## 4 Cracking Analysis of the Xulong High Arch Dam  
### Effect of Temperature Load on Stress and Displacement of the Xulong Arch Dam  
For the analysis cases 1 and 10, the displacement and stress distribution of the dam (Figure 7), characteristic stresses (Table 4), and maximum displacement along river direction at different key \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Bulk Density (t/m\({}^{3}\))**} & \multirow{2}{*}{**Deformation Modulus (GPa)**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multicolumn{2}{c}{**Shear Strength**} \\ \cline{5-5}  & & & & \(C^{\prime}\) (MPa) & \(F^{\prime}\) \\ \hline Dam concrete & 2.40 & 25.0 & 0.167 & 5.0 & 1.7 \\ Rock of type II & 2.70 & 24.0 & 0.22 & 1.2 & 1.1 \\ Rock of type III & 2.60 & 17.5 & 0.24 & 1.05 & 1.0 \\ Rock of type III & 2.55 & 12.5 & 0.26 & 1.0 & 0.95 \\ Rock of type IV & 2.50 & 6.0 & 0.30 & 0.65 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical-mechanical parameters of the rock masses and dam materials. Figure 6: The 3D numerical model. (**a**) dam-foundation overall model; (**b**) main faults distribution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Normal Water Level + Temperature Rise**} & \multicolumn{2}{c}{**Normal Water Level + Temperature Drop**} \\ \hline \multirow{2}{*}{**EL (m)**} & \multirow{2}{*}{**Mean Temperature**} & \multirow{2}{*}{**Linear Temperature**} & \multirow{2}{*}{**Mean Temperature**} & \multirow{2}{*}{**Linear Temperature**} \\  & & & & \\ \hline
2308 & 9.40 & 0.00 & 2.65 & 0.00 \\
2302 & 7.67 & 3.09 & 3.22 & \(-0.49\) \\
2290 & 4.75 & 8.65 & 2.06 & 2.06 \\
2270 & 2.42 & 12.54 & 0.68 & 5.67 \\
2245 & 2.24 & 14.18 & 0.92 & 7.99 \\
2220 & 2.79 & 14.66 & 1.67 & 8.98 \\
2195 & 3.60 & 14.85 & 2.62 & 9.29 \\
2170 & 3.58 & 14.72 & 2.65 & 9.45 \\
2145 & 1.43 & 9.96 & 0.83 & 6.53 \\
2120 & \(-0.97\) & 4.74 & \(-1.35\) & 2.60 \\
2095 & \(-1.88\) & 2.66 & \(-2.12\) & 1.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mean and linear temperature difference under normal water level. locations (Table 5) are obtained. The maximum displacement along river direction is 32.9 mm near the EL 2189-2226 m (case 1) and 20.2 mm at the dam crest (case 10). The dam tensile stress of case 1 is slightly greater than that of case 10. The maximum tensile stress near the left arch abutment is bigger than that of the right arch abutment. This is related to different geological conditions on the left and right bank of the arch dam. The sudden drop in temperature has a greater impact on the tensile stress and the displacement of the arch dam, which increases the possibility of dam cracking. This is why the temperature drop loads are applied to the arch dam in cases 1 to 9. The insulation work of the arch dam should be done in February and March, especially at the crest and outlets of the dam. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Location** & **Content** & **Case 1** & **Case 2** \\ \hline \multirow{3}{*}{Upstream surface} & Maximum tensile stress of dam heel & 0.9 & 0.89 \\  & Maximum tensile stress near left arch abutment & 1.18 & 1.17 \\  & Maximum tensile stress near right arch abutment & 0.97 & 0.94 \\ \hline \multirow{3}{*}{Downstream surface} & Maximum compression stress of dam toe & 6.93 & 7.35 \\  & Maximum compression stress near left arch abutment & 8.76 & 8.88 \\  & Maximum compression stress near right arch abutment & 8.53 & 8.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristic stresses at different key locations under analysis cases 1 & 10 (unit: MPa).