Simulation of Debris Flow Deposit in Mt. Umyeon

Abstract

Debris flow is a representative natural disaster in Korea and occurs frequently every year. Recently, it has caused considerable damage to property and considerable loss of life in both mountainous and urban regions. Therefore, It is necessary to estimate the scope of damage for a large area in order to predict the debris flow. A response model such as the random walk model(RWM) can be used as a useful tool instead of a physics-based numerical model. RWM is a probability model that simplifies both debris flows and sedimentation characteristics as a factor of slopes for a subjective site and represents a relatively simple calculation method compared to other debris flow behavior calculation models. Although RWM can be used to analyzing and predicting the scope of damage caused by a debris flow, input variables for terrain conditions are yet to be determined. In this study, optimal input variables were estimated using DEM generated from the Aerial Photograph and LiDAR data of Mt. Umyeon, Seoul, where a large-scale debris flow occurred in 2011. Further, the deposition volume resulting from the debris flow was predicted using the input variables for a specific area in which the deposition volume could not be calculated because of work restoration and the passage of time even though a debris flow occurred there. The accuracy of the model was verified by comparing the result of predicting the deposition volume in the debris flow with the result obtained from a debris flow behavior analysis model, Debris 2D.

1. Introduction

A debris flow refers to the phenomenon in which a landslide due to a typhoon or a severe rainstorm causes debris along with water to strongly drift downstream. In particular, in Korea, debris flows mostly occur from June to August each year, causing tremendous damage to properties and human lives.

The representative debris flows were recorded by typhoons, ‘RUSA’ and ‘MAEMI’ that occurred in 2002 and 2003, respectively, and caused considerable damage in Gangwon-do, as shown in Fig. 1. The debris flow was caused by a localized torrential downpour around Pyeongchanggun and Inje-gun, Gangwon-do, in 2006 and resulted in considerable property damage and loss of life (Choi, 2001; Lee et al., 2013). Debris flows rapidly cause considerable damage in a large area without any unusual movements and their danger has reached serious proportions (Lee, 2005; Ko et al., 2014). In Korea, an annual average of 68 casualties and property damage worth 2.1 trillion won was observed for 10 years (2001~2010), and currently, the number of casualties in cities is increasing. Further, casualties caused by debris flows in rural areas have recently in creased. As shown in Fig. 2, the relief expenditure for damage caused by landslides and debris flows has increased from year to year (Koo and Chae, 2013).

Fig. 1.Debris flow damage cases (Lee et al., 2013)

Fig. 2.Increases in debris flow recovery costs (Koo and Chae, 2013)

To minimize the damage caused by debris flows, it is very important to install erosion control dams in the expected moving path and the deposition region of these flows (Miyamoto, 2002). However, it is very difficult to install such an erosion control dam for every possible case of debris flow because doing so requires huge construction costs. Therefore, construction of disaster protection facilities according to accurate predictions for the scope of debris flow damage is an important and effective method to address the abovementioned issue, and several studies on the development of such a method have been conducted thus far (Chun et al., 1997; Kim, 2011; Kim, 2012; Lee et al., 2012; Kim, 2013).

Owing to the improvements in computing performance resulting from developments of science and technology, we can consider the approach of a debris flow behavior analysis model, which is different from that of a physical model, which is based on not only slopes in damaged areas but also flow and sedimentation mechanisms. However, the predicted results are not satisfactorily accurate (O’Brien et al., 1993; Suzuki et al., 2003; Hirakawa et al., 2006). Therefore, a response model such as the random walk model (RWM), a useful tool for predicting the scope of damage due to debris flows in a large area, is used instead of a physics-based numerical model. RWM is a probability model that simplifies both debris flows and sedimentation characteristics as a factor of slopes for a subjective site and represents a relatively simple calculation method compared to other debris flow behavior calculation models. Further, it is necessary to determine the input variables for terrain conditions beforehand even when RWM can be used for analyzing and predicting the scope of damage caused by debris flows (Kim et al., 2014).

Studies on RWM have been actively conducted up to the present. Imamura and Sugita (1980), who first introduced the RWM, implemented their study by determining input variables based on site investigations of subjective test sites and theoretical values. Interestingly, Lee et al. (2011) investigated optimal input variables in actual debris flow-damaged areas. Kim et al. (2014), on the other hand, implemented a program with the Visual C++ language by adding lattice distances and the mass point volumes, in addition to the major input variables of the RWM, and estimated the optimal input variables by analyzing the overlap rate in sedimentation areas according to the input variables. The precedent study estimated the input variables by considering the overlap rate in sedimentation areas, but the results of the debris flow simulation, which was implemented using the estimated input variables, were not appropriately verified.

