Climate change is resulting in more frequent rainstorms and more rain-induced debris flows in mountainous areas. The prediction of likely hazard zones is important for debris flow risk assessment and management. Existing numerical methods for debris flow analysis often require the input of hydrographs at prescribed initiation locations, ignoring the initiation process and leading to large uncertainties in debris flow initiation locations, times, and volumes when applied to regional debris flow analysis. The evolution of the flowing mixture in time and space is also barely addressed. This paper presents a new integrated numerical model, EDDA 2.0, to simulate the whole process of debris flow initiation, motion, entrainment, deposition, and property changes. Two physical initiation mechanisms are modelled: transformation from slope failures and surface erosion. Three numerical tests and field application to a catastrophic debris flow event are conducted to verify the model components and evaluate the model performance. The results indicate that the integrated model is capable of simulating the initiation and subsequent flowing process of rain-induced debris flows, as well as the physical evolution of the flowing mixture. The integrated model provides a powerful tool for analysing multi-hazard processes, hazard interactions, and regional debris flow risk assessment in the future.
Debris flows are one of the most catastrophic hazards in mountainous areas (e.g. Zhang et al., 2013; Raia et al., 2014), and can pose high risks to society (e.g. Tang et al., 2011; Gao et al., 2016). They are often triggered by heavy rainfall and sensitive to climate change (e.g. Wong, 2009; Lee et al., 2010). As extreme rainstorms become more frequent, coping with rain-induced debris flows becomes more critical in debris flow prone regions such as Italy, Japan, Hong Kong, and earthquake-affected areas in Sichuan, China.
During a storm, debris flows may be initiated by surface erosion, slope failures, or dam breaching (e.g. Takahashi, 2007), and enlarged during the subsequent flowing process (e.g. Iverson, 1997). The debris flow mixture finally deposits in a flatter area, while the interstice fluid still flows along the debris flow track without further material entrainment as rainfall continues. The evolution of the flowing mixture includes three phases in terms of sediment concentration: clear water flow, hyperconcentrated flow, and debris flow. The transition of the flowing mixture between any two phases occurs spatially and temporally during the whole rainfall process.
Many numerical programs have been successfully developed for debris flow analysis, such as DAMBRK (Boss Corporation, 1989), FLO-2D (O'Brien et al., 1993), DAN (Hungr, 1995), DMM (Kwan and Sun, 2006), Debris2D (Liu and Huang, 2006), FLATModel (Medina et al., 2008), MassMov2D (Beguería et al., 2009), DAN3D (Hungr and McDougall, 2009), PASTOR (Pastor et al., 2009), RAMMS (Bartelt et al., 2013), EDDA 1.0 (Chen and Zhang, 2015), DebrisInterMixing (von Boetticher et al., 2016), and AschFlow (Quan Luna et al., 2016). These programs can simulate the debris flow movement with either constant or varying properties of the flowing mixture. The entrainment and deposition processes can also be considered, such as in EDDA 1.0 (Chen and Zhang, 2015).
Until now, numerical simulation of the physical process of debris flow initiation has been largely avoided in the literature. Moreover, little attempt has been made to simulate the entire process from the initiation to the subsequent debris flow motion and deposition in an integrated manner. We address these two research gaps in this paper.
Experimental studies and field monitoring have been conducted to study the initiation mechanics of rain-induced debris flows (e.g. Johnson and Sitar, 1990; Cui, 1992; Cannon et al., 2001). A few physical models have been proposed (e.g. Takahashi, 1981; Iverson et al., 1997) to reveal the mechanisms of initiation using infinite slope stability models which are mathematically one-dimensional and statically determinate, leading to unambiguous quantitative results. However, these models do not simulate the debris flow initiation process, particularly the transformation from a slope failure to a debris flow. Statistical models have also been proposed to relate debris flow initiation to rainfall (e.g. Caine, 1980; Wieczorek, 1987; Chen et al., 2005; Godt et al., 2006; Cannon et al., 2008; Coe et al., 2008; Guzzetti et al., 2008; Baum and Godt, 2010; Berti et al., 2012; Staley et al., 2013; Zhou and Tang, 2014; De Luca and Versace, 2017a, b; Gao et al., 2017a) and other parameters such as surface runoff discharge (Berti and Simoni, 2005) or clay content (Chen et al., 2010). These models are not physically based.
