## 5 Summary and Conclusions  
Crest cracking is one of the most common damage types for high earth-rockfill dams and is closely related to the deformation behavior of high earth-rockfill dams, specifically the crest settlement inclination. Dam crest is susceptible to cracking as the crest settlement inclination exceeds a certain threshold, however the dam crest does not necessarily crack immediately. Whereas, if the abnormal state (i.e., the crest settlement inclination exceeds the threshold value) is sustained for a long time, the potential of crest cracking becomes large and increases with the duration of abnormal state. Due to complex physical mechanisms and stochastic factors, the duration of abnormal state before crest cracking is uncertain and could be regarded as a random variable. Consequently, crest cracking risk can be evaluated with probabilistic approaches. In this paper, a methodology for dynamic risk evaluation and early warning of crest cracking for high earth-rockfill dams is proposed. The key components of the methodology include: (a) The discrimination of abnormal state related to crest cracking, which is implemented by comparing the crest settlement inclination (which is computed using FEM with the calibrated constitutive model parameters based on the in-situ deformation monitoring data) with the threshold value. (b) Computation of crest cracking probability and estimation of cracking time. The exponential  
Figure 16: The early warning times (i.e., the period between the actual cracking time and the estimated lower limit of cracking time) for the crest cracking events. distribution is adopted to represent the probability distribution of the duration \(T_{AS}\) of abnormal state before crest cracking. Then as the abnormal state of dam crest deformation occurs and continues, the crest cracking probability in a given time can be computed by integration with respect to \(T_{AS}\). Inversely, the cracking time (i.e., the time interval from the beginning of abnormal state until the occurrence of crest cracking) corresponding to a given probability can be estimated. (c) Determination of the values of probability adopted to early warn crest cracking, which are suggested to be selected by statistical analysis of the calculated probabilities at the observed cracking times. In this paper, the mean values and confidence intervals of the calculated probabilities are used. (d) Bayesian estimation and updating of probability distribution of the parameter \(\lambda\) in the PDF of \(T_{AS}\), which is the expected value of the duration of abnormal state before crest cracking. Since historical information regarding the parameter \(\lambda\) is insufficient, the epistemic uncertainty in \(\lambda\) is characterized quantitatively by subjective probability and Bayesian theory is applied to dynamically estimate and update the probability distribution of \(\lambda\), according to observed durations of abnormal state before crest cracking. The methodology is illustrated and verified by the risk evaluation and early warning of crest cracking for an actual earth-rockfill dam. The dam crest cracking and recracking (i.e., the sealed cracks were split again and again) events were observed during the periods of high reservoir level. The probability distribution for \(\lambda\) is progressively updated according to the observed values of \(T_{AS}\). It is observed that the dispersion of the updated distributions of \(\lambda\) gradually decreases with the accumulation of relevant information. The cracking probability of dam crest increases with the duration of abnormal state and the width of confidence interval of the estimated cracking probability progressively contracts with the updating of the distribution for \(\lambda\). Finally, the early warning of crest cracking for the dam is investigated by estimating the lower limit of cracking time.