Introduction

The most catastrophic landslide events in Korea are debris flows initiated by landslides due to extreme rainfall. These rapid to extremely rapid processes are characterized by materials comprising coarse and fine particle matrices with varying levels of water saturation. The socio-economic damage caused by destructive debris flows has been well documented throughout the world and specifically in Korea (KSCE 2012; Quan Luna 2012). Therefore, a need arises to design and manage a near-real-time early warning system that can provide information regarding the risk related to an extreme rainfall-induced debris flow. The hazard component of a near-real-time early warning system would require the evaluation of debris flow intensity factors, such as velocity, volume, or flow depth, to conduct the risk assessment-based dissemination of warnings. A sequential-based hazard framework was introduced to analyze the debris flow intensity factors at a detailed scale using near-real-time rainfall information at a small scale (Nikhil 2016). At a detailed scale, the hazard analysis always requires the estimation of a larger number of parameters, as well as knowledge of the initial conditions and boundary conditions. This complexity, however, cannot be overlooked, particularly in regions with high urban populations and important infrastructures, and can be eased by establishing databases. Currently, sophisticated dynamic models using depth-averaged equations of motion with single-phase rheology defining the internal stress and basal shear resistance are popular, owing to their simplicity and fast implementation. Most of the dynamic methods based on the equivalent fluid concept require input factors such as the initial volume, rheological parameters, and erosion coefficient for forward analysis of a debris flow. Researchers have tried to couple rainfall with the results from empirical-based landslide susceptibility or infinite slope stability-based models to determine the initial volume that existed prior to the debris flow (Wang et al. 2013; Park et al. 2016). However, the data-dependent models correspond to particular landslide types, initial conditions, and boundary conditions that cannot be easily adapted to Korean conditions, while the 1D- or 2D-based slope stability models within the GIS environment would give an overly conservative initial volume estimate, producing isolated, unstable cells.

The most common and easiest method for modeling these intricately complex debris flow phenomena is to use rheological models, with the parameters of which can be determined via either lab experiments or calibration. Lab experiments that include rheometers, flumes, or ring shear tests, although scale dependent, cannot capture the multifaceted interactions, yet it remains scientifically appealing to conduct measurements in a lab-controlled environment (Pirulli 2010). However, a calibration-based method using landslide inventories is the easiest and fastest approach for determining the material values that implicitly capture the complexities of interactions and other phenomena involved during a flow. Several studies on back-calibration of the rheological and entrainment parameters for channelized and non-channelized debris flow events using numerical models have been conducted (McDougall and Hungr 2004; Pirulli and Pastor 2012; Cuomo et al. 2016). However, no clear methodology or approach exists that outlines how the established databases for back-analyzed values can be used in the predictive debris flow hazard assessment.

Large databases have been developed for debris flow rheological models like the Voellmy, Bingham, and frictional by several researchers (O'Brien and Julien 1988; GEO 2012; Quan Luna 2012). The use of the above databases for debris flow hazard prediction in a local setting is difficult because of the lack of information related to the local geomorphological or geotechnical factors influencing a particular rheology in addition to uncertainties induced by calibration method, choice of digital elevation model (DEM) resolution, and numerical model adopted.

Thus, in this study, a method to develop database for input parameters: initial volume, bulk frictional angle, and growth rate, was put forward for predictive-based debris flow hazard assessment under extreme rainfall at a site-specific scale. At first, the initial volume database was established using a one-way coupled seepage slope stability modeling. Subsequently, the prediction of the bulk frictional angle was carried out using a newly developed artificial neural network (ANN) model incorporating geomorphological and geotechnical factors. Finally, a database for the user-defined growth rate within the watershed was developed using the initial volume, final volume, and approximate runout length.

Study area and materials

The Raemian watershed, located in the Woomyeon mountain region, Seoul (Fig. 1a), was selected to conduct the case study. A 2-m DEM of the topography needed for the analysis was extracted using the spatial analyst tool in ArcGIS 10.1 and showed the highest elevation of 295 m above sea level (Fig. 1b). The Raemian slope exhibits a colluvium layer comprised of sand and gravel mixture in a silty matrix, up to 3-m thickness, and a gneiss bedrock layer.

Fig. 1
figure 1

a The Woomyeon mountain region in Seoul considered for debris flow hazard assessment. b Digital elevation map of the Raemian slope

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Database development for the initial volume

After the catastrophic event on 27 July 2011, about six geotechnical investigation boreholes were drilled at the site under consideration for the collection of soil, hydrological, and geological information (KGS 2011; KSCE 2012). The soil water characteristic curve (SWCC) (Fig. 2a), unsaturated hydraulic conductivity (Fig. 2b), and shear strength (Table 1) were obtained from pressure plate, Fredlund, and Xing relative permeability equation (Fredlund et al. 1994), and direct shear test, respectively.

