Coupled modeling framework for proactive design of debris-flow barrier placements

Abstract

This study presents a coupled modeling framework for the proactive design of debris-flow mitigation strategies, with a particular focus on optimizing barrier placements. In response to the increasing risks posed by debris flows in mountainous regions, the framework integrates physically based modeling and data-driven methods across four interlinked phases: shallow landslide initiation, debris-flow mobilization, runout simulation, and barrier design. Site-specific geomorphological, geotechnical, and hydrogeological conditions were incorporated to enhance modeling accuracy. Key debris-flow parameters—including initial volume, entrainment rate, and basal friction angle—were estimated using field-based indices and statistical regressions, then applied to the DAN3D dynamic model for simulating debris-flow behavior. Monte Carlo simulations produced velocity and thickness distributions with mean values of 20.86 m/s and 4.09 m, and 99th percentile values (28 m/s and 4.5 m). These extreme-case predictions aligned well with observed peaks from the 2011 Mt. Umyeon debris-flow event, supporting the reliability of the proposed framework. Barrier performance evaluations for two alternative configurations showed that strategic placement significantly reduces downstream impact intensity. Despite remaining uncertainties, such as spatial variability in material properties and real-world complexities, the framework offers a systematic and adaptable approach to debris-flow hazard assessment and infrastructure protection, supporting informed disaster risk reduction in mountainous terrains.

Introduction

Debris flows are one of the most destructive natural hazards in mountainous regions, particularly in Korea, where steep slopes and intense summer rainfall contribute to their frequent occurrence. Notably, the 2011 Mt. Umyeon debris flow in Seoul caused 16 fatalities and severe urban damage, and more than 150 landslides were recorded in the area during that single event¹. Similar events have continued to occur in Korea. In 2019, heavy rainfall in Gangwon Province triggered a series of debris flows in mountainous areas, including Inje and Pyeongchang, resulting in residential damage and emergency evacuations². More recently, in the summer of 2023, record-breaking monsoon rainfall triggered widespread landslides and debris flows, resulting in at least 13 fatalities and severe damage across mountainous regions, as reported by Statistics Korea³. These recurring disasters highlight the urgent need for proactive hazard mitigation planning. In recent years, the frequency and severity of debris-flow events have increased significantly due to global climate change and uncontrolled development in high-risk areas, leading to severe loss of life and infrastructure damage⁴. Effective debris-flow hazard mitigation requires not only reliable prediction of debris-flow dynamics but also a quantitative framework that supports the optimized design of site-specific structural measures^5,6. In this study, we demonstrate the application of this framework through a case study involving closed-type check dams.

Various methods have been developed to assess debris-flow hazards and support the design of countermeasures. Empirical approaches^7,8 rely on historical datasets to estimate debris-flow characteristics such as velocity, volume, and runout distance. These methods are widely used due to their simplicity and rapid applicability. For example, Rickenmann⁷ proposed empirical relationships to predict key debris-flow characteristics—such as peak discharge, front velocity, and runout distance—using catchment area, channel slope, elevation drop, and fan geometry, based on data from approximately 60 debris-flow events in the European Alps. However, empirical methods are often site-specific and struggle to generalize to new or significantly different conditions. Moreover, they rarely consider spatially distributed flow behavior or temporal evolution, making them less suitable for designing mitigation structures in dynamic environments.

In contrast, dynamic modeling approaches⁹ employ physics-based principles, including mass and momentum conservation, to simulate complex debris-flow behavior. These models provide detailed hazard information and can assess the impact of different mitigation strategies. However, their application is often limited by the difficulty of selecting appropriate rheological parameters and geotechnical properties, which govern debris-flow mobility and interaction with the terrain¹⁰. As a result, dynamic models are often used for back-analysis of past events rather than for proactive hazard assessment and mitigation planning. Additionally, while tools such as FLO-2D¹¹ and DEBRIS-2D¹² have been widely used, they tend to simplify erosion and entrainment processes, limiting their applicability in high-gradient, erosion-prone terrains like those found in Korea.

To overcome these limitations, coupled modeling frameworks have been developed by integrating multiple approaches. For example, Park et al.¹³ proposed a hybrid model that combines TRIGRS (for landslide susceptibility mapping), an empirical debris-flow initiation criterion, and FLOW-R (a stochastic model for runout analysis) to generate debris-flow susceptibility maps. While this approach provides valuable insight into potential debris-flow paths, it does not incorporate quantitative predictions of debris-flow velocity, thickness, or volume, limiting its usefulness in designing mitigation structures. Most notably, existing frameworks do not explicitly connect debris-flow simulation outputs to the actual placement and configuration of physical mitigation measures such as check dams. This creates a critical gap between hazard prediction and engineering design. Therefore, there remains a significant need for an integrated framework that not only predicts debris-flow intensity and runout behavior, but also utilizes this information to proactively design site-specific mitigation structures.

This study presents a coupled modeling framework for proactive design of debris-flow barrier placements. The proposed framework combines physically based and statistical approaches to estimate key hazard parameters, including initial debris volume, entrainment growth rate, and basal friction angle, which are then used as inputs for the DAN3D dynamic model. The framework incorporates erosion, entrainment, and rheological variability, enabling realistic simulations of debris-flow behavior in complex mountainous terrains. Unlike conventional approaches, it also connects these simulations to mitigation planning by optimizing the placement and configuration of debris barriers.

To evaluate the effectiveness of this framework, we applied it to a case study of the 2011 debris-flow event at Mt. Umyeon. By simulating debris-flow behavior and assessing the impact of different barrier configurations, we demonstrate how proactive barrier placement can effectively mitigate debris-flow hazards. The findings of this study aim to provide a practical framework for disaster risk reduction by linking hazard intensity prediction to structural mitigation design. While the proposed methodology is broadly applicable, we illustrate its use through a focused case study involving closed-type check dams.

