite deformation behavior of rock under the disturbance stress paths, a series of mechanical tests are initially conducted under designed disturbance stress paths (hydrostatic stress stage (HSS), initial loading–unloading stage (ILUS), and disturbance stage (DS)). Additionally, low disturbance (LD), medium disturbance (MD), and high disturbance (HD) modes are taken into consideration. Then, the finite deformation theory is employed to study the nonlinear behavior. This nonlinear behavior can be regarded as a nonlinear relationship between the stress and strain of rock under loading, especially the initial compression stage and plastic stage, as well as a complex deformation field, which is described by the finite deformation theory and featured by the mean rotation angle (Θ). Afterwards, the damage variable (DV) regarding Θ is proposed and used to establish a novel strength criterion (NSC) based on the current Hoek–Brown strength criterion. Finally, by considering the NSC, an associated elasto-plastic constitutive model is developed. The results show that the initial confining pressure (ICP) and disturbance mode have a significant effect on the elastic modulus (E). Meanwhile, the ICP has a higher effect on E than the disturbance mode. Then, the evolution of Θ is closely associated with the nonlinear deformation of rock masses because the σ1−Θ curves can be divided into three stages. Those stages can match well with the initial compression stage, elastic stage, and plastic stage, respectively. Regarding Θ as a parameter of the damage variable (DV), the NSC is established. Additionally, it can be observed that the failure envelopes of the NSC scale down gradually with increasing Θ on the deviatoric plane. Meanwhile, as the value of the coefficient of determination (DC) is higher than that of other strength criteria, the NSC may exhibit better agreement with the experimental data. Furthermore, a constitutive model based on the aforementioned strength criterion and the hardening function that takes Θ and the disturbance of rock masses (D) into account is proposed and validated as a solution to predict the nonlinear behavior of rock specimens under the disturbance stress paths.