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ORIGINAL RESEARCH article

Front. Earth Sci., 27 September 2022
Sec. Geohazards and Georisks
This article is part of the Research Topic Water-Related Natural Disasters in Mountainous Area, volume II View all 16 articles

Influence of soil mechanical and hydraulic parameters on the definition of rainfall intensity and duration thresholds based on Transient rainfall infiltration and grid-based regional slope-stability model (TRIGRS)

Sen ZhangSen Zhang1Qigang Jiang
Qigang Jiang1*Xitong XuXitong Xu1Guofang TaoGuofang Tao1Zhenchao ZhangZhenchao Zhang1Xin GaoXin Gao1Chunlong HeChunlong He1
  • 1College of Geo-exploration Science and Technology, Jilin University, Changchun, China

As a supplement to empirical-statistical methods, physically based methods can be employed to define rainfall thresholds for triggering landslides in areas lacking records of landslides. The transient rainfall infiltration and grid-based regional slope-stability model (TRIGRS), as a physically based model, has been applied to define rainfall thresholds at the basin, slope unit, and grid cell scales. However, as far as we know to date, the influence of soil mechanical and hydraulic parameters on defining rainfall thresholds at various scales has not been comprehensively evaluated. In this study, TRIGRS was used to define rainfall intensity (I) and duration (D) thresholds at various scales for Buzhe village, Pu’an county, Guizhou province, China, under the conditions of different soil physical parameters. The results show that the number of rainfall thresholds decreased with cohesion (c) and internal friction angle (φ) and increased with soil unit weight (γs), excluding the basin scale. Threshold position varied positively with c and φ and negatively with γs. Soil mechanical parameters have a greater influence on the definition of rainfall thresholds based on TRIGRS than hydraulic parameters.

Introduction

Rainfall-induced shallow landslides mainly occur on slopes covered by a layer of colluvium or residual soil (Salciarini et al., 2006; Montrasio and Valentino, 2007; Montrasio and Valentino, 2008). Rainfall infiltration in slopes increases the pore-water pressure and decreases the shear strength, thereby triggering landslides (Lim et al., 1996; Vanapalli et al., 1996). Thus, rainfall is recognized as the primary trigger of shallow landslides (Campbell, 1975; Keefer et al., 1987; Wilson, 2005), and rainfall thresholds are the most used tools to forecast landslides (Caine, 1980; Aleotti, 2004; Guzzetti et al., 2007; Guzzetti et al., 2008; Li et al., 2017; He et al., 2020). Guizhou province is located in the mountainous area of southwest China. As one of the landslide-prone provinces in China, shallow landslides frequently occur in Guizhou province (Yu et al., 2016; Zhang et al., 2017; Lin and Wang, 2018; Ma et al., 2020). However, only few defined rainfall thresholds or landslide early warning systems (LEWSs) exist in this area to address the risk of shallow landslides.

Empirical-statistical and physically based methods can be used to define rainfall thresholds (Aleotti, 2004; Guzzetti et al., 2007; Park et al., 2019). Empirical-statistical rainfall methods define rainfall thresholds through the statistical analysis of rainfall conditions that have triggered landslides (Brunetti et al., 2010; Peruccacci et al., 2012; Melillo et al., 2018). Currently, empirical-statistical rainfall thresholds have become the most common landslide model (i.e., the functional relationship between weather conditions and landslide events) in LEWSs (Calvello, 2017; Piciullo et al., 2018; Guzzetti et al., 2020). However, empirical-statistical methods mainly rely on the availability and quality of landslide records (Peres and Cancelliere, 2014). They are severely limited for the areas with incomplete or unavailable landslide records. In this case, physically based methods are the ideal alternative.