Methodology

This study proposes a coupled modeling framework for the proactive design of debris-flow barrier placements, consisting of the following main processes (Fig. 1): (1) shallow landslide initiation, (2) debris-flow mobilization, (3) debris-flow runout, and (4) barrier placement design modeling using a dynamic numerical model.

Fig. 1

Coupled modeling framework for proactive design of debris-flow barrier placements.

Shallow landslide initiation model

Debris flows, which transition from shallow landslides retaining large amounts of water and exhibit rapid movement, are the most typical type of landslide occurring on natural slopes in mountainous regions of Korea¹⁴. To predict mechanically unstable areas that are at risk of imminent sliding due to rainfall, a physically-based landslide susceptibility analysis is conducted as the first step. This analysis allows spatiotemporal analysis of rainfall impacts without requiring historical landslide inventory. The physically-based model applied here includes a rainfall infiltration analysis to calculate pore-water pressure in the soil and an infinite slope stability analysis to identify unstable areas on a GIS platform.

This framework does not simulate surface runoff generation or overland flow routing, as it focuses specifically on rainfall-induced, landslide-triggered debris flows rather than those driven by concentrated runoff.

The primary input required for this modeling stage is rainfall data. In this study, the actual rainfall event that caused severe debris-flow damage during the 2011 Mt. Umyeon landslide—one of Korea’s most catastrophic landslide disasters—was used to validate the framework under realistic and extreme hazard conditions. The second input dataset is terrain data, specifically slope gradient information necessary for slope stability analysis. This data can be readily extracted from high-resolution digital elevation models (DEMs) using GIS platforms.

Lastly, geo-hydraulic data required for infiltration analysis and geotechnical data necessary for slope stability analysis were primarily obtained through field sampling and laboratory testing in this study. To facilitate future applications over broader regions, the use of AI or machine learning-based estimation techniques has been proposed in the literature for parameters such as SWCC^15,16 using readily measurable data like grain size distribution or sand/clay content. However, these AI-based models must be supported and validated with reliable experimental or field measurements to ensure accuracy and applicability. A more detailed description of these input datasets is provided in the section titled “Database”.

Rainfall infiltration analysis

Rainfall infiltration significantly influences slope stability by altering the pore water pressure and wetting front in unsaturated soils¹⁷. In slopes with unsaturated soil, the infiltrating water changes the pore water pressure profile and weakens the soil’s shear strength, affecting slope stability. This study uses the SEEP/W (Geostudio 2020 version) finite element software for a 1-D rainfall infiltration analysis, which computes transient flow through soil profiles and determines the advancement of wetting fronts under varied rainfall intensities.

The infiltration process in unsaturated soil can be described using Darcy’s Law:

$$v=ki$$

(1)

where v is the Darcian velocity, k is the hydraulic conductivity, and i is the gradient of total hydraulic head. According to the mass balance with Darcy’s Law, a governing equation for transient flow through unsaturated soil can be derived as follows¹⁸:

$$\frac{\partial}{\partial\:x}\left({k}_{x}\frac{\partial\:H}{\partial\:x}\right)+\frac{\partial}{\partial\:y}\left({k}_{y}\frac{\partial\:H}{\partial\:y}\right)=\frac{\partial\:\theta}{\partial\:t}$$

(2)

where H is the total head, k_x is the hydraulic conductivity in the x-direction, k_y is the hydraulic conductivity in the y-direction, Q is the applied boundary flux, $\theta\:$ is the volumetric water content, and t is the time. This equation, known as the Richards equation, is solved iteratively in SEEP/W using boundary and initial conditions, allowing the wetting front’s advancement through unsaturated soil to be computed.

The model domain was simplified to a 2 m-deep soil column, as supported by post-event field investigations of the 2011 Mt. Umyeon landslide, which reported typical failure depths ranging from 1.0 m to 1.5 m¹⁹. A rectangular grid of quadrilateral elements was used to represent the soil layers. Initial matric suction was set at 80 kPa across all depths based on field measurements²⁰ ensuring the model starts under realistic field conditions. The historical rainfall dataset from the Seocho weather station was used, and surface runoff conditions that prevent surface ponding were included, given the sloping nature of the ground surface.

Infinite slope stability analysis

Slope stability analysis was performed in a GIS environment, where each cell was treated as an infinite slope. The Mohr-Coulomb failure criterion was applied to evaluate both saturated and unsaturated conditions²¹. The factor of safety (FS) for each cell was calculated using the following infinite slope equation²²:

$$FS=\frac{{tan}\phi^{\prime}}{{tan}\beta}+\frac{c{\prime}-{\sigma}^{s}{tan}\phi^{\prime}}{{z}_{w}(\gamma\:\cdot\:{sin}\beta\:\cdot\:{cos}\beta\:)}$$

(3)

where $\varnothing^{\prime}$ is the effective internal friction angle, c’ is the effective cohesion, ${\sigma}^{s}$ is the suction stress, $\beta\:$ is the slope angle, z_w is the vertical depth of soil, and $\gamma\:$ is the soil unit weight dependent on the water content, which can be derived using the equation $\gamma\:={\gamma}_{d}+{\theta}_{w}\cdot\:{\rho}_{w}$ (${\theta}_{w}$ is the volumetric water content,$\:{\rho}_{w}$ is the density of water, and ${\gamma}_{d}$ is the dry unit weight (= 14.7 kN/m³). The suction stress was derived using the general formula:

$${\sigma}^{s}=-{S}_{e}({u}_{a}-{u}_{w})$$

(4)

$${S}_{e}=\frac{{\theta}_{w}-{\theta}_{r}}{{\theta}_{s}-{\theta}_{r}}={\left[\frac{1}{1+\left\{\alpha\:\right({u}_{a}-{u}_{w}){\}}^{n}}\right]}^{m}$$

(5)

where S_e is the degree of saturation, u_a is the pore-air pressure (assumed to be zero, equal to atmospheric pressure), and u_w is the pore-water pressure²³.

