# Mechanical Behavior of Weathered Granite Exposed to Water
## 4 Modeling
### Validation of Model  
This study first takes finding the post-peak stress-strain curve of a fully weathered rock sample under a confining pressure of 500 kPa as an example to verify the developed model. To this end, we obtain the elastic modulus of the weathered rock sample before the peak (\(E_{0}\)), defined as the ratio of the axial stress at the peak to the axial strain at peak, and substitute it into Equation (3) along with the residual stress on the rock mass and the residual strain of the rock mass; then, the \(\varepsilon_{1r}^{p}\) of the weathered rock sample at the residual strength point can be calculated. Then, from substituting these data into Equations (4) and (5), it can be concluded that a corresponding \(c\) and \(\varphi\) can be obtained for each given \(\varepsilon_{1}^{p}\). Next, Equation (6) calculates \(\sigma_{1}\) in the strain-softening stage, and, finally, Equation (3) gives \(\varepsilon_{1}\). This work selects a total of 18 data points according to the test results.  
On the basis of the one-to-one correspondence of the relevant quantities in Table 4, the strain-softening stress-strain curve of the strongly weathered rock can be determined, as plotted in Figure 9. The drawing process of the stress-strain curve of the rock sample is shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(p\) (kPa) & \(\varepsilon_{1}^{p}\) (\%) & \(\varphi\) (\({}^{\circ}\)) & \(c\) (kPa) & \(\sigma_{1}\) (kPa) & \(\varepsilon_{1}\) (\%) \\ \hline \multirow{8}{*}{500} & 0 & 18.6 & 39.08 & 202.04 & 1.87 \\  & 1.55 & 19.5 & 38.05 & 250.48 & 3.87 \\  & 3.1 & 20.4 & 36.98 & 271.46 & 5.61 \\  & 4.65 & 21.3 & 35.98 & 283.29 & 7.27 \\  & 6.2 & 22.2 & 34.94 & 291.45 & 8.90 \\  & 7.75 & 23.1 & 33.93 & 297.78 & 10.51 \\  & 9.3 & 24 & 33.01 & 303.20 & 12.11 \\  & 10.85 & 24.9 & 32.02 & 306.79 & 13.69 \\  & 12.4 & 25.8 & 31.21 & 307.63 & 15.25 \\  & 13.95 & 26.7 & 30.20 & 306.64 & 16.79 \\  & 15.5 & 27.6 & 29.38 & 305.65 & 18.33 \\  & 17.05 & 28.5 & 28.59 & 303.75 & 19.86 \\  & 18.6 & 29.4 & 27.99 & 302.00 & 21.40 \\  & 20.15 & 30.3 & 27.40 & 300.12 & 22.93 \\  & 21.7 & 31.2 & 26.91 & 298.22 & 24.46 \\  & 23.25 & 32.1 & 26.52 & 296.63 & 26.00 \\  & 24.8 & 33 & 26.48 & 294.56 & 27.53 \\  & 26.35 & 33.9 & 25.03 & 293.00 & 29.06 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The softening parameters of the fully weathered rock (SA-1).  
Figure 9: The calculated stress–strain curve fitted to the test data.  
In the same way, the above method can be utilized to calculate the strain-softening parameters of the other fully weathered granites under a confining pressure of 500 kPa and those of the sandy weathered granites and fragmented weathered granites under a confining pressure of 600 and 680 kPa, respectively. Figure 11a-c represents the models fitted to each group of the experimental data. Except for the individual samples, the changing trend of the stress-strain curves of the weathered granites determined by this model is consistent with the measured data. The calculated results have a high degree of fit to the test results, and the dispersion is small (the goodness of fit \(R^{2}\) of all samples is greater than 0.9). In addition, this paper employs the experimental data of [PERSON] [35], [PERSON] [27], and [PERSON] [36] to further verify the accuracy of the model, as depicted in Figure 11d. The calculated stress-strain curve of the weathered granite well agrees with the test data, indicating that the proposed model offers appropriate predictions.  
Figure 11: _Cont._  
Figure 10: Stress–strain curve flow chart.