Physically based methods define rainfall thresholds by simulating the hydrological process of soil and slope stability during rainfall infiltration (Salciarini et al., 2008; Salciarini et al., 2012). TRIGRS is a physically based model for shallow landslide prediction (Baum et al., 2002; Baum et al., 2008; Baum et al., 2010; Alvioli and Baum, 2016). Thus, TRIGRS is widely used in modeling the timing and distribution of shallow landslides (Vieira et al., 2010; Lee et al., 2017; Tran et al., 2018; He et al., 2021; Ip et al., 2021) and landslide susceptibility mapping (Baum et al., 2005; Park et al., 2013; Marin and Mattos, 2020). In addition to these widespread applications, TRIGRS is applied in defining physically based rainfall thresholds given its ability to describe the scaling behavior of rainfall thresholds (Alvioli et al., 2014).

The Sendai Framework for Disaster Risk Reduction proposes the goal of substantially increasing the availability and access to multi-hazard early warning systems and disaster risk information and assessments to people by 2030 (UNISDR, 2015). Guzzetti et al. (2020) proposed that LEWSs can be deployed and operated worldwide, and suggested increasing the rate of LEWS deployment for landslide-prone areas. In some landslide-prone areas of China, the quality of records of landslides is poor. Although this situation has improved in recent years, the time span and quality of existing landslide records are insufficient to support the definition of empirical-statistical rainfall thresholds. For these areas, physically based methods can extend the application scenarios of LEWS based on rainfall thresholds, which is important for LEWS deployment.

TRIGRS can be employed to define rainfall thresholds at three scales, namely, basin, slope unit, and grid cell scales. At the basin scale, the rainfall threshold is defined for the whole area. Rainfall conditions exceeding the defined rainfall threshold can trigger several landslides in the entire area. Alvioli et al. (2018) used TRIGRS to define the rainfall event-duration (E-D) threshold for Upper Tiber River Basin in Italy. Bordoni et al. (2019) used TRIGRS to define the E-D threshold for an area of Oltrepò Pavese in Italy. Marin and Velásquez (2020) used TRIGRS to define the I-D thresholds for the Envigado Basin of Colombia under the conditions of different soil hydraulic properties. Marin et al. (2020) used TRIGRS to define the I-D thresholds for 93 small basins in Colombian Andes and analyzed the effect of basin morphometric parameters on defined I-D thresholds. Marin et al. (2021) used TRIGRS to define the I-D thresholds for La Arenosa and La Liboriana Basins in Colombian Andes. At the slope unit scale, rainfall thresholds are defined for slope units with critical rainfall. Rainfall conditions exceeding the defined rainfall thresholds can trigger landslides in the corresponding slope units. Alvioli et al. (2014) used TRIGRS to define the I-D thresholds for several sub-basins of the Upper Tiber River Basin. Zhang et al. (2022) divided Dabang village, Pu’an County, Guizhou Province, China, into several slope units and used TRIGRS to define the I-D thresholds for the slope units with critical rainfall. At the grid cell scale, rainfall thresholds are defined for grid cells with critical rainfall. Rainfall conditions exceeding the defined rainfall thresholds can trigger landslides in the area of the corresponding grid cells. Marin (2020) used TRIGRS to define the I-D thresholds for grid cells with critical rainfall in the Envigado Basin. Marin et al. (2021) used TRIGRS to define the I-D thresholds for grid cells with critical rainfall of La Arenosa and La Liboriana Basins.

Detailed and accurate soil parameters (e.g., soil depth, soil mechanical, and hydraulic parameters) are required to properly apply TRIGRS. However, obtaining substantial information on distributed soil properties at a large scale is a challenge, especially regarding soil physical properties (i.e., mechanical and hydraulic parameters) (Gariano and Guzzetti, 2016; Zhang et al., 2018). Uncertainties in soil parameters are caused by complex geological conditions, spatial variability, and laboratory measurement (Catani et al., 2010; Ho et al., 2012; Corominas et al., 2014; Bicocchi et al., 2015), which make it impossible to eliminate all uncertainties. In terms of using TRIGRS to predict the spatiotemporal information of shallow landslides and landslide susceptibility mapping, the influence of soil mechanical and hydraulic parameters on the prediction and mapping results has been extensively explored (Salciarini et al., 2006; Montrasio et al., 2011; Bordoni et al., 2015; Gioia et al., 2016; He et al., 2016; Ciurleo et al., 2017; de Lima Neves Seefelder et al., 2017; Weidner et al., 2018; Ciurleo et al., 2019). Some probabilistic approaches have been adopted with TRIGRS to quantitatively account for soil parameter uncertainties (Raia et al., 2014; Salciarini et al., 2017). In these probabilistic approaches, the input parameters are considered random variables, and the output is the probability of failure.