Debris-flow mobilization model

The debris-flow mobilization model aims to identify areas within landslide-susceptible zones that are likely to evolve into active debris flows. This study employed the artificial neural network (ANN)-based criterion proposed by Kang et al.²⁴ to distinguish debris-flow sources from general landslide-prone areas. The model uses eight geomorphological predictors, including slope gradient, curvature, and upslope contributing area (UCA). The mobilization threshold was determined based on the following relationship:

$$\beta \ge 34\exp (0.003 \cdot {\text{UCA}}) + 14.32\quad ({\text{UCA} \ge 5}00\;{\text{m}}^{{\text{2}}} )$$

(6)

where $\beta\:$ is the slope gradient (°) and UCA is the upslope contributing area (m²). Areas meeting this criterion were designated as debris-flow initiation zones and used as source locations for assigning initial debris volumes in the runout simulations.

Debris-flow runout model

The DAN3D model⁹ using a smoothed-particle hydrodynamics code, was selected for its effectiveness in simulating debris-flow dynamics, especially the entrainment of material along the flow path. The model utilizes a semi-empirical approach with governing equations based on mass and momentum conservation. The DAN3D program requires the information of initial debris volume, entrainment growth rate, and rheological parameters as input data for the debris-flow runout analysis. The estimation of the three input parameters ultimately enables the predictive modeling of debris-flow hazards. The model domain boundaries were delineated based on documented debris-flow traces, including the initiation and deposition areas, to ensure full coverage of the flow path within the simulation.

Entrainment growth rate estimation

The entrainment phenomenon refers to the increase in debris-flow volume due to the addition of water and the erosion of bed materials along the flow path. Park et al.²⁵ demonstrated that the initial debris-flow volume typically increases by 10 to 20 times, with extreme cases reaching up to 100 times. This highlights the importance of considering entrainment in debris-flow simulations. In DAN3D, debris-flow volume is assumed to increase exponentially along the flow path, as expressed in Eq. (7):

$$\overline{{E_{s} }} = \frac{{\ln (V_{f} /V_{o} )}}{S}$$

(7)

where $\overline{{E_{s} }}$ is the average entrainment growth rate, V_f is the final debris-flow volume, V_i is the initial volume, and S is the average path length.

Park et al.²⁵ developed a statistical formula (Eq. (8)) to estimate the average entrainment growth rate ($\overline{{E_{s} }}$) using geomorphological and geotechnical variables. The formula is expressed as:

$$\overline{{E_{s} }} = 0.04717 - 0.002246\ln \left( {L_{{cp}} \cdot Basin_{{30}} } \right) - \frac{{0.000148}}{{D_{{50}} }}$$

(8)

where ${L}_{cp}$ is the channel path length, ${Basin}_{30}$ is basin area with slope inclinations of 30% or greater, and ${D}_{50}$ is the median of grain-size distribution. Although this formula was developed from datasets in other debris-flow-prone Korean catchments, the geomorphological characteristics are comparable to those of the Mt. Umyeon watershed. Thus, the formula is considered suitable for first-order estimation under similar local conditions. All input variables (${L}_{cp}$, ${Basin}_{30}$, ${D}_{50}$) were measured within the Raemian watershed to ensure site-specific applicability. This entrainment estimate was not used for precise calibration but rather to support realistic parameterization in DAN3D simulations.

Rheological parameter estimation

Rheological properties are critical for accurately modeling debris-flow behavior, as they govern the internal deformation and flow dynamics of the material during movement. DAN3D provides five rheological models (Newtonian, Plastic, Bingham, Frictional, and Voellmy) to simulate debris-flow characteristics under varying environmental conditions. Each model calculates basal shear stress, which resists the debris-flow movement.

For this study, the Frictional model was selected due to its simplicity and reliability in requiring only a single input parameter: the bulk basal friction angle (​${\phi}_{b}$). The shear stress (τ) is defined as follows⁹:

$$\tau\:=(\sigma\:-u){tan}\phi\:$$

(9)

where is σ is the total bed-normal stress, u is the pore water pressure, and ϕ is the basal friction angle. Using the pore pressure ratio (r_u = u/σ), the equation simplifies to:

$$\tau\:=\sigma\:(1-{r}_{u}){tan}\phi\:$$

(10)

To simplify further, the ​${\phi}_{b}$is introduced, which represents an effective friction angle accounting for pore-water pressure effects. This is expressed as:

$${{tan}\phi}_{b}=(1-{r}_{u}){tan}\phi\:$$

(11)

Thus, the basal shear stress can be rewritten as:

$$\tau\:=\sigma\:{{tan}\phi}_{b}$$

(12)

This formulation allows the rheological property to be characterized by a single parameter, ${\phi}_{b}$, which can be estimated via stochastic methods. The stochastic methods, such as Monte Carlo simulations, are particularly advantageous as these account for variability and uncertainty in field conditions.

For this study, the ${\phi}_{b}$ was determined through Monte Carlo simulations, using a back-analyzed database of past debris-flow events. A comprehensive database on basal friction angles was established by Lee²⁶ through back-analysis of 37 debris-flow cases in the central region of Korea, including events characterized by high mobility and long runout distances under saturated conditions.