Fig. 2
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a SWCC. b Hydraulic conductivity

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Table 1 Soil hydraulic and strength characteristics
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To assess the most critical failure volume, a coupled finite element method (FEM)-based 3D seepage analysis and limit equilibrium-based slope stability analysis was conducted for the extreme rainfall event of 26–27 July 2011 (Fig. 3). The frequency plot shown in Fig. 4a, based on a database of 1003 landslides collected from several parts of Korea (Seoul, Yongin, Sangju, Pohang, Sokcho, Muju, JangSu, Jumunjin, Youngok, and Pyeongchang), was used to determine the aspect ratio (ratio of width to length) (mean value = 0.38) of the 3D slip surface to reduce the computational time without compromising the reliability of the analysis. Additionally, instead of meshing and analyzing the entire slope, with a length of 600 m, a slope length of approximately 180 m was selected since most of the landslides had a length of less than 100 m (Fig. 4b), and an average relative elevation of 81.62% was observed, indicating that most landslides occurred near the highest elevation (Fig. 4c). The 3D slope geometry shown in Fig. 5 was meshed, with approximately 15,669 triangular elements and 26,690 nodes, and the no-flow boundary condition was used at the side slopes, upslope, and downslope. Additionally, the groundwater table was modeled at the bedrock level, as suggested based on a field investigation (KSCE 2012; Jeong et al. 2015).

Fig. 3
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Rainfall pattern for initial volume estimation in Raemian slope and factor of safety versus time

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Fig. 4
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Landslide morphological frequency distribution for a aspect ratio, b landslide length, and c relative elevation

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Fig. 5
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3-D numerical model for the initial volume estimation in Raemian slope

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Database development for the bulk frictional angle

The ANN-based bulk frictional angle model consists of eight parameters: plan curvature, profile curvature, percentage of fine content, D50, initial unit weight, initial volume, relative relief ratio, and channel length. The geomorphological parameters were determined from the DEM at a resolution of 10 m using the spatial analyst tool in ArcGIS 10.1. Table 2 shows the values of input parameters estimated for the Raemian slope.

Table 2 Input parameters used in ANN-based bulk frictional angle model for Raemian slope
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Database development for erosion growth rate

To determine the final volume that may be mobilized by the debris flow in Raemian slope, watersheds corresponding to the drainage line determined using the 2-m DEM in ArcGIS 10.1 are created using the hydrological tool. Once the watershed is created, the total area of the watershed is multiplied by the soil depth obtained from the forestry map purchased from the Korea Forest Service (Park et al. 2016). The conservative estimate, due to the use of a large watershed area, will be balanced by the uncertainty in the soil depth map. The average depth obtained from the site investigation is approximately 4.3 times that obtained from the soil depth map for the Raemian slope. The runout length is determined based on the drainage line length using the add surface information tool in ArcGIS 10.1.

Method

The reliable estimation of the input parameters for debris flow prediction is usually quite complex and involves several uncertainties which motivate the development of a framework to establish the input parameter database for predictive debris flow runout assessment using single-phased models (Fig. 6).

Fig. 6
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Framework for input parameter database establishment to predict debris flow hazard

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The use of DAN-3D code necessitates the estimation of three input parameters: initial volume, rheological model parameter, and growth rate (McDougall and Hungr 2004).

Initial volume assessment

The initial volume has a positive influence on the debris flow hazard factors such as velocity, runout length, and area. A study by De Haas et al. (2015) showed nearly linear increase in runout length, area, and velocity with an increase in initial volume. For predictive purposes, the initial landslide volume can be estimated using a simplified hydrological model coupled with infinite slope stability scheme (Baum et al. 2010). However, the approach leads to overestimation of the initial volume and is more suited over a medium or regional scale. The application of a 3D-based analysis was vital not only owing to the advantage of direct volume estimation but also to closely model the field condition, in which the slope failure surfaces are non-symmetric and do not extend infinitely (Reyes and Parra 2014). In addition, it encompasses the lateral variation of topography, shear strength, and pore pressure (Reid et al. 2015). Ignoring these effects would result in extremely conservative and inaccurate results (Stark and Eid 1998; Bromhead et al. 2002) with 15 and 50% differences in the lowest factor of safety (FOS) (Gitirana et al. 2008).

