## 5 Method of Determining Parameters by Field Experiments
### Parameter Identification of Circular Rigid Bearing Plate Test  
A circular rigid pressure-bearing plate with an area of 2000 cm\({}^{2}\) was used to test the shale section on the downstream side of the second stage hoist foundation of the Tectonic Beach Hydropower Station for compression creep [26]. The displacement measuring instrument was situated beneath the circular rigid bearing plate, and the load was applied by the jack above the bearing plate. The stress distribution transferred to the rock by the circular rigid bearing plate is as follows [33]:  
\[p(r)=\frac{P}{2\pi r\sqrt{R_{0}^{2}-r^{2}}} \tag{25}\]  
where \(P\) is the total pressure on the bearing plate, \(P=\pi R_{0}^{2}q\); \(q\) is the normal uniform load applied by the jack. The elastic and viscoelastic solutions of settlement at the measuring point are calculated using Equations (7), (12) and (25), in which F(\(x,y\)) is expressed in polar coordinates as follows:  
\[F(x,y)=F(0\leq r\leq R_{0})=\frac{\pi^{2}R_{0}q}{2} \tag{26}\]  
The results of the rheological model parameter inversions of the rock are obtained using the same parameter inversion method as in the previous section (Tables 4 and 5). Figure 11 also shows the comparisons between the theoretical displacement curves of the two models and the measurements obtained.  
Figure 10: Comparisons between the theoretical displacements based on the two rheological models and the measured results: (**A**) \(p\)= 2 MPa, (**B**) \(p\) = 3 MPa and (**C**) \(p\) = 4 MPa.  
Figure 11 shows that both the calculated displacements based on the integer- and fractional-order models can be consistent with the measurements obtained at different stress levels; however, as time increases, the creep deformations predicted by the integer-order model are smaller than those of the fractional-order model. Tables 4 and 5 show the coefficients of determination of the calculated displacements and the measurements  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(q\) (MPa) & \(K\) (GPa) & \(G_{1}\) (GPa) & \(G_{2}\) (GPa) & \(\eta\) (GPa-h) & \(\alpha\) & \(R^{2}\) \\ \hline
1.2 & 34.77 & 20.86 & 49.95 & 171.04 & 0.707 & 0.9913 \\
1.5 & 33.77 & 20.26 & 62.81 & 277.65 & 0.757 & 0.9833 \\
1.7 & 30.29 & 18.18 & 74.19 & 1000 & 0.389 & 0.9526 \\
2.0 & 31.89 & 19.13 & 55.89 & 557.66 & 0.496 & 0.9944 \\
2.2 & 29.61 & 17.77 & 88.50 & 1000 & 0.786 & 0.9855 \\
2.5 & 29.68 & 17.81 & 43.42 & 1000 & 0.613 & 0.9858 \\
2.9 & 28.82 & 17.29 & 61.48 & 633.92 & 0.852 & 0.9827 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Inverse analysis results based on the fractional-order model.  
Figure 11: Comparisons between the theoretical displacements based on the two rheological models and the measured results.  
obtained for the two models. The fractional-order model's coefficients of determination are larger than those of the integer-order model at different stress levels, and the fractional-order model's coefficients of determination are greater than 0.95. Therefore, the model's theoretical displacements correlate highly with the measurements obtained and can better describe and predict the rock's creep deformation.