Many of the existing computer programs do not simulate the initiation of debris flows. Instead, they require a predefined empirical hydrograph, created based on the estimated volumes of rainfall runoff and source materials, to initiate a debris flow, which is so-called “two-step” analysis (Fig. 1). Two-step analysis leads to large uncertainties in debris flow initiation locations, times, and volumes when applied to regional debris flow analysis. For instance, Shen et al. (2017) simulated hillslope debris flows initiated from surface erosion, in which the initiation location is artificially intervened (Fig. 1) and the slope failure mechanisms are not included. The integrated simulation of the whole process of debris flow (Fig. 1) remains an open challenge. In addition, the physical rainfall runoff and overland flow processes before the initiation of debris flows are overlooked. Currently, the study of the full evolution of the flowing mixture in time and space is limited.
Comparison between “two-step” simulation and integrated simulation of rain-induced debris flows.
Numerical tools have been developed for simulating single types of hazards (e.g. H. X. Chen et al., 2015; Shen et al., 2017). However, multiple types of hazards may be induced by a rainstorm (i.e. slope failures, debris flows, and flooding) (e.g. Zhang et al., 2014; Zhang and Zhang, 2017). One hazard can be the cause of another (e.g. rainfall triggers slope failures that in turn trigger debris flows). Different types of hazards can also interact with each other (e.g. several small debris flows from sub-channels can merge into a larger one). Therefore, hazard risk assessment requires hydrological, landslide, and debris flow analyses at a regional scale (e.g. Formetta et al., 2011; Archfield et al., 2013). The simulation of the complete processes of possible hazards and their interactions at a regional scale can be a powerful tool to help identify likely hazards, potentially affected areas, and elements at risk. However, the ability to numerically analyse hazard interactions is still limited (e.g. Kappes et al., 2012; Marzocchi et al., 2012). Using the existing “two-step” tools (Fig. 1) to analyse potential regional hazards can be challenging, as they involve tremendous uncertainties and it is time-consuming to conduct “two-step” analyses for each of all potential hazard locations (e.g. Chen and Zhang, 2015; Gao et al., 2016; Shen et al., 2017). Hence, the development of an integrated model for simulating multi-hazard processes and interactions (Fig. 1) is of great theoretical and practical importance.
The objectives of this paper are as follows: (1) to physically incorporate debris flow initiation into the debris flow motion simulation to enable the simulation of the whole process of rain-induced debris flows, (2) to study the full evolution of the flowing mixture in time and space during the whole rainfall process, and (3) to develop a tool to simulate multi-hazard processes and analyse hazard interactions.
Intense rainfall in mountainous regions could trigger debris flows from loose soil deposits on hillslopes or in channels. A conceptual model for rain-induced debris flows and likely initiation mechanisms are shown in Fig. 2. Debris flows can be initiated by three mechanisms: transformation from landslides, surface erosion, and dam breaching. Due to rainfall infiltration the hillslope gradually becomes saturated, and the soil loses its strength, causing shallow seated slope failures (Zhang et al., 2011). During a rainstorm, slope failures can occur at different times in space within a catchment. Some of the detached material may move into channels and form landslide dams, and some may directly transform into debris flows. As the surface runoff accumulates the landslide dam formed earlier in the channel may break, initiating a channelized debris flow (e.g. Liu et al., 2009; Chen et al., 2012; Peng and Zhang, 2012). At the same time, the surface runoff may cause bed erosion and initiate hillslope debris flows (e.g. Cannon et al., 2001). Some of the separate debris flows may merge in the main channel of the drainage basin, forming a larger catastrophic debris flow event (e.g. Iverson et al., 1997). The final magnitude of a debris flow could be many times that of its initial volume due to entrainment of materials along the path from additional slope failures, bed erosion, or bank collapses (e.g. Iverson et al., 2011; Chen et al., 2012; Ouyang et al., 2015). If the debris flow reaches a flat residential area downstream in the basin, it can cause severe loss of life and property.
Conceptual model of a rain-induced debris flow and three typical initiation mechanisms of debris flows: bed erosion, transformation from landslide, and dam breach.
Based on the conceptual model for the whole process of debris flow in Fig. 2 the strategy of the integrated model, including two debris flow initiation mechanisms (i.e. bed erosion and transformation from landslides), is shown in Fig. 3. The integrated model consists of a digital terrain module, a rainfall module, an infiltration module, an overland flow module, a slope stability module, a surface erosion module, a debris flow dynamics module, and a deposition module. The digital terrain module discretizes the study area into a grid system with geological, hydrological, and geotechnical information assigned for each cell. All the computations are based on the concept of cell. As the primary triggering factor, rainfall is simulated in the rainfall module. Water infiltration into the ground is then simulated to analyse the pore water pressure profile and compute the surface runoff. The slope stability and surface erosion are then evaluated in the slope stability module and surface erosion module, respectively. Once debris flows are initiated by the two physical mechanisms, the motion of the flowing mixture is analysed through the debris flow dynamics module. Material entrainment may occur along the flow path, incorporating solid materials from additional slope failures and surface erosion. Finally, the deposition process is assessed through the deposition module. The runout distance, inundation area, and deposition volume of the debris flows can all be assessed.
