Rainfall-induced Debris Flows Research Articles

Monitoring cases of rainfall-induced debris flows in China

Monitoring cases of rainfall-induced debris flows in China

Deep learning prediction of rainfall-driven debris flows considering the similar critical thresholds within comparable background conditions

Machine learning has been widely applied to predict the spatial or temporal likelihood of debris flows by leveraging its powerful capability to fit nonlinear features and uncover underlying patterns or rules in the complex formation mechanisms of debris flows. However, traditional approaches, including some current machine learning-based prediction models, still have limitations when used for debris flow prediction. These include the lack of a specific network structure or model to consider the updating of debris flow critical conditions in relation to geographical background conditions, limiting the universality of prediction models when transferring them to different places. In this study, this article proposes a deep learning network designed to predict the spatiotemporal probability of rainfall-induced debris flows, incorporating the Similarity Mechanism of Debris Flow Critical Conditions (SM-DFCC). The model comprehensively integrates the mining of rainfall-triggering features and couples them with geographical background features to fit the nonlinear relationship with debris flow formation. The model underwent training using data on various historical debris flows triggered by different storms across Liangshan Prefecture from 2020 to 2022. The results indicated that: (i) the method is effective in predicting the spatiotemporal likelihood of debris flows under catchment units, with accuracy scores (ACC) ranging from 0.724 to 0.835; (ii) after optimization using the AVOA algorithm, the predictive performance of the model significantly improved, with an increase of 27.24% in ACC scores for SVC and 8.81% for XGBoost; and (iii) factor importance analysis revealed that rainfall triggering factors have higher cumulative contribution rates when distinguishing between the occurrence and non-occurrence of debris flows. In addition, taking a rainfall storm on 06, September 2020 as a case, this research quantitatively revealed the pattern of debris flow formation, where high-frequency disaster areas exhibit lower rainfall thresholds of debris flows, represented by absolute energy (AE). Despite these findings, the accuracy and reliability of rainfall data still remain the most challenging obstacle in basin/regional-scale debris flow prediction when applying this method. The integration of multiple sources of rainfall data, including station data, satellite rainfall, radar rainfall, etc., is necessary to accurately quantify the impact of rainfall on debris flow formation when applying this method to debris flow monitoring and early warning tasks. Overall, this method shows great potential in providing a scientific reference for the construction of debris flow monitoring and early warning systems in the future.

Prediction of rainfall-induced debris flow using Random Forests and Bayesian Optimization in Yingxiu Town, Wenchuan County, China

Prediction of rainfall-induced debris flow using Random Forests and Bayesian Optimization in Yingxiu Town, Wenchuan County, China

Debris flow at Luib on the A87 strategic road: Isle of Skye, Scotland

A rainfall-induced debris flow occurred on 30 September 2022, closing the A87 trunk (strategic) road on the Isle of Skye for around 2 h. Ground-based and aerial drone inspections were used to describe the event and a comprehensive rainfall analysis was undertaken. It is concluded that the event was triggered by overland water flow from the slopes above the source zone as a result of high rainfall. The resulting translational slide transitioned into a debris flow that reached a pre-existing channel where entrained superficial deposits were deposited, adding to pre-existing levee structures before reaching the road. The rainfall that led to the debris flow was high intensity–low duration; the rainfall analysis encompasses annual, monthly, daily, hourly and 15 min data, each aiding understanding of the climate of the area and/or the event rainfall. Comparison is made with a rainfall event the following month, which was of a greater magnitude but of longer duration and lower intensity. The hazard at this location is a concern but the risk is emphasized by the proximity of the road to the steep slopes above and the lack of a viable detour. Thematic collection: This article is part of the Geo-resilience and infrastructure collection available at: https://www.lyellcollection.org/topic/collections/geo-resilience-and-infrastructure

Numerical-model-derived intensity–duration thresholds for early warning of rainfall-induced debris flows in a Himalayan catchment