In this research, a coupled 3D infiltration and limit equilibrium-based slope stability model was used for the assessment of the initial volume that will mobilize into a debris flow at a slope scale. The transient 3D seepage analysis is carried out using the commercial code SVFLUX (SVOFFICE 5 2016). The resulting spatially varying pore pressure was incorporated into the 3D slope stability analysis using a commercial code SVSLOPE (SVOFFICE 5 2016). The 3D Bishop’s limit equilibrium method satisfying the moment equilibrium condition was selected to balance the result accuracy and the computational time.

Rheological model and parameter estimation

Several of the existing debris flow codes use rheological models such as the Bingham, Voellmy, and frictional to define the basal shear stress (McDougall and Hungr 2004; Medina et al. 2008; Pirulli 2010; Rickenmann et al. 2006). The Bingham model requires parameters from a rheometer test, which involves significant uncertainty because of data gaps with respect to the appropriate flow water content and the percentages of sand, fine, and gravel content during the flow. The model is mostly appropriate for fine-grained soil but is still too simple to capture the overall flow behavior (Iverson 1997; Jeong 2010). On the other hand, the Voellmy model, developed for modeling avalanches using a combination of the frictional and drag coefficient, has been successfully used by several researchers to model debris flows (Hungr et al. 2002; Medina et al. 2008; Pirulli 2010). Currently, back-calibration is the only technique to estimate the frictional and the drag coefficient parameters. However, the presence of two parameters adds to the complexity of optimization, and therefore, it is difficult to develop a reliable model for prediction of Voellmy parameters. Studies by Iverson and Vallance (2001) and D’Agostino et al. (2013) have shown, via experiments, that the Mohr-Coulomb equation can well predict the effective intergranular stresses in a rapid, gravity-driven flow. The undrained ring shear tests on both loose and dense soils have shown that the effective stress path after reaching the failure line gradually followed the line until the residual shear resistance in steady state was achieved (Okada et al. 2004). Therefore, in this study, a frictional rheology is selected to model the basal shear stress of debris flow consisting of silty-sand-type material, and the bulk frictional angle is estimated using an ANN-based model. The bulk frictional angle is back-calibrated using an optimization code incorporated into the DAN-3D model. The code is used because a manual trial-and-error-based method is time consuming and has limitations with regard to exploring the entire parameter space and possible non-identification of the existence of non-uniqueness. The optimization minimizes the difference between the model and field observations (Aaron et al. 2016).

Table 3 shows the bulk frictional angle determined via both back-analysis and experiments for previous case studies. In all the cases, the bulk frictional angle is determined either through an experiment or by utilizing flow depth or the deposition characteristics as the main constraining parameter rather than velocity. This non-consideration of velocity as a constraining parameter will lead to an underestimation of the impact pressure (proportional to square of the velocity) and thus the lower vulnerability and risk-level assessment.

Table 3 Bulk frictional angle values from previous studies
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There are several geomorphological and geotechnical factors that influence the bulk frictional angle value for a debris flow. In this study, eight factors, namely, plan curvature, profile curvature, percentage of fine content, D50, initial unit weight, initial volume, relative relief ratio, and channel length, were selected based on a detailed literature survey.