Framework of the integrated simulation of debris flows.
The core of the proposed integrated analysis is the debris flow dynamics
simulation and constitutive modelling of the flowing mixture. The governing
equations for debris flow dynamics describe the mixture movement and changes
in debris flow properties, which are depth-integrated mass conservation
equations (Eqs. 1 and 2) and momentum conservation equations (Eq. 3) (Chen
and Zhang, 2015):
One of the requirements of the integrated analysis is modelling different
flowing mixtures simultaneously. The flowing mixture can be classified into
three types: clear water flow, hyperconcentrated flow, and fully developed
debris flow based on sediment concentration, combining grain-size
distribution and particle densities (Pierson, 2005). In this study, the
flowing types of mixtures are classified using the volumetric solid
concentration If If 0.2 If 0.45
Therefore, a proper rheological model must involve
Under heavy rainfall, excess rainwater becomes surface runoff when the
rainfall intensity exceeds the infiltration capacity. In EDDA 2.0, the
infiltration capacity is assumed to be the saturated permeability of the
surface soil. The surface runoff process is simulated by solving the
governing equations (Eqs. 1–3) and the Manning equation with
Water infiltration will increase the subsurface pore water pressure, causing slope failures that are normally shallow-seated. The infiltration process is simulated in EDDA 2.0 by solving the Richards equation with a forward-time central-difference numerical solution. A non-uniform grid is created along the soil depth to enhance the accuracy of the solution near boundaries and interfaces. The integrated program calculates the instant pore water pressure profile to facilitate evaluating the slope stability of each cell at each time step.
A debris flow may be initiated by the transformation of a mass flow of slope failure material at any location and at any time during a storm. The possible locations and approximate failing time can be identified in a cell-based slope stability analysis, if the topography, geology, soil properties etc. are properly defined. To consider this initiation mechanism, the slope instability evaluation must be performed over all the computational cells at each time step.
With the knowledge of real-time pore water pressure profiles provided by the
infiltration module, a real-time slope instability analysis can follow.
Considering that these rain-induced slope failures are shallow seated, the
thickness of the failure mass is small compared to the large plan dimensions
of these slopes. Therefore, an infinite slope model for two-layer soil slopes
is a reasonable option to evaluate the factor of safety (
Intense rainfall can generate plentiful surface runoff, and the soil bed
will erode in the runoff water. The initially clear overland flow can
gradually develop into a hyperconcentrated flow and finally into a hillslope
debris flow, as its
We consider the occurrence of erosion under the condition that the bed shear
stress is equal to or larger than the critical erosive shear stress of the bed
material and the volumetric sediment concentration is smaller than an
equilibrium value. The equilibrium value proposed by Takahashi et al. (1992)
is adopted in this study:
Many researchers have studied the relationship between the soil erosion rate
and shear stress. A form of exponential expression has been used for bed
erosion in the literature (e.g. Roberts et al., 1998; Z. Chen et al.,
2015). More widely
used is a linear function of shear stress (e.g. Graf, 1984; Hanson and Simon,
2001; Julian and Torres, 2006; Chang et al., 2011; Chen and Zhang, 2015):
Material exchange occurs as a debris flow marches along its flowing path, including material entrainment (solid mass gain from outside of the flowing mixture) and deposition (solid mass loss from inside of the flowing mixture).
Entrainment from additional bed erosion or slope failure materials along
its trajectory plays a significant role in debris flow volume amplification.
The final volume of the debris flow deposit can be many times that of its
initial volume. An excellent example of this is the 1990 Tsing Shan debris flow,
which was the largest ever observed in Hong Kong. An originally small slip of
350 m
After flowing into a flatter area, deposition of some solid material will
occur. Deposition is deemed to occur if the flow velocity is smaller than a
critical value and
The terrain is discretized into a grid of cells. Each cell is assigned with
the input data, including topography, soil depth, geotechnical soil
properties, rheological model parameters, and so on. There are eight flow
directions in each cell: four compass directions and four diagonal
directions. In each time step, the infiltration is first evaluated to
compute the surface runoff and slope stability at each cell. Then changes in
flow depth
After all the computations have been completed in each time step, numerical
stability criteria are checked for each cell to limit the time step and avoid
surging while allowing for large time steps. Three convergence criteria are
adopted:
The Courant–Friedrichs–Lewy (CFL) condition, with the physical
interpretation that a particle of fluid should not travel more than the cell
size in one time step (Fletcher, 1990), is mostly used in explicit schemes.