However, few studies have explored the influence of soil mechanical and hydraulic parameters on the definition of rainfall thresholds based on TRIGRS. Only Marin and Velásquez (2020) explored the effect of soil hydraulic parameters on the position of rainfall thresholds defined at the basin scale. The performance of the rainfall threshold requires evaluation before applying it in LEWSs (Piciullo et al., 2017; Segoni et al., 2018). Exploring the influence of soil physical parameters on the rainfall thresholds defined by using TRIGRS can facilitate the evaluation of the physically based rainfall thresholds.

In this study, Buzhe village, Pu’an county, Guizhou province of China was taken as the study area. The soil mechanical and hydraulic parameters measured by field sampling were taken as standard values. In each TRIGRS simulation, a parameter was varied by the given proportion and the rest remained constant. Then, the I-D thresholds at various scales were defined under the conditions of given physical parameters. Finally, the influence of soil physical parameters on the number and position of rainfall thresholds was explored by comparing the simulated Fs maps and defined thresholds.

Study area

Pu’an county, which is located in southwest Guizhou province of China (Figure 1), has tremendous undulating terrains, and the dissolution and erosion of landforms are staggered. Moreover, soft rocks such as siltstone and sandstone are widespread. These soft rocks are easily weathered into the eluvium and slope wash. As for rainfall, the average annual precipitation of Pu’an county is 1,443 mm. Owing to the complex geological setting and rainy environment, Pu’an county is one of the landslide-prone counties in Guizhou province.

FIGURE 1
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FIGURE 1. (A) Location of Pu’an county (image source: SRTM data) and (B) location of the study area.

Lower Triassic sandstone and clay rock, Upper Permian siltstone, sandstone, and clay rock, and Upper Permian limestone and siltstone are distributed in the study area (Figure 2A). The soil types in the study area are red loam and lime soil (Figure 2B). The distribution of each soil type is consistent with the corresponding soil parent material. Red loam is distributed on sandstone, siltstone, and clay rock. Lime soil is distributed on limestone.

FIGURE 2
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FIGURE 2. (A) Geology map of the study area and (B) spatial distribution of soil types.

Data

Digital elevation model

The input data for TRIGRS are topographic factors, soil parameters, soil thickness, and initial conditions for surface flux and groundwater table. As for topographic factors, the 10-m resolution DEM was taken as input. Other required input slopes and flow direction maps were generated using ArcGIS software based on the DEM data.

Soil parameters

The input soil mechanical parameters include γs, φ, and c. The input hydraulic parameters include saturated hydraulic conductivity (Ks), hydraulic diffusivity (D0), saturated water content (θs), residual water content (θr), and fitting parameter (αG) of Gardner’s model for the soil water characteristic curve (SWCC) (Gardner, 1958). A total of 18 samples of red loam and 10 samples of lime soil were collected at the 14 sampling locations (Figure 2B). The mechanical parameters were measured through laboratory static triaxial experiments. The hydraulic parameters were measured through laboratory variable tap penetration experiments. For each parameter, the average of the measurements was taken as the standard value (Table 1). Regarding θs, θr, and αG, this study determined the parameters for the Gardner model (used in TRIGRS) based on the Van Genuchten model (Van Genuchten, 1980) for SWCC of typical soil types in Guizhou province (Zhao, 2021). The volumetric water contents were the same in the two models for each soil type, and αG was fitted to be within the limits of the Van Genuchten curves, as suggested by Marin (2020).

