The Impact of Geological and Rainfall Characteristics on Slope Stability Analysis in Shallow Landslide Modelling using the TRIGRS Model

West Java Province has a high potential for susceptibility to landslides. West Bandung Regency is one of the regions in West Java which has high occurrences of landslides triggered by rainfalls. Rainfall-induced landslides in this region have occurred 165 times during rainfall in the last ten (10) years. An effort to predict the landslide occurrences in this region requires the knowledge of factors affecting the hillslope stability. This paper aims to (1) evaluate the parameters affecting slope stability, (2) determine rainfall characteristics affecting slope, and (3) evaluate the performance of TRIGRS model - ling. This study applies a deterministic method using the model of TRIGRS to analyze the effect of one-day antecedent rainfall intensity on the instability of hillslopes. The parameters used in this study are based on field investigation, geo - logical and topographical maps, soil engineering properties, and historical rainfall data. The effect of one-day antecedent rainfall intensity was considered in two scenarios, i.e. 6 hours and 12 hours of antecedent rainfall. Modelling results show that hillslope instability in the study areas is affected by many factors, such as hilly morphology, steep slopes, low shear strength parameters, weathering of volcanic rocks, and the lineament density of geological structures. The modelling simulation also indicates that landslide occurrences in this study area are initiated by a long antecedent rainfall period. Based on ROC analysis, the TRIGRS model shows that the model performance evaluation is in good agreement for mod - elling slope stability against actual landslide events.


Introduction
In Indonesia, landslides are geological disasters that often occur.Landslides are widespread during long periods of heavy rain (Tohari, 2018).The main parameter that triggers landslides is rainfall (Polemio and Petrucci, 2000;Farahmand and Kouchak, 2013).Landslides triggered by rain are generally shallow (Lepore et al., 2012;Tranet al., 2017) and are associated with reduced shear strength soils and soil weathering grade (Sugianti et al., 2022).Rain infiltration induces a rise in groundwater tables and causes the soil to saturate due to increased pore water pressure, causing a reduction of soil strength properties and decreasing slope stability, thus triggering landslides (Iverson, 2000).
The efforts to minimize landslide risk require a better understanding of rainfall intensity characteristics as triggering factors of landslides.Researchers have studied the correlation between the characteristics of rainfall and landslide events as fundamental to determining and de-veloping the warning system for real-time regional landslides (Lateh et al., 2013;Hong et al., 2018).The increase in rainfall intensity as a triggering factor for landslides causes an additional load on the slopes and an increase in pore-water pressure (Iverson, 2000;Muntohar and Liao, 2008).Landslides can occur even over long periods of rainfall, and the rainfall intensity will be lower due to the effect of previous rainfall (Huang and Lin, 2002;Bai et al., 2014).Landslide disasters can cause natural damage, social and economic losses, injuries, and deaths (Turner, 2018;Aristizábal and Sánchez, 2020).Mitigation and preparedness efforts to reduce landslide risk require analysis of slope stability in landslide risk areas and awareness of the causes of slope instability.
West Java Province has a high potential for susceptibility to landslides.The West Bandung Regency in West Java has the highest landslide hazard triggered by heavy rainfall.Regarding the landslide susceptibility map for West Java of the Geological Agency, Center for Volcanology and Geological Hazard Mitigation from Indonesia, the West Bandung area has a medium to high level of susceptibility.Figure 1 shows that landslides occurred 178 times in the West Bandung area during rainfall in one decade.So, landslide disasters have occurred almost yearly in the last decade in this region.Thus, to minimize the landslide hazard risk in West Bandung, knowledge of how rainfall influences landslide susceptibility in this region is necessary.This knowledge is obtained through a spatial landslide susceptibility modelling study.
Previous researchers have carried out various modelling using GIS (Geographical Information System) methods for landslide susceptibility.Several studies, including Lee and Sambath (2006), and Chauhan et al.
