4.2. Probability Analysis of Extreme Rainfall
The main inducing factor of deformation and failure of the Shiyantan Landslide is rainfall, and the capacity and dynamic change process of rainfall have an important impact on the stability of the slope. The significant deformation and instability of the landslide are often induced by extreme rainfall processes. The reliability calculation of landslide stability, in the complete sense, can be achieved by analyzing the probability of extreme rainfall in a certain period of time and the possibility of landslide occurrence under this extreme rainfall condition.
It is rainy from June to August in the study area. The Shiyantan Landslide is a shallow rock landslide, where the influence of rainfall is mainly slope infiltration [41
]. In this paper, the Pearson-III distribution was used to study extreme rainfall, and the probability density function is [42
is the rainfall data; a0
, and β
are the location parameter, shape, and scale of Pearson III distribution, respectively, which can be expressed as
; E (x)
is the mathematical expectation; CV
are the off-potential coefficient and skewness coefficient. The density function can be determined after a0
, α, and β are determined.
The exceeding cumulative probability of x can be expressed as
be the variance yield, then the above formula can be transferred into
It can be seen that P is a function of α and . After transformation, it is not difficult to find that the rainfall frequency curve can be obtained after knowing E(x), Cv, and Cs.
In this paper, the annual maximum method was employed to select the samples, and the maximum value of the rainfall extreme value index from 2005 to 2018 was used for frequency distribution statistics. The extreme value index was the maximum cumulative rainfall of 1 day, 3 days, 5 days, and 7 days, and the reappearing period was 10 years, 50 years, and 100 years. Then, the parameters under different rainfall durations were obtained by using the curve-fitting method to fit the Pearson III curve, as shown in Table 4
Based on the above calculation, the Green-Ampt model was used to calculate the rainfall infiltration intensity under certain rainfall intensities [38
is the infiltration depth, t is the rainfall time, q is the rainfall intensity, α is the slope gradient,
is the saturated water content, and
is the initial water content. The calculation of rainfall infiltration depth in different reappearing periods is shown in Table 5
4.3. Risk Assessment of Landslide
The thickness of the sliding body of the Shiyantan Landslide is about 7–8 m. According to the analysis of the calculation results in Table 4
, the calculation conditions of the landslide stability were divided into the following three types: 1. Only considering the weight of the sliding body, that is, the natural state; 2. Considering the weight of the sliding body and once rainfall in 10 years and 3-day rainstorm, that is, the semi-saturated state; 3. Considering the weight of the sliding body, that is, once 7-day rainfall in 50 years, that is, the complete saturation state. In this paper, Geo-studio/Seep and slope modules were used to calculate the stability and failure probability of the slope under the above conditions. The results are shown in Table 6
. The slope is relatively stable under normal conditions (natural state). When rainfall causes the rock and soil to be semi-saturated, the slope is stable. However, in the case of rare continuous heavy rainfall, with the increase in the rainfall intensity and reappearing period, the depth of rainwater infiltration will gradually increase, so that the rock and soil will be completely saturated, the weight will increase, the cohesion and internal friction angle will decrease, the stability of the slope will decrease, and the probability of instability will increase abruptly. Meanwhile, houses are built at the foot of the slope without taking any reinforcement measures, which causes a serious threat to the life and property safety of residents at the foot of the slope.
To evaluate the vulnerability of the disaster-bearing body, the influence range of the landslide should be first determined. The influence range of the landslide was mainly determined by the farthest sliding distance. According to the actual investigation and calculation, its farthest sliding distance was 170.8 m. Based on the structural characteristics of the slope, the affected area of the landslide was divided into four zones: the landslide mass was Zone 1, the region from the foot of the landslide slope to the first row of buildings is Zone 2, the region from the highway and the second row of buildings to 170.8 m of the leading edge of the landslide is Zone 3, and the post-expansion range of the landslide is Zone 4. The post-expansion range of the landslide was obtained according to the topography, field investigation, and engineering geological experience, as shown in Figure 16
Uzielli et al. proposed the formula for calculating the vulnerability of hazard-bearing bodies, as follows:
where I refers to the action intensity of the landslide disaster;
represents the vulnerability of the hazard-bearing body;
represent the structural type, maintenance condition, service life of the building, and the included angle between the direction of the landslide force and the axial direction of the building;
represents the impact force index of the landslide;
represents the thickness index of the moving sliding mass.
