A Model of Debris Flow Forecast Based on the Water-Soil Coupling Mechanism

0. INTRODUCTION

Debris flow triggered by the heavy rainfall is a common natural disaster in mountain areas. Due to its unexpectedly erupted attribution, the debris flow often causes serious casualties and property loss. As an important means of the disaster mitigation, the debris flow forecast has been paid much attention by searchers. The formation mechanism of debris flow is considered as the theory foundation of debris flow forecast. However, because the formation mechanism of debris flow was understood not well, many researchers (Pan et al., 2013; Bacchini and Zannoni, 2003; Cheng et al., 1998; Caine, 1980; Campbell, 1975) had to employ statistical analysis method to study the empirical relationship between the rainfall and debris flow events, then determine the threshold depending on the combinations of rainfall parameters, such as antecedent rainfall, rainfall duration, intensity, cumulative rainfall, etc.. In the early study (Campbell, 1975), the single rainfall parameter, such as the critical cumulative rainfall and the rainfall intensity, was adopted as the forecast factor. Along with the development of the research of debris flow forecast, the combinations of rainfall parameters were used to establish the identification formula for the forecast. The I-D curve (rainfall intensity-duration) was proposed in 1980 (Caine, 1980) and became a common method for debris flow forecast. In later research (Wilson and Jayko, 1997), the similar combination mode of rainfall intensity and duration was also used for mapping rainfall thresholds of debris flow in San Francisco region. In addition, other combination modes of defining a threshold for debris flow activity in terms of mean intensity, duration and mean annual precipitation was also presented for the debris flow prediction of dolomites, northeastern Italy (Bacchini and Zannoni, 2003). These forecast methods relied on the critical rainfall, but in fact, it's very difficult to determine an exact critical rainfall for a region, even for a valley. This is the main reason why the accuracy rate is not high. As a consequence, it has a high risk using "occurrence" or "nonoccurrence" to express forecast results of the debris flow. To avoid this risk, Wei et al.(2007, 2006, 2004) established an extenics model of debris flow forecast using the fuzzy mathematics. The critical rainfall was divided into a series of grade intervals according to the different conditions of debris flow formations. The formation probability of debris flow would be determined according to underlying surface conditions and the interval range where the forecast rainfall of the forecast region is located. Although the influence of the underlying surface on the formation of debris flow was considered in this forecast method, the essential relation between underlying-surface factors and the rainfall factor was not actually established using the formation mechanism of debris flow. So this forecast method still did not break through the mode of statistical forecast, and owing to the grid element used as the basic forecast unit, the forecast results should be revised manually according to the watershed analysis.

In recent years, some scholars (Berti and Simoni, 2005; Iverson et al., 1997; Cui, 1991; Iverson and LaHusen 1989; Takahashi, 1978) have carried out the studies on the slope stability in the condition of mechanical property variation of the soil mass and established the model of debris flow initiation. It has been found experimentally (Iverson and LaHusen, 1989) that the fluctuation of the pore water pressure at the shear plane of the soil mass would lead to the contact stress failure between the soil particles. And based on this discovery, Iverson et al.(1997) has derived the initiation model of debris flow based on the Mohr-Coulomb rule and further studied the influence of the pore water pressure on the formation process of debris flow using the flume experiment in USGS. Takahashi (1978) studied the formation mechanism of debris flow under the action of the hydrodynamics and then presented the critical identification formula for the debris flow formation. Cui (1991) established the stress state function with the variables of soil water content, bed slope and the fines content to predict the formation of debris flow. Zhang et al. (2006) presented an identification model of debris flow formation aiming at the single slope. However, owing to the single slope taken as the main study object, these models mentioned above can not give a judgment whether there is debris flow formation at the watershed scale. Additionally, although some studies (e.g., Tang and Zhang, 2008) have mentioned the debris flow forecast of the watershed scale by distributed hydrological model, no definite model or method was established in their research and consequently can't be applied to the debris flow forecast at the watershed scale.

In order to break through the statistics-based forecast mode of debris flow, this paper will analyze the soil mass stability of the slope by the advantage of achievements in the formation mechanism of debris flow, study the water-soil coupling relationship at the watershed scale and develop a model of debris flow forecast based on the water-soil coupling mechanism.

1. BASIC PRINCIPLES

The debris flow usually occurs in the relatively small watershed. According to Wei et al. (2008), the watershed area of debris flow varies from 1 to 100 km², and more than eighty percent of them are less than 10 km². Generally, the formation process of debris flow in this small watershed contains two water-soil coupling phases. The first one, the coupling of the rainfall and the soil mass of the slope, leads to the soil mass instable. The second one, the coupling of the runoff and instable soil, leads to the formation of debris flow. Both of them are taken as the basic principles for the forecast model of debris flow based on the water-soil coupling at the watershed scale. In the model, the rainfall is the trigger factor in the two phases and runs through the whole process of debris flow formation.

