# Study on Damage Constitutive Model of Rock under Freeze-Thaw-Confining Pressure-Acid Erosion
## 5 Conclusions  
By introducing chemical damage variables, freeze-thaw damage variables, and force damage variables, this paper derives the total damage variables of the acid-corroded rock under the coupling effect of freezing-thawing and confining pressure. Based on the assumption that the microelement strength of the rock obeys the Weibull distribution, adopt damage mechanics theory, D-P criterion is selected. Adopting the Lemaitre strain equivalence hypothesis, a constitutive model including freeze-thaw-confining pressure coupled damage evolution equation of acid-etched rock is established to study the damage evolution characteristics of rock failure.  
(1) Comparing the theoretical curve peak point of the damage constitutive model established in this paper with the peak point of the experimental data curve, the results show that the two are in suitable agreement, indicating that the established damage constitutive model can better reflect the triaxial compression process of the rock the stress-strain peak characteristics. It has particular practical significance for geotechnical engineering construction in cold area engineering.  
(2) The peak strain at the peak point of the theoretical curve of the damage constitutive model established in this paper does not change much with the number of freeze-thaw cycles, and the peak stress will fluctuate slightly with the number of freeze-thaw cycles. Generally speaking, with the change of the number of freeze-thaw cycles, the peak point of the theoretical curve and the peak point of the experimental data curve are in suitable agreement.  
(3) In the constitutive model established in this paper, the model parameter \(F_{0}\) related to the peak stress of the rock has obvious mechanical significance. As the peak stress increases, the value of \(F_{0}\) gradually increases, and with the continuous increase in confining pressure, the value of \(F_{0}\) also keeps increasing.  
(4) The damage constitutive model established in this paper does not have specific rock type parameters. The required model parameters can be obtained through routine triaxial tests in the laboratory. It has nothing to do with lithology and can be applied to  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Freeze-Thaw** & **Fitting Expression** & **Elastic Modulus Fitted Value** \\
**Cycles n** & & \(E_{\text{n}}\)/GPa \\ \hline
0 & & 1.649 \\
5 & \(E_{\text{n}}\)\(=2.298\text{E}-4\times\text{n}^{2}-\) & 1.520 \\
10 & \(0.027\times\text{n}+1.649\) & 1.402 \\
20 & \(0.027\times\text{n}+1.649\) & 1.201 \\
40 & & 0.937 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Fitting values of elastic modulus of red sandstone under different freeze-thaw cycles.  
all kinds of hard rock. It is convenient for engineering applications and has features of wide applicability.  
Conceptualization, Y.C. and P.X.; methodology, P.X.; software, P.X.; validation, P.X., X.D., T.M.F.-S., R.A. and S.W.; formal analysis, P.X.; investigation, P.X.; resources, P.X.; data curation, P.X.; writing--original draft preparation, P.X.; writing--review and editing, Y.C. and P.X.; supervision, Y.C.; project administration, Y.C.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
The study was supported by \"the National Natural Science Foundation of China (Project No. 10872133)\". The study was supported by \"Shanghai soft Science Research Key Project (Project No.18692106100)\".  
The authors declare no conflict of interest.