The time step is limited by The percent change of flow depth in one time step should not exceed a
specified tolerant value, TOLP( The change in flow depth in one time step should not exceed a specified
tolerant value, TOL(
Adjusting these three criteria, the computational time and accuracy could reach a good balance. If all the numerical stability criteria are successfully satisfied, the time step can be increased for the next computational cycle. Otherwise the time step is reduced and the computation restarted. The volume conservation is computed at the end of each time step for the inflow, outflow, grid system storage, and infiltration loss.
A satellite image of the study area taken shortly after the Xiaojiagou debris flow on 14 August 2010.
The previous version, EDDA 1.0 (Chen and Zhang, 2015), passed several
verification tests including debris flow dynamics, erosion, and deposition. In
this new version of integrated analysis, the new modules for surface runoff,
coupled infiltration, and slope stability analysis, and the integrated program
require further verification. The response of Xiaojiagou Ravine during a
rainstorm in August 2010 is used to verify the new modules. The in situ
conditions shortly after the 2010 Xiaojiagou debris flow event are shown in
Fig. 4. The Xiaojiagou Ravine has an area of 7.84 km
Rainfall process of the August 2010 rainstorm.
First the performance of the rainfall runoff module of the integrated program is compared with a commonly used program FLO-2D (FLO-2D Software Inc., 2009). The infiltration module is then checked against an analytical solution under steady rainfall. The slope stability analysis is verified by comparing it with the landslide satellite image and the computation results by Chen and Zhang (2014). Finally, the performance of the integrated model is checked against the 2010 Xiaojiagou debris flow event in Sect. 4.
Comparison of the maximum surface runoff flow depths and flow
velocities simulated using FLO-2D
The same input data are used in EDDA 2.0 and FLO-2D, including the digital
elevation model, the Manning coefficient (
The results from the two programs are compared in Fig. 6, including the distributions of the maximum flow depth and flow velocity. The result from FlO-2D (Fig. 6a and c) differ only slightly from those of EDDA 2.0 (Fig. 6b and d). During the rainstorm process, the maximum flow depth computed by FLO-2D is 3.2 m, while that computed by EDDA 2.0 is 3.4 m. The outflow hydrographs recorded at the mouth of the ravine of the two programs are shown in Fig. 7. The computed overall discharge processes from both programs are very close.
Before applying the infiltration module to compute the pore water pressure profiles under the actual rainfall event, four cases of infiltration under steady rainfall are adopted to verify the infiltration module. The results are compared with those from an analytical solution by Srivastava and Yeh (1991) and Zhan et al. (2013). The scenario of two-layer soil is considered, which is also used in the field application. Table 1 presents the input parameters for the four cases. Four combinations are set up to represent likely in situ conditions. The results from the numerical infiltration module and the analytical solution are compared in Fig. 8. For all the four cases, the module performance is satisfactory.
Parameters used in the infiltration module verification.
Notes:
Properties of four types of superficial materials.
Notes:
Soil properties for debris flow simulation.
Notes:
Constitutive (rheological) parameters for debris flow simulation.
Notes:
Comparison of the outflow hydrographs at the ravine mouth using FLO-2D and EDDA 2.0.
Pore water pressure profiles at various times:
The 2008 Wenchuan earthquake triggered over 50 000 landslides within the
earthquake region, leaving a large amount of loose materials on hillslopes
and in channels (Fig. 4). These materials became the source of numerous
post-earthquake rain-induced landslides and debris flows. Presently, nearly
80 % of such material remains in the mountain regions, posing great
potential threats (Zhang et al., 2016). EDDA 2.0 is used to reproduce the
slope failures under the rainstorm conditions from August 2010 (Fig. 5) by Chen and
Zhang (2014), who evaluated the slope stability of a 164.5 km
A heavy rainstorm swept the epicentre of the event, Yinxiu town, and its vicinity. The
rainstorm lasted about 40 h from 12 to 14 August 2010, delivering a total of about 220 mm
of precipitation (Fig. 5). A catastrophic debris flow was triggered
by the storm in Xiaojiagou Ravine (Fig. 4). The debris flow was witnessed at
the ravine mouth at approximately 05:00 LT on 14 August and lasted about 30 min.
Roughly 1.17
Computed unstable cells vs. landslide scars on the satellite image.
