## 2 Establishment and Analysis of Damaged Components
### Effects of Chemical Corrosion and Temperature on Viscoelastic Strain  
According to the creep test of rock under the coupled action of different chemical corrosion and temperatures, the rock's creep rate and variable changes with the pH and temperature; damage variables, including pH and temperature, are established based on the variation law of rock creep with pH and temperature under different coupling conditions. Formula (3) shows the damage variable's expression.  
\[D=1-e^{\frac{-a(T-T_{0})}{[pH-pH_{0}]}} \tag{3}\]  
where \(T\) is the temperature of the rock mass during the test; \(T_{0}\) is the room temperature during the test (the room temperature in this test is 20 \({}^{\circ}\)C); \(pH\) is the \(pH\) of the rock mass during the test; \(pH_{0}\) is the \(pH\) of the comparative solution (the \(pH\) of the comparative solution in this test is 6.7); \(\alpha\) is a model parameter (related to \(pH\) and others).  
Figure 2 shows the viscoelastic element constructed in this study under the coupled effect of temperature and pH. Its composition is made up of elastic and viscous elements connected in series. According to the theory of the combined model, the stress expression of the viscoelastic element under the coupled action of temperature and pH is given as follows:  
\[\sigma_{\rm TC}=E_{2}\varepsilon_{3}+\eta_{2}(T,pH)\hat{\varepsilon}_{3} \tag{4}\]  
\(\eta_{2}(T,pH)\) is the viscosity damping coefficient affected by temperature and pH, \(\eta_{2}(T,pH)=\eta_{2}(1-D)\).  
After combining Equations (3) and (4), the strain of the viscoelastic element under the joint action of temperature and pH can be obtained as follows:  
\[\varepsilon_{3}=\frac{\sigma_{TC}}{E_{2}}\left(1-e^{\frac{\frac{a(T-T_{0})}{ [pH-pH_{0}]}}{\eta_{2}}}t\right) \tag{5}\]  
After deriving Formula (5), the strain rate of the viscoelastic element under the coupled action of temperature and pH can be obtained as follows:  
\[\hat{\varepsilon}_{3}=e^{\frac{a(T-T_{0})}{[pH-pH_{0}]}}\times\frac{\sigma_{ \rm TC}}{\eta_{2}}\times e^{-\frac{\frac{a(T-T_{0})}{[pH-pH_{0}]}}{\eta_{2}}}t \tag{6}\]  
According to the boundary conditions and test data of this test, take \(\sigma_{\rm TC}\) = 16 MPa, \(E_{2}\) = 2500 MPa, \(\eta_{2}\) = 2800 GPa-h, \(a\) = 0.15, \(T_{0}\) = 20 \({}^{\circ}\)C, and \(pH_{0}\) = 6.7.  
When using \(T\) = 50 \({}^{\circ}\)C, substitute \(pH\) = 1 and 13 into Formula (5) to obtain a set of creep curves with the same temperature but different \(pH\).  
Figure 2: Viscoelastic Elements with Temperature and pH.  
Figure 3 shows the effect of temperature on the strain of viscoelastic elements in an acidic environment. The figure shows that when other parameters are the same, the creep strain and rate of the viscoelastic element gradually increase as the temperature increases.  
Figure 4 shows the effect of pH on the strain of the viscoelastic element at the same temperature. The figure shows that when other parameters are the same, the creep strain and rate of the viscoelastic element in an acidic environment exceed those in an alkaline environment.  
The viscoelastic element constructed in this study under the coupled action of temperature and pH can accurately describe the effects of temperature and pH on rock creep strain and rate.