Thus, the objective of this study is to improve the reliability of estimating input variables by comparing the overlap rate between the area of an actual debris flow and the sedimentation area estimated by an experiment in addition to considering the studies of Lee et al. (2011) and Kim et al. (2014) in which only the overlap rate of the sedimentation area covered by the debris flows was taken into account. Further, the scope of damage caused by debris flows was predicted using the input variables for a specific area in which the deposition volume could not be calculated because of work restoration and the passage of time even though a debris flow occurred there. The accuracy of the estimation model was verified by comparing the predicted deposition volume in the debris flow with the values obtained from a debris behavior analysis model, Debris 2D.

 

2. Theory and Methods

2.1 Debris flow mechanism in the debris flow behavior analysis model(RWM and Debris 2D)

In this study, RWM was used for predicting debris flows in the experimental area. As mentioned in Introduction, RWM is a statistical model that simplifies both debris flows and sedimentation characteristics as a factor of slopes. A more specific theoretical background and method were referenced by the previous studies of Imamura and Sugita (1980), Lee et al. (2011), and Kim et al. (2014).

RWM basically simulates the flow and the deposition of debris flows by using DEM and uses a simulation technique that behaves similarly to the actual natural phenomenon through the diversification of the flow on the basis of random number generation. RWM applies the following assumptions for the prediction of the debris flow.

First, collapsed soils in the areas of debris flows are released downstream by dividing it into a specific amount of soil. Second, the specific amount of soil starts to move in the range of the DEM, which is divided into cells, and the movement route is determined by the direction that has the highest probability of showing the movement through a comparison of the route in an arbitrary cell with the slopes of the neighboring cells. The probability of presenting the movement for each direction is determined by the slopes, inertia, and weights presented by random numbers. Third, if the slopes are found to be below a specific level for all points neighboring a certain point where the soil deposition settles, debris flows would be suspended and would accumulate at this point. The simulation results are presented by the route of debris flows, deposition point, and deposition volume (Lee et al., 2011).

The Debris 2D model was used for verifying the reliability of the debris flow data, which was predicted by using RWM in the experimental area. This model was developed by Liu and Huang (2006) by using the relationship between shear stress and strain proposed by Julien and Lan (1991). The input variables for implementing the model in the simulation of debris flows were shear yield stress, coordinate values, height, and amount of debris flow at the mass point volumes. In the Debris 2D model, the detailed theoretical background and simulation method of debris flows were referenced by the previous studies of Julien and Lan (1991) and Tsai et al. (2011).

Fig. 3 shows the relationship between the input variables, volume, and yield stress, at an mass point volumes in Debris 2D. Fig. 3(a) represents the behavior of debris flows according to the changes in volume (amount of debris flow) with a fixed input of yield stress, and Fig. 3(b) shows the behavior of the debris flow according to the changes in yield stress with a fixed input of the volume at an mass point (Liu et al., 2009; Tsai et al., 2011).

Fig. 3.Relationship between the volume and the yield stress at an mass point in the Debris 2D model (Wu, 2013)

For implementing a simulation based on the RWM mechanism as shown in 2.1, input variables such as mass point volumes, inertia weights, and critical deposition angle need to be estimated. For estimating the input variables of RWM, the aerial images and DEM data in a subject site of the debris flows and the Monte-Carlo simulation method are used. The Monte-Carlo simulation method is used for determining the maximum and minimum values of the input variables that need to be extracted, as the range and the tendency of the input variables, which are obtained by implementing the model repeatedly with a specific interval, are analyzed for determining the optimal input variables (Lee et al., 2011). Although this method has a disadvantage, which is considerable time consumption in its process, it allows us to clearly understand the correlation between the physical phenomena of debris flows and the input variables based on an accurate analysis of the relationship between the input variables. Further, it is a very effective method to determine appropriate input variables by using simplifying complex phenomena, which are difficult to predict in detail compared to other physical models (Kim et al., 2014).

Fig. 4 represents the proposed process of analyzing and predicting the movement of debris flows. This process revised the previous studies of Lee et al. (2011) and Kim et al. (2014) and complemented it in which the simulation results obtained by using RWM were verified using the Debris 2D model.

Fig. 4.Debris flow analysis and prediction process

2.2 Analysis of the overlap rate between flow and deposition areas

With respect to the overlap rate analysis, the overlap rates of the deposition areas were compared to predict the parameter in the existing research cases. In this research, however, the overlap rates of the flow areas of the debris flow, as well as the deposition areas, were compared, and the overlap rate experimental process is shown in Fig. 5. The simulation results are represented in the range of –1.0 to +1.0 in which –1.0 denotes no overlap between the simulation and the actual deposition area without any overlaps and +1.0 represents a perfect overlap between these two areas (Kim, 2015). For the mass point volume, the simulation was performed by increasing the soil deposition from the mass point volumes by considering both the average flow area slopes and erosions, and the deposition volume was determined by analyzing the deposition area and the deposition volume. Then, the simulation was repeatedly performed by controlling the deposition volume on the basis of the analysis of the types of deposition areas.

