Assessment of Risks of Regional Shallow Slope
Failures
H.X. CHEN a and L.M. ZHANG b a
Research Assistant, Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, China
b
Professor, Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, China
Abstract. Shallow slope failures are one of the most frequent geological hazards in mountainous areas, which pose great danger to people and properties in affected areas. This paper presents a cell-based platform for quantitative risk assessment for shallow slope failures at a regional scale. There are five components in this platform; namely, a digital terrain module, a spatial rainfall distribution module, a slope stability and reliability evaluation module, a movement prediction module, and a risk assessment module. The locations and volumes of the slope failures are estimated using the slope stability and reliability evaluation module. The movement prediction module is used to predict the potential movement traces of the detached material, which moves along the steepest path. The risks of the slope failures are finally assessed using the risk assessment module, which can be used as an indicator for early warning. The vulnerability of a person to slope failure is determined by the volume of slope failure and angle of reach. The platform is applied to a 164.5 km2 hilly terrain in the Wenchuan earthquake zone to test its performance in quantitative risk assessment for regional shallow slope failures. The platform evaluates the risks of shallow slope failures at a regional scale efficiently.
Keywords. Landslides, slope failure, travel distance, risk assessment, Wenchuan earthquake
1. Introduction
Shallow slope failures are one of the most frequent geological hazards in hilly terrains, which can cause enormous casualties and economic losses. Quantitative risk assessment for slope failures is a powerful tool for hazard mitigation, which has been widely applied around the world (e.g. Finlay et al., 1999; Dai et al., 2002; van Westen et al., 2002). Several problems may arise in assessing the risks in a large area where widespread shallow slope failures may occur. How does one assess the risk in the large area efficiently? Sometimes more than one slope failures may happen simultaneously or successively, and affect the same element at risk. How does one assess the risk considering the relationships among different slope failures? Vulnerability is an important component for risk assessment. How does one assess the vulnerability of persons to slope failures properly? In this study the authors attempt to address these problems. The objective of this study is to develop a cell-based
quantitative risk assessment platform for regional shallow slope failures, which provides basis for risk-based early warning.
2. Platform Framework
The framework of the platform is shown in Figure 1. The platform comprises five components; namely, a digital terrain module, a spatial rainfall distribution module, a slope stability and reliability evaluation module, a movement prediction module, and a risk assessment module. The first three components have been described in detail by Chen and Zhang (2014). In this study, the risk of slope failures to travellers along a road is considered.
The digital terrain is discretized into a grid first, with the properties in each cell assigned (e.g. geology, topography, soil properties, hydrological parameters). Each cell is a computational unit. All the analyses are based on concept of cell.
T. Schweckendiek et al. (Eds.) © 2015 The authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License. doi:10.3233/978-1-61499-580-7-250
Figure 1. Framework of the cell-based quantitative risk assessment platform.
Rainfall is a triggering factor for slope failures; hence it is essential to obtain the spatial rainfall distribution. Very often only a limited number of rain gauges are installed in a certain area. Universal kriging has been widely applied to obtain spatial rainfall distribution, which is adopted in this study.
Once the spatial rainfall information is obtained, infiltration analysis can be conducted to obtain spatial and temporal pore-water pressure profile of each cell. The stability and reliability of each cell can be evaluated afterwards using the slope stability and reliability evaluation module.
After the locations, volumes, and occurrence probabilities of the slope failures are determined, the impact area of the detached material can be assessed by the movement prediction module.
Finally, the risk is assessed through the risk assessment module, which considers the relationships among different slope failures.
3. Prediction of Slope Failure Movement
After the stability of each cell is assessed, unstable cells that are bounded at one side or one corner or more are grouped together and each group is viewed as an individual slope failure. The reason to group unstable cells is to consider the size effect of slope failures since a larger
slope failure moves farther if other conditions are the same due to energy balance.
An empirical method is developed to present the movement of slope failures on a three-dimensional digital terrain. Data of 20 rain-induced shallow slope failures and 31 earthquake-induced slope failures in the Wenchuan earthquake zone are used to develop an empirical relationship for predicting the travel distance of the detached material:
logL 0.184 0.069 log V0.830 logH (1) where H, L and V are the fall height, travel distance, and volume of the slope failure, respectively. The Pearson coefficient of correlation for this relationship is 0.92. The empirical relationship is taken as the movement cessation criterion. The detached material of slope failures is assumed to move along the steepest path to lower cells until the maximum travel distance is reached.
