# Study on Elastoplastic Damage Coupling of Reservoir Mudstone Considering Permeability Change
## 4 Simulation Verification of the Model  
### Mechanical Model Parameters  
The elastoplastic damage coupling mechanical model contains eight parameters, which are the sum of two elastic parameters \(E\) and \(\
u\), five plastic parameters \(A\), \(C_{0}\), \(\alpha_{p}^{0}\), \(b\), \(\eta\), and one damage parameter \(m\). Among them, \(E\) and \(\
u\) are the elastic modulus and the Poisson' s ratio, which can be obtained according to the slope of the linear elastic section, the ratio of the axial strain \(\varepsilon_{1}\) and the lateral strain \(\varepsilon_{3}\) of the stress-strain curve, respectively. \(A\) and \(C_{0}\) can be determined using the intercept and slope of the average stress \(p\) and deviatoric stress \(q\) curve under the limit yield stress state. \(\alpha_{p}^{0}\) can be determined using the average stress \(p\) and deviatoric stress \(q\) curve of the initial yield surface. \(b\) can be determined using the hardening function \(\alpha_{p}\) and plastic internal variable \(\gamma_{p}\) relationship. \(\eta\) can be determined using the stress state of the transformation from volumetric compression to expansion [29]. The damage parameter \(m\) can be determined using the damage evolution curve.  
The sensitivity analysis of some parameters of the model was carried out, including the plastic parameters \(b\) and \(\eta\) and damage parameter \(m\). The parameter \(b\) has effects on the hardening rate, plastic deformation and damage evolution (Figure 7). Before the peak stress, the smaller the value \(b\), the more obvious the plastic hardening, the peak stress increases, and the plastic deformation increases. After the peak stress, the smaller the value of \(b\) and the faster the stress drop, indicating the greater the post-peak damage. When the value of \(b\) is close to 0, there is no plastic hardening stage before the peak, and the stress-strain curve is linear; damage leads to the decrease in post-peak stress, and the elastoplastic damage coupling model degenerates into the elastic damage model. The parameter \(\eta\) is closely related to the compression-expansion conversion of material volume deformation (Figure 8). \(\eta\) has a small influence on peak stress and post-peak residual strength. The larger the value of \(\eta\), the earlier the compression-expansion inflection point will appear, and the expansion effect of the volume deformation is more obvious.  
The parameter \(m\) is related to damage evolution (Figure 9). It has little effect on the pre-peak deformation. With the decrease in \(m\), the peak stress decreases, and the damage variable at the peak point increases. The influence of \(m\) on the post-peak deformation is obvious. The smaller the value of \(m\), the faster the stress drop rate after the peak, the more obvious the deformation under the same stress, the lower the post-peak residual strength and the faster the growth rate of the damage variable, resulting in greater damage. When \(m\) is approaching infinity, the stress-strain curve has no post-peak softening stage, and the  
Figure 8: Sensitivity analysis of parameter \(\eta\).  
Figure 7: Sensitivity analysis of parameter \(b\).  
model degenerates into an elastoplastic constitutive model. When \(m\) approaches infinity and \(b\) approaches 0, the model degenerates into an ideal elastoplastic model.