(2010) used a logistic regression method that related the probability of landslide occurrence to independent variable parameters and the analytical hierarchy process (AHP) methods that consider many objective and subjective factors in ranking weighting (Hadji et al., 2018;Zhao et al., 2017) in statistical approaches to create landslide hazard zone maps.Other research has been conducted to map landslide hazards using the weighted value method (Sugianti et al., 2014).Models of probabilistic evaluation utilize multiple logistic regression analysis (Kawagoe et al., 2010;Lee and Pradhan, 2006).Landslide susceptibility statistical models highly depend on the input data of historical landslides.Some studies also focused on the landslide processes using the deterministic approach to predict regional-scale landslides (Baum et al., 2005;Simoni et al., 2008).
According to the landslide mechanism, rainfall infiltration can cause an increase in pore-water pressure from negative to positive pore-water pressure on shallow landslides.The role of rainwater infiltration in slope stability is very complex (Tran et al., 2017).Previous research combines a model of the physical-based model and the hydrogeological model for mapping shallow slope stability triggered by rainwater infiltration, such as the SINMAP, SHALSTAB, TRIGRS, GEOtop-FS, and TiVaSS models.The SINMAP considers a model of the parallel failure plane to the soil surface that calculates the stability of an infinite slope that complements the stability of gravity, soil shear angle, and cohesion in the failure plane on the soil surface of the slope (Kawagoe et al., 2010).The SHALSTAB model combines the analysis of infinite slope stability and the model of a steady-state hydrological condition for assessment areas with the potential for landslides (Pack et al., 1998).The GEOtop FS method is the most complex physics model based on the prediction of landslide susceptibility spatially and temporally by involving an association of twodimensional surface runoff with three-dimensional unsaturated subsurface flow (Dietrich et al., 1998).The development of TRIGRS is based on a one-dimensional model of vertical infiltration to predict the simple stability of an infinite slope (Baum et al., 2005).Meanwhile, the TiVaSS model is a physically based model that uses Richards' 3-D formulation and stability of the infinite slope basic equation for landslides of shallow depth due to rainfall (Simoni et al., 2008).
In order to predict the susceptibility of hillslopes to rainfall-triggered shallow landslides, the TRIGRS model -a grid-based regional slope stability model, is most commonly used (Baum et al., 2002).TRIGRS calculates the change of the transient pore pressure and an attendant change in the slope safety factor due to rainfall infiltration using the linearized Richards formula by Iverson (2000) and Baum et al. (2002).In contrast, other physical models do not consider the transient transformation of saturation induced by rainfall infiltration (Baum et al., 2002).The advantage of TRIGRS is that the model is capable of estimating trigger factors that are sensitive to landslides (Baum et al., 2010), zoning susceptibility maps (Pack et al., 2013;Sugianti et al., 2016), and predicting landslides (Zhuang et al., 2017).Although previous studies have shown that the TRIGRS performance is comparable with other models, such as the TiVaSS (Tran et al., 2017), and SHALSTAB (Marin et al., 2021b), however, its capability to analyze the change of transient pore-water pressure provides good results in identifying landslide-susceptible areas (König et al., 2021).
An effort to predict landslide occurrences requires the knowledge of factors affecting the hillslope stability.Previous papers have discussed the landslide susceptibility of the West Bandung Regency region using the TRIGRS method approach (Hermawan, 2023).However, this study has not yet considered the effect of different rainfall intensities on shallow landslide susceptibility in the region.In this current study, we used the TRIGRS model to analyze the effect of rainfall intensity characteristics on shallow landslide susceptibility in the West Bandung Region.This study aims to (1) evaluate the parameters that affect slope stability, (2) determine the characteristics of rainfall that affect slope stability, and (3) assess the TRIGRS model performance to identify potential landslides triggered by rainfall.In this Copyright held(s) by author(s), publishing rights belongs to publisher, pp.147-166, DOI: 10.17794/rgn.2023.4.12 study, the TRIGRS model is implemented to produce a landslide susceptibility map under the effect of the oneday antecedent rainfall intensity.The results of the initial condition model are compared with those of 6-hour and 12-hour rainfall models to determine rainfall characteristics triggering landslides.The receiver operating characteristics (ROC) analysis is used to evaluate the capabilities and effectiveness of the TRIGRS model in predicting areas prone to shallow landslides.Furthermore, the paper also thoroughly analyzes causative factors that influence landslide prediction in the study location.

