## 4 Verification of the Established Rock Constitutive Model
### Comparison of the Numerical and Model Test Results  
In order for a comparison with the model test results, the nodes near the stress measurement points in the corresponding model test samples were selected in each numerical model, and the radial stress time history curves at this point were obtained under the combined effect of different biaxial pressures and blasting loads. The waveforms of the measured and numerical stress time history curves at the same locations in different model test samples were firstly compared, and the measured and numerical stress time curves of the stress measurement points 17 and 18 in the T1, T2, and T3 test samples were selected under the biaxial pressure conditions of 0, 0.75 MPa, 1.5 MPa, and 3 MPa in both the model tests and numerical simulations as shown in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Intact Rock** & **Joint** & **Seamless Steel pipe** \\ \hline Compressive strength/MPa & 5.864 & / & 645 \\ Tensile strength/MPa & 0.613 & / & 400 \\ Elastic modulus/GPa & 5.226 & / & 206 \\ Internal friction angle/\({}^{\circ}\) & 23.2 & / & / \\ Cohesion/MPa & 1.49 & / & / \\ Poisson ratio & 0.203 & / & 0.3 \\ Initial normal stiffness/GPa/m & / & 12 & / \\ Initial shear stiffness/GPa/m & / & 7.53 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical parameters of the intact rock, joint, and seamless steel pipe. Figure 8: Measured blast load and applied schematic: (**a**) measured blasting load time curve; (**b**) blasting load application. Figure 9: Measured and numerical stress wave curve at P17 and P18 points in each sample under different static loads: (**a**) T1 sample; (**b**) T2 sample; (**c**) T3 sample. As seen in Figure 9, the measured and numerical stress wave curves recorded at P17 and P18 stress measurement points in each model test sample under different biaxial pressures were relatively similar in form and amplitude, and the stress wave amplitude decreased as the biaxial pressure increased. The above phenomena demonstrate the feasibility and accuracy of the numerical calculations based on a combination of the BB model describing the nonlinearity of the joints and the established Mohr-Coulomb elasto-plastic rock constitutive model considering the initial damage. In order to verify the rationality of the established rock constitutive model from the perspective of stress wave propagation, the stress wave transmission coefficients of the jointed rock masses contained in each numerical model under different biaxial pressures were used for comparing the numerical and experimental results, as shown in Figure 10. It should be noted that the stress wave transmission coefficients of rock masses with a different number and angle joints in the model test were determined by the incident wave and the transmitted wave collected by the stress sensors arranged before and after the rock masses, which was the ratio of the amplitude of the transmitted stress wave to the incident wave. For example, for the T1, T2, and T3 test samples in Figure 2, the amplitude ratios of the stress wave recorded by the stress measuring points 22 and 21 were the stress wave transmission coefficients of the 90\({}^{\circ}\) single-joint rock mass, the 90\({}^{\circ}\) double-joints rock mass, and the 90\({}^{\circ}\) three-joints rock mass, respectively. In the numerical modeling, the nodes corresponding to the stress measuring points in the model test samples were selected in the numerical model to determine the incident and transmitted stress wave of the rock mass, and the numerical transmission coefficients were obtained. Meanwhile, the applied confining pressures in the model tests were 0, 0.75 MPa, 1.5 MPa, and 3 MPa, respectively, but the range of confining pressures was increased in the numerical calculations, which were from 0 to 7.5 MPa, with an interval of 0.75 MPa, for a total 11 different confining pressures.