Fig. 5.Overlap rate analysis of the flow and deposition areas (Kim, 2015)

2.3 Study sites and data sets for analyzing the behavior of debris flows

In this study, the study site for analyzing the behavior of debris flows was on Mt. Umyeon located in Seocho-gu, Seoul. A heavy rain with a cumulative rainfall of 595 mm within three days in July 2001 caused considerable damage to property and loss of life.

Mt. Umyeon is divided into a total of 31 hydrology-related watersheds. As shown in Table 1 and Fig. 6, six areas (A–F), which represent clear differences between before and after the occurrence of debris flows, were selected for this analysis. In these six areas, three of them (B, C, and E) showed no loss of deposition and allowed us to measure the deposition volume. Further, the optimal input variables for the RWM debris flow behavior prediction model were predicted through the analyses of the overlap rate in these areas. For other areas (A, D, and F), the scope of the damage caused by debris flows was predicted using the optimal input variables.

Table 1.Information of study sites

Fig. 6.Study sites

The data used in this study were produced using the aerial images taken before and after the damage to investigate the changes in the terrain before and after the occurrence of debris flows. The images of conditions before and after the damage were taken in August 2009 and August 2011, respectively. The spatial resolution of the images taken before and after the damage was 25 cm. DEM was generated from the data surveyed using an aerial LiDAR for both before and after the damage. The spatial resolution of the aerial LiDAR-surveyed data was 56 cm and was interpolated by 1 m. The input variables, such as mass point volumes, destruction types, and critical deposition volumes, were obtained from an actual site investigation. Fig. 7 shows the dataset used in this study.

Fig. 7.Data set

 

3. Debris Flow Simulation and Analysis Results

3.1 Configuration of input variables and the estimation of optimal input variables

For estimating the optimal input variables, a simulation was performed on the basis of B1~B2, C1~C2, and E, in which areas showed no loss of deposition. Table 2 shows the ranges of the three input variables, namely the mass point volumes, inertia weights, and critical deposition angle, in RWM. Further, the value that represents a high distribution rate in the overlap rate was analyzed.

Table 2.Estimation range of input variables

The most important factor in estimating the scope of damage caused by debris flows is the determination of mass point volumes from debris flows. Because the RWM only dispenses the mass point volumes in a debris flow by dividing it with a specific amount, it cannot consider the deposition volume generated from the movement of debris flows. Thus, the actual deposition volume was smaller than simulated one. For resolving this problem, the optimal input variables were determined by increasing the erosions released from the mass point volumes through the consideration of the deposition volume in the flow areas.

As shown in Table 3, it was possible to deduce the correlation between the slopes of flow areas and the critical deposition angle conditions during a debris flow simulation under different conditions configured for estimating the input variables.

Table 3.Critical deposition angle conditions for the average slopes in flow areas

The critical deposition volumes obtained from the RWM simulation and the actual site were compared and presented in Table 4 on the basis of the simulations of areas B1~B2, C1~C2, and E. Table 5 shows the estimated optimal input variables that lead to the results in Table 4. The items of the mass point volumes and the critical deposition angle conditions showed high overlap rates within a specific range, but the inertia weights represented constant values in all areas. The overlap rates in the flow and deposition areas were 0.38~0.41 and 0.40~0.47, respectively. In the distribution of the optimal input variables, the mass point volumes were 4~5 times larger than those of the mass point volumes, while the inertial weights were 1.1~1.2 and the critical deposition angle conditions were 4°~5°. Although the inertia weights showed results similar to those of the study of Kim et al. (2014), the critical deposition angle conditions showed some differences. An improvement in the overlap rate was observed in this study as compared to the study of Kim et al. (2014). The reliability of the input variables deduced in this study is higher than that of the previous studies.

Table 4.Comparison of the deposition volume between RWM and the actual site

Table 5.Estimated optimal input variables in the study area

3.2 Estimation of the damaged range in debris flows

The optimal input variables were deduced on the basis of the critical deposition angle conditions according to the average slope in the flow areas and the relationship between the mass point volume and the inertia weight in the study area. The damage ranges and critical deposition volumes in three areas, A1~A3, D1~D3, and F, where the deposition area loss was estimated.