Area general condition
The study area is located in the West Bandung Regency on the coordinates 9216779 -9250979 N and  751683.7 -785108.7 E in UTM 48 S Zone, on the west side of the Bandung basin, West Java Province, Indonesia (see Figure 2).This study area covers approximately 1,145 km 2 .Figure 2 shows the digital elevation model of the study area based on 1:25.000digital maps produced by DEMNAS, Geospatial Information Agency, Indonesia (https://tanahair.indonesia.go.id/demnas/#/ demnas).The highest elevation is 2,049 meters above sea level.According to Figure 2, the geomorphology of the study area mainly consists of hilly landscapes to high hills.This geomorphological condition contributes to the landslide susceptibility of the hilly landscape during the rainy season.

Geology of the research area
Based on the regional geological map shown in Figure 3, the study area stratigraphy is made up of rock formations ranging from old to young, namely the Rajamandala Formation of Oligocene -Early Miocene with lithological characteristics of clay, marl clay, marl, quartz sandstone, and conglomerate; the Jampang Formation composed of dacite tuff sandstone, pumice tuff, breccia, and tuffaceous clay (Koesmono and Kusnama, 1996); the Citarum Formation of Miocene age, characterized by breccia lithology, sandstone, siltstone; the Jatiluhur Formation of Early Miocene age with lithological characteristics of limestone, marl, quartz sandstone, basalt, and tuffaceous breccia; the Beser Formation of Early Miocene to Middle Miocene age, with tuffaceous breccia and lava lithology and andesite to basalt composition; the Cimandiri Formation of the older Middle Miocene composed of alternating claystone and light to medium gray siltstones, and yellowish-brown sand-stones, locally calcareous, locally consisting of lava deposits composed of tuff, andesite breccias, and tuff breccias; the Cantayan Formation of Middle Miocene age with lithological characteristics of clay, marl, sandstone, limestone, shale, and breccia; the Subang Formation of Late Miocene, dominated by breccia, claystone, and sandstone lithology; the Cilanang Formation of Late Miocene with characteristics of the lithology of sandstone with molluscs, marl, limestone; the Citalang Formation of Pliocene age with lithology characteristics of tuffaceous marl, interspersed by tuffaceous sandstones and conglomerates (Silitonga, 1973); the Pleistocene intrusion of hornblende andesite, pyroxene andesite, and andesite; Quaternary Old Volcanic deposits characterized by breccia lithology, lahars, and layered tuff sandstone with a gentle slope; and Quaternary Young Volcanic deposits with lithology characteristics in the form of tuffaceous sandstone, lapilli, tuffaceous breccia, lava, and agglomerates originating from Mount Tangkubanparahu and Mount Tampomas.
Other rock formations of the fluvial depositional environment are also present in the study area, namely, Holocene Lake Deposits composed of lithology silt, clay, fine sand, coarse sand, gravel, and tuffaceous conglomerates; and Holocene Alluvium consisting of silt, clay, fine sand, coarse sand, and gravel sand as well as chunks of igneous and sedimentary rocks.
The regional geological structure developed in this study location is characterized by folds and faults (Sudjatmiko, 1972).They consist of the Cipongkor syncline, the normal fault in the Cipatat area of the Rajamandala Formation Citarum Formation and Beser Formation, and the strike-slip fault in the Cipeundeuy area of the Ja-

Topographic slope
For the analysis of digital topographic maps, input data for topographic slope parameters are acquired from DEM-NAS with a scale of 1:25,000.The digital elevation model (DEM) of the study area was created using the GIS software.The DEM was divided into grids of 25 m×25 m (see Figure 4).Data sets of local landslide inventory were collected from field surveys, visual identification from Google Earth, and the database of the Center for Volcanology and Geological Hazard Mitigation, Indonesia, with a total of 113 landslide events.The study area is mainly located at the elevation of 500-1,000 meters above sea level around 64.3% of the total area.The landslide event in this study is approximately 70.8% distributed in that elevation (see Figure 4, shown in yellow).
The DEM is then used to generate raster maps of flow direction and slope.The DEM is also used to produce the slope gradient distribution of each cell.Figure 5 depicts the characteristics of a hilly morphology mainly consisting of hilly landscapes to high hills in the north-east and southwest.Besides, the transformation from flat to hilly area is well seen in the central areas to the east.As indicated in Figure 5, the history of landslide events is prevalent in hilly areas with moderate to steep slopes with slope angles ranging from 21% to 54%.Thus, slope angles significantly contribute to landslide occurrences in the study area.In implementing runoff routing calculations, it is necessary to know the direction of the downslope cells that limit the steepest in correspondence with each cell in the TRIGRS model.
The research location was dominated by the northward flow direction covering an area of 226 km 2 to the Cipatat, Cililin, and Gununghalu area, the westward flow direction covering an area of 223 km 2 to the Cililin, Cipatat, Padalarang, and Cisarua area, and the south-  ward flow covering an area of 189 km 2 to the Padalarang, Ngamrah, Parompong, and Batujajar area, and the eastward flow direction covering an area of 172 km 2 up to the Gununghalu, Cililin, and Sindangkerta area.The landslide distribution is located in eight directions: north (22% of events), south (19% of events), west (16% of events), east (19% of events), northwest (10% of events), southeast (19% of events), southwest (19% of events), and northeast (19% of events) shown by an arrow (see Figure 6).