Abstract. Debris flows triggered by rainfall are catastrophic geohazards that occur compounded during extreme events. Few early warning systems for shallow landslides and debris flows at the territorial scale use thresholds of rainfall intensity–duration (ID). ID thresholds are mostly defined using hourly rainfall. Due to instrumental and operational challenges, current early warning systems have difficulty forecasting sub-daily time series of weather for landslides in the Himalayas. Here, we present a framework that employs a spatio-temporal numerical model preceded by the Weather Research And Forecast (WRF) Model for analysing debris flows induced by rainfall. The WRF model runs at 1.8 km × 1.8 km resolution to produce hourly rainfall. The hourly rainfall is then used as an input boundary condition in the spatio-temporal numerical model for debris flows. The debris flow model is an updated version of Van Asch et al. (2014) in which sensitivity to volumetric water content, moisture-content-dependent hydraulic conductivity, and seepage routines are introduced within the governing equations. The spatio-temporal numerical model of debris flows is first calibrated for the mass movements in the Kedarnath catchment that occurred during the 2013 North India floods. Various precipitation intensities based on the glossary of the India Meteorological Department (IMD) are set, and parametric numerical simulations are run identifying ID thresholds of debris flows. Our findings suggest that the WRF model combined with the debris flow numerical model shall be used to establish ID thresholds in territorial landslide early warning systems (Te-LEWSs).

Copula-Based Probabilistic Hazard Assessment Model for Debris Flow Considering the Uncertainties of Multiple Influencing Factors

This paper proposes a probabilistic hazard assessment model for debris flows considering the uncertainties of multiple influencing factors based on copula approaches. Fifty-nine rainfall-induced debris flows occurred between 2001 and 2009 in Taiwan are taken as an illustrative example to validate the proposed approaches. A copula-based probabilistic model is developed to model the joint probability distribution of debris-flow volume V and its influencing factors (e.g., rainfall intensity, RI and landslide area, AL). The developed model is then used to make probabilistic prediction of debris-flow volume for a specific hazard level, and compared with the empirical approaches. The proposed probabilistic model is also used to develop the exceedance probability charts of quantities for a specific debris-flow basin. Results show that the developed V–RI–AL probabilistic model can provide reasonable estimates of debris-flow volume in Taiwan for a specific probability level of 0.94, and show better predictive performance than the empirical relationships by using an independent debris-flow dataset in Taiwan for validation. The developed multivariate joint probabilistic model can also provide the exceedance probability of debris flows through considering the uncertainties of debris flow and its influencing factors, providing a preliminary reference for hazard assessment of the debris flows.

Numerical simulation of rainfall-induced debris flow in the Hongchun gully based on the coupling of the LHT model and the Pudasaini model

Numerical simulation of rainfall-induced debris flow in the Hongchun gully based on the coupling of the LHT model and the Pudasaini model

Characteristics, Dynamic Analyses and Hazard Assessment of Debris Flows in Niumiangou Valley of Wenchuan County

Niumiangou valley, the epicenter of the 12 May 2008 Wenchuan earthquake (MS 8.0), became an area with frequent and dense debris flow disasters post-earthquake. Based on the in situ investigations after the earthquake on 14 August 2010 and a series of gathered data, characteristics and dynamic analyses of post-earthquake debris flows in Niumiangou valley were conducted, and then their hazard degree was assessed. Some research conclusions are obtained: (1) these post-earthquake debris flows have some typical characteristics, such as rainstorm viscous-type debris flow, happening usually between 11 p.m. and 5 a.m., broken out in the main channel as well as six branch gullies at the same time and also induced in the branches with good vegetation; (2) the dynamic parameters of Niumiangou debris flow (including volumetric weight, velocity, peak discharge, impact force, total amount of debris flow, total amount of solid materials washed out by single debris flow, maximum height of the debris flow rises and super elevation in bend) are relatively significant, and due to which it can be indicated that these debris flow disasters have great destructive power and harmfulness; (3) the hazard degree of debris flow in Niumiangou valley is very high, compared with the debris flows that occurred in the years of 2008 and 2013 in Niumiangou valley post-Wenchuan earthquake, and the comparison result shows that the hazard degree of debris flow in Niumiangou valley is relatively higher, which is consistent with the current situation. Therefore, according to these results, debris flows in Niumiangou valley are in the development phase and large-scale rainfall-induced debris flow disasters, with greater damage and stronger wallop, will easily occur in the rainy seasons of the 20 years after the earthquake.

