## 3 Establishment of Structural Model and Verification
### Verification of Structural Model  
A numerical model corresponding to the proposed structural model in this section was established using the commercial finite element software ABAQUS. The size of the numerical model was \(20\times 20\times 40\) mm\({}^{3}\). The settings of the numerical model, meshing, and boundary conditions are shown in Figure 6a. 3D solid elements (C3D8R in ABAQUS notation) were used in this numerical model, which contained 60,544 elements in total. The numerical model was loaded with a speed of 0.02 mm/min on the top surface. Equation (1) is obtained by fitting the nonlinear stage of the stress-strain curve in Figure 2a,  
\[\sigma=-1.56\varepsilon^{3}+1.86\varepsilon^{2}-0.77\varepsilon+1109\quad(436 0\leq\varepsilon\leq 4790\mu\varepsilon) \tag{1}\]  
where \(\sigma\) is the stress, \(\varepsilon\) is the strain, and \(\mu\varepsilon\) (\(10^{-6}\)\(\varepsilon\)) is the micro-strain.  
For the finite element simulation, it is assumed that the material remains elastic before deformation localization begins. The global mechanical behavior enters non-linear evolution, which is related to the material stiffness mode on the shear band [5]. After reaching the peak value, the stress reduction is related to the interface sliding of the shear band. Corresponding to three deformation stages of the presented structural model, the finite element simulation was also divided into three stages. The first deformation stage of the numerical model was equivalent to uniaxial compression of the homogeneous material. The elastic modulus of all the elements was 12 GPa, and Poisson's ratio was 0.25. For the second stage, the evolution process of the DLB equivalent to the gradual decrease in the elastic modulus of the elements at the \"weak interlayer\" position and the other elements were invariant. The law of elastic modulus decreasing can be obtained by deriving Equation (1). For the third stage of deformation, the elastic modulus of the elements was the same as that in the second stage. After the DLB formed, a contact surface was set up in the finite element model to simulate the relative dislocation of the rock structure under uniaxial compression [41]. The shear strain field of the structural model obtained using the FEM is shown in Figure 6b. The average loading and average displacement of the nodes on the top edge of the numerical model were taken as the global mechanical response of the specimen. The stress-strain curve obtained by the FEM is shown in Figure 6c, and \(\mu\varepsilon\) is micro-strain. The strain  
Figure 5: (**a**) Sketches of stress–strain curve; (**b**) structural model.  
maps 1, 2, and 3 in Figure 6b, respectively, correspond to points of non-linear starting, peak stress and failure in Figure 6c.  
When the weak interlayer with the control effect appears in the rock specimen, the proposed structural model can be used to describe the global mechanical behavior. The simulation results show that the proposed structural model can reproduce the linear and non-linear mechanical behaviors of the rock specimen. Further, the structural model can reflect the process of deformation localization with the weak interlayer, which has the control effect. Thus, it is reasonable to characterize the mechanical behavior of the rock specimen with the proposed structural model. However, the proposed structural model is not suitable for the DLB without a control effect.