Simulation results of the Xiaojiagou debris flow:
Comparison of the simulated and observed deposition zones:
Outflow hydrograph and changes in
Distributions of
In EDDA 1.0, the study area has to be divided into two domains for rainfall runoff
simulation and debris flow runout simulation respectively. However, in
the integrated simulation by EDDA 2.0, only one grid of 9500 30
We examine the final output of the integrated simulation first. Erosion plays
an important role in the volume magnification of debris flows. The final
erosion depths in the eroded areas are shown in Fig. 10a. The most eroded
areas during the Xiaojiagou debris flow event were in channels, where a huge
amount of loose solid material was present (Chen et al., 2012). Loose
deposits on the hillslopes also eroded after the landslide bodies detached
from their original locations and slid down the slopes. The distribution of
the eroded areas reflects that the debris flows were initiated from both
slope failures and surface erosion, then developed along the channels by
further erosion and entrainment of the slope failure materials; these are the
two mechanisms considered in the integrated model. The distribution of the
maximum flow velocity is shown in Fig. 10b, with the maximum value being 9.5
m s
The simulated and observed deposition areas are compared in Fig. 11. It is
seen that the simulation results (Fig. 11a) match the observation (Fig. 11b)
reasonably well. The simulated deposition depth is approximately 20 m, very
close to that of the observed thickness of the deposit fan during the field
investigations. The total volume of the observed deposition fan is about
1.17
The changes in the volumetric sediment concentration
To demonstrate the evolution of the flowing mixture within the drainage
basin, the distributions of
We have successfully extended the “two-step” debris flow simulation to an
integrated simulation of the whole process of rain-induced debris flows.
However, there are still limitations in the underlying assumptions and
simplifications:
EDDA 2.0 considers the initiation of debris flows from the transformation of
slope failures and surface erosion. However, the initiation from dam
breaching has not yet been tested. The studies consider material entrainment from surface erosion and slope
failure detachment, but the entrainment from bank failures can only be
considered using an empirical rate, instead of via a three-dimensional
physical model. The governing equations are in a depth-integrated form; hence, particle
segregation in the vertical direction cannot be considered. The rheological models for the hyperconcentrated flow, fully developed
debris flow, and slope failure mass flow need further study. The
slope failure mass movement is particularly critical for estimating the transformation
rate from a slope failure to a debris flow.
A new integrated simulation model is developed for simulating rain-induced debris flow initiation, motion, entrainment, deposition, and property changes. The model is unique in that it simulates the whole process of rain-induced debris flow evolution and two physical initiation mechanisms (i.e. transformation from landslides and surface erosion). Previous “two-step analysis” with an assumed inflow hydrograph and an inflow location can now be conducted at once, scientifically, and without subjective assumptions.
Three numerical tests have been conducted to verify the performance of the newly added modules of the integrated model. The Xiaojiagou Ravine landslides and debris flows triggered by the rainstorm in August 2010 were used as a verification case. In test 1, the rainfall runoff simulation by EDDA 2.0 was compared to FLO-2D. The simulation results from the two models are very close, which indicates that EDDA 2.0 simulates rainfall runoff well. In test 2, an analytical solution for evaluating the pore water pressure profile under infiltration is adopted. Comparison between the model solution and the analytical solution indicates that the integrated model evaluates the infiltration process well. The regional slope stability within the study area under the same rainstorm was evaluated using the integrated model in test 3. The computed unstable cells compare well with the observations from the satellite image and the results from previous studies.
The new integrated model was finally applied to reproduce the Xiaojiagou debris flow event. The model can simulate the entire evolution process of rain-induced debris flows, and estimates the volume, inundated area, and runout distance of the debris flow reasonably well . It is concluded that the new integrated debris flow simulation model, EDDA 2.0, is capable of (1) simulating the whole process of rain-induced debris flow from debris flow initiation to post-initiation debris flow motion, entrainment and deposition, and (2) tracing the evolution of the flowing mixture in time and space during the whole process of rainfall. The integrated model will serve as a powerful tool for analysing multi-hazard processes and hazard interactions, and the assessment of regional debris flow risks in the future.
EDDA 2.0 is written in FORTRAN, which can be compiled
using Intel FORTRAN compilers. A doi has been generated for the source code
and the source code is available online at
The supplement related to this article is available online at:
LZ and PS conceived the methodology and formulated the model. PS programmed the analysis code and performed the analysis. HC and RF evaluated the model results. All authors contributed to the writing of the manuscript.
The authors declare that they have no conflict of interest.
The authors acknowledge support from the Research Grants Council of the Hong Kong SAR (grant numbers C6012-15G and 16206217). Edited by: Bethanna Jackson Reviewed by: two anonymous referees