Rainfall-induced debris flows and shallow landslides in Ribeira Valley, Brazil: Main characteristics and inventory mapping

Debris flows are one of Brazil's most frequent mass movement processes, triggered by extreme rainfall events and initial volume provided by shallow landslides. Despite the recurrence of catastrophic occurrences, Brazil still lacks basic data containing the main characteristics of previous events. In this way, this research aimed to make a morphometric characterization of the event and to provide debris-flow and shallow landslides inventories. For the morphometric analysis, a Digital Elevation Model (DEM) was used. For the inventory map of debris flow runout and shallow landslides scars, a post-event free access image from Google Earth Pro and satellite images from RapidEye were used. The results show that debris flows had two main flows that affected different areas of the city of Itaóca. Also, one single shallow landslide contributed as initial volume to the debris flows that reach the city downtown, demonstrating the importance of entrainment. Shallow landslides analysis shows its concentration in slopes between 20.1 – 30°, with orientation South and Southeast, elevation between 600 – 800m, and in concave curvatures. The results helped to better understand debris flows in Brazil, highlighting their relationship with the occurrence of shallow landslides as one of the main triggering factors. Those data are crucial to mitigation action of possible new events.

Debris flow susceptibility analysis using a bivariate statistical analysis in the Panataran River, Kg Melangkap, Sabah, Malaysia

This study area is part of the Kadamaian watershed and is located on the North-West flank of Mount Kinabalu, composed of sedimentary rock from the Crocker Formation and the Mt. Kinabalu granitic pluton. Many loose seismic materials were found on the slopes during the 2015 Sabah Earthquake with a moment magnitude of 6.0. These materials later served as the source material for rainfall-induced debris flows or shallow landslides. The community closest to the Panataran river in the Kg Melangkap area is the most affected. Therefore, the objective of this study is to study the debris flow susceptibility analysis using a bivariate statistical analysis approach, namely the Frequency Ratio (FR) model. Forty-eight landslides were identified using remote sensing interpretation. Characteristics of the research area, such as slope gradient, elevation, slope aspect, lithology, slope curvature, and topographic wetness index, were selected as the factors to evaluate the debris flow susceptibility analysis. The correlations between these factors and the occurrence of landslides were established, and the results were assessed and validated based on those results. Validation findings demonstrate that this technique provides high accuracy, with an AUC of 81.8 for success rate. As a result, it can be stated that this model accurately predicted landslide susceptibility in the research area, and that it can help local authority with future land-use planning, as well as give tools for hazard mitigation.

Changes in debris-flow susceptibility after the Wenchuan earthquake revealed by meteorological and hydro-meteorological thresholds

After the 2008 Wenchuan earthquake (Mw 7.9), an increase in rainfall-induced debris flows was initially observed in the earthquake-hit region (Sichuan, China). In the following years, the frequency of debris flows gradually reduced, indicating a recovery of stability of debris deposits originated from the earthquake. To assess these dynamically changing conditions, empirical thresholds have been identified to predict post-seismic debris flow occurrences with two approaches: a meteorological approach based only on precipitation characteristics, and a hydrometeorological approach that also considers the hydrologic conditions before the onset of rainfall. Both used the available record of precipitations and debris flows that occurred in the years 2008–2015 in Wenchuan county. Hydrometeorological thresholds for debris flows have been identified at the catchment scale by assessing the water balance with a simplified lumped hydrological model, based on the Budyko framework, and using catchment water storage as a proxy of the moisture state of the slopes. The results indicate that both meteorological and hydrometeorological thresholds allow catching the progressive recovery of stability of the debris deposits. In particular, the assessment of water balance at the catchment scale highlights the role played by the hydrological processes affecting the slopes, leading to the definition of reliable and robust thresholds. The hydrometeorological approach is thus recommended to define thresholds for early warning of debris flows at the catchment scale.

Assessment and Analysis of a Rainfall–Time-Lagging Water-Related Disaster in Mountainous Areas