It is important to note that the ${\phi}_{b}$ values used in this study were not obtained from laboratory or field testing, but were derived through numerical back-analysis to match observed debris-flow behavior. In particular, extreme cases with highly fluidized, clay-rich or fine-grained materials—commonly seen in Korean debris flows—led to friction angles as low as 1–2°.

Based on this study, the probability density function (PDF) of the ${\phi}_{b}$ was determined to follow a log-logistic distribution, as shown in Fig. 2a. The mean and variance of the basal friction angle were calculated as 4.15° and 2.96°, respectively. Despite appearing low from a physical standpoint, these values are suitable for dynamic modeling as they reproduce real-world debris-flow behavior in complex mountainous terrains. These values served as essential inputs for the DAN3D model, enabling the simulation of debris-flow dynamics with realistic parameter variability.

The detailed Monte Carlo simulation procedure is illustrated in Fig. 2b:

• Step 1. Establishing a database of ϕ_b values from previous events.

• Step 2. Fitting the data to a PDF.

• Step 3. Randomly sampling ϕ_b values from the PDF for 2,000 model runs in DAN3D.

• Step 4. Plotting the results (velocity and thickness) as PDF and cumulative distribution function (CDF).

This stochastic approach ensures the framework accounts for variability in rheological properties and provides probabilistic predictions of debris-flow hazards.

Fig. 2

Parameter uncertainty characterization and debris-flow runout modeling process: (a) Log-logistic distribution of the basal friction angle from the input parameter database; (b) Flowchart illustrating the application of the Monte Carlo method for debris-flow runout simulation using randomly sampled input parameters.

Barrier placement design: optimal number and location

Based on the predictive debris-flow hazard intensity information—such as velocity and thickness—derived from the previously introduced modeling framework, various mitigation measures can be proactively designed. In this study, a case-based approach was employed to determine the optimal placement of closed-type check dams by comparing two design scenarios with different numbers and configurations of these structures.

The placement and configuration of the closed-type check dams were guided by a combination of debris-flow initiation characteristics, model-predicted runout behavior, and terrain morphology. Specifically, three main criteria were applied:

• (1) the locations of debris-flow initiation zones identified through susceptibility mapping,

• (2) simulation results of flow paths, velocities, and debris-flow thickness distributions obtained from the DAN3D model,

• (3) topographic features such as slope breaks, channel convergence points, and natural deposition zones.

In Case 1, a single closed-type check dam was installed immediately downstream of the lowest initiation source area, where the channel slope sharply decreases and flow accumulation is intensified. This placement aimed to intercept debris before reaching downstream infrastructure. In Case 2, a two-tier barrier configuration was applied: one dam near the uppermost initiation source area to reduce flow momentum in the early stage, and a second dam at the same location as in Case 1. This configuration was intended to evaluate the performance of sequential interception in mitigating flow energy and reducing downstream vulnerability.

The dam locations were aligned with points where the DAN3D simulation indicated a rapid increase in flow thickness and velocity, as well as morphological transitions in the channel profile. The effectiveness of each barrier scenario was quantitatively assessed using a vulnerability index, which incorporates debris-flow velocity and thickness to estimate potential structural damage in the downstream area. A schematic overview is provided in Fig. 3. The vulnerability index, which quantifies potential building damage, was calculated using the following formulas²⁷:

$$V=1-{e}^{(-0.1703{h}^{1.537})}$$

(13)

$$V=1-{e}^{(-0.0094{v}^{2.775})}$$

(14)

where V is the vulnerability index, h is the flow thickness (m), and v is the flow velocity (m/s). Kang and Kim²⁷ suggested four levels of classification for building damage and they distinguished degrees of damage based on the vulnerability index (Table 1).

Fig. 3

Description of the closed-type check dam locations in this study.

Table 1 Classification of building damage by debris flows (Kang and Kim²⁷).

The closed-type check dams were installed to be perpendicular to the debris-flow directions of the reference case. Surface erosion near the barrier was prevented by setting a no erosion zone, which was half the width of the check dams (check dam 1: 35 m, check dam 2: 15 m). The specifications of closed-type check dams are summarized in Table 2.

Table 2 Specification of the closed-type check dams.

Study area

The study area is the Raemian watershed located on the northern slope of Mt. Umyeon, as shown in Fig. 4a. This watershed has an area of 75,600 m² with average slope angles of 44° at the initiation area and 19° along the channel path¹. Here, the initiation area refers to the upper slope segments that contributed directly to the main debris-flow path, as identified through field investigation and post-event imagery. The debris flow in this area traveled a runout distance of 606.7 m, with a maximum observed eroded depth of 4 m, resulting in a final debris volume of approximately 46,500 m³, as derived from post-event field investigation reports by Korean Geotechnical Society (KGS)¹⁹ and Korean Society of Civil Engineers (KSCE)²⁸. This debris-flow event directly impacted nearby apartment buildings, causing significant damage up to the fourth floor, as illustrated in Fig. 4b.

Fig. 4

Overview of the 2011 debris-flow disaster in the Mt. Umyeon area: (a) Location of the target area (red dashed box) and the number of fatalities in each region on July 27, 2011. Point A indicates the Raemian region, where debris-flow behavior was directly observed, including flow velocity and thickness; (b) Debris-flow impact and key geomorphic zones in the Raemian watershed. This figure includes an upper right photograph of the initiation zone (originally cited as Yune et al.²⁹) and a lower right photograph of the deposition zone (originally cited as Jeong et al.¹) within the figure.

