Prediksi Jarak Luncur Longsoran Berdasarkan Parameter Geometri Lereng dan Tipe Batuan Landslide Distance Prediction Based on Slope Geometry and Rock Type Parameters

Indonesia is a country that has great potential to experience natural disasters, one of which is a landslide disaster. Based on this fact, a method is needed to predict the range of landslides to minimize the impact of disaster losses. The empirical statistical method is one of the methods that can be used to predict landslides by taking input data from the history of previous landslide events. This research aims to find the best modeling form for sliding distance prediction and which parameters influence a landslide's sliding distance prediction. This study used multiple linear regression methods. The data used in this study are geometric slope parameters in the form of slope height (H), original slope (θ), landslide area (A), and rock type (RT). The data was taken from the 2015-2021 PVMBG landslide investigation report and used the Google Earth and Global Mapper program. Based on the analysis of the best empirical model that can predict the sliding distance of a landslide log Lmax = 0,387 – 0,097 RT + 0,230 log H + 0,458 log A – 0,220 tan θ with an R 2 value of 0,94 and an average estimated error of 31,56%. The parameter that has the most influence on the prediction of sliding distance is the area affected by the landslide (A).


INTRODUCTION
Indonesia is one of the countries that have a great potential to experience natural disasters because Indonesia is located between the confluence of three major world plates, namely the Indo-Australian Plate, the Eurasian Plate, and the Pacific Plate (Subardjo, 2005). As a result of the contact of these plates, Indonesia is a country experiencing quite an active earthquake and volcanic activity. Apart from that, other impacts of the movement of the earth's plates result in various forms of the earth's surface, such as mountainous areas with steep slopes. Steep slopes have the potential to experience landslides when there is heavy rainfall accompanied by ground movement (Rahman, 2015). Topography, climate, geology, and land use, cause slope failure (Nordiana et al., 2018).
Based on the modeling results on slope safety, the combination of loading and soil parameters is the cause of the slope in critical conditions and high landslide potential (Apriani et al., 2021). It is crucial to make predictions about the extent of the impact of landslide events as input into mitigation strategies and plans for strengthening structures, including restrictions on land use. However, topographical factors, landslide mass mechanics, and slope properties make predicting the sliding distance challenging to perform (Roering et al., 2005), meanwhile making landslide models in the laboratory is difficult because modeling the heterogeneity of the flow material in the field is difficult to replicate in the laboratory (Ward & Day, 2006). Statistical models can be used as a primary analysis tool in predicting landslides because the initial conditions of the landslide and the parameters during the landslide are challenging to determine (Crosta et al., 2006). Statistical modeling relates the physical properties of slopes to areas affected by landslides (McKinnon, 2010). The empirical model describes the sliding distance of a landslide based on the relationship between parameters obtained from observations of landslide events in the field. Slopes that fail can provide helpful information about the condition of the soil parameters on a slope at the time of failure and an opportunity to evaluate the stability of other slopes (Apriani et al., 2020). However, this model produces an unclear interpretation, so a geometric, geomorphological, and volume change approach is needed to reduce the error of the resulting model (Hungr et al., 2005). If used, the statistical, empirical method will estimate the extent of the landslide, the extent of the debris flow area, and the various mass movements (Rickenmann, 1999). In addition, statistical, empirical methods can also provide data regarding geological properties that can be applied in the mathematical modeling of landslide mass movement (Rickenmann, 2007). In addition, statistical, empirical methods can also provide data regarding geological properties that can be applied to the mathematical modeling of landslide mass movement (Devoli et al., 2009).
This study describes the physical characteristics of landslides in Indonesia based on the landslide event data that PVMBG has summarized. The data that has been summarized will be analyzed using statistical analysis using the multiple linear regression method using the Statistical Package for the Social Sciences (SPSS) program using the required parameters. Qarinur (2014) proposed a landslide run-out distance prediction model based on geometric parameters but did not consider soil-type parameters. Guo (2013) stated in his research that the rock type is one of the parameters that affect the sliding distance of the landslide, and the height of the slope (H) is the most influential parameter compared to the volume of the landslide source (V) and the slope of the slope (θ) (Apriani et al., 2022).
This research is focused on the prediction model of the sliding distance prediction by considering geometric factors, including the parameter of slope height (H), original slope (θ), and rock type (RT), which has not been done in previous research for cases of avalanches in Indonesia. Hence, This study aims to obtain the best model to predict the sliding distance in Indonesia and to obtain the parameters that most influence the sliding distance of the landslide. The analysis was conducted using the SPSS program to obtain the best model and see the relationship between the review variables. The research results are expected to be used as an initial mitigation effort to minimize the impact of landslide losses.