TABLE 1
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TABLE 1. The range and average of soil samples measurements in the study area.

c, φ, and γs were taken 0.8, 0.9, 1.1, and 1.2 times the standard values as input. Ks and D0 were taken 0.7, 0.8, 1.2, and 1.3 times standard values as input. The input mechanical and hydraulic parameters were assigned to each grid cell according to the spatial distribution of soil types in the study area (Figure 2B). One parameter was changed, and the remaining parameters were kept constant for each simulation. A total of 20 simulations were performed.

Soil thickness significantly influences the simulation results of TRIGRS (Tran et al., 2018). Many studies have shown that the linear relation of slope angle and soil thickness to characterize the soil thickness map can obtain suitable simulation results of TRIGRS (Viet et al., 2017; Tran et al., 2018; He et al., 2021). The relationship assumes that soil thickness (y) is in inverse proportion to slope angle (x), that is, the minimum soil thickness (0.1 m) corresponds to the maximum slope (69.41°) and the maximum soil thickness (3.3 m) corresponds to the minimum slope (0.1°). From the relationship, the soil thickness map was generated by the linear equation (Eq. 1). The units of y and x are meter and degree, respectively.

y=0.04617x+3.3.(1)

The input initial conditions include initial surface flux (Iz) and initial groundwater table. Given the complex properties of soil (e.g., void and uniformity), Iz is difficult to measure using laboratory tests. Thus, the empirical relationship between Iz and Ks was used to determine Iz. This study set Iz to be 0.01 of Ks and set the initial groundwater table to be the same as the soil thickness, as suggested by Kim et al. (2010), Park et al. (2013), Lee et al. (2017), and Viet et al. (2017).

Methods

TRIGRS model

The TRIGRS model is designed for simulating the timing and distribution of shallow landslides by computing the transient pore-pressure changes and attendant changes in the factor of safety of slope caused by rainfall infiltration (Baum et al., 2002; Baum et al., 2008; Baum et al., 2010; Alvioli and Baum, 2016). Infiltration models include the models for saturated initial and unsaturated initial conditions. For saturated initial conditions, infiltration models in TRIGRS adopt Iverson’s linearized solution (Iverson, 2000) of the Richards equation (Richards, 1931). For unsaturated initial conditions, infiltration models in TRIGRS adopt the analytical solution of the Richards equation for unsaturated soil proposed by Srivastava and Yeh (1991) to approximate the infiltration process and the Gardner model to describe SWCC (Gardner, 1958). TRIGRS simulates the slope stability based on the infinite-slope model (Taylor, 1948). The slope stability is represented by Fs, which is calculated as follows:

Fs(Z,t)=tanϕtanδ+cψ(Z,t)γwtanϕγSZsinδcosδ,(2)

where γw and γS represent the unit weights of water and soil, respectively; c is the effective soil cohesion; ϕ is the effective soil internal friction angle; δ is the slope angle; and ψ(Z,t) is the pressure head as a function of depth Z and time t. Failure is predicted when Fs<1, and stability holds when Fs1. The simulation results of Fs are visualized on GIS software. The latest version (v2.1) of TRIGRS was used in this study (Alvioli and Baum, 2016).

Definition of I-D thresholds at the basin scale

In this study, the method proposed by Marin and Velásquez (2020), Marin et al. (2020), and Marin et al. (2021) was used to define the I-D thresholds at the basin scale. This method proposed two ratios, namely, the critical failure area ratio (ac) and failing area ratio (af), where ac is the ratio that excludes unconditionally unstable grid cells (i.e., Fs<1 without rainfall). At the basin scale, af is calculated as the ratio of the area of grid cells with Fs<1 to the area of study area.