Several institutions, such as the KGS and the KSCE, conducted immediate field surveys after the debris-flow event. They recorded essential data, including the geotechnical properties and geological changes caused by the event, which provided a detailed basis for quantitative debris-flow analysis. In particular, the Raemian watershed incident was well-documented through video evidence from vehicle dashcams, CCTVs, and mobile phones, enabling the direct observation of debris-flow behavior. The velocity of the debris flow was estimated to be 28 m/s based on the travel time and distance covered across the affected area, a notably high speed compared to similar events worldwide.

The exceptional mobility of the debris flow in this region is attributed to high liquidity caused by excessive rainfall that saturated the slope just before the event¹³. This increased water content and reduced debris sediment concentration, further enhancing debris mobility. These unique site characteristics make the Raemian watershed a critical case study for analyzing extreme debris-flow hazards and testing the effectiveness of mitigation measures, while aiming for the ultimate goal of strategically placing debris barriers in advance of actual disaster occurrences.

Database

The debris-flow modeling relies on a comprehensive dataset, encompassing geotechnical, hydraulic, meteorological, and terrain-related information. These data sources are essential for accurately modeling a sequential process of debris flows that spans from shallow landsliding, debris-flow mobilization, and runout behavior within the Raemian watershed.

Rainfall data

Rainfall data is a crucial component of the shallow landslide modeling, as heavy rainfall events are a primary trigger for debris flows in the study area. For this analysis, rainfall data were obtained from the Seocho weather station, which recorded hourly measurements during the storm event on 25–27 July 2011 (Fig. 5). Although this study utilized actual rainfall data from a past event for validation purposes, for general predictive modeling, hazard assessment can be performed by applying a constant rainfall intensity of 10 mm/hr and continuing the rainfall until slope instability occurs, following the methodology developed by Park et al.³⁰. This threshold, though not extremely high, has been shown to yield high predictive accuracy for landslide initiation in Korea, where slopes are particularly sensitive due to the moderate permeability of local weathered soils (~ 10 mm/hr or 2.8 × 10⁻⁶ m/s).

Fig. 5

Hourly and continuous rainfall distribution on 25–27 July 2011 obtained by the Seocho weather station.

Geotechnical and terrain data

Geotechnical properties play a fundamental role in assessing slope stability. For this study, the values of effective cohesion ($c{\prime}$) and internal friction angle ($\phi^{\prime}$) (Table 3) were obtained from Kim et al.³¹based on field shear tests conducted in boreholes and laboratory tests on trial pit soils, as illustrated in Fig. 6a. The cohesion values ranged from 6.9 to 11.8 kPa, with an average value of 7.5 kPa applied for spatial interpolation in the GIS model using the kriging method. Similarly, the effective internal friction angle varied between 21.7° and 25.1°, with a mean value of 22.3° utilized for the infinite slope stability analysis. The interpolation results are illustrated in the geotechnical property maps for cohesion and friction angle (Fig. 6b and c, respectively).

Although the sampling points (PT1–4 and B1–2) are not evenly distributed across the study area, all available data were used to improve the spatial representation of soil parameters. Compared to relying on a single measurement value, the use of multiple data points, even with spatial imbalance, offers a more reasonable and informative basis for geotechnical analysis. It is noted that the interpolation results are intended to provide generalized spatial trends, rather than detailed local heterogeneity.

Soil dry unit weight (γ) was determined through field density tests on both saturated and unsaturated soil samples and set at 14.7 kN/m³ across the study area. The slope gradient and elevation, were extracted from 5 m-resolution DEM of the Raemian watershed (Fig. 6d). The slope angle across the area varies between 0° and 50°.

Fig. 6

Spatial distribution of investigation points and geotechnical parameters (refer to Kim et al.³¹): (a) Location map of boreholes and trial pits; (b) distribution of friction angle; (c) spatial distribution of cohesion; (d) spatial map of slope angle.

Table 3 Geotechnical properties of the soil (refer to Kim et al.³¹).

Geo-hydraulic data

Hydraulic properties of unsaturated soil are critical for accurately simulating rainfall infiltration and its effect on slope stability. The saturated permeability was determined to be 8.0 × 10^− 6 m/s, based on permeability tests conducted on representative soil samples from the site. The soil-water characteristic curve (SWCC) and permeability functions, which represents the relationship between soil moisture content and matric suction, was derived using van Genuchten³²’s empirical equations (Eqs. (15) and (16), respectively), as follows:

$${\theta}_{w}={\theta}_{r}+({\theta}_{s}-{\theta}_{r}){\left[\frac{1}{1+(\alpha\:\psi\:{)}^{n}}\right]}^{m}$$

(15)

$$k={k}_{s}\frac{[1-(\alpha\:\psi\:{)}^{n-1}\{1+(\alpha\:\psi\:{)}^{n}{\}}^{-m}{]}^{2}}{\{1+(\alpha\:\psi\:{)}^{n}{\}}^{m/2}}$$

(16)

where ${\theta}_{w}$ is the volumetric water content, ${\theta}_{s}$ is the saturated volumetric water content, ${\theta}_{r}$ is the residual volumetric water content, $\psi\:$is the matric suction, $k$ is the coefficient of permeability, ${k}_{s}$ is the saturated coefficient of permeability, $\alpha\:\:$and n are the empirical fitting parameters, and m = 1–1/n. These properties, as illustrated in Table 4; Fig. 7, were critical for capturing infiltration behavior and simulating transient pore water pressure accurately.

Fig. 7

Hydraulic properties of unsaturated soil used in this study: (a) SWCC; (b) coefficient of permeability curve.

Table 4 Hydraulic properties of unsaturated soil used in this study (refer to Kim et al.³¹).