The 27 debris flow data were collected via a field investigation and literature review for Yongin, Icheon, Chuncheon, Yeoju, and Gwangju areas. Figure 7 shows the box plot of the eight independent factors used in the ANN model development. The topographic curvature causing the obstruction, convergence, or divergence of a flow influences the flow dynamics because of transverse shearing and cross-stream momentum transport (Pudasaini et al. 2005). The profile curvature is defined as the curvature of the terrain in the direction of the slope. This factor induces centripetal acceleration of the flow, which alters the bed-normal stress and therefore can affect the basal and internal stresses (McDougall and Hungr 2004). Additionally, the presence of a concave curvature can lead to the ponding of water, which may decrease the bulk frictional angle of the moving debris mass. The left-skewed distribution of the profile data shown in Fig. 7a exhibits an interquartile (IQR) range of 0.58, indicating that most of the data are concentrated around the average value of 0.64 and thus low variation. It is also observed that 25% of the data lie above the third quartile value of 0.96, with the maximum value of the profile curvature existing at 7.96. On the other hand, the plan curvature is defined as the curvature perpendicular to the slope direction, and the negative type considers the effect of confinement of the debris flow in the channel leading to the convergence and thus positively favoring the occurrence of a rapid flow. Figure 7b shows the plan curvature data, which are right-skewed, with an average value of − 3.69; 50% of the data lie between the second and third quartile values of − 5.18 and − 2.13, respectively. The relative relief ratio is defined as the difference between the highest and the lowest elevation points along the slope. This factor indicates the availability of the potential energy for the flow downslope and can implicitly account for grain collision and velocity fluctuation controlling the debris flow travel distance (D’Agostino et al. 2010). The data distribution of the relative relief ratio (Fig. 7c) is almost normal, with an average of 16.18%; however, the data have considerable variation owing to an IQR of 4.94%. The figure also shows the minimum and maximum values of the relative relief ratio, i.e., 8.22 and 24.82%, respectively. Channel length is another important factor influencing the travel distance of the flow. If the channel length is small, then debris flow will be mobilized at a bulk frictional angle with a value much higher than that in the case of a longer channel. This is because the large strains induced in debris flow traveling for a longer distance will cause the basal stress to be decreased to a much lower value relative to that to a shorter distance (De Alba and Ballestero 2006). Figure 7d exhibits the left-skewed, non-normal distribution of the channel length, with an average of 158 m. The upper extremum value of 529.07 m lies relatively far away from the average, in comparison to the lower extremum value of 69.73 m. The percentage of fine content denotes the proportion of silt or clay content in soil, which, according to the research of Wang and Sassa (2003), can significantly affect the maintenance of the pore pressure ratio during a flow and thus is an important factor that can change the bulk frictional angle during a flow. A higher percentage of fine content may maintain the excess pore water pressure for a longer time and hence result in mobilization of a debris flow at a lower bulk frictional angle in comparison to flow with a lower percentage of fine content. The highly left-skewed data for the percentage of fine content, shown in Fig. 7e, has an average value of 5.52%. Approximately 50% of the fine content data lie between the second and third quartiles of 1.75 and 9.17%; the data display a low spread and exhibit a minimum and maximum value of 1.71 and 54.2%, respectively. D50, representing the average grain size in the soil bed of a slope, is also considered. The presence of a higher grain size will result in an increase in the bulk frictional angle because of higher frictional contact between the particles. Additionally, a higher grain size in the flow will increase the number of grain-to-grain interactions and result in a higher effective normal stress, resulting in a higher bulk frictional angle (Bagnold 1954; Sassa 2000). The D50 data distribution, as shown in Fig. 7f, is slightly skewed towards the right, with an average of 1.13. The box plot also shows an IQR of 0.67, indicating a spread towards the higher side, with the minimum and maximum grain size influencing the bulk frictional angle, with values of 0.05 and 1.96, respectively. The differences in initial conditions such as porosity, thickness, and landslide momentum influence the bifurcation of the landslide behavior in terms of the basal pore water pressure and hence the basal bulk frictional angle (Iverson et al. 2015). The unit weight can be considered analogous to the initial porosity, where if the initial porosity is higher than a critical value; it may result in high-speed landslides because of abrupt pore water increases within the shear zone (Iverson 1997; Moriwaki et al. 2004). The box plot shows that the right-skewed unit weight data distribution (Fig. 7g) has an average of 15.04 kg/m3 and that 75% of the data exist above 14.59 kg/m3. The variation of the initial volume generated would also influence the bulk frictional angle, which occurs because of the grain-crushing mechanism at the basal shear zone. Assuming an undrained condition, the grain crushing that occurs under high normal stress decreases the volume and leads to an increase in the excess pore water pressure, causing localized liquefaction (Okada and Ochiai 2007). Additionally, a study by Sato et al. (2009) shows a systematic increase in mobility with the increase in volume because of the temporary small friction coefficient induced by the highly sheared zone, which would subsequently transition into shear diffusion throughout the body. Therefore, the initial volume and the bulk frictional angle would have an inverse relationship. Figure 7h demonstrates an average debris flow volume of 110.01 m3 for the left-skewed distributed data, with 50% of the data lying between 76.94 and 170.13 m3 showing significant variation.

Fig. 7
figure 7

Box plot of the independent factors used in the ANN model development. a Profile curvature. b Plan curvature. c Relative relief ratio. d Channel length. e Percent fines. f D50. g Unit weight. h Initial volume

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In this study, back-calibration was conducted for 27 field cases to ascertain the bulk frictional angle using the debris flow path footprint and the superelevation velocity. The debris flow path footprint information was obtained using the field investigation and digital elevation models; on the other hand, the lack of direct velocity measurement prompted an indirect estimation using the velocity at superelevation given by the forced vortex equation (Eq. (1)) (Prochaska et al. 2008):

$$ v=\sqrt{\frac{R_c g\varDelta h}{kb}} $$
(1)

where v is the mean velocity, Rc is the channel’s radius of curvature, g is the acceleration due to gravity, Δh is the superelevation height, k is the correction factor for viscosity and vertical sorting (in this study, k = 1 (Prochaska et al. 2008)), and b is the flow width.

