## 2 Statistical Analyses of Individual Hazards
### Risk Assessment of River Blockage Caused by Landslides  
The river blockage caused by landslides can be classified into complete blockage and partial blockage, as shown in Figure 1. In the case of a partial blockage, the landslide deposit blocks part of the river channel and the river still flows through the unblocked channel. In the case of a complete blockage, the landslide deposit completely blocks the river channel and forms a landslide dam, which promotes the formation of a barrier lake. Therefore, assessing the degree of river blockage is the primary task of risk assessment. [PERSON] et al. [13] investigated the relationship between the formation of landslide dams and two critical conditions, namely landslide volume and valley width, and proposed an assessment index, named the morphological obstruction index (MOI), as follows:  
\[\text{MOI}=\lg(V_{L}/W_{V}) \tag{1}\]  
where \(V_{L}\) denotes the landslide's volume (m\({}^{3}\)) and \(W_{V}\) denotes the valley's width (m). When MOI \(>\) 4.6, a landslide dam forms; when MOI \(<\) 3.00, a landslide dam does not form; and landslide dams are uncertain when 3.00 \(\leq\) MOI \(\leq\) 4.6. The advantage of this formula is that the valley's width and the landslide's volume can easily be measured, so it is suitable for rapid assessments of the risk of river blockage. However, the accuracy of the MOI is poor. Only 57.9% of the cases in the database could be assessed correctly (Table A1) by this method. This is because the risk of a landslide blocking the river is also related to many other factors, such as the valley's shape, the riverbank's slope, and the landslide's materials. The accuracy needs to be improved by taking more factors into consideration. A landslide formed on a steeper slope is more likely to induce a landslide dam, as the landslide generates more kinetic energy [10]. According to the database, the relationship between the steepness of the slope and the degree of river blockage can be statistically analyzed, as shown in Figure 2. This illustrates that a landslide with a steeper slope is more likely to completely block the river and form a landslide dam. Moreover, landslide materials with larger particles are also more likely to accumulate directly at the bottom of the river and form a landslide dam. It is also easier for a landslide dam to form in a V-shaped valley than in a U-shaped valley [27]. Figure 1: The difference between complete blockage and partial blockage. Figure 2: The percentages of landslide cases with different slope steepness, resulting in partial and complete river blockages. [PERSON] et al. [28] and [PERSON] et al. [29] collected many cases of river blockages caused by landslides in China and Italy. Some cases with complete data were selected to establish a database of 57 events. According to the database (Table A1), an index based on the MOI was proposed, named the Landslide Blocking River Index (LBRI). The valley's shape, the landslide's materials, and the steepness of the slope were considered in the LBRI to make it more accurate and enhance its applicability. Because some cases lacked a description of the valley's shape, the shapes of these cases were considered to be V-shape valleys for a conservative evaluation:  
\[\text{LBRI}=\frac{A_{C}}{\cos\varphi}\log_{10}(V_{L}/W_{V}) \tag{2}\]  
where \(\varphi\) denotes the steepness of the landslide slope (\({}^{\circ}\)) and \(A_{C}\) denotes the \"accumulation coefficient\", which is related to the valley's shape and the particle size of landslide materials. According to the analysis results of database, different values of \(A_{C}\) are suggested for various landslide materials and different valley shapes, as shown in Table 1.  
In Figure 3, the results calculated for the LBRI were divided into two different domains, i.e., complete blockage and partial blockage. According to the statistical analysis of these data, when LBRI \(<\) 4.5, the river is partly blocked; when LBRI \(\geq\) 4.5, the river is completely blocked.