Results

In this section, the applicability of the modeling framework proposed in the section titled “Methodology” was evaluated through a case study of the Mt. Umyeon landslide area. The framework was applied under the assumption of a pre-landslide scenario, reflecting conditions prior to the occurrence of the actual Mt. Umyeon landslide. Each analysis step was sequentially conducted to design and implement mitigation measures in a virtual environment. The results were then compared to the observed outcomes of the actual landslide event (reference case) to assess the framework’s accuracy and validity. This preliminary study demonstrated the framework’s potential as a mitigation tool by effectively reducing simulated debris-flow impacts in the study area.

Shallow landslide initiation

A key objective of this step was to evaluate the spatiotemporal predictability of unstable areas in the Raemian watershed by combining 1-D infiltration analysis (using SEEP/W) and infinite slope stability analysis (using ArcGIS). The infiltration analysis simulated the impact of rainfall from 0 h (before rainfall onset) to 17 h (when the debris flow occurred). The results provide crucial insights into the hydrological and mechanical processes leading to slope failure.

Figure 8a and b show the vertical profiles of pore water pressure and suction stress, respectively. The pore water pressure and suction stress progressively diminished from the surface to deeper layers as the wetting front advanced toward the bedrock. By 17 h, the pore water pressure and suction stress reached approximately 0 kPa up to a depth of 1.3 m, indicating saturated conditions conducive to slope failure. Notably, between 15 h and 17 h, the rainfall intensity exceeded the saturated permeability (28 mm/hr), creating conditions for potential run-off. While run-off was not explicitly modeled, it likely influenced the rapid debris flow observed in the field.

The infinite slope stability analysis, as shown in Fig. 8c, highlights that the FS decreased with increasing rainfall infiltration. At 15 h, FS reached 1.3 at a depth of 1.0 m, suggesting potential landslide warnings could be issued. By 17 h, FS dropped to 1.0 at a depth of 1.3 m, signaling imminent failure. Spatial analysis results (Fig. 9) reveal how unstable areas expanded over time, emphasizing the utility of time-varying landslide maps in forecasting hazardous zones.

Fig. 8

Vertical profile results of infiltration and slope stability analysis over time: (a) pore water pressure; (b) suction stress; (c) safety factor.

Fig. 9

Results of time-varying landslide susceptibility analysis in the Raemian watershed: (a) 14 h; (b) 15 h; (c) 16 h; (d) 17 h (at the time of debris-flow occurrence).

Debris-flow mobilization

The main objectives in this step are to identify the locations of debris-flow initiation points from the unstable areas derived in the section titled “Shallow landslide initiation” and then to extract the initial volumes from these landslide sources by applying the debris-flow mobilization criterion. Figure 10a illustrates the potential initiation points within the unstable areas in the Raemian watershed, which satisfy the specified geomorphological criterion for debris-flow mobilization. The application of the debris-flow mobilization criterion produced the results that were in good agreement with the evidence provided by historical debris-flow sources with a total of four, which occupied 11.2% of the entire watershed area.

As shown in Fig. 10b, there were no initial debris-flow sources prior to 16 h of rainfall among the unstable areas. The debris-flow initiation points began to occur in the vicinity of Sources 1, 3, and 4 at 17 h of rainfall (Fig. 10c). The predicted debris-flow initial volume was estimated as 747.5 m³. However, Source 2 could not be detected, which may be due to the uncertainty of the geotechnical properties and subsurface geometry assumed in the 1-D rainfall infiltration and infinite slope analyses.

Fig. 10

Prediction of debris-flow initiation using the mobilization criterion: (a) application result of the debris-flow mobilization criterion in the Raemian watershed; (b) landslide susceptibility analysis at 14–16 h (no predicted source areas); (c) predicted debris-flow initiation source at 17 h.

Debris-flow runout

The DAN3D dynamic model simulated debris-flow behaviors, including velocity, thickness, and flow path. For this purpose, input data regarding the initial debris volume were generated and applied based on the results derived in the section titled “Debris-flow mobilization”. The values of geomorphological and geotechnical variables required for the statistical formula calculation of the average entrainment growth rate ($\stackrel{-}{{E}_{s}}$) in the Raemian region were as follows: the ${L}_{cp}$ was 647 m, the ${Basin}_{30}$ was 56,434 m², and the ${D}_{50}$ was 0.27 mm. Substituting these values into Eq. (10), $\stackrel{-}{{E}_{s}}$ was calculated as 0.0075%/m. Monte Carlo simulations using basal friction angle distributions (Fig. 2a) provided detailed velocity and thickness distributions (Fig. 11) at the point A, as previously illustrated in Fig. 4.

Fig. 11

Log-logistic distribution of debris-flow velocity and thickness at point A: (a) PDF of velocity; (b) CDF of velocity; (c) PDF of thickness; (d) CDF of thickness.

The probabilistic Monte Carlo simulations yielded a debris-flow velocity distribution with a mean of 20.86 m/s (range: 17.65–28.31 m/s) and a thickness distribution with a mean of 4.09 m (range: 3.81–4.62 m). While the predicted mean values were lower than the observed peak values, the 99th percentile results closely matched the observed velocity (28 m/s) and thickness (4.5 m), indicating that the model effectively captured the extreme behavior of the debris flow. These findings suggest that the debris flow in the Raemian watershed was exceptionally rapid and hazardous, likely influenced by significant run-off contributions.

In addition to flow velocity and thickness, erosion depth along the flow path was also analyzed by comparing DAN3D simulation results with observed pre- and post-event surface elevation profiles. Figure 12 illustrates a comparison of the simulated erosion depth with field-measured surface change along the gully. Although some localized underestimation of erosion was observed in the DAN3D output, the model effectively represented the general trend of erosion accumulation along the flow path, consistent with its exponential erosion assumption.