Figure 3A shows the flowchart of the definition of I-D thresholds at the basin scale. TRIGRS was run with a set of I-D conditions to simulate. In the simulation, I was increased from 2 mm/h to 30 mm/h, with an increment step of 2 mm/h. D was increased from 2 to 60 h, ranging from 2 to 20 h with an increment step of 2 h and ranging from 20 to 60 h with an increment step of 4 h. For each I-D condition, af was calculated and compared with ac. If afac, the I-D condition was regarded to cause instability. This study defined rainfall thresholds using the ac of 1%.

FIGURE 3
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FIGURE 3. The flowchart of the definition of I-D thresholds based on TRIGRS (A) at the basin scale and (B) at the slope unit scale.

Before fitting, the I-D conditions that cause instability were screened to exclude the I-D conditions with the same I or D values (Zhang et al., 2022). Then, the screened I-D conditions were plotted in a log–log plot (logI vs logD). Also, the distribution of I-D conditions was fit to be the linear equation of Eq. 3.

logI=βlogD+logα,(3)

where I is the rainfall intensity (mm/h), D is the rainfall duration (h), β is the slope, and logα is the intercept. After getting the α and β, Eq. 3 was transferred into the power law equation (Eq. 4).

I=αDβ,(4)

Definition of I-D thresholds at the slope unit scale.

In this study, the method proposed by Zhang et al. (2022) was used to define I-D thresholds at the slope unit scale. The slope units were delineated based on ridge and valley lines obtained by using hydrology analysis tools in ArcGIS. (Xie et al., 2004; Wei et al., 2018).

The flowchart of the definition of I-D thresholds at the slope unit scale is shown in Figure 3B. The definition of rainfall thresholds at the slope unit scale involves defining rainfall thresholds for slope units with critical rainfall (i.e., under the given rainfall conditions, the slope units can reach instability). For each slope unit, af was calculated as the area of unstable grid cells within its range to the area of the slope unit. The remaining steps were the same as those for the basin scale.

Definition of I-D thresholds at the grid cell scale.

In this study, the method proposed by Marin (2020) was used to define I-D thresholds at the grid cell scale. Defining rainfall thresholds at the grid cell scale involves defining rainfall thresholds for grid cells with critical rainfall, that is, under the given rainfall conditions, the grid cells can reach instability. At the grid cell scale, the rule for determining I-D conditions causing instability was Fs<1. The remaining steps were the same as the abovementioned methods (Figure 4).

FIGURE 4
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FIGURE 4. The flowchart of the definition of I-D thresholds based on TRIGRS at the grid cell scale.

Rainfall thresholds defined at any scale are not applicable to rainfall events of any rainfall duration. The defined rainfall thresholds are valid for a range of duration with initial and final durations. The initial duration is the duration that causes the whole study area or each slope unit unstable for the first time. The final duration is the maximum duration at which the increase in duration no longer affects the stability for the given range of intensities.

Results

Factor of safety maps

When I and D are at the maximum, that is, I = 30 mm/h and D = 60 h, the Fs maps under different soil mechanical and hydraulic parameters conditions can reflect the number of slope units and grid cells with critical rainfall and whether the whole study area has critical rainfall.

Supplementary Video 1 (in the supplementary material) shows the distribution variation of grid cells with Fs<1 under the maximum I-D condition when c, φ, and γs were 0.8, 0.9, 1.1, and 1.2 times the standard values. The whole study area had critical rainfall under given soil mechanical parameters. Figure 5 shows the number of slope units and grid cells with critical rainfall under given soil physical parameters. When c was 0.8, 0.9, 1.1, and 1.2 times the standard value, the number of slope units with critical rainfall was 46, 45, 39, and 36, respectively. The number of grid cells with critical rainfall was 13,518, 11,585, 7,613, and 3,414, respectively. The number of slope units and grid cells with critical rainfall decreased when c increased. When φ was 0.8, 0.9, 1.1, and 1.2 times the standard value, the number of slope units with critical rainfall was 45, 44, 40, and 40, respectively. The number of slope units with critical rainfall was 10,930, 10,201, 8,800, and 8,122, respectively. The number of slope units and grid cells with critical rainfall decreased when φ increased. When γs was 0.8, 0.9, 1.1, and 1.2 times the standard value, the number of slope units with critical rainfall was 37, 40, 45, and 45, respectively. The number of grid cells with critical rainfall was 4,324, 7,789, 10,680, and 11,639, respectively. The number of slope units and grid cells with critical rainfall increased when γs increased.