Soil engineering properties
In this research, undisturbed soil samples were taken from several locations representing different geological units using a soil sampler (see Figure 7) to obtain physical and engineering soil properties required for the infiltration process and slope stability calculation in the TRI-GRS model.Laboratory tests include soil unit weight (γ w ) test and shear strength test.Shear strength parameters, the effective soil cohesion (c'), and the effective shear angle (φ') were obtained from triaxial compression tests in consolidated undrained conditions.The saturated hydraulic conductivity coefficient (Ks) was determined using the falling head permeameter tested.Table 1 shows the summarized soil properties for each geological unit.
TRIGRS modelling also requires input parameters related to soil hydraulic diffusivity.Soil hydraulic diffusivity, D 0 , was determined as the correlation of the coefficients of saturated hydraulic conductivity (Ks), where previous studies found approximately 10-500 times the hydraulic conductivity value in colluvium soil (Park et al., 2013).This study assumes that 100 times the Ks value (Baum et al., 2005) given by: Figure 8 presents maps of soil engineering properties overlayed with landslide location distributions obtained based on Table 1.Because the soil properties data are rare for each rock formation, the spatial join analysis tool available in GIS software was used to create a map of soil engineering properties using Table 1.This analytical method was also used in the study of regional rainfall-induced slope failures in Malaysia (Saadatkhah et al., 2015).A raster map of soil engineering properties was created using the polygon to raster GIS conversion tool for all value parameters for each geological unit.Figure 8A presents the distribution of landslide occurrence in the soil unit weight map.Most of the landslide occurrences are located in hilly areas of low soil unit weight.In Figure 8B, the landslide incidents are dominantly distributed in hilly areas with low saturated hydraulic conductivity coefficients.Low hydraulic conductivity indicates the slope surface capability to pass water at a prolonged flow rate in these areas.So, when the hydraulic conductivity of the soil is poorer, the water is retained longer, and the soil becomes more saturated.Soil saturation can occur when there has been a lot of rain for a long time (Hong et al., 2018;Huang and Lin, 2002).Saturation causes an increase in the pressure of pore water and eventually causes a decrease in the strength of soil shear, consequently triggering susceptibility landslides.It is evident in Figure 8C and Figure 8D that most landslide occurrences are mainly in hilly areas with low soil cohesion and friction angles.In other words, the hilly areas with low soil shear strength are very prone to rainfall-induced landslides.

Soil Thickness
Morphology and relief are factors that influence the formation process of soil thickness.In areas with high elevations or in the hills, the soil layer is thinner due to erosion, whereas a thicker soil layer is formed due to the sedimentation process in flat areas.So, for the effective soil thickness parameter, it is assumed spatially using the linear equation function of the elevation.The soil thickness is also an essential parameter in the TRIGRS model (Baum et al., 2002).Soil thickness affects infiltration and soil cohesion in deterministic shallow landslide models.
Mapping soil thickness is complex, costly, and timeconsuming.Several methods of spatial interpolation are applied to mapping various soil thicknesses using the function of terrain attributes: elevation (

Groundwater table
Shallow slope failure occurrences are mainly due to rising groundwater tables and pore water pressure.So, the groundwater table is one of the hillslope stability controlling parameters.In this study area, the measurement of groundwater depth conducted in 6 dug wells at landslide locations indicates that a shallow groundwater level was of about 1 to 4 m with an average depth of 2.5 m present in the study area (see Figure 7).Therefore, based on TRIGRS' ability to predict the occurrence of shallow slides with slip planes near the surface slopes, this study applied an average groundwater depth of 2.5 m in the TRIGRS modelling.

Rain intensity and return period
Rainfall data for this study was collected over 35 years from several meteorological stations distributed in the study area.Based on the collected rainfall data, the daily maximum rainfall data were determined (see Figure 10) and then analyzed using the Gumbel distribution theory to obtain probability and rainfall distribution curves (see Figure 11).
As mentioned previously, there has been an increase in landslide occurrences in the study area during the last ten years.According to Figure 11, the rainfall for a 10year return period is 111 mm/day, with a probability of around 68%. Two scenarios of rainfall intensity and duration were considered for the susceptibility modelling to evaluate the influence of different rainfall characteristics on landslide susceptibility in the study area.Scenario A considered a short period of rainfall, which was assumed to last for 6 hours in one day prior to the landslide.In scenario B, a long period of rainfall was considered to last for 12 hours one day prior to the landslide incident.Long-duration rainfall causes fewer antecedent rainfall-induced landslides (Huang and Lin, 2002).The rainfall intensity for short and long-period scenarios was determined using Mononobe's formula (Fang and Chen, 1995) as shown in Equation 3, as follows: (3) Where: I -the rain intensity plan (in mm/hour), R 24 -the daily maximum rainfall in 24 hours (in mm/ day), t -rain duration (in an hour).Table 2 shows rainfall intensity and duration determined using Mononobe's formula for each scenario used in the TRIGRS model.For scenario A, a short period of heavy rain of 6 hours was characterized by a rainfall intensity of 11.65 mm/hour.Meanwhile, the rainfall intensity of 7.43 mm/hour for 12 hours represents the long period of light rain in scenario B.