The database of 27 real debris flow cases for ANN-based model development using MATLAB is divided into training (80%), testing (10%), and validation (10%) data. The training is conducted using the Levenberg-Marquardt (Marquardt 1963) back-propagation algorithm for different numbers of neurons in the hidden layer.

After conducting trial and error for different combinations of independent parameters, the best model was obtained using eight independent factors with a single hidden layer consisting of 15 neurons by using the tangent-sigmoid transfer function (Fig. 8a). The eight independent factors, i.e., percentage of fine content, D50, unit weight, relative relief ratio, channel length, initial volume, plan curvature, and profile curvature, yielded high model performance, as shown in Fig. 8b, with high R-square values of 0.97, 0.77, and 0.82 obtained for the training, validation, and testing data, respectively.

Fig. 8
figure 8

a Neural network. b RMSE for training, testing, and validation dataset

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Erosion rate estimation

Entrainment mainly refers to bulking of a flow through incorporation of fluid and solid boundary materials owing to progressive scouring of bed materials or channel bank collapse (Iverson 2012). The final volume, runout distance, and spreading are mainly influenced by the amount of soil entrained during the debris flow runout. The initiation of erosion/deposition has been studied using empirical laws (Egashira et al. 2001; McDougall and Hungr 2004) and soil mechanic concept considering static stress equilibrium conditions (Medina et al. 2008; Quan Luna 2012; Takahashi et al. 1992). The entrainment estimated using soil mechanics concepts are limited in use owing to the lack of information on the slope bed regarding the shear strength variation at various depth (Jakob and Hungr 2005). The entrainment method based on empirical law calculates the erosion rates as a function of the flow velocity or the flow depth. In DAN-3D (McDougall and Hungr 2004), the entrainment mechanism is implemented using a user-defined erosion depth and growth rate parameter which is independent of the flow velocity. The growth rate parameter is calculated as

$$ {E}_s=\frac{\ln \left({V}_f/{V}_o\right)}{L} $$
(2)

where Vf is the final volume, Vo is the initial volume, and L is the approximate runout length.

Results

The variation of pore water pressure for the cross section at Y = 30 m, where a 22-h-long rainfall occurred, is illustrated in Fig. 9. At time t = 14:00 on 26 July (Fig. 9a), the top surface had an initial matric suction value of 5.8 kPa, while the value at the bottom (bedrock) decreased to a saturated condition because of the presence of a ground water table. Figure 9b shows the pore water pressure distribution at 19:00, 3 h after the start of rainfall, during which a drop in matric suction was observed and a pore water pressure of 15 kPa developed at the bedrock. The 3-h dry period from 22:00 on 26 July exhibited the recovery of matric suction from − 9.67 to − 11.98 kPa in a few convex (− ve profile curvature) regions along the section (Fig. 9c). On the other hand, at the bottom part of the slope, a rise in pore water pressure to values greater than 20 kPa was seen (Fig. 9c). After a 3-h non-rainfall period, the rainfall until 04:00 on 27 July added approximately 70 mm of rainwater, saturating a large area of the slope, especially at the downslope and converging sections of the slope, while the top portion had a relatively high matric suction of 15 kPa (Fig. 9d). In the early morning, between 04:00 and 09:00 (Fig. 3), an extremely large amount of rainfall of 230 mm occurred, which is approximately 2.5 times that of the cumulative rainfall value at 04:00, with a peak intensity of 86.5 mm/h. This extremely high rainfall caused the water table to reach the top of the colluvium soil throughout the slope, thereby eliminating regions with negative pore water pressure, as shown in Fig. 9e, except in a small region existing at the highest elevation of the slope, which had a small matric suction of approximately 2 kPa (Fig. 10e). Figure 10a, b plots the initial matric suction distribution of 5.8 kPa and the matric suction distribution at 19:00, respectively, demonstrating a general decrease in negative pore water pressure because of the rainfall infiltration. The matric suction recovery was mainly exhibited at the top part of the slope and in the regions with a convex topography, while saturation in the regions along the converging topography was observed (Fig. 10c). An increase in spatial distribution of the saturated area was generally exhibited from the slope base and along the drainage channel from 02:00 on 27 July (Fig. 10d), with complete saturation occurring just before 09:00 (Fig. 10e). However, 3 h after the high rainfall intensity of 80 mm/h (12:00), the topsoil gradually desaturated, with the matric suction reaching 2.5 kPa (Fig. 10f).

