# Analysis of Cement Sheath-Rock Damage Mechanism--A Case Study on Water Injection Wells
## 3 Validation of the Damage Model  
The direct shear tests mentioned in the literature were conducted specifically on the RMT-150 system, which is a well-established and widely used apparatus in the field, as shown in Figure 2. The maximum normal force and shear force were 1000 kN and 500 kN, respectively. In compliance with the methodologies prescribed by the International Society for Rock Mechanics (ISRM), this machine possesses the capability to perform direct shear tests. It operates by applying shear stress at a controlled rate of 0.005 mm/s, facilitating a clear observation of the post-peak behavior exhibited by the cohesive interface. Comsol Multiphysics is a powerful finite element analysis software that can be used for the simulation and solving of various physical phenomena. It features high flexibility, user-friendliness, and high scalability, making it an important tool in scientific research and engineering design. In this study, COMSOL software was utilized, and a newly developed constitutive model was employed for numerical simulations. The introduced novel damage function D2 was utilized to investigate the damage evolution behavior of interface rock in the study. To ascertain the efficacy of the damage model, a comprehensive evaluation was carried out by comparing the numerical simulation results with experimental findings. The size of the model was set at 150 mm \(\times\) 150 mm, with the bottom fixed and the top boundary subjected to a pressure of 2 MPa. The model underwent a shearing displacement rate of 0.005 mm/s along the cement-rock interface, with a total of 2642 grid nodes. The dimensions, loading speed, and applied pressure in the numerical model were carefully matched with the laboratory test parameters to ensure precise validation results. A damage model was formulated by utilizing the available experimental data as a foundation. The peak displacements were \(\mathrm{\delta_{f}=0.65\ mm}\) and \(\mathrm{\delta_{c}=0.91\ mm}\). The fundamental parameters are presented in Table 1.  
To validate the effectiveness of the damage model, a comprehensive comparison was conducted between the numerical simulation results and the experimental findings. The occurrence of simultaneous complete rock damage and fracture along the interface is visually depicted in Figure 3. As shown in (a), the experimental observations demonstrate the appearance of interface cracks within the composite rock. In a corresponding manner, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Material Elastic Modulus** & **Cohesion** & **Frictional Angle** \\  & **(GPa)** & **(MPa)** & **(°)** \\ \hline Rock & 24 & 1.1 & 48 \\ Concrete & 33 & 1.5 & 52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of the composite rock model [19]. Figure 2: The RMT-150 equipment is specifically used for conducting direct shear tests to measure shear stress [19]. the numerical simulation outputs presented in (b) indicate that the rock damage along the interface primarily manifested at the junction between the rock and cement sheath. This manifestation occurred under the influence of shear stress, aligning with the observed experimental results. Formula (5) is defined as the uncorrected bonding force, while Formula (6) represents the established model for the corrected bonding force. In Figure 4, when the normal pressure is 2 MPa, the curve of the corrected bonding force shows significantly improved accuracy compared to the uncorrected curve. It is worth noting that the adjusted curve exhibits a peak stress of 4.37 MPa. When compared to the experimental data, the error in peak stress is only 0.68%. In contrast, the uncorrected curve indicates a peak stress of 4.1 MPa, deviating from the measured experimental value by 6.82%. Therefore, once the bonding force is corrected, the numerical simulation results demonstrate a significant enhancement in accuracy, as shown in Table 2.  
Figure 4: Stress–displacement curve of rock bonded interface in numerical simulation of the model.