1.1 Failure of Soil Mass under the Action of the Rainfall

The rainfall infiltration is the crucial trigger factor of influencing the soil mass stability and finally leading to the shallow landslide, and the instable depth of the shallow landslide generally varies from 0.5 to 2 m. Before the rainfall infiltration, the soil mass of the slope within the watershed is mainly in the unsaturated state. Along with the rainfall infiltration, the increase of the soil water content will decrease the matrix suction of the soil mass, and the decrease of the matrix suction leads to the failure of soil mass. In this study, the slope stability under the action of the rainfall infiltration is analyzed based on the infinite slope model using the factor of safety (F_s). The shallow failure surface governed by the Mohr-Coulomb rule is assumed to be parallel to the slope surface (Fig. 1).

Figure  1.  Infinite slope model to analyze soil mass stability under the action of rainfall infiltration.

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The shear strength formula of the unsaturated soil proposed by Fredlund and Rahardjo (1993) is shown as follow

So, based on the Eq. 1, the limit equilibrium formula can be expressed as follows

The shear force F that triggers the slope instability at the shear plane is defined by downslope parallel component of the soil mass gravity. It can be expressed as follows

The normal stress at the shear plane can be expressed as follows

By combining the Eqs. 2, 3 and 4, the final form of limit equilibrium formula can be derived.

where c is the soil cohesion force, φ is the internal friction an- gle, u_a is the atmosphere pressure and equal to zero, φ^b is re- lated to the matrix suction (It is close to the internal friction angle (φ) in the condition of the low matrix suction), H_s is the soil depth, ψ=(u_a–u_w) is the matrix suction of the soil (it is the function of the soil water content described by the Van Genuchten model) (Van Genuchten, 1980)

where S_e is the saturated degree, θ_s is the saturated water con- tent of the soil, θ_r is the residual water content of the soil, θ is the soil water content of the current hour, α, n and m are the parameters of the curve, and n=1–1/m.

1.2 Coupling of the Runoff and the Instable Soil

The further coupling process between the runoff and the instable soil mass will lead to the formation of debris flow at the watershed. The process is so complicate that there is no numerical model or physical model to describe it in present researches. From the view of the field observation, debris flow is a water-soil mixture with a biggish density. As a characteris- tic value of the debris flow, the density is an important index to distinguish the hyper-concentration flow, dilute debris flow and viscous debris flow, which also represents the soil material quantity of the debris flow. It's a necessary condition for debris flow formation in watershed scale that the density of the mixture reaches a certain value, but it is not the sufficient condition. So the mixture density can be employed to evaluate the possi- bility of debris flow formation in a watershed, but we can't determine that debris flow will certainly happen. Apparently, the density value of mixture is bigger and the formation prob- ability of debris flow is larger, but there is no a function to de- scribe this relationship now. According to Kang et al. (2004), the density of debris flow varies from 1.1 to 2.3 g·cm^-3. If the density of the mixture is divided into a series of reference in- tervals as Table 1, the formation probability of debris flow is larger and larger from 1st interval to 5th interval of the density. Five grades of debris flow warning are defined according to these density intervals as Table 1.

Table  1.  Probability of debris flow formation according to the water-soil mixture density

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The density of mixture in a watershed is the key factor of this model, which can be estimated by runoff and volume of failure soil mass under the action of rainfall with following equation

where ρ is the density of the water-soil mixture, ρ_w is the den- sity of water, ρ_s is the density of solid particle (generally, ρ_s=2.7 g.cm^-3), v_w is the volume of the water and v_s is the volume of failure soil mass.

2. FORECAST METHOD OF DEBRIS FLOW BASED ON WATER-SOIL COUPLING AT THE WATERSHED SCALE

2.1 Simulation of Hydrological Process and Acquisition of Key Parameters under the Action of Rainfall

According to the water-soil coupling Eq. 8, in order to use the mixture density ρ for publishing the forecast information of the debris flow watershed, the total volume of the instable soil mass v_s and runoff v_w in a watershed under the action of rainfall should be estimated in real time. The two key parameters are closely linked with the variation of soil water content, matrix suction and runoff under the action of the rainfall, so the hy- drological process in a watershed should be simulated to get these hydrological parameters. In this study, the distributed hydrological model GBHM (Cong et al., 2009; Yang et al., 2002) is employed to simulate the hydrological process of in- terception, infiltration and runoff etc. in a watershed.