The TRIGRS Model
The USGS developed a Transient Rainfall Infiltration and Grid-based Regional Slope-Stability Analysis.The model is called TRIGRS.This model was applied to analyze rainfall-induced landslides in this study (Baum et al., 2002).TRIGRS is a model used to compute slope stability using analytical solutions to calculate the safety factor value to transient pore water pressure using an infinite slope analysis approach to rainfall-induced ( BaumCopyright held(s) by author(s), publishing rights belongs to publisher, pp.147-166, DOI: 10.17794/rgn.2023.4.12 et al., 2002; Baum et al., 2010).This model was designed using the FORTRAN programming language.TRIGRS is crucial for mapping landslide occurrence, prevention, and investigations.TRIGRS can be used as a land-use design for regional areas against landslide hazards.TRIGRS requires input parameters, i.e. soil hydraulic condition, parameters of shear strength soil, and rainfall infiltration.Except for the rainfall rate parameter, input parameters for this TRIGRS modelling in this study vary spatially (see Table 3).
The infiltration in the TRIGRS model applied a linear principle (Iverson, 2000) and an extension of Richard's formula.Iverson's infiltration formula consists of steady and transient conditions.A steady state is a condition at the initial filtration input rate and the inclination angle where the flow is in an unbalanced direction (Iverson, 2000).Transient infiltration is a condition that considers the flow of vertical downward, the surface flux of varying time series for variable intensity and duration, and the condition of zero-flux at times more than the early border of infinitely deep basal (see Figure 12).
The following formula gave the pore pressure for layers saturated of the basal zone with ψ as the groundwater pressure head at depth Z and time t.Z originates z/cos δ where Z is positive in the downward direction and depth below the ground surface; δ is the slope angle; z is normal to the slope angle and the t parameter is the time.d is the steady-state depth of the water table measured in the vertical direction, d LZ is the saturated layer depth in the basal zone measured vertically, β = cos 2 δ −(I ZLT /Ks), Ks is the saturated hydraulic conductivity in the Z direction, I ZLT is the steady surface flow, I nZ as the surface flow of a given intensity for the nth time interval.Further, D1 originates D0/ cos 2 δ, the saturated hydraulic diffusivity (D0) = Ks/ Ss, the saturated hydraulic conductivity (Ks), and the specific storage (Ss).N is the total number of time intervals; H(t−tn) is the Heaviside step function, and tn is the time at the nth time interval in the rainfall infiltration sequence; erfc(η) is the complementary error function: ierfc(η) = (1/√π) exp(−η 2 )− ηerfc(η) m is the index of infinite series displaying an odd term in the complementary error function, given by Baum et al. 2002: (4) In this model study, the safety factor (SF) calculation uses an analytical formula to analyze the failure of an infinite slope, described as the ratio of the resistive force to the driving force on the slope.A safety factor formula of an infinite slope in the model uses parameters including φ' as the effective friction angle of the soil and c' as the effective soil cohesion.Further, ψ (Z,t) is the pres-  Copyright held(s) by author(s), publishing rights belongs to publisher, pp.147-166, DOI: 10.17794/rgn.2023.4.12 sure head in the saturated zone at depth Z and time t, γ s is the unit weight, γ w is the unit weight of water, and θ is the sliding plane angle for each grid cell given by (Iverson, 2000): (5) The slope safety factor is controlled by the strength of resistance and stress shear acting in the slip plane.A safety factor is a value that states the condition of slope stability abbreviated with the SF value.The slope is stable on the condition that an SF value of more than 1.0; otherwise if it has an SF value less than 1.0, it is unstable.Equations (4) and ( 5) are combinations of the value of the safety spatial distribution calculated based on rainfall and parameter input data.
Soil engineering properties were determined from laboratory tests on undisturbed samples from different geological units that formed raster with cell pixels 25x25 m.

ROC (Receiver Operating Characteristic) curve
In modelling, a method to illustrate the classification model performance of all classification thresholds uses analysis of the receiver operating characteristic curve (ROC).The ROC curve is a method to visualize, organize, and select the classifier based on model performance (Fawcett, 2006).ROC is a two-dimensional graph with the proportion of false positives (specificity) as the prediction rate on the horizontal axis and the proportion of true positives (sensitivity) as the success rate on the vertical axis (see Figure 13).In this respect, the ROC curve as an independent threshold method is used to evaluate the influence of the causal factor parameters on landslides (threshold-independent method) (Chung and Fabbri, 2003).The ROC forms part of the unit square area whose value is between 0 and 1.0, called AUC or Area Under Curve.In other words, the AUC is an area under the ROC curve to measure an ability model classifier.The AUC value is one type of statistical accuracy for predictive (probability) models in natural disaster assessment analysis.Evaluation of model performance accuracy based on the AUC value of the ROC curve can be classified into five groups (see Table 4).In this study, the ROC curve analysis was conducted to evaluate the level of significance of each parameter in controlling the landslide susceptibility of the TRIGRS modelling results.
The AUC calculation formula used in this study by Beguería (2006) is as follows: Where: x i -the proportion of landslide area (%) y i -the proportion of landslide events (%).

