## 2 Brief Descriptions of an Actual Earth-Rockfill Dam and Its Crest Cracking
### The Dam Crest Cracking  
After the reservoir level first reached the normal water level, on 14 November 2010, longitudinal cracks were observed in the dam crest. After that, the cracks were sealed with asphalt materials. However, in the following years, the sealed cracks were split again and again during the periods of high reservoir level. The dates of crest cracking and recracking are listed in Table 1. The cracks extend along the dam axis and are mainly distributed between cross sections 0 + 187.84 m\(\sim\)0 + 234.14 m, 0 + 250.14 m-0 + 300.14 m and 0 + 308.5 m-0 + 419.0 m. The maximum crack width is 6 mm. The distribution ranges and the photograph of the cracks are shown in Figure 3. In order to investigate  
Figure 1: The highest cross section of the dam and foundation, where the red spots represent the monitoring points for calibration of the constitutive model parameters.  
Figure 2: The dam filling process and the water level of the reservoir.  
the depths of the cracks, the dam owner carried out three field surveys in 2010, 2012 and 2019, respectively. The depths of all the cracks were detected using electrical resistivity tomography and ground penetrating radar. Moreover, the downward propagations of cracks in several locations were revealed by excavation. The revealed cracks in exploratory pits are shown in Figure 4. The maximum depth of the cracks is inferred to be about 1.5 m according to the field survey results. The vertical distance between the dam crest and the top of the gravelly soil core is 2 m, thus the cracks may not penetrate into the gravelly soil core. In addition, the monitoring data from piezometers did not show any anomaly of the seepage in the gravelly soil core.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crest Cracking Event** & **Start Date of Abnormal State (y/m/d)** & **Date of Crest Cracking (y/m/d)** & **Duration of Abnormal State (d)** \\ \hline The first cracking & 2010/8/10 & 2010/12/21 & 133 \\ The second cracking & 2011/7/17 & 2011/10/18 & 93 \\ The third cracking & 2012/7/6 & 2012/11/09 & 126 \\ The forth cracking & 2013/7/26 & 2013/11/25 & 122 \\ The fifth cracking & 2014/7/17 & 2014/09/27 & 72 \\ The sixth cracking & 2015/7/26 & 2015/10/13 & 79 \\ The seventh cracking & 2016/8/24 & 2016/11/3 & 71 \\ The eighth cracking & 2017/7/13 & 2017/10/15 & 94 \\ The ninth cracking & 2018/7/13 & 2018/9/24 & 73 \\ The tenth cracking & 2019/8/3 & 2019/10/24 & 82 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The dates of crest cracking and recracking as well as the corresponding durations of abnormal state.  
Figure 3: The distribution ranges and the photograph of the cracks.  
Although the cracks did not directly harm the safety of the gravelly soil core, the cracks should be duly sealed, since rains will flow into the cracks and erode the materials inside the dam. Therefore, it is worth estimating the time range of the dam crest cracking and remediation measures can be prepared in advance. In the following sections, we propose a methodology for dynamic risk evaluation and early warning of crest cracking for high earth-rockfill dams in the Bayesian framework and apply it to the dam mentioned above.