The GBHM uses the finite difference method to discrete the one-dimensional Richard differential equation and uses the mechanism of runoff generation over infiltration to control the upper bounder of rainfall infiltration. This model can be em- ployed to simulate the variation rule of soil water content and the runoff within the watershed under the action of the rainfall infiltration as well as the variation rule of the matrix suction in the condition of the soil water content variation. So the GBHM can be used to provide these hydrological parameters to calcu- late the instable soil mass v_s and runoff v_w in real time.

The distributed hydrological model GBHM has been successfully applied to the simulation of the runoff in Yangtze River watershed (Xu, 2007). The basic data required in this model mainly includes digital elevation model (DEM), the space-distribution data of rainfall within the watershed, land use type, soil type, hydrological-mechanical parameters relating to the soil type and the vegetation index, etc.. The DEM with a certain precision can be generalized from the topographic map of the study zone by using ArcGIS. In the DEM, the study zone is discretiezed into a series of grids. The space-distribution data of rainfall can be supplied by the numerical weather forecast system and resampled by ArcGIS to correspond the grids of the DEM. In addition, the land use type, soil type and the vegeta- tion index can be obtained from the corresponding database. These data are also needed to be resampled to corresponding grids of the DEM.

2.2 Real-Time Estimation on the Total Volume of Instable Soil Mass

For each discretiezed grid within the watershed, its un- saturated soil depth is supposed 2 m and divided into seven layers with thickness 0.05, 0.1, 0.15, 0.2, 0.3, 0.5, 0.7 m from the top layer to bottom layer. The limit equilibrium Eq. 5 is employed to calculate the safety factor (F_s) of each soil layer, and the total volume of the instable soil mass v_s is estimated in real time through confirming the instable depth of each grid within the watershed.

The limit equilibrium formula of the unsaturated soil in- dicates that the safety factor F_s of a grid is mainly controlled by the matrix suction and the cohesion force of the soil (both of them decrease along with the gradually increasing of the soil water content). The soil mass of the grid will be considered to be instable when F_s < 1. So, the real-time estimation on the total volume of the instable soil mass mainly depends on the real- time calculation of the soil water content and the matrix suction (namely, the negative pore water pressure) within the watershed. In this study, with the soil water content and the matrix suction obtained from the distributed hydrological model (GBHM) as the dynamic inputs, the safety factor F_s of each soil layer of grids within the watershed will be identified, and the total volume of the instable soil mass within the watershed can be estimated in real time by the Eq. 9.

where Sum_ins is the total volume of the instable soil mass at the time t, D_ins is the instable depth of each grid, A_i is the grid area, N_ins is the total quantity of the instable grids at the time t.

2.3 Real-Time Estimation on the Total Volume of Runoff

Based on the mechanism of runoff generation over infil- tration, the overland flow is described by the GBHM using the Manning formula, then the runoff depth D_r of each grid in the condition of rainfall is calculated in real time. The total volume of runoff v_w caused by the rainfall at the time t can be calculated through the Eq. 10.

where Sum_r is the total volume of the runoff at the time t, D_r is the runoff depth of each grid, A_i is the grid area, and N is the total number of the grids within the watershed.

Finally, the density ρ of the soil-water mixture at the time t within the watershed can be calculated through combining the Eqs. 9 and 10 with the Eq. 8. Then the warning grade of debris flow formation can be determined by comparing the mixture density ρ with the reference Table 1.

3. VERIFICATION OF THE FORECAST METHOD

3.1 Study Zone

Jiangjia Gulley (Fig. 2) with the length of 12.1 km and watershed area of 47.1 km² is a tributary of Xiaojiang River, which is located in Dongchuan, Yunnan Province, China. It is a typical small watershed with several debris flow events each year (Kang et al., 2007, 2006) where the Dongchuan Debris Flow Observation and Research Station, Chinese Academy of Sciences is located. The frequently-happened debris flow events and the completed observation data of the Station pro- vide an effective way to verify the forecast method of the de- bris flow proposed in this study.

Figure  2.  Location of the Jiangjia Gulley.