4. Assessment of Risks Posed by Regional Slope Failures
4.1. Concepts of Risk Assessment
Morgan et al. (1992) proposed a general equation to express societal risk posed by a landslide:
>
( ) ( | ) ( | ) ( | )@
e n LOL i i i i i i R¦
P H uP S H uP T S uV L T uE (2) where RLOL is the societal risk, which indicatesthe potential loss of life; ne is the number of hazard events; P(H) is the occurrence probability of the landslide event; P(S|H) is the probability of the spatial impact given the event happens;
P(T|S) is the probability of temporal impact
given the spatial impact; V(L|T) is the vulnerability of the individual given the landslide impact (i.e. fatality rate); E is the element at risk. The above equation does not consider the relationships among different hazards.
The occurrence probability of slope failure is estimated using the first-order second-moment (FOSM) method (Chen and Zhang, 2014).
P(S|H) can be determined by the slope stability
analysis and the movement analysis. If the moving material reaches a cell, P(S|H) is taken as 1; otherwise, P(S|H) is 0. Travellers are assumed to present uniformly along the road so
P(T|S) is always 1.0 in this study. A vulnerability
matrix for roads and other facilities proposed by Lo and Cheung (2004) is adopted for estimating the vulnerability of persons in vehicle to slope failures, which is determined by the size of slope failure and angle of reach. Although roads and facilities are less vulnerable than a human being to a fast moving slope failure, a person driving a vehicle can detect a slope failure and become less vulnerable.
4.2. QRA for Regional Slope Failures
One cell of the road may be affected by several hazard events in a short period (Figure 2). These events can be viewed as a serial system. The range of the probability of spatial impact is
1 max( ) 1 (1 ) e n i I i i P dP d
P (3)where Pi is the probability of a cell being affected by slope failure i; PI is the probability that the cell is affected by any of the slope failures; ne is the number of slope failures that may affect the cell. The lower bound of PI refers to a perfectly dependent scenario while the upper
bound of PI refers to a completely independent scenario.
Figure 2. Slope failures affecting the same road. As shown in Figure 2, there are two slope failures. Cells 1-37 belong to slope failure I while cells 38-74 belong to slope failure II. Unstable cells that belong to the same slope failure are assumed to be perfectly dependent. A road cell (e.g. cell 75) may be buried by the detached material of different cells that belong to the same slope failure (cells 1 and 2). The maximum failure probability of the cells (cells 1 and 2) is used according to Eq. (3). Unstable cells that belong to different slope failures are assumed to be independent. A road cell (e.g. cell 77) may be buried by detached material of different cells that belong to different slope failures (cells 7, 27, 38, and 60). If the detached material of the four cells reaches cell 77, then the probability that cell 77 is affected by the detached material is
>
@
^
7&27`
^
>
38&60@
`
1 1 max ( ) 1 max ( ) I P P H u P H (4)The vulnerability factor for a traveller in a vehicle is
1 2
( | ) 1 1 ( | )sf 1 ( | )sf V L T ª¬ V L T º ª¼ ¬u V L T º¼ (5)
where sf1 and sf2 represent slope failure I and slope failure II, respectively.
In general, the probability that one specific road cell is affected by the detached material can be calculated as
1 1 [1 ( ) ] e n I i i P
P H (6)where ne is the number of slope failures of which the detached material can reach the specific road cell; P(H)i is the maximum failure probability of the cells that affect the road cell in group i. The vulnerability factor for a traveller in a vehicle can be calculated as 1 ( | ) 1 [1 ( | ) ] e n i i V L T
V L T (7)5. Application to Slope Failures Triggered by the 13 August 2010 Storm Event
5.1. Study Area
The study area includes a section of Provincial Road 303 (PR303) from milestone K0 (Yingxiu) to K18 (Gengda) and its vicinity near the epicentre of the Wenchuan earthquake, Yingxiu (Figure 3). The total study area is 164.5 km2, discretized into 182,417 cells. The cell size is 30 u 30 m. The alignment of PR303 between K0 and K18 is primarily along the Yuzixi River that is bounded by terrains with elevations from 880 to 4,140 m. The risk of slope failures to travellers along the road is considered in the application.
Figure 3. Locations of the study area and six rain gauges. The 2008 Wenchuan earthquake triggered a large number of landslides in the study area. Based on Quick-bird satellite images taken on 30 May 2008 with a resolution of 0.6 m and field
investigations, a total of 305 hill-slope deposits were identified (Zhang et al., 2012), with a total volume of 54.3 u 106
m3. The study area is classified into four types based on the surface geology; namely, loose soil deposit, vegetated land, bedrock, and riverbed. Bedrock and riverbed are set to be stable. The soil parameters and soil thickness have been introduced in detail by Chen and Zhang (2014).