Fig. 12

Comparison of pre- and post-debris flow surface elevation profiles and simulated erosion depth along the channel (The pre- and post-event surface data were reproduced from Kim et al.³¹ while the simulated erosion depth was obtained from DAN3D modeling conducted in this study).

In the proposed coupled modeling framework, the debris-flow runout modeling results corresponding to the 99th percentile velocity were utilized in the subsequent barrier placement design phase to ensure that the barriers would effectively handle extreme scenarios. Both flow velocity and debris thickness were used independently as design criteria in the barrier placement process. The Monte Carlo simulations provided statistical distributions for both parameters, reflecting their respective sensitivities to rheological variability and their distinct roles in influencing debris-flow impact forces and barrier design requirements.

Barrier placement design

In this step, a comparative study was conducted to assess how different locations and numbers of closed-type check dams influence the reduction of debris-flow hazards, based on the debris-flow runout modeling results corresponding to the 99th percentile velocity derived from the section titled “Debris-flow runout”. These modeling results, representing conditions without check dams (Fig. 13a), serve as the reference case for comparison with the outcomes from debris-flow runout analyses (hereafter referred to as Case 1 and 2) conducted under identical debris-flow scenarios but incorporating check dams.

In Case 1, a single check dam was installed at the end of a debris-flow initiation source area (Source 1 in Fig. 13b). The results indicated reductions in debris-flow velocity, thickness, and volume by 50%, 73%, and 55%, respectively, compared to the reference case. However, as observed in the modeling result at 40s (Fig. 13b), debris flows originating from Sources 3 and 4 overflowed Check Dam 1 and reached the Raemian apartments. While the vulnerability index for thickness decreased significantly from 0.76 to 0.2, suggesting only slight structural damage to the buildings, the vulnerability index for velocity showed negligible reduction, indicating that complete damage would still be expected. Therefore, Case 1 proved inadequate for mitigating debris-flow hazards effectively.

In contrast, Case 2 (Fig. 13c) involve d the installation of two check dams at the start and end of the potential initiation source areas. This configuration fully protected the Raemian apartments from debris-flow impacts, demonstrating the importance of strategic placement and additional barriers for effective hazard mitigation.

Fig. 13

Comparison of debris-flow thickness distribution over time for three design scenarios: (a) reference model (no check dam); (b) Case 1 (one check dam); (c) Case 2 (two check dams). Each panel shows debris-flow thickness at multiple time steps.

As shown in Table 5, the reference case closely matches the debris-flow hazard intensities documented during the historical 2011 debris-flow event in the Raemian watershed. Furthermore, the check dam configurations implemented in Case 2 effectively reduced both velocity and thickness to zero at point A, resulting in a vulnerability index of 0.

Table 5 Results of debris-flow hazard reduction according to the number of check dams.

Discussion

The findings of this study provide valuable insights for both hazard assessment and mitigation planning. The time-varying landslide stability maps demonstrated the potential for issuing timely landslide warnings, which could facilitate early evacuation and reduce human casualties. By identifying the threshold FS value of 1.3 as a critical indicator, the study offers a practical framework for landslide forecasting in similar geomorphological settings.

Compared to previous studies, the proposed framework offers notable improvements in both modeling depth and its applicability to structural design. Empirical approaches, although useful, often lack the capacity to simulate flow-path evolution and energy accumulation, making them unsuitable for detailed structural planning. The earlier framework, such as that proposed by Park et al.¹³effectively identifies high-risk zones but does not quantify debris-flow intensities such as velocity or thickness. It also fails to incorporate structural mitigation components like barrier placement or optimization.

Furthermore, numerical tools like FLO-2D¹¹ or Debris-2D¹² are widely applied. However, they often do not adequately simulate erosion or entrainment processes. This limits their use in modeling high-speed, volume-increasing debris flows characteristic of Korean terrains. In contrast, the present study links rainfall-induced slope instability, probabilistic entrainment modeling, and dynamic runout simulation in a unified framework that directly supports the design and evaluation of check dams under extreme hazard scenarios.

To date, only a few studies have attempted to integrate entrainment into dynamic flow simulations in conjunction with structural mitigation design. One such study is Choi et al.³³ who used DAN3D to numerically reconstruct a past debris-flow event and evaluate the effectiveness of a check dam configuration. While their study considered entrainment and dynamic flow behavior, it was focused on retrospective analysis and did not aim to develop a predictive or design-oriented framework. The present study builds upon such efforts by introducing a forward-looking methodology for evaluating multiple structural configurations under uncertain future conditions.

The extreme velocity observed in the Mt. Umyeon debris flow (28 m/s) can be partially explained by entrainment-driven momentum growth, as demonstrated by Iverson et al.³⁴ who showed that debris flows traveling over saturated, erodible beds can accelerate due to positive pore-pressure feedback and dynamic entrainment. In comparison, Revellino et al.³⁵ conducted a dynamic back-analysis of debris avalanches in Sarno and Cervinara, Italy, and found velocities typically ranging from 5 to 15 m/s, with extreme cases reaching 20 m/s. In another study, Abe et al.³⁶ performed a numerical simulation of debris-flow runout using a depth-averaged material point method and reported a maximum velocity of 60 m/s, which was consistent with results from a Newtonian fluid model.

These cases highlight the potential for extremely high mobility in debris flows, especially under fluidized and saturated conditions. They underscore the necessity of designing debris-flow mitigation structures with a focus on extreme-case scenarios, as average or historical conditions may significantly underestimate impact forces. By incorporating time-varying entrainment, pore-pressure feedback, and Monte Carlo-based rheological uncertainties, the proposed framework improves upon earlier approaches and aligns well with field-scale observations across diverse geographic regions.

The preliminary study on check dam deployment highlighted the importance of strategic placement and optimal number of dams in mitigating debris-flow hazards. While a single check dam in Case 1 reduced debris-flow velocity, thickness, and volume, this mitigation was insufficient to fully protect vulnerable structures, particularly when dealing with large source volumes or multiple initiation points. In Case 2, the addition of a second check dam near the highest initiation source demonstrated complete mitigation of debris-flow impacts in this specific case. This highlights the advantage of targeting initiation sources to reduce potential debris-flow energy and entrainment along the flow path.

However, it is essential to note that using multiple check dams is not universally better. The findings emphasize that the effectiveness of check dam installations depends on site-specific conditions, including debris-flow source volume, initiation point locations, and the geomorphological characteristics of the watershed. For instance, knowing the precise locations and volumes of debris sources allows for a more targeted and effective defense, as demonstrated in Case 2.

Despite its contributions, this study has several limitations that should be addressed in future research. First, the modeling framework does not include surface runoff generation or flow routing processes. While this exclusion is reasonable for landslide-triggered debris flows primarily driven by infiltration, it limits the applicability of the framework to runoff-triggered debris flows, which require different hydrological modeling approaches. This limitation should be considered when applying the framework to regions where surface flow accumulation is a dominant triggering mechanism.

Second, the check dams modeled in this study were assumed to be empty at the onset of the debris-flow event and were evaluated for a single extreme scenario. In practice, the effectiveness of closed-type check dams would decline in multi-event situations unless regular sediment removal and maintenance are conducted. This modeling simplification highlights the need for future studies to incorporate sediment retention dynamics and event-to-event recovery cycles into design evaluations.

Additionally, the study’s focus on closed-type check dam location and number did not extend to variations in dam design, size, or type. Investigating alternative barrier designs, such as slit dams or ring nets, could help identify more cost-effective and environmentally sustainable solutions. Finally, uncertainties in the geotechnical properties used in the analysis may have influenced prediction accuracy and should be addressed through sensitivity analyses or probabilistic modeling approaches to improve reliability.

In summary, while previous methods have either focused on empirical estimation⁷ or regional susceptibility mapping¹⁴ this study proposes a proactive framework that bridges hazard prediction with structural design through dynamic simulation. This integration enhances the practical utility of hazard assessments and provides quantitative criteria for mitigation planning—an area often underexplored in earlier literature.

Overall, the study demonstrates a robust approach to enable anticipatory modeling of extreme debris-flow scenarios by incorporating site-specific characteristics and subsequently designing optimized configurations of mitigation measures. However, incorporating additional factors and addressing the outlined limitations would further enhance its applicability and reliability, particularly under extreme rainfall scenarios. Future research should build on these findings to develop comprehensive, multi-faceted strategies for debris-flow disaster prevention and mitigation.

Conclusions

This study presented a robust coupled modeling framework aimed at the proactive design of debris-flow barrier placements. The framework consists of the following sequential modeling phases: shallow landslide initiation, debris-flow mobilization, debris-flow runout, and, finally, barrier placement design. In each modeling phase leading up to the final design stage, physically-based or data-driven approaches were applied to simulate debris-flow scenarios under the most extreme conditions that could potentially occur, based on site-specific geomorphological, geo-hydraulic, geotechnical, and geological characteristics. A case study in the Raemian watershed validated the framework’s effectiveness in debris-flow hazard prediction and mitigation planning.

In the first modeling phase, the physically-based landslide susceptibility analysis identified unstable areas beginning at 15 h of rainfall. By 17 h, these areas satisfied the debris-flow mobilization criterion, and the initial debris-flow volume was estimated at 747.5 m³. The entrainment growth rate, calculated using the statistical formula, was determined to be 0.0075%/m. The probabilistic Monte Carlo simulation yielded a debris-flow velocity distribution with a mean of 20.86 m/s and a range of 17.65–28.31 m/s, while the thickness distribution had a mean of 4.09 m and ranged from 3.81 to 4.62 m. The observed debris-flow hazards—28 m/s velocity and 4.5 m thickness—were confirmed to fall within the 99th percentile of the predicted hazard range, providing a reasonable basis within the coupled modeling framework for determining an extreme debris-flow scenario for barrier design.

Building on the predicted hazard information, a preliminary study explored the effectiveness of different closed-type check dam configurations. A single check dam placed at the end of the potential initiation source reduced debris-flow thickness and volume but failed to mitigate velocity hazards sufficiently, leaving the buildings vulnerable. The addition of a second check dam near the highest initiation source completely prevented debris-flow impacts in this specific case. However, the study emphasizes that this result is context-specific and should not be generalized. Instead, it highlights the importance of strategic check dam design, where the number, location, and type of dams are tailored to site-specific conditions for optimal hazard reduction and resource efficiency.

This framework offers a systematic and data-driven approach to debris-flow hazard assessment and mitigation, providing actionable insights for disaster prevention managers. By enabling proactive simulations of site-specific extreme debris-flow scenarios and evaluating the performance of mitigation measures, the framework facilitates cost-effective and environmentally sustainable planning for barrier installations. Additionally, further improvements could be achieved by incorporating real-time monitoring data and comprehensive economic analyses into the modeling approach, thereby providing more holistic and practical guidelines for mitigation measures. Future research should also aim to investigate real-world barrier performance and structural resilience under extreme debris-flow conditions.