Effect of rainfall on spatial and temporal slope stability
Figure 14 shows the results of the TRIGRS model for the initial condition for scenarios A and B, which indicates the hillslopes in the study area are in a dominantly stable condition (SF > 1.0).The unstable hill slope (SF < 1.0) was dominantly distributed only in the northeastern part of the study area as indicated by a blue circle, characterized by steep to very steep slopes and thin soil thickness.Thus, factors such as slope angles and soil thickness are

AUC index values
Classification 0.9 -1.0 Very Good 0.8 -0.9 Good 0.7 -0.8 Fairly Good 0.6 -0.7 Bad 0.5 -0.6 Incorrect The results of slope stability modelling for each scenario, represented in Figure 15 and Figure 16, show that the unstable hillslope areas significantly in both scenarios at the end of the rainfall period.This proves that any rainfall intensity of a given duration affects the stability of hillslopes in the study area, especially on moderate-to-steep hillslopes.The modelling results also revealed that steep hillslope areas with high stability remain stable for both scenarios.Referring to Figure 8, the cohesion and friction angles of the steep hillslopes are significantly high.This modelling result demonstrates that rainfall infiltration could not reduce the stability of steep hillslopes made up of soil layers of higher shear strength.In other words, soil shear strength plays an important role in maintaining the stability of steep hillslopes during a rainfall period.

Effect of rainfall characteristics on landslide susceptibility
Based on the results of the TRIGRS modelling, the histogram graph shows a decrease in the stable slopes area and an increase in the unstable slopes area from the first hour to the last hour.Figure 17 and Figure 18 show the expansion of the unstable slope area by approximately 11.5% in scenario A and 16.4% in scenario B. These results implied that the rainfall intensity can affect the stability of the hillslope, from stable to unstable condi-tions, as indicated by a decrease in the slope safety factor (SF) value, hence, the hillslope is prone to landslides.
Based on the comparison, the modelling result shows that the influence of the one-day antecedent rainfall was perceived in two scenarios, i.e. 6 hours and 12 hours.Figure 19 shows that a long period of antecedent rainfall affects the hillslope stability more significantly than a short period of rainfall in the study area.Based on this figure, it is very obvious that rainfall of long duration makes the slopes more unstable (scenario B) because rainwater that infiltrates into the slopes is retained longer, and hence, the slopes become more saturated than short durations (scenario A).Therefore, the duration of rainfall has a more significant impact on slope stability than rainfall intensity.

Relationship between landslide susceptibility and geological conditions
The relationships between the landslide inventory data and the TRIGRS modelling results for every rock formation are shown in Figures 20 and Figure 21.Based on these figures, events mainly occurred in the Beser Formation which is dominantly composed of volcanic rocks.The TRIGRS modelling also shows the unstable hillslope mainly concentrated in the Beser Formation.Thus, the TRIGRS modelling results have a good correlation with the landslide inventory data.
The TRIGRS modelling results demonstrate that the landslide susceptible areas increase with rainfall duration in both scenarios.In scenario A, the unstable hillslope areas cover up to 63.67 km 2 in the Beser Formation, 20.68 km 2 in the Citalang Formation, and 11.22  km 2 in the Citarum Formation when the rainfall period ends (see Figure 20).Similarly, the landslide-susceptible areas in scenario B increase from T0 to T12, reaching up to 80.97 km 2 in the Beser Formation, 49.18 km 2 in the Citalang Formation, and 19.23 km 2 in the Citarum Formation (see Figure 21).Thus, according to the modelling results, the rock formation also affects the land-slide susceptibility in the study area.In all rainfall scenarios, the Beser rock formation is more prone to landslides than other rock formations, and its susceptibility increases more significantly under the increase in rainfall duration.In other words, rainfall duration has a more pronounced effect than rainfall intensity on landslide susceptibility in the study area.Figure 22 shows the distribution of unstable hillslopes in areas that have developed geological structures.From this figure, it can be seen that some historical landslide events were distributed in the areas of high lineament density.Thus, the geological structure can be one of the controlling factors of landslide susceptibility because it is associated with the weathering process of the rock, by which the rock becomes more permeable.Consequently, the rainwater can infiltrate the rock through the weathered weak zone.The distribution of unstable hillslopes is also found in steep hilly areas without geological structure in the Cililin and Sinandgkerta areas (shown in the blue rectangle).These areas are geologically made up of volcanic rocks (see Figure 3).Referring to Figure 3 and Figure 8, the hillslopes of the Beser Formation are very prone to landslides because the soils have low shear strength.Thus, the hilly areas without any geological structure influences, soil shear strength will control the susceptibility of the areas to landslides.
Other soil property parameters, such as hydraulic conductivity (Ks) and unit weight of soils (gs) also have a significant control on the hillslope susceptibility to landslide.Referring to unit weight and hydraulic conductivity maps (see Figure 8A and Figure 8B) and the TRIGRS modelling result (see Figure 16B), hillslopes with low to medium Ks and g s are more susceptible to landslides than those with high Ks and g s .Low soil coefficients of hydraulic conductivity cause the soil to retain the rainwater for a long time, resulting in the saturation of the soil layer during a rainfall period.Thus, infiltration of rainwater into low hydraulic conductivity soils is more sensitive to rainfall duration than to rainfall intensity (Aristizábal et al., 2020).Similarly, hillslopes with a low soil unit weight are also more prone to landslides because the hillslopes are made up of clay-rich soils of low hydraulic conductivity that will control the soil saturation as explained previously.Thus, it is clear that the physical and mechanical properties of soils may influence the landslide occurrences in the study area.Some previous studies (Mugagga et al., 2011;Zung et al., 2009) also indicated that the stability of any hillslope is       influenced by specific soil parameters such as bulk density, and shear strength, among others.
The influence of soil type on landslide susceptibility in the study area is also examined.made up of andosol soils around Cisarua, Cililin, and Cipongkor (see blue rectangle).Other landslide-susceptible areas are made up of latosol soils.Thus, the most dominant soil types sensitive to landslides are andosol and latosol soils, and both have resulted from weathering volcanic rocks.A landslide study in Karanganyar Regency Central Java also found that these two soil types are sensitive to landslides (Priyono et al., 2023).