FIGURE 5
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FIGURE 5. The number of objects with critical rainfall (A) slope units and (B) grid cells.

Supplementary Video 2 (in the supplementary material) shows the distribution variation of grid cells with Fs<1 under the maximum I-D condition when Ks and D0 were 0.7, 0.8, 1.2, and 1.3 times the standard values. In these cases, the whole study area had critical rainfall. The number of slope units and grid cells with critical rainfall was 41 and 9,502. The number of slope units and grid cells with critical rainfall did not vary with Ks or D0.

I-D thresholds at the basin scale

Supplementary Video 3 (in the supplementary material) show the variation of I-D thresholds defined at the basin scale when c, φ, and γs were 0.8, 0.9, 1.1, and 1.2 times the standard values. Figures 6A–C show the comparison of thresholds defined at the basin scale under given c, φ, and γs values, respectively. The results showed that the threshold with higher c or φ was located on the higher part of the graph. The threshold with higher γs was located on the lower part of the graph.

FIGURE 6
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FIGURE 6. I-D thresholds defined at the basin scale under given soil mechanical and hydraulic parameters: (A) c, (B) φ (the thresholds were the same under the condition of 1.1φ and 1.2φ), (C) γs, and (D) Ks.

Supplementary Video 4 (in the supplementary material) and Figure 7 show the variation of thresholds defined at the basin scale when Ks and D0 were 0.7, 0.8, 1.2, and 1.3 times the standard values. Figure 6D shows the comparison of thresholds defined at the basin scale under given Ks values. The results showed that the variation in Ks did not significantly influence the position of thresholds defined at the basin scale. The threshold with higher Ks had a larger applicable duration range. Meanwhile, under the condition evaluated, D0 did not influence the position of thresholds defined at the basin scale.

FIGURE 7
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FIGURE 7. I-D thresholds defined at the basin scale under the conditions: (A) 0.8D0, (B) 0.9D0, (C) 1.1D0, and (D) 1.2D0.

I-D thresholds at the slope unit scale

Supplementary Video 5 (in the supplementary material) show the variation of I-D thresholds defined at the slope unit scale whenc, φ, and γs were 0.8, 0.9, 1.1, and 1.2 times the standard values. Figures 8A–C show the comparison of thresholds defined at the slope unit scale under given c, φ, and γs values, respectively. The results showed that the thresholds with higher c or φ tended to be the higher part of the graph. The thresholds with higher γs tended to be the lower part of the graph.

FIGURE 8
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FIGURE 8. I-D thresholds defined at the slope unit scale under given soil mechanical and hydraulic parameters: (A) c, (B) φ, (C) γs, and (D) Ks.

Supplementary Video 6 (in the supplementary material) and Figure 9 show the variation of thresholds defined at the slope unit scale when Ks and D0 were 0.7, 0.9, 1.1, and 1.2 times the standard values. Figure 8D shows the comparison of thresholds defined at the slope unit scale under given Ks values. The results showed that the variation in Ks did significantly influence the position of thresholds defined at the slope unit scale. The thresholds with higher Ks tended to be applicable to large duration ranges. D0 did not influence the position of thresholds defined at the slope unit scale under the condition evaluated.

FIGURE 9
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FIGURE 9. I-D thresholds defined at the slope unit scale under the conditions: (A) 0.8D0, (B) 0.9D0, (C) 1.1D0, and (D) 1.2D0.