Fig. 9
figure 9

Pore water pressure distribution at section Y = 30 m: a at 14:00, b at 19:00, c at 00:00, d at 04:00, e at 09:00, and f at 12:00

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Fig. 10
figure 10

Pore water pressure distribution at the top surface: a at 14:00, b at 19:00, c at 00:00, d at 04:00, e at 09:00, and f at 12:00

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The 3D-based FOS analysis for the Raemian slope was conducted under the pore water pressure conditions of 19:00, 00:00, 04:00, 09:00, and 12:00 for the given extreme rainfall pattern. Figure 3 displays the high FOS value of 1.62 obtained under the initial condition before rainfall, which dropped to 1.339 at 19:00 for a cumulative rainfall of 47.5 mm. The FOS value continuously decreased with rainfall progression and reached a minimum of 1.10 at 09:00 on 27 July 2011 for a cumulative rainfall of 387 mm; it then remained constant at 10:00 and 12:00. The critical FOS at 09:00 resulted in a slip volume of approximately 4032 m3.

The final volume, a prerequisite for the growth rate estimation, was calculated based on a conservative methodology considering the entire watershed area and the average soil depth. The Raemian watershed under consideration had an area of 79,455.35 m2 and an average soil depth of 0.71 m was carefully chosen from the KFRI map using ArcGIS 10.1. Thus, the tentative maximum final volume was approximately 56,413.3 m3. Additionally, the runout distance, measured from the initiation area to the end of the watershed using the COGO tool in ArcGIS 10.1, was approximately 619.34 m. Thus, the growth rate can be estimated using the previously assessed initial volume as follows:

$$ {E}_s=\frac{\ln \left(56413.3/4032\right)}{619.34}=0.0042\ {\mathrm{m}}^{-1} $$
(3)

Table 4 shows the predicted and the field observed values of input used for the debris flow runout analysis of the Raemian slope as well as the final output.

Table 4 Predicted and field observed values of factors in Raemian slope
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Figure 11 delineates the debris flow thickness position and distribution at various times from 0 to 40 s. The failed soil mass, with a maximum thickness of 3 m (Fig. 11a), collapsed as the flow started (Fig. 11b). After 10 s of the debris material motion, the front part of the flow had a thickness of less than 0.5 m, and overall lengthening of the flow was observed (Fig. 11c). Figure 11d, e shows the movement of the debris flow along the channel bend and some overflow of materials outside of the channel. The flow left the mountain channel and reached the road at approximately 25 s, as displayed in Fig. 11f. The front part of the flow impacted the apartments, with a flow thickness of less than 0.5 m, while the rest of the flow, with a thickness larger than 2.1 m, only reached the road (Fig. 11h). The flow, upon leaving the channel confinement, spread out laterally along the road, and the average thickness of the thicker zones at the rear end of the flow decreased as the flow spread in the deposition region (Fig. 11i).

Fig. 11
figure 11figure 11

Debris flow thickness distribution: a initial time, b 5 s, c 10 s, d 15 s, e 20 s, f 25 s, g 30 s, h 35 s, and i 40 s

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Figure 12 exhibits the predicted maximum velocity of the channelized debris flow versus distance. The figure demonstrates the evolution of velocity as the channeled flow progresses downslope, with a velocity of approximately 25 m/s being attained around the bend ~250 m away from the source. The flow accelerated after the channel bend and attained a maximum velocity of 30 m/s before decelerating downstream as the channel slope decreased. The debris flow runout, upon reaching the end of the watershed and entering the road, had a speed close to 26.81 m/s, which is very similar to that observed during the actual 2011 event, i.e., 28 m/s. The figure confirms the general trend of the debris flow, in which the flow rapidly accelerated to an extremely high velocity of approximately 30 m/s within the channel and then decreased to a value between 20 and 25 m/s in the settlement area. In DAN-3D, the flow stopped after the user-defined time was reached; hence, at 40 s, the flow still had considerable momentum and continued to move. However, in the field, the momentum was lost upon impact with the surrounding buildings.

Fig. 12
figure 12

Debris flow average velocity versus distance

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Figure 13a shows the variation of the volume with distance and time. The increase in volume as the flow distance and time increased indicates the influence of entrainment, which removed soil at a growth rate of 0.0042 m−1, resulting in a final volume of approximately 53,067.9 m3.