Both global climate change and human activities are continuously impacting the abruptness and frequency of water-related natural disasters such as flash floods, debris flows, and landslides in mountainous areas, greatly threatening the safety of lives and properties. A recent rainfall-induced debris flow event happened on July 6, 2020 in the Chenghuangmiao Gully, in Sichuan Province, China, resulting in severe damage to buildings at the outlet. An integrated analysis of the consequence and triggering mechanism of this debris flow event was conducted with hydrologic information, topographic details, vegetation regimes, and drone aerial imagery. The result shows that the entire runout of the debris flow differs from that of common ones (debris flow and rainfall were highly related and synchronized), which happened 4 h after the stop of the rainfall. The hysteretic feature increases the difficulty of the prediction and warning of the debris flow due to lack of a responsible triggering mechanism. The hillslope surface is well covered by vegetation, hindering regular observation and cleaning up of long-term deposited wood and sediment debris. This effect increases the crypticity and abruptness of potential debris flows. With field evidence and analysis, it is speculated that long-term accumulative processes of dead wood sand sediment deposition formed a small-scale debris dam, and the continuous water release from the watershed led to dam breaching, subsequently triggering the initiation of the debris flow. Multiple steps distributing along the gully of an average slope of 15.65° contributed to the amplification of the debris flow once the breach of the upstream wood and sediment dam occurred. Along the gully, small-scale landslide scars can be observed, possibly amplifying the scale of the debris flow and disaster impact. This debris event gives a lesson of necessary demands of predicting and managing the risks of a low-frequency debris flow non-synchronized with rainfall events.

The relationship of human activities and rainfall-induced landslide and debris flow hazards in Central China

Human activities have been recognized as one of the significant influencing factors on natural hazard, yet studies of quantitative relationship between human activities and natural hazard have been limited. The relations of human activities and hazards (landslide and debris flow) induced by heavy rainfall are quantitatively analyzed in this study and suggestions are provided for the integrated hazard mitigation management in the study area of Central China. The results show that human activities index (HAI) is an effective indicator to characterize spatiotemporal changes of human activities. The relations of rainfall-induced landslide, debris flow hazards and human activities are significant as shown in spatial distribution. The probability of rainfall-induced landslide, debris flow hazards is highly correlated with the intensity of human activities and the changes of HAI. However, in terms of temporal relations, human activities have more direct impact on rainfall-induced landslide hazard than on rainfall-induced debris flow hazard, as the frequency of landslide hazard shows a 2-year delay with HAI changing, in general, according to the cross-wavelet transform analysis. In comparison, no significant correlating period is shown between the changing human activities and the frequency of rainfall-induced debris flow hazard. Specifically, there are three types of time relationship between the changing human activities and rainfall-induced landslide, debris flow hazards in the affected counties: (1) concurrent changing, accounting for 30% of landslide and 18% of debris flow; (2) lagging relationship, accounting for 54% of landslide and 30% of debris flow; (3) no direct relationship, accounting for 16% of landslide and 52% of debris flow. The results in this study suggest that HAI is a simple and effective index for the local governments to manage human impacts on rainfall-induced landslide and debris flow hazards, and integrated prevention measures are suggested to be executed when HAI reaches 0.072. In addition, the types of human activities also impact landslide, as the ratio of Economy factor to Land use factor (E/L) is significantly (P < 0.05) higher in counties with concurrent relationship of changing human activities and frequency of rainfall-induced landslide hazard. The results should assist the policy-making for integrated mitigation of rainfall-induced landslide and debris flow hazards at local/regional level, while balancing economic development and natural hazard.

Study of kinematic characteristics of a rock avalanche and subsequent erosion process due to a debris flow in Wenjia gully, Sichuan, China

This paper aims to systematically study kinematic characteristics of Wenjiagou rock avalanche triggered by the M8.0 2008 Wenchuan earthquake and one of subsequent debris flows that occurred on August 13, 2010 (8.13 debris flow), using a numerical approach. The kinematic characteristics of the rock avalanche are back-calculated using an energy-based runout model. The erosion process of the subsequent rainfall-induced debris flow is analyzed using a progressive scouring entrainment model incorporated in the energy-based runout model. The results indicate that Wenjiagou rock avalanche traveled farther than most other rock avalanches with a maximum velocity of approximately 73 m/s detected at about 1700 m away from the source zone. The erosion of the 8.13 debris flow mainly occurred right after the dam failure which contributes to more than 97% of the total eroded volume. Besides, four different scenarios, including no blockage of the runoff (scenario I), no dam failure (scenario II), dam failure at the end of precipitation (scenario III), and no erodible material (scenario IV), are supposed to study the effect of the failure of a check dam on the erosion characteristics of the debris flow. The results reveal that the blockage of the channel without failure could reduce 86% of the total volume and the failure of check dams is the main reason for the destructive consequence of the 8.13 debris flow. This paper proposes an approach to explore kinematic characteristics of a rock avalanche and erosion process of the subsequent rainfall-induced debris flows and also innovatively provides a method to indirectly assess mitigation strategies that can be used for the design of mitigation projects.