The estimation results in these three areas are presented in Fig. 8 and Table 6. The critical deposition angle conditions were 3°~4°, and the additional erosions were five times larger than those of the mass point volumes. The estimated critical deposition volumes in the areas with the loss of deposition areas were determined further, it was found that A1~A3: 8,315 ㎥, D1~D3: 4,499.0 ㎥, and F: 750 ㎥.

Fig. 8.Debris flow damage predictions

Table 6.Estimation results of the critical deposition volumes using the optimal input variables

3.3 Comparison of the simulation results of debris flows

The estimated critical deposition volumes in the areas with a loss of deposition areas were compared with the results obtained from the Debris 2D model. As shown in Fig. 9, the similarity between the movement of debris flows and the position of deposition areas according to the changes in volumes under the same condition was verified. Further, as shown in Fig. 10, the critical deposition volumes in these two models were presented as a graph according to the quantitative analysis of the data in these models.

Fig. 9.Comparison of the movements according to changes in volumes in the same area(A1~A3)

Fig. 10.Comparison of the critical deposition volumes according to changes in volumes in the same area (A1~A3)

With respect to the movement and position of deposition areas according to the changes in volumes in the same area, there were some differences in the movement but the direction and position of the deposition areas were similar in these two models. In the case of the deposition volume, the RWM model generated a constant pattern, but the Debris 2D model represented a relatively irregular pattern as compared to that of the RWM model. However, the quantitative critical deposition volumes in these two models were similar.

The estimated critical deposition volumes obtained from the RWM simulation for the areas with a loss of deposition areas (A1~A3, D1~D3, and F) were compared with those from the Debris 2D model. In the comparison, the yield stress in the Debris 2D model was fixed at 150 Pa, which is a condition similar to the characteristics of the debris flows, and the additional erosions were the same as in the RWM model. Although a test in which the yield stresses were varied within a range of 100 Pa ~ 1,200 Pa was previously performed, there was no relationship between the yield stress and the deposition volume, as shown in Fig. 3. As a result, the critical deposition volumes in these two models were very similar, as presented in Table 7. It also showed a relatively accurate level of estimating the movement of debris flows and the deposition volume in the RWM model.

Table 7.Comparison of the simulations of debris flows

 

4. Conclusion

This study is to improve the reliability of estimating input variables by comparing the overlap rate between the area of an actual debris flow and the sedimentation area estimated by an experiment in addition to considering the past studies in which only the overlap rate of the sedimentation area covered by the debris flows was taken into account. Further, the scope of damage caused by debris flows was predicted using the input variables for a specific area in which the deposition volume could not be calculated because of work restoration and the passage of time even though a debris flow occurred there. The accuracy of the estimation model was verified by comparing the predicted deposition volume in the debris flow with the values obtained from a debris behavior analysis model, Debris 2D.

Mt. Umyeon is divided into a total of 31 hydrology-related watersheds in which six areas (A~F), which represent clear differences between before and after the occurrence of debris flows, were selected in this study. In these six areas, three areas (B, C, and E) showed no loss of sediment and allowed us to measure the deposition volume. Further, the optimal input variables in the RWM were predicted through analyses of the overlap rates in these areas. In the distribution of the optimal input variables, the mass point volumes were 4~5 times larger than those of the mass point volumes, while the inertial weights were 1.1~1.2 and the critical deposition angle conditions were 4°~5°. Although the estimated values showed results similar to those of the previous study, the critical deposition angle conditions exhibited some differences. The reliability of the input variables deduced in this study is higher than that of the previous studies.

The damage ranges in other areas (A, D, and F) in which the deposition volume cannot be measured were estimated using the optimal input variables. The estimated results were compared with those from the Debris 2D model for different movements of debris flows, positions of deposition areas, and critical deposition volumes. For the same area, there were some differences in the movements but the direction and position of the deposition areas were similar in these two models. For the deposition volume, the RWM model exhibited a constant pattern, but the Debris 2D model represented a relatively irregular pattern as compared to the RWM model. However, the quantitative critical deposition volumes in these two models were found to be similar.

Finally, the estimated deposition volume in the areas with a loss of deposition areas (A, D, and F) was compared with those from the Debris 2D model. As a result, the critical deposition volumes in these two models were found to be very similar. Therefore, the RWM model was relatively accurate in estimating the movement of the debris flows and the deposition volume.

RWM is a probability model with respect to slopes, and the Debris 2D model is a yield stress-based physical model. These two models are limited with respect to the deposition volume. Inevitably, in this study, the critical deposition volumes were calculated by adding weights, which are considered to be erosions, to the deposition volume. Therefore, a more accurate behavior analysis of debris flows and damage predictions will be conducted when the relationship between the debris flow behavior and erosion will be applied to the model in a future study.