Fig. 13
figure 13

Debris flow. a Average volume versus time and distance. b Velocity without entrainment versus velocity with entrainment. c Longitudinal profile of eroded depth

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Discussion

The coupled 3D seepage and slope stability-based analysis gave a volume of 4032 m3 in comparison to a large volume of 13,600 m3 (Park et al. 2013) assessed using the 2D TRIGRS model. This overly conservative estimate of the volume, which is approximately four times the actual volume, can be attributed to non-consideration of the 3D geometry effect, side shear resistance, and end effects (Stark and Eid 1998; Reid et al. 2015). The pore pressure distribution of the 3D seepage analysis, unlike in the 1D- or 2D-based analysis, was influenced by infiltrated rainfall propagation in the X, Y, and Z directions of the topography, especially during heavy rainfall; thus, the FOS continued to decrease even when there was no rainfall for a small time period (Fig. 10). A study conducted using the same rainfall conditions as in the Woomyeon mountain region by means of an infinite slope stability-based model (TRIGRS) exhibited a significant matric suction recovery during the non-rainfall period and subsequently an increase in the FOS value (Kang 2017). The 3D-based LE analysis gave a higher FOS value in comparison to the 2D-based models, which agrees with most of the studies conducted previously (Cavounidis 1987; Xie et al. 2011). The current analysis can take into consideration the influence of curvatures on the initial volume. The predicted volume, approximately 18.58% larger than that observed in the field, occurs at the upstream end of the concave topography and near the outlet of the convex profile curvature of the slope because of the higher influence of the profile curvature (local slope) compared to the plan curvature (Talebi et al. 2007). However, the 3D-based volume assessment can be cumbersome at the site-specific scale owing to the need to obtain initial conditions (matric suction, water table), soil hydrological and shear strength properties, soil depth, and boundary conditions which may vary spatially.

The mobilization of the failed soil mass into a debris flow can be assigned to the large runoff because of the rainfall intensity being approximately 1.78 times the saturated permeability. Also, the soil in the Raemian watershed has an approximate mobility index (AMI) of 1.39, which is greater than 1 (ratio of average in situ saturated water content (50.25%) to average water content at liquid limit (36.18%)), signifying that the soil has higher saturated water content available than its liquid limit, causing the mass to easily flow upon remolding (Ellen and Fleming 1987).

The study clearly demonstrates the approach for a rheological parameter prediction incorporating the site-specific geomorphological and geotechnical conditions. The back-calculated bulk frictional angle model can implicitly consider the rheological variation, e.g., dilution owing to runoff water controlled by the site morphology. There are several existing mechanisms which can explain the decrease in shear resistance for debris mass propagation, e.g., the maintenance of excess pore water pressure due to grain crushing or the presence of fine content, or the Kelvin-Helmholtz-type mechanism, where the pressure wave generated relieves the overburden pressure and thus the shear resistance (Foda 1994). In the current bulk frictional angle model, however, the exact mechanism resulting in a decrease in shear resistance is difficult to be pinpointed because of a lack of detailed experiments and laboratory tests specific to Korean site conditions. The analysis of bulk frictional angle in Raemian slope shows the effective friction angle to decrease by approximately 93.15%, highlighting the major role of pore water pressure in accelerating the flow to extremely high speeds. The extremely low predicted bulk frictional angle of 1.56°, although it is not the actual value of the mobilized residual friction angle, results in extremely high predicted debris flow velocity of 26.81 m/s. The predicted debris flow velocity is comparable to that observed (28 m/s) by the black boxes of CCTV within damaged cars when the debris flow reached the road (Park et al. 2016). A study on the frictional rheological model using the ring shear test for the Gamahara debris flow event of 1996 and the 1997 Harihara debris flow revealed an extremely low bulk frictional angle of 3.6° and 8°~9°, respectively (Table 3). The study determined that the low bulk frictional angle value resulted from the generation and maintenance of excess pore water pressure and verified the efficacy of the effective stress concept in explaining the mechanism. Although the described experimental-based methodologies are commendable in helping to decrease the existing knowledge gaps in the estimation of the basal frictional angle, the insurmountable influence of field conditions such as channel constraints, curvatures, erosion, and water along the path results in extreme variability in the basal friction during a flow. These effects are difficult to simulate in a laboratory and hence require a back-calculation using real events. Also, the adoption of any statistically based rheological parameter prediction model to another site requires a need to evaluate for similarity in the geomorphological and geotechnical conditions.