For Zone 1, the buildings on the landslide body were easy to collapse due to the overall damage of the landslide mass, and the vulnerability of personnel increased with the increase in the vulnerability of the buildings, so the vulnerability was taken as 1.
In Zone 2, there were dense buildings, and most of them were 1–3-floor rural houses with brick or brick and wood structures. Their maintenance condition was general, and the included angle between the impact direction of the sliding mass and the axial direction of the building was close to 0–5°. Using the engineering category method and related empirical parameters, specific parameters and building vulnerability results are shown in Table 7
; In Zone 2, the landslide at the foot of the slope was the direct impact zone, and the time for indoor personnel to avoid disasters was short, so the vulnerability of personnel was 0.45.
Due to the obstruction of buildings in Zone 2, the impact force on buildings in Zone 3 would be reduced, and the vulnerability value of buildings in Zone 3 would also be reduced. After a comprehensive analysis, the vulnerability of buildings in this zone was 0.45, and the vulnerability of personnel was 0.05.
Since there were no buildings at the trailing edge of the landslide in Zone 4, the building vulnerability and personnel vulnerability were not considered.
Landslide risk is generally defined as the casualties and property losses caused by landslide disasters in a certain period of time. Therefore, the quantitative risk determination of geological disasters mainly involves the frequency analysis of geological disasters and the vulnerability calculation of hazard-bearing bodies. In this paper, the most frequently used economic risk calculation model was adopted to calculate the economic risk, and the calculation formula is as follows:
is the economic risk;
is the annual probability of landslide instability;
is the probability that the landslide reaches the disaster-bearing body, which needs to consider the sliding distance and sliding direction of the landslide;
is the space-time distribution probability of the hazard-bearing body, and it can be 1.0 for houses and other buildings located in fixed positions;
is the vulnerability value; E is the value of the hazard-bearing body, such as the net value of houses, roads, factories, etc.
For the loss of human life, the individual risk can be calculated by the following formula:
is the individual risk value;
is the vulnerability of personnel; the definition of
is similar to economic risk.
According to the field investigation, the disaster-bearing bodies within the slope scope of the Shiyantan Landslide were mainly considered economic disaster-bearing bodies (buildings, roads, and farmland) and indoor personnel. The landslide mainly threatened rural self-built residential buildings, residents, village roads, and 103 residents on and at the foot of the slope. The specific economic values are shown in Table 8
. According to the estimation in the scene, the average distance between the building and the leading edge of the landslide was about 17 m, and the arrival probability of the landslide mass was
. As for the space-time probability, the buildings were the fixed hazard-bearing bodies, so their space-time probability was 1; the space-time probability of people in the houses could be obtained through the investigation, and it could be known that in one of the houses, people lived 305 days a year and stayed 18 h a day, so the space–time probability of people was P (S:T) = (305/365) * (18/24) = 0.627.
Thus, the risk determination of the Shiyantan Landslide was carried out, and the results are shown in the Table 9
At present, the Shiyantan landslide has undergone emergency treatment, including drainage ditches and retaining walls, but there are still some problems. Therefore, the following prevention and control suggestions are put forward: (1) Anti-slide piles. The inclined house plays the role of presser feet, but it has a greater risk. It is recommended to strengthen it. At the same time, anti-slide piles are used to support the shallow part of the front of the landslide. The pile ends should be embedded in the bedrock to a certain depth. (2) The intercepting ditch should be built at the trailing edge of the landslide. It forms an organic whole with the annular intercepting ditch on both sides and in the middle of the landslide, so that the surface water in the landslide area can be fully and effectively discharged during the rainy season to reduce the softening effect of the rock and soil in the landslide area. (3) It is necessary to pack the cracks on the landslide to prevent rainwater from seeping into the landslide. (4) Residents threatened by the sliding body have been partially relocated, but there are still many residents on the leading edge, so they should be relocated in time. In addition, the continuous deformation signs of the landslide shall be monitored continuously, and warning signs shall be set on both sides of it. The water level of the Jinjiang River shall be monitored. When the water level reaches or exceeds the historical maximum water level of 177 m, the front edge of the landslide is soaked by the river water to prevent the secondary sliding of the landslide.
In conclusion, this article takes Mayang County as an example to quantitatively characterize the landslide disaster risk, which provides an example for the follow-up landslide risk assessment and prevention work. In addition, there are still many defects in the research. It is hoped that in the following research, the vulnerability analysis can be more systematic and in-depth, for example, considering the age structure of personnel, building infrastructure, etc.