5.2. Slope Failures Triggered by the 13 August 2010 Storm Event
From 11:00 on 12 August 2010 to 9:00 on 14 August 2010, a storm swept Yingxiu and its vicinity, with a duration of 46 h, which was the heaviest storm event after the 2008 Wenchuan earthquake in the study area up to 2010. The locations of six rain gauges are shown in Figure 3; namely, Dujiangyan, Yingxiu, Shuimo, Yinxing, Xuankou, and Gengda. The rain data and interpolation results have been introduced in detail by Chen and Zhang (2014). Widespread slope failures were triggered by the storm. A total of 351 fresh rainfall-induced slope failures were identified in the study area, and the total volume of the slope failures was approximately 21.5 u 106
m3.
5.3. Risk Assessment for the Slope Failures
Four snapshots are selected for analysis; namely
t = 5 h, 15 h, 36 h, and 46 h. T = 5 h is at the
early stage of the storm; t = 15 h is the moment when the storm started to be heavy; t = 36 h is the moment of peak rainfall intensity; and t = 46 h is at the end of the storm. It is assumed that all slope failures occur simultaneously at each analysis moment and the stability, reliability, and movement analyses at one moment are independent from those at other moments. The traffic flow is assumed remain at 35 persons per kilometre (Zhang et al., 2012).
Figure 4. Hazard map at the end of the storm: (a) unstable cells; (b) probability of failure of cells; (c) movement traces of detached material; (d) final deposition locations.
The distributions of unstable cells, probability of failure of cells, movement traces, and final deposition locations of the detached material at the end of the storm are shown in
Figure 4 as an example. The performance of the platform in predicting the locations and occurrence probability of slope failures has been verified by Chen and Zhang (2014).
Figure 4a gives the locations of computed slope failures. The volume of the slope failure is determined by the cell area and the depth of failure surface. Figure 4b gives the probability of failure of the cells. Figures 4c and 4d give the impact area of the detached material. Therefore, the results in Figures 4b,c,d define the probability of spatial impact. The angle of reach of the slope failure is determined by the fall height and travel distance of the detached material. The vulnerability of traveller to slope failure is determined by the volume of the computed slope failure and angle of reach.
The societal risks posed by the slope failures from K0 to K18 during the storm are summarized in Table 1. At the early stage of the storm (t = 15 h), section K3-K4 is the most dangerous. At the late stage of the storm, section K13-K14 becomes the most dangerous. When the storm starts to be heavy (t = 15 h), the societal risk reaches a rather high level (85.83). The reason is that the loose materials on steep terrain are quasi-stable shortly after the earthquake and can easily lose stability under rainfall.
The results indicate that the road is extremely dangerous since the potential loss of life (223.5) is about 35% of the total number of travellers on the road (630) if the traffic flow remains at 35 persons per kilometre. The actual fatalities were much smaller than 223.5 due to two reasons. The first reason is that travellers were not uniformly distributed during the storm. They tended to stay in safe places or find shelters when the slope failures occurred. The second reason is that when the storm became heavy in the evening, few travellers entered the road. Therefore, the computed potential loss of life only reflects the impact of slope failures to the road when the traffic flow reaches the design flow and no redistribution happens.
6. Summary and Conclusions
A risk assessment platform for regional shallow slope failures has been reported in this paper.
(a)
(b)
(c)
There are five components in this platform; namely, a digital terrain module, a spatial rainfall distribution module, a slope stability and reliability evaluation module, a movement prediction module, and a risk assessment module.
The locations and volumes of the detached material are estimated using the slope stability and reliability evaluation module. The movement prediction module is used to predict the potential movement traces of the detached material, which moves along the steepest path. The risks of the slope failures are finally assessed using the risk assessment module. The vulnerability to slope
failures is determined based on the size and angle of reach of each slope failure. The platform considers the relationships among different slope failures to some extent.
The method is applied to a 164.5 km2 hilly terrain in the Wenchuan earthquake zone to test its performance in the assessment of the risk of regional shallow slope failures. The results indicate that the risk level increases continuously until end of the storm. Serious loss of life would happen if the traffic flow is at the assumed level of 35 persons per kilometre.
Table 1. Societal risks of the slope failures from K0 to K18 during the 13 August 2010 storm.
t RLOL per km Total RLOL
Maximum value Minimum value
Value Road section Value Road section
5 h 0.00 - 0.0 - 0
15 h 13.02 K3-K4 0.01 K16-K17 85.83
36 h 22.00 K13- K14 2.11 K6-K7 197.00
46 h 24.85 K13- K14 2.81 K6-K7 223.50
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