I-D thresholds at the grid cell scale

A monitored unstable slope is located near a coal mine in the study area. A buffer zone was built with a radius of 50 m around the unstable slope (Figure 10). I-D thresholds were defined for the grid cells with critical rainfall in the buffer zone.

FIGURE 10
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FIGURE 10. Location of the monitored unstable slope, coal mine, and built buffer zone.

Supplementary Video 7 (in the supplementary material) show the variation of I-D thresholds defined at the grid cell scale when c, φ, and γs were 0.8, 0.9, 1.1, and 1.2 times the standard values. Figures 11A–C show the comparison of thresholds defined at the grid cell scale under given c, φ, and γs values, respectively. The results showed that the thresholds with higher c or φ tended to be the higher part of the graph. The thresholds with higher γs tended to be the lower part of the graph.

FIGURE 11
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FIGURE 11. I-D thresholds defined at the grid cell scale under different soil mechanical and hydraulic parameters: (A) c, (B) φ (the thresholds were the same under the condition of 1.1φ and 1.2φ), (C) γs, and (D) Ks.

Supplementary Video 8 (in the supplementary material) and Figure 12 show the variation of I-D thresholds defined at the grid cell scale when Ks and D0 were 0.7, 0.9, 1.1, and 1.2 times the standard values. Figure 11D shows the comparison of thresholds defined at the gird cell scale under given Ks values. The results showed that the variation in Ks did significantly influence the position of thresholds defined at the grid cell scale. The thresholds with higher Ks tended to be applicable to large duration ranges. D0 did not influence the position of thresholds defined at the grid cell scale under the condition evaluated.

FIGURE 12
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FIGURE 12. I-D thresholds defined at the grid cell scale under the conditions: (A) 0.8D0, (B) 0.9D0, (C) 1.1D0, and (D) 1.2D0.

Discussion

The methods of defining rainfall thresholds at different scales have their own characteristics. At the basin scale, given that the threshold is defined for the entire area, the process is the simplest. However, the defined threshold can only judge the occurrence of landslides and cannot provide detailed spatial information for landslide prediction. At the slope unit scale, given that the thresholds are defined for slope units with critical rainfall, the process is relatively complicated. The defined thresholds can provide spatial information specific to the range of slope units for prediction. At the grid cell scale, given that the thresholds are defined for grid cells with critical rainfall, the process is the most complicated. The defined thresholds can provide the most spatial information (i.e., specific to the range of grid cells) for prediction. When defining rainfall thresholds at the basin and slope unit scales, an additional condition is used to determine whether I-D conditions cause instability (af>ac). When defining rainfall thresholds at the grid cell scale, the rule for determining whether I-D conditions cause instability is simply Fs<1 without additional conditions.

Soil physical parameters influence the number and position of rainfall thresholds defined at various scales. The number of rainfall thresholds is the number of objects warned by thresholds (i.e., the objects with critical rainfall). At the basin scale, the rainfall threshold was defined for the entire study area, and the entire study area had critical rainfall under the considered conditions in this study. At the slope unit and grid cell scales, the number of rainfall thresholds was positively correlated with γs and negatively correlated with c and φ. Ks and D0 did not cause any variation (Figure 5).

For threshold position, the position of thresholds varied positively with c and φ and varied negatively with γs. Under the considered conditions, Ks did not significantly influence the threshold position. The thresholds with higher Ks were applicable to larger duration ranges. D0 did not influence the threshold position. Marin and Velásquez (2020) discovered that Ks did not produce a noticeable variation on the position of the I-D threshold defined at the basin scale, and D0 did not affect the position of threshold, which are in line with the results of this study. Wu et al. (2017) conducted a sensitivity analysis of soil physical parameters to evaluate the rainfall threshold determined by using TRIGRS. In the literature (Wu et al., 2017), rainfall threshold is defined as the critical rainfall condition causing the simulated Fs to be less than a specific critical value under a specific warning duration. Actually, this study conducted the sensitivity analysis of soil physical parameters to Fs. Wu et al. (2017) proposed that Fs varied positively with c and φ, negatively with γs. c, and φ, and γs affected Fs more significantly than Ks and D0. Thus, the influence of soil physical parameters on the position of rainfall thresholds is the same as the influence on Fs.