Probabilistic rainfall thresholds for debris flows occurred after the Wenchuan earthquake using a Bayesian technique

Empirically derived rainfall thresholds of debris flows are used for regional-scale early warning. However, triggering rainfall intensities of post-seismic debris flows evolve with time, causing high false alarms since thresholds estimated by conventional methods ignore the uncertainty of non-triggering rainfall events. Based on 172 triggering rainfalls and 2396 non-triggering rainfalls from 2008 to 2013 after the Wenchuan earthquake, we analyzed the evolution of probabilistic rainfall thresholds for post-seismic debris flows using a Bayesian technique. We found, rainfall thresholds significantly decrease compared with pre-earthquake events initially and later tend to increase annually. Meanwhile, the triggering rainfall characteristics tend to gradually change from a short-duration high-intensity pattern to a long-duration and low-intensity pattern. We also checked the effect of antecedent precipitation on debris flows by defining an IET (inter-event time). Our results suggest the antecedent precipitation plays an important role in low-intensity long-duration rainfall-induced debris flows and has little effect on the short-duration high-intensity rainfall-induced debris flows. The characteristics of triggering rainfall for debris flows after the Wenchuan earthquake can be best reflected by IET = 7 h. By employing a Naïve Bayes algorithm, uncertainties of three rainfall threshold models, I-D (mean intensity-duration), IT-D (triggering intensity-duration), and IT-E (triggering intensity-cumulative rainfall) were investigated, and the IT-D model was found to perform best. The characteristics and evolution of debris flow rainfall thresholds over the years after the Wenchuan earthquake was best presented by the Bayesian probabilistic rainfall thresholds. We believe the results can be used to improve the precision of an early warning system for post-seismic debris flows.

Paraglacial adjustment of sediment slopes during and immediately after glacial debuttressing

Daily time lapse imagery and pixel tracking was used to monitor and track spatial and temporal changes in sediment-mantled hillslopes, during and immediately after glacier retreat in the Fox Glacier/Te Moeka o Tuawe valley, New Zealand. Observations from 2014 to 2018 of the Fox Glacier and surrounding hillslopes show hillslope failure is primarily coincident with, and triggered by, glacier retreat with rainfall accelerating movement of the hillslope. During glacier retreat, failure of the hillslope primarily occurred through sediment sliding, internal deformation of the sediment and occasional surficial debris falls, flows and avalanches delivering approximately 9.2 M m3 of sediment directly to the underside of the glacier over the study period with a maximum daily averaged movement of 0.4 m per day of the main sediment mass. Following debuttressing, hillslope failure became dominated by localised rainfall-induced debris flows which initiated gullying of the sediment-mantled slope. Ongoing instability of the slope and associated movement is maintained by toe erosion from the Fox River and melting dead ice, while continued rapid failure is facilitated through localised debris flows. The tracking of temporal and spatial changes of sediment-mantled hillslopes during glacier retreat has shown broad-scale hillslope response to occur quickly within days of rainfall or accelerated glacier retreat, particularly during summer. Debris flows, commonly thought to be a dominant erosion process within paraglacial environments, only occur following complete debuttressing and are supply-limited, only occurring after sediment sliding has occurred. Unlike many other case studies, sediment connectivity immediately following glacier retreat is high due to a lack of storage space and high rainfall inducing mass movements, efficiently delivering hillslope sediments to the proglacial stream channel. Attempts to quantify displaced volumes of sediment from paraglacial systems are likely underestimated due to a) a lack of focus on the early and latter stages of debuttressing b) a reliance on debris flows being a primary transport mechanism, and c) sediment being delivered sub-glacially rather than supra-glacially, further enhancing connectivity.

