## 3 Methodology for Dynamic Risk Evaluation and Early Warning of Crest Cracking
### Computation of Crest Cracking Probability and Estimation of Cracking Time
The seepage coefficient of core wall of Pubugou Dam is \(1\times 10^{-5}\) cm/s, which is far smaller than that of rockfill body (\(1\times 10^{-1}\) cm/s). Thus, the core wall can be regarded as an impermeable structure. In this paper, the seepage process within the dam body is not considered, and the water load is applied to the upstream surface of the core wall directly. [PERSON] adopts the same calculation method [3]. Thus, during the water level simulation, the buoyancy in the upstream saturated rockfill shell and the hydraulic pressure acting on the upstream face of gravelly soil core are considered. In addition, the wetting deformation of the upstream rockfill shell is computed in the first reservoir impoundment. In order to improve the accuracy of the calculated settlements, the constitutive model parameters for the finite element simulation are calibrated using the recorded deformation data at four monitoring points. These monitoring points are selected for their reliable performances and representativeness. Of the selected monitoring points, TP14, SG18 and SG25 are for measuring the external and internal settlements of the dam respectively, while CH19 is for measuring the internal horizontal displacement of the dam. The individual locations of the monitoring points are indicated in Figure 1. Response surface method (RSM) was utilized to replace the time-consuming finite element calculations of the displacements at the monitoring points [23], and particle swarm optimization (PSO) method was used to minimize the objective function and calibrate the parameters [7]. Figure 2 shows that there was a period from 20 December 2009 to 20 May 2010, during which the water level was relatively stable, and the monitoring data of this period was selected for back analysis of creep parameters by RSM-PSO method. Then, these creep model parameters can be used for the complete computation and the Duncan-Chang parameters and wetting model parameters can be calibrated in the same way. The deformation back analysis procedure is shown in Figure 7. The calibrated values of the constitutive model parameters are listed in Tables 2-4. Figure 6: 2D finite element model of the dam and foundation. The deformations of the dam and foundation are calculated using FEM with the calibrated values of the constitutive model parameters. The measured and computed time series of displacements of the monitoring points TP14, SG18, SG25 and CH19 are compared in Figure 8. It can be seen that the computed displacements are in good agreement with the measured displacements, and the overall relative error between the measured and computed displacements is less than 6%. Thus, the finite element simulation is able to well predict the deformation behavior of the dam during operation. The contours of settlement and horizontal displacement of the dam, when the reservoir level first reaches the normal water level, are shown in Figures 9 and 10 respectively. It is observed that the deformation of the dam is consistent with the general deformation pattern of high earth-rockfill dams. The maximum settlement of the dam is 2.20 m and the maximum upstream and downstream horizontal displacements are 0.96 m and 0.29 m respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathbf{c_{w}}\) & \(\mathbf{n_{w}}\) & \(\mathbf{d_{w}}\) \\ \hline Upstream rockfills & \(5.47\times 10^{-4}\) & 1.367 & \(2.65\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibrated parameters of the wetting deformation model for the upstream rockfills.