TRIGRS does not have a function for defining rainfall thresholds. Rainfall thresholds are defined by analyzing the relationship between the output Fs grid and the input rainfall conditions of TRIGRS. The conditions for determining landslide occurrence differ in defining rainfall thresholds at various scales. The methods at the basin and slope unit scales take the condition that serval grid cells with Fs<1 exist for given rainfall conditions to determine landslide occurrence, which is to analyze the overall behavior of unstable grid cells. The method at the grid cell scale analyzes the individual behavior of a single unstable grid cell by treating a single grid cell with Fs<1 as a landslide. The variation of Fs of a random single grid cell directly influences the definition of rainfall thresholds at the grid cell scale. For example, under the conditions of c was 0.8 and 1.2 times the standard value, the variation in the number of grid cells with Fs<1 is 10,104. The variation directly caused the variation of 10,104 for the number of rainfall thresholds defined at the grid cell scale. However, the variation only caused the variation of 10 for the number of rainfall thresholds defined at the slope unit scale. Thus, the method at the grid cell scale is easier affected by the uncertainty and spatial variability of soil physical parameters.

Conclusion

The influence of soil mechanical and hydraulic parameters on the definition of I-D thresholds based on TRIGRS can be divided into the influence on the number of rainfall thresholds and threshold position.

The number of rainfall thresholds defined at the slope unit and grid cell scale decreased with c and φ, increased with γs, and did not vary with Ks and D0. Under the considered conditions, the number of thresholds defined at the basin scale was not affected by soil physical parameters.

The position of rainfall thresholds varied positively with c and φ and negatively with γs. Ks did not produce a noticeable variation in the threshold position. D0 did not influence the threshold position. The thresholds with greater Ks were applicable to larger duration ranges.

Soil mechanical and hydraulic parameters have less effect on rainfall thresholds defined by analyzing the overall behavior of unstable grid cells (i.e., basin and slope unit scales) than the thresholds defined by analyzing the individual behavior of unstable grid cells (i.e., grid cell scale).

Data availability statement

The data analyzed in this study are subject to the following licenses/restrictions: The data presented in this research are available from the corresponding author by reasonable request. Requests to access these datasets should be directed to Qigang Jiang, jiangqigang@jlu.edu.cn.

Author contributions

SZ collected the soil samples, designed the analysis, performed the analysis, and wrote the original draft. XX developed a Python program for the definition of rainfall thresholds. The other authors helped to draft the manuscript.

Funding

This study was supported by The First Surveying and Mapping Institute of Guizhou Province under Grant number GZWH-2021-4536Y.

Acknowledgments

We thank The First Surveying and Mapping Institute of Guizhou Province for the assistance in the field sampling.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2022.971655/full#supplementary-material

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Keywords: shallow landslides, rainfall thresholds, I-D thresholds, TRIGRS, physically based method, soil mechanical and hydraulic parameters

Citation: Zhang S, Jiang Q, Xu X, Tao G, Zhang Z, Gao X and He C (2022) Influence of soil mechanical and hydraulic parameters on the definition of rainfall intensity and duration thresholds based on Transient rainfall infiltration and grid-based regional slope-stability model (TRIGRS). Front. Earth Sci. 10:971655. doi: 10.3389/feart.2022.971655

Received: 17 June 2022; Accepted: 31 August 2022;
Published: 27 September 2022.

Edited by:

Jia-wen Zhou, Sichuan University, China

Reviewed by:

Min Xiong, Tongji University, China
Elena Benedetta Masi, University of Florence, Italy

Copyright © 2022 Zhang, Jiang, Xu, Tao, Zhang, Gao and He. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Qigang Jiang, jiangqigang@jlu.edu.cn

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