Validation and evaluation of TRIGRS landslide susceptibility
Validation was performed using landslide inventory data obtained from the Center for Volcanology and Geological Hazard Mitigation data, field mapping, and landslide identification via Google Earth.This validation helps evaluate the level of influence of parameter calculations on the slope SF for each input parameter of the TRIGRS modelling.A validation process was also implemented on the modelling results of TRIGRS to evaluate the success rate of predicting slope stability and determining the model performance of rainfall-induced landslides in the study area.

ROC curve for parameter
The ROC curve analysis shows that the AUC of each parameter value has a reasonably good validation value in modelling slope stability.The AUC value ranges from 0.57 to 0.9 for all slope stability controlling parameters.Referring to Table 4, slope inclination, elevation, and soil thickness are the parameters that will have a significant effect on slope stability modelling.Meanwhile, the saturated hydraulic conductivity, diffusivity, shear strength parameters, and unit weight of soils have less significant control on the modelling (see Figure 24).Thus, this result indicates that slope inclination, elevation, and soil thickness have a more substantial control on slope stability modelling than the shear strength parameters of the soil in the study area.In contrast, the flow direction is the lowest parameter affecting slope stability.This is because this parameter is only used in the TopoIndex program to calculate runoff routes and is not directly involved in the TRIGRS modelling to calculate the SF of the slope.

ROC curve for model
Figure 25 shows the ROC curves to validate the TRI-GRS modelling results for each scenario using the AUC value for each rainfall duration.The models were validated by comparing the percentage of landslides generated from the TRIGRS model in scenarios A and B to the

Effect of rainfall characteristic on hillslope stability
Figure 26 and Figure 27 show the graph of change in the safety factor of hillslope instability models for six historical landslide locations, from the initial condition (T0) to the final condition (T6 and T12) for each rainfall scenario.In the validation process, there are 60.7% of validated inventory data in scenario A and 63.4% in scenario B. The graphs show the safety factor decreases with the increase in rainfall duration to reach the value of less than 1.0.Thus, it is clear that long-duration rainfall of low intensity causes more hillslopes to become unstable.Thus, this study demonstrates that rainfall duration will have a more significant effect than rainfall intensity on the hillslope stability.This is because rainwater that infiltrates into the slope surface is retained longer, causing more soil layers to get saturated, and the developed pore-water pressures become higher during a longer period of rainfall.The landslide study in northwestern Colombia Andes using physically-based models indicates a greater influence of rainfall duration instead of rainfall intensity (Aristizábal et al., 2020).Recent landslide events that happened in the Emilia Romagna, area (Italy) in the middle of May 2023 are an example of the effect of long-duration rainfall on triggering landslides.The landslide initiation required 36 hours of antecedent rainfall with a total rainfall of 300 mm, almost the same amount of rain, that usually falls in seven months.In contrast, Guzzetti et al. (2008) state that average rainfall intensity is more important than rainfall duration to evaluate rainfall conditions triggering shallow landslides and debris flows.

Conclusions
The study presented in this paper evaluates the effect of rainfall characteristics on landslide susceptibility in  Copyright held(s) by author(s), publishing rights belongs to publisher, pp.147-166, DOI: 10.17794/rgn.2023.4.12 the West Java Regency through physically-based models, incorporating the intensity and duration of rainfall, as well as the spatial variability of geological conditions, morphometry, and soil parameters.The study suggests that many factors affect the stability of the hillslopes, among which the slope inclination, elevation, and soil thickness have a primary control on the hill slopes stability in the study area.
The results of TRIGRS modelling indicate that the stability of a hillslope decreases to a critical condition with the increase in rainfall duration because more rainwater will infiltrate into the hillslope and will be retained longer in the soil layer to cause more saturation of the hillslope, and hence, decrease in the hillslope stability.The evaluation of the modelling results suggests that long-duration rainfall of low intensity has a more significant impact on triggering landslides than short-duration rainfall of high intensity.Although this study has predicted the hillslope areas susceptible to rainfall-induced landslide with fair accuracy (AUC = 0.7 -0.8), however, the current landslide susceptibility modelling is still subject to revision.More accurate landslide prediction using the TRIGRS model can be obtained when soil hydraulic and engineering properties data are available for each lithology.So, more detailed geological engineering mapping to obtain soil samples for each lithology for laboratory soil properties determination is recommended.
The results of physically-based shallow landslide prediction using the TRIGRS model provide a baseline for more detailed landslide hazard study and landslide risk assessment.In addition, establishing a landslide susceptibility map can substantially contribute to the landslide hazard mitigation strategies and landslide risk-based spatial planning in the West Bandung Regency.

