The probabilistic stability analysis of a three-dimensional rock slope is studied in this paper. The deterministic computation of the critical slope height is based on the kinematic approach of limit analysis, for which the generalized Hoek-Brown failure criterion is adopted to characterize the failure of rock masses. Sparse polynomial chaos expansion is taken to perform the probabilistic analysis using a response surface method. The uncertainties considered involve the Hoek-Brown parameters ($m_i$ , GSI, ${\sigma }_c$ , and $D_i$ ), slope geometry parameters ($\beta$ , $H$ , and $B/H$ ), and rock mass unit weight ($\gamma$ ). The influences of the uncertainty level, correlation relationships between the Hoek-Brown parameters, and distribution types are discussed. Finally, a reliability-based design chart is provided to evaluate the safety factor of a slope required for a target failure probability.

Debris flows are natural disasters that frequently occur in mountainous areas, usually accompanied by serious loss of lives and properties. One of the most commonly used approaches to mitigate the risk associated with debris flows is the implementation of early warning systems based on well-calibrated rainfall thresholds. However, many mountainous areas have little data regarding rainfall and hazards, especially in debris-flow-forming regions. Therefore, the traditional statistical analysis method that determines the empirical relationship between rainstorms and debris flow events cannot be effectively used to calculate reliable rainfall thresholds in these areas. After the severe Wenchuan earthquake, there were plenty of deposits deposited in the gullies, which resulted in several debris flow events. The triggering rainfall threshold has decreased obviously. To get a reliable and accurate rainfall threshold and improve the accuracy of debris flow early warning, this paper developed a quantitative method, which is suitable for debris flow triggering mechanisms in meizoseismal areas, to identify rainfall threshold for debris flow early warning in areas with a scarcity of data based on the initiation mechanism of hydraulic-driven debris flow. First, we studied the characteristics of the study area, including meteorology, hydrology, topography and physical characteristics of the loose solid materials. Then, the rainfall threshold was calculated by the initiation mechanism of the hydraulic debris flow. The comparison with other models and with alternate configurations demonstrates that the proposed rainfall threshold curve is a function of the antecedent precipitation index (API) and 1 h rainfall. To test the proposed method, we selected the Guojuanyan gully, a typical debris flow valley that during the 2008–2013 period experienced several debris flow events, located in the meizoseismal areas of the Wenchuan earthquake, as a case study. The comparison with other threshold models and configurations shows that the selected approach is the most promising starting point for further studies on debris flow early warning systems in areas with a scarcity of data.

Although tunnels typically experience a lower rate of damage than surface structures during an earthquake, some tunnels have experienced considerable damage during recent strong earthquakes. Hence, seismic response analysis of tunnels located in high-intensity earthquake zones is an important issue for tunnel engineers. In this study, a three-dimensional numerical model of a tunnel was developed to analyse the dynamic energy response and damage evolution of tunnel linings under the influence of seismic waves. A nonlinear concrete damage model for the tunnel lining and a special infinite element boundary technique were employed to investigate the damage pattern and damage evolution process for tunnel lining structures. In addition, the concept of seismic layer is proposed on the basis of the flexibility ratio (a measure of the flexural stiffness of a tunnel relative to the surrounding ground) as a countermeasure against seismic damage. Subsequently, numerical simulation results are compared with field observation data for tunnels damaged during the Wenchuan earthquake. The crack patterns revealed in the damage analysis of the numerical model have also been observed in the field investigation of several mountain tunnels damaged during the Wenchuan earthquake. The similarities between the damage patterns of the lining structures in the field observation and in the damage analysis provide additional evidence of the considerable influence of seismic waves on the damage patterns.