RESEARCH METHODS
The slope geometry parameters used in his research are described in Figure 1. The difference between the highest point of the landslide event (crown of the landslide) and the perpendicular to the sloping point (foot of the slope) is called the slope height (H). The sliding reach (L) is the horizontal distance from the line perpendicular to the crown of the slide to the farthest reach of the slide movement. The sliding angle (α) is an angle between the landslide crown's highest point and the slide material's most distant direction. Perception of the shadow angle (β) to determine the farthest reach of the rock collapse. The shadow angle (β) is defined as the angle resulting from the line connecting the farthest point of the slide with the slide block. The slope angle (θ) is from the line that unites the highest point of the rockfall down the slope with the three intervals of slope height (Hungr et al., 2005). The type of rock is one of the parameters that affect the sliding distance of the landslide. Soil type (RT) is divided into 4 parts which will be attached in Table 1. (Guo et al., 2014). Landslides consist of softer soil (smaller RT) so that the resulting kinetic energy is consumed more by the friction of the soil. Therefore, these failed ground movements will have shorter glide distances (Guo et al., 2014).
Models with one independent variable were analyzed using simple linear regression. Meanwhile, a multiple linear regression model consisting of slope height and inclination was used to describe the relationship between the dependent variable, the sliding distance of a landslide, and more than one independent variable. Normality, heteroscedasticity, F test, and Ttest are part of the classic assumption test used in this study. Table 2 shows the level of relationship between variables determined based on the value of the coefficient of determination in the resulting model. The higher the coefficient of determination, the stronger the relationship between the parameters reviewed, meaning that the model represents the conditions of the examined parameters.

σ ≤ 15
2) Strongly weathered hard rock 3) Moderately~strongly weathered tuff, phyllite, marl, sandy mudstone, etc. Source: Guo et al., 2014  The partial test or T test is intended to describe the effect of each independent variable on the dependent variable. To explain the individual correlation between the independent variables and the dependent variable, therefore assumptions are made based on the following Equations (1) and (2) as follows.
Equation (1) has a hypothesis that it cannot affect the independent variables with the dependent variable, while Equation (2) has a hypothesis that there is a relevant effect of the independent variables on the dependent variable.
The F test is a test of all independent variables in a model. This test is conducted to prove whether the independent variable significantly impacts the dependent variable. The main conditions for withdrawal of action are: p-value > 0,05 and Fhitung < Ftabel then H0 is approved (3) p-value < 0,05 and Fhitung > Ftabel then H1 is approved (4) So it is assumed that, H0: No simultaneous impact between the independent variable and the dependent variable. H1: Has a simultaneous effect between the independent and dependent variables. The data used in this research is data obtained from PVMBG and using assistive programs from Google Earth and Global Mapper. The first stage of data processing is creating landslide-affected areas on Google Earth based on the ground motion situation map in the PVMBG ground motion report in Kemloko III Hamlet, Kenalan Village, Borobudur District, Magelang Regency, Central Java, as shown in Figure 2. In contrast, Figure 3 is the result of creating areas affected by landslides which were processed using Google Earth based on reports of ground motions in Hamlet Kemloko III. Figure 3 shows 3 points, namely E1, E2, and E3. E1 is the highest elevation point in the landslide-affected area, E2 is the point in the landslide area with a flat elevation, and E3 is the lowest in the landslide-affected area. Based on these points, the variables needed in this study are obtained: the slope length before the landslide (L0) and the distance after the landslide (L). The L0 value is obtained between points E1 and E2, while the L value is obtained between points E1 and E3.
The affected area obtained in the Google Earth application will be reused to assist the analysis process in the Global Mapper application so that a contour map of the area affected by the landslide is produced, as illustrated in Figure 4.  After getting the H and L0 values, a calculation can be carried out to obtain the θ value by calculating the inverse tangent angle of the H and L0 values. Then the RT value is obtained by classifying the soil types contained in the ground motion report and the PVMBG geological map in Figure 6. with the classification of soil types in Table 1.