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3.2 Data Preparation

The DEM of Jiangjia Gulley (Fig. 3) with grid size 30 m×30 m is generalized from the 1 : 10 000 topographic map. The soil types and their hydrological-mechanical parameters (Table 2) with the resolution ratio of 1 000 m are obtained from the national soil database and the vegetable index obtained from MODIS image with resolution ratio of 250 m. The land use map is the version of 2 000 with 1 : 100 000 scale (Fig. 4) and the parameters of each land use type (such as the leaf area index and evaporation factor of plants) are obtained from http://www.fao.org/geonetwork/srv/en/main.home. The rainfalls data observed by 7 rain-gauges of the station and some meteorological stations of Dongchuan are used to make the distribution of rainfalls in the watershed. These data are trans- formed into the map with the same grids of the DEM.

Figure  3.  Digital Elevation Model of Jiangjia Gulley.

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Table  2.  Soil types and their hydrological-mechanical parameters

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Figure  4.  Distribution of the land use in Jiangjia Gulley.

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The cohesion force (c) and the internal friction angle (φ) of the soil mass in Jiangjia Gulley are obtained from the direc- tion shear test. The fitted variation relationships (Fig. 5) of the cohesion force and the internal friction angle with the soil water content indicate that the cohesion force of soil mass is suscep- tible to the soil water content marked with an obvious inflection point. The cohesion force and internal friction angle of the soil mass corresponding to the soil water content at the t time by following equations based on the direction shear test.

Figure  5.  Fitting curve of the cohesion force (c) and internal friction angle (φ).

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where θ is the mass water content, c is the cohesion force and φ is the internal friction angle of the soil mass.

3.3 Verification Results

The software of ArcGIS and Fortran 6.6 are employed to deal with the data and run the program of debris flow forecast model. In this verification, the Jiangjia Gulley is discretiezed into 65 372 grids. Four debris flow events observed in 2006 (Table 3) are used to verify this forecast method of debris flow.

Table  3.  Debris flow events observed in Jiangjia Gulley in 2006

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The dynamic variation processes of the total volume of the instable soil mass, the total volume of the runoff and the mix- ture density ρ are shown in Fig. 6. The four figures contained in Fig. 6 can be classified into the three types: the type of creeping to peak value (Figs. 6a and 6b), the type of remaining unique value throughout the period (Fig. 6c) and the type of jumping to the peak value type (Fig. 6d). The three types are mainly caused by the interaction of the antecedent rainfall and the rainfall triggering the debris flow on the same day with differ- ent distribution of the rainfall intensity. Taking the events of Jul. 5 and Jul. 6 for examples, the early warning information at 01:00 on Jul. 5 should have been published with the 5th grade, but the corresponding total volume of the instable soil mass with about 1 000 m³ may be inadequate for the requirement quantity of debris flow formation in Jiangjia Gulley, because the observed minimum quantity of the soil mass is about 5 000 m³ in Jiangjia Gulley according to the collected data (Zhuang et al., 2009; Kang et al., 2007, 2006). So, taking this value as the lower limit value of the forecast model, the early warning in- formation on Jul. 5 should be published at 11:00. As for the event of Jul. 6, the density of the mixture was in the interval corresponding to highest grade of debris flow warning from 2:00 to 6:00, according to the observation, the debris flow event of July 6 happened at 03:55 and ended at 08:30.

Figure  6.  Dynamic early warning information of debris flow. (a) Jul. 5; (b) Jul. 6; (c) Aug. 15; (d) Aug. 20.

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Comparing with the observation of debris flow events and the result of forecast calculated by the model, the forecasts of 3 events are successful, but it is failing for the event of July 5 (Table 4). This verification shows the model of debris flow forecast based on the water-soil coupling mechanism is effective and most of debris flow events coincide to the forecast result.

Table  4.  Early warning results of debris flows

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4. CONCLUSIONS

A model of debris flow forecast at watershed scale has been established by the research of the water-soil coupling mechanism in a watershed, and its feasibility has been tested by a case study in Jiangjia Gulley. According to the research, some conclusions can be drawn as follows.

(1) The coupling of water and soil leads to the failure of soil mass on the slopes because the variation of soil mechanical property with the rainfall infiltration influences the stability of soil mass on the slopes. An instable identification model of the unsaturated soil in a watershed was set up to estimate the vol- ume of failure soil mass in real time under the action of rainfall.

(2) The coupling of runoff and failure soil mass controls the formation of debris flow because the debris flow is a soil-water mixture with a biggish density. Because the density is an important index to distinguish debris flow from hyper- concentration flow and it's a necessary condition for debris flow formation in watershed scale that the density of the mix- ture reaches a certain value, the mixture density can be em- ployed to evaluate the possibility of debris flow formation in a watershed. The density of mixture is proposed to be divided into five reference intervals to coincide the formation probability of debris flow.

(3) The Jiangjia Gulley is chosen as a case study water- shed to test the feasibility of