The predicted growth rate of 0.0042 for Raemian slope is quite low in comparison to that of the other 31 debris flow cases collected across South Korea (Park 2015) primarily due to the relatively higher unit weight, percent fines, and longer first-order drainage channel length. The separation of the resistances terms owing to basal shear and momentum transfer due to entrainment in DAN-3D helps in identifying the influence of erosion on the general flow characteristics. In this study, it is observed that extremely high debris flow velocities (~100 m/s) without the consideration of erosion can be reached in contrast to that upon considering the entrainment mechanism (Fig. 13b). Thus, the resistance due to momentum transfer effect considerably reduces the velocity and the difference between velocities for both the cases keeps on increasing as the flow progresses downslope. Finally, near to the impact on apartment, the velocity without entrainment becomes about 3.33 times that of that with entrainment mechanism. Thus, the inertial resistance owing to momentum transfer effect under high erosion rate of the bed is not upstaged by the low effective basal shear strength (φbulk=1.56°), and therefore, it significantly influences the observed debris flow velocity.

A final volume of 53,067.9 m3 was obtained from the runout analysis and is approximately 15.05% larger than the actual volume observed in the field. The reason for this difference can be attributed mainly to the choice of a conservative value of the displacement-dependent erosion rate. The large final volume, which is approximately 13.16 times the initial volume, indicates the intense erosion that occurred along the Raemian watershed slopes. The field investigation of the debris flow gullies in Raemian after the 27 July 2011 event showed a maximum entrained depth of 2.0 m at the upper portion and 0.1–1.0 m at the lower portion of the channel bed (Jeong et al. 2015). Figure 13c exhibits a maximum depth of approximately 2.0 m at 350 m, and the scouring depth decreases rapidly to approximately 0.1 m along the lower part of the channel because of the decrease in erosion energy. Thus, the erosion trend modeled by DAN-3D using the predicted growth rate matches quite well with that observed in the field. The portion of the debris flow impacting the Raemian apartments had an average thickness of 0.5 m. If a model considering the fluid-structure interaction was simulated, the actual impact could be modeled and may correspond to that shown in Fig. 14, wherein the debris flow impacted more than two floors of the buildings. The predictive debris flow runout assessment conducted for the Raemian slope using the input parameter database establishing method gives a conservative estimate of the total entrained volume, while it estimates an almost similar assessment of the velocity in comparison to the real event. The user-defined growth rate estimation method considered in the framework is not sufficient to create several hazard scenarios corresponding to different initial volumes for a high-risk slope. The limitation can be overcome by the use of soil mechanic-based entrainment models or a statistical growth rate model integrating geotechnical and morphological properties.

Fig. 14
figure 14

Debris flow impact on buildings (Jang Seung-Yoon 2011/Getty images, Truth Leem/Reuters)

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Conclusion

The reliability of the predictive debris flow hazard modeling largely depends on the quality of the input parameter database. Though several methods and approaches for the estimation of initial source volume, rheological parameter, and entrainment growth rate exists, however, there is a lack of thorough research into how the existing methods shall be appropriately used to develop the database of input factors for predictive debris flow assessment especially at a site-specific scale. In this research, therefore, a framework is advanced for estimating the parameters used in the DAN-3D code for debris flow runout modeling at a site-specific scale. The framework was applied to the Raemian slope in the Woomyeon mountain region, Seoul, where an extreme rainfall event on 27 July 2011 triggered a debris flow resulting in several casualties. The initial volume of 4032 m3 was estimated using a 3D-based infiltration and slope stability analysis. Also, a back-calibrated ANN-based model for the bulk frictional angle assessment and an empirical growth rate predicted a debris flow final volume of 53,067.9 m3, a maximum velocity upon arrival on the road of 26.81 m/s, and a debris thickness of approximately 0.5 m concentrated near the Raemian apartments. Notwithstanding limitations like site-specific variations in initial conditions (matric suction, water table), soil hydrological and shear strength properties, soil depth, and boundary conditions, the use of 3D-based analysis for slope stability prediction can yield a more reliable estimate relative to 2D-based analysis.

The proposed approach can be extended to other 3D single-phase-based debris flow codes incorporating entrainment for, e.g., RASH-3D (Pirulli 2010), DFEM-2D (Rickenmann et al. 2006), FLAT-2D (Medina et al. 2008), GEO-SPH (Pastor et al. 2009), and RAMMS (Christen et al. 2010). However, in these codes, the rheological or the entrainment model adopted might be different from that used in this study, and therefore, a suitable estimation of corresponding input parameters (integrating site-specific geomorphological and geotechnical settings) should be undertaken. The prediction of debris flow hazard characteristics can be used for impact analysis and risk scenario generation leading to appropriate design of active or passive countermeasures.