RESULT AND DISCUSSION
The data summarized in Table 3. will be analyzed using the SPSS auxiliary program with the multiple linear regression method. Guo (2014) applied in his research that the L max value was obtained based on the following Equation (5) Where L max is the distance of the furthest slide, RT is the type of rock, V is the volume of the slide, β is the slope transition angle, PHA is the peak horizontal acceleration of the earthquake load, n is the coefficient of the analysis of each variable, and θ is the slope angle. The PHA parameter was not used in this study because the landslide event data used in this study were not related to earthquake activity but due to soil types that quickly decay if rainfall increases and slopes are steep (PVMBG, 2021). Parameter β is also not used because its value is not obtained. As shown in Figure 1, to obtain the value of the slope transition angle, it is necessary to calculate the inverse tangent angle from the slide plane's height to the landslide material's reach length. However, the height value of the slip surface cannot be defined due to limited data, so the slope transition angle or β cannot be calculated. Then the landslide volume value or V is also not used because the landslide volume data obtained is too tiny to do regression analysis. The data obtained are summarized in Table 3. The parameters RT and θ are still used in this study because the rock type and slope angle affect the sliding distance of the slide (Guo et al., 2014). The area of the landslide influences the sliding distance of the landslide (Legros, 2002), so parameter A is added to add comparative data when carrying out the regression analysis. Therefore, the data on landslide events are in Table 3 before carrying out multiple regression analysis. It is converted following Equation (6) to produce an Equation that will be used as follows.  The data is attached to Table 4 and will be used to prove that the results of SPSS modeling can be applied by conducting a T-test and F-test. Tests were carried out using data on 4 variables, namely RT, H, A, and θ according to Equation (6) because these data have the highest coefficient of determination (R 2 ) compared to other data, equal to 0,940 according to Table 4. The T-test was carried out to prove whether or not there was an influence between the geometric parameters of the slope on Lmax. The results of the T-test data are attached in Table 5.
Parameters that influence the sliding distance of the slide must meet the requirements with a p-value < α and t-stat > t-test, so the p-value of 0,000 is smaller than 0,05. The t-stat value is 4,718, more significant than 2,16 so that it can meet the assumptions in Equation (2) so; that out of 4 parameters, there is only one parameter that meets the assumptions in Equation (2), namely parameter n3 in Equation (6) namely parameter A or the area affected by the landslide. The F test is carried out to prove whether the geometric parameters on L max cause a simultaneous effect. The results of the F test calculations are described in Table 6  The results obtained from the F Test experiment proved that the p-value of 0,000 was less than 0,05 and the f-stat value of 51,088 was more significant than 3,11, so it was concluded that the geometric parameters of the slope had an impact simultaneously on the sliding distance of the landslide based on hypothesis on Equation (4).
The coefficient of determination (R 2 ) used as a benchmark in this study uses the highest R 2 value from the modeling results in Table 4, namely on the data of 4 variables. The R 2 value obtained was 0,940. It can be concluded that the variation in the distance of the landslide slide can be explained by the geometric parameters of the slope of 94% so that the level of relationship between the parameters reviewed is very strong, meaning that the model represents the conditions of the parameters studied (Sugiyono, 2014). Therefore, modeling is used to predict the sliding distance of the landslide using the following Equation (7). Testing the proposed model is very difficult because validation using back-analysis using post-hoc parameters only proves the model's adaptability (Iverson, 2003), even though the coefficient of determination shows the level of relationship between the parameters reviewed is very strong. The model represents the conditions of the parameters examined. It is necessary to test the model on field measurements (Guo et al., 2014) so that Equation (7) can predict the distance of moving landslide material using 5 landslide event data at PVMBG in the 2018 to 2019 timeframe. Landslides predicted by regression modeling will be compared with the sliding distances that occur in the field. In addition, it is also necessary to calculate the error value, namely by using the following Equation (8).
The results of the landslide sliding distance values in each case are modeled by Equation (7) compared to the landslide sliding distance values obtained from the PVMBG report, and the recapitulation results can be seen in Table 7 below. The data in Table 7 shows the results of the statistical modeling validation. The estimated error generated for each landslide event has different effects. The resulting model represents the landslide events in the Sepaku area because it produces a minor percentage error of 9,44%. In comparison, the statistical model does not represent the landslide conditions in Cikalong Wetan because it has a difference between the sliding distance of the model slide and the largest field, equal to 61,76%. The average estimated error of 5 landslide events was 31,56%. Based on the percentage error estimation data in Table 7, some data at the incident location has a substantial percentage value, namely at the Cibeber, Cikalong Wetan, and Ciloto locations. The high estimated error percentage value is not because the model obtained is not good but because the resulting empirical model has different location characteristics from the location data used for model validation. Therefore, the greater the percentage value of the estimated error, the further the characteristics of the location of the validation data are from the resulting empirical model. Vice versa, if the percentage value of the estimated error is small, the more similar the location characteristics of the validation data are to the resulting empirical model. Because the average value of the resulting error estimates is relatively small, it can be concluded that the modeling used can be applied. Then the parameters that have the most influence on this modeling can be seen in the results of the T-test in Table 5, namely the parameter of the landslide area (A) because only parameter A meets the qualifications of the hypothesis in Equation (2).

CONCLUSION
The analysis results show that the best empirical model capable of predicting slide distance is log Lmax = 0,387 -0,097 RT + 0,230 log H + 0,458 log A -0,220 tan θ, with R 2 equals 0,94 with a very strong level of relationship between the parameters being reviewed, meaning that the model represents the conditions of the parameters being studied. The difference between the predicted landslide sliding distance from the modeling results and the events in the field is 31,56 %, so the model has almost the same location characteristics as the data used. Based on the T parameter test that has the most influence on the prediction of the sliding distance of the landslide is the parameter of the area affected by the landslide (A) compared to the parameter of slope height (H), original slope (θ), and rock type (RT). The results from the F Test experiment prove that the slope's geometric parameters simultaneously impact the sliding distance of the slide.