## 3 Nonlinear Creep Model of AS
### Determination of Creep Parameters
#### 3.3.2 Determination of the Remaining Creep Parameters
Equation (28) can be solved as follows:  
* Arbitrarily select initial values of a set of coefficients \(b_{1}\) to \(b_{7}\);
* Calculate \(a_{kj},\ C_{k}\);
* Substitute \(a_{kj}\) and \(C_{k}\) into \((2-46)\) (28) to obtain \(\delta_{1}\) to \(\delta_{7}\);
* Take \(b_{1}+\delta_{1},\ b_{2}+\delta_{2},\ldots,\ b_{7}+\delta_{7}\) as the approximate values of the regression coefficients;
* Using \(b_{1}+\delta_{1},\ b_{2}+\delta_{2},\ldots,\ b_{7}+\delta_{7}\) as the initial values of the regression coefficients, repeat the above steps until \(\delta_{1},\delta_{2},\ldots,\delta_{7}\) are small enough;
* Obtain the final values of the creep model parameters \(K,\ G_{0},\ G_{1},\ \eta_{1},\ \eta_{2},\ \eta_{c}\) and the rheological index \(n\), which are the values of the final iterative regression coefficients \(b_{1}\) to \(b_{7}\). The nonlinear creep model parameters of AS samples under different confining pressures and loading levels were obtained by the above methods. As shown in Table 4, the model could reflect the creep behaviors of AS. A comparison between the experimental data and the fitting value is shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\boldsymbol{C/MPa}\) & \(\boldsymbol{\alpha_{c}/MPa}\) & \(\boldsymbol{K}\) & \(\boldsymbol{G_{0}/GPa}\) & \(\boldsymbol{G_{1}/GPa}\) & \(\boldsymbol{\eta_{1}/GPa\cdot h}\) & \(\boldsymbol{\eta_{2}/GPa\cdot h}\) & \(\boldsymbol{\eta_{c}/GPa\cdot h}\) & \(\boldsymbol{n}\) \\ \hline \multirow{4}{*}{3} & 23.5 & 9.33 & 8.31 & 48.32 & 865.71 & - & - & - \\  & 26.9 & 17.52 & 2.43 & 23.24 & 280.35 & - & - & - \\  & 30.3 & 3.14 & 2.17 & 17.57 & 215.63 & 3.6 & - & - \\  & 33.7 & 8.57 & 5.70 & 188.23 & 670.53 & 1660.12 & 51.31 & 2 \\ \hline \multirow{4}{*}{6} & 26.4 & 9.98 & 7.83 & 281.56 & 755.48 & - & - & - \\  & 30.7 & 10.37 & 6.72 & 260.34 & 691.35 & - & - & - \\  & 35.0 & 9.84 & 6.02 & 210.73 & 466.83 & 3434.97 & - & \\  & 39.3 & 9.96 & 5.87 & 169.85 & 349.77 & 556.42 & 49.10 & 3 \\ \hline \multirow{4}{*}{9} & 30.3 & 10.55 & 6.73 & 281.53 & 841.71 & - & - & - \\  & 34.4 & 10.78 & 5.75 & 226.87 & 768.69 & - & - & - \\  & 38.5 & 10.63 & 5.15 & 189.38 & 647.36 & 1436.64 & - & - \\  & 42.6 & 10.63 & 4.83 & 167.38 & 527.84 & 690.32 & 50.44 & 4 \\ \hline \multirow{4}{*}{12} & 33.6 & 11.35 & 6.47 & 298.46 & 954.37 & - & - & - \\  & 37.7 & 12.02 & 6.68 & 260.14 & 857.67 & - & - & - \\  & 41.8 & 11.15 & 5.53 & 210.35 & 724.68 & 2857.64 & - & - \\  & 45.9 & 10.86 & 5.66 & 170.75 & 687.63 & 1557.86 & 57.48 & 4 \\ \hline \multirow{4}{*}{15} & 36.9 & 12.12 & 7.56 & 360.93 & 1033.75 & - & - & - \\  & 40.2 & 12.45 & 7.54 & 326.67 & 957.34 & - & - & - \\  & 43.5 & 11.55 & 7.01 & 291.64 & 890.48 & - & - & - \\  & 46.8 & 11.68 & 6.82 & 242.88 & 824.35 & 3687.85 & - & - \\  & 50.1 & 11.48 & 5.82 & 190.51 & 783.42 & 1868.52 & 58.81 & 5 \\ \hline \multirow{4}{*}{18} & 39.6 & 12.13 & 8.37 & 409.65 & 1247.55 & - & - & - \\  & 43.9 & 12.84 & 7.87 & 341.67 & 1001.58 & - & - & - \\ \cline{1-1}  & 48.2 & 12.69 & 6.36 & 317.64 & 1034.75 & - & - & - \\ \cline{1-1}  & 52.5 & 11.77 & 6.82 & 271.53 & 977.46 & 2436.32 & - & - \\ \cline{1-1}  & 56.8 & 12.03 & 6.52 & 217.32 & 960.73 & 1982.54 & 55.53 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Creep parameters of AS under different confining pressures.