Figure 3 :
Figure 3: Geological map of the study area in West Bandung Regency.

Figure 6 :
Figure 6: Flow direction raster map and landslide locations.

Figure 5 :
Figure 5: Raster map of the slope angles and occurrences of landslide.

Figure 8 :
Figure 8: The landslide occurrences distribution on soil engineering properties map; (A) unit weight, (B) saturated hydraulic conductivity, (C) effective cohesion, and (D) effective friction angle.
Saulnier et al., 1997), slope inclination (Schilirò et al., 2018), and slope curvature (Montgomery and Dietrich, 1994; Mehnatkesh et al., 2013).Field soil depth observations and the topographic factors derived from DEM produced good soil depth correlation.Thus, this study used a simple relationship that assumes the soil thickness associated with the elevation derived from the DEM map.In this study, the soil depth uses a linear drop elevation function to map spatially (Saulnier et al., 1997), expressed as: m i = m max -(m max -m min /z max -z min ) x (z i -z min )) (2) Where: m min -the minimum effective soil thickness (m), m max -the maximum effective soil thickness in a cell (m), z i -the elevation at point i in a cell (m), z min and z max -the minimum and maximum elevation at a cell, respectively (m).The distribution of soil thickness is shown in Figure 9.The values of the minimum and the maximum soil thickness are 0.05 m and 7.0 m, respectively.
Figure9indicates landslide occurrences are mainly located in hilly areas with a soil layer of 0.58 to 6.85 m thick.As a result, landslides are restricted to hilly areas with soil thicknesses less than 7.0 m in this area.

Figure 9 :
Figure 9: Distribution of landslide occurrences against soil layer thickness.

Figure 11 :
Figure 11: Gumbel's method of the probability distribution curve.

Figure 14 :
Figure 14: TRIGRS modelling results at initial condition scenario A (A) and scenario B (B).

Figure 16 :Figure 15 :
Figure 16: TRIGRS modelling results in scenario B for the 12-hour duration (A) the first 4 hours and (B) 12 hours.

Figure 19 :
Figure 19: Comparison of the area of unstable slopes in scenarios A and B.

Figure 17 :
Figure 17: The area of stable and unstable slopes in scenario A.

Figure 18 :
Figure 18: The area of stable and unstable slopes in scenario B.

Figure 20 :
Figure 20: The total unstable area in each rock formation in scenario A.

Figure 21 :
Figure 21: The total unstable area in each rock formation in scenario B.

Figure 22 :
Figure 22: Relationship between the unstable hillslope area and geological structures.

Figure 23 :
Figure 23: Distribution of soil types on unstable slopes.
Figure 23 shows the slope stability map of the TRIGRS model overlapped with soil type maps for the study area.According to this figure and the slope stability modelling result (see Figure 16b), the unstable hillslopes are mainly in hilly areas Copyright held(s) by author(s), publishing rights belongs to publisher, pp.147-166, DOI: 10.17794/rgn.2023.4.12

Figure 25 :
Figure 25: ROC curve for the models for both scenarios.
(a) AUC for each rainfall duration in Scenario A (b) AUC for each rainfall duration in Scenario B percentage of landslide inventory data.TRIGRS modelling in scenarios A and B have AUC values ranging from 0.7 to 0.77, respectively.The results of this study show that the TRIGRS modelling has fairly good accuracy in predicting rainfall-triggered hillslope instability in this study area.This study proved that rainfall intensity has a significant effect on the decreased hillslope stability.

Figure 27 :
Figure 27: Variation of SF value of hillslope in scenario B for landslide locations shown in the map.

Figure 26 :
Figure 26: Variation of SF value of hillslope in scenario A for landslide locations shown in the map.

Table 1 :
The results of laboratory tests for soil engineering properties.Code Location Effective cohesion c' (Pa) Unit weight (N/m 3 ) Effective friction angle phi' (θ) Porosity (n) Saturated hydraulic conductivity, Ks (m/s) Infiltration rate (m/s) Hydraulic diffusivity, D 0 (m/s)

Table 2 :
Rainfall intensity scenarios used in the landslide susceptibility modelling.

Table 3 :
Input parameters for the TRIGRS model in this study.