Sensitivity analysis of influencing parameters on slit-type barrier performance against debris flow using 3D-based numerical approach

Extreme rainfall-induced debris flow can be catastrophic to an urban area, and installation of slit-type barriers can prevent such damage while minimizing negative impact on environments. However, the performance of slit-type barriers against debris flows remains poorly identified partly due to the innate complexity in interactions between debris flow and solid structure. This paper investigated the flow behaviors of debris affected by slit-type barriers using the computational fluid dynamics (CFD) method, in which the numerical model based on the volume of fluid method was verified using the physical modeling results. The sensitivity analysis was performed by building metamodels to determine the primary parameters influencing the barrier performance against debris flows among various variables, in which the effect of input properties and design parameters, particularly the soil concentration in fluidized debris, initial velocity and volume of debris, the barrier height, and the opening ratio, was evaluated from the perspectives of the flow energy reduction and debris trapping. The initial velocity and volume of debris were found to play a significant role in determining the debris flow characteristics. A decrease in the opening ratio in the channel primarily facilitated the energy reduction and trapping due to the reduced opening size. However, the barrier height exhibited a limited effect when the height was sufficiently high to block the debris flow volume. In addition, it was observed that the double barrier system effectively increased the energy reduction while keeping the benefit of open-type barrier. The developed simulation method and obtained results provide an effective tool and an insight that can contribute to an optimum design of the debris-flow barrier.

GIS-based assessment of debris flow hazards in Kulekhani Watershed, Nepal

Debris flows are a hazardous natural calamity in mountainous regions of Nepal. Torrential rainfall within a very short period of the year is the main triggering factor for instability of slopes and initiation of landslides in these regions. Furthermore, the topography of the mountains and poor land use practices are additional factors that contribute to these instabilities. In this research, a GIS model has been developed to assess the debris flow hazard in mountainous regions of Nepal. Landslide-triggering threshold rainfall frequency is related to the frequency of landslides and the debris flow hazard in these mountains. Rainfall records from 1980 to 2013 are computed for one- to seven-day cumulative annual maximum rainfall. The expected rainfall for 1 in 10 to 1 in 1000 years of return periods is analyzed. The expected threshold rainfall is modeled in the GIS environment to identify the factor of safety of mountain slopes in a study watershed. A relation between the frequency of rainfall and debris flow hazard area is derived for return periods of 25, 50, 100, and 200 years. The debris flow hazard results from the analysis are compared with a known event in the watershed and found to agree. This method can be applied to anticipated rainfall-induced debris flow from the live rainfall record to warn the hazard-prone community in these mountains.

Susceptibility assessment of rainfall induced debris flow zones in Ladakh–Nubra region, Indian Himalaya

In recent past, rainfall-induced debris flow events in Ladakh–Nubra region have caused loss of lives and damages to civil infrastructures and army locations. Therefore, there is a need of high spatial and temporal monitoring of precipitation, and further to assess susceptible rainfall-induced debris flow zones in the area. We assessed the rainfall data collected at two gauge stations and observed a significant increase in the rainfall amount over the study region during summer-monsoonal period 1997–2017. Increasing trend was also observed from CRU gridded precipitation dataset. A GIS-based multi-criteria evaluation (MCE) method was performed by combining topographical, environmental and hydrological parameters for mapping of rainfall-induced susceptible zones. Suitability analysis of precipitation forecasts from WRF model at higher resolution (3 km) was also performed. A good agreement (r = 0.76) was observed between 4-day model forecast and field observed rainfall. Further, the simulated precipitation from WRF was incorporated into GIS model for assessment of debris flow susceptible zones for two cases of heavy precipitation events. The modelled high, medium, low and very low risk susceptible zones identified for the year 2015 events are validated with field survey and pre-post satellite imageries, and found in good agreement (ROC = 76.6%). The model was able to identify affected areas during the Leh cloud burst event in year 2010. In addition, a threshold value of rainfall for initiation of debris flow in the region was also reported.

A combined method for modeling the triggering and propagation of debris flows

This study describes a combined method for rainfall-induced debris flow initiations (landslides) and propagations including a series of numerical analyses. In this study, the debris is assumed as a mixture of soils and water which is physically non-Newtonian fluid. The emphasis is placed on applying the effect of the combination of rainfall-induced landslides and debris flows to the numerical analysis. An analysis of rainfall-induced landslides is conducted to identify the thickness and location of the initial volume of debris flow. The movement of debris flow is subsequently simulated considering entrainments affected by the initial wetting condition (wetting front) estimated from the rainfall-infiltration analysis. The proposed method can simulate a sequential process from the initiation of the debris flows to the deposition based on the prediction of slope failure by rainfall, fluid dynamics based on Navier–Stokes equation, and the analysis of entrainments by considering the effect of the weight of debris and the wetting condition of soil beds. Based on the numerical results of this study, the proposed method could be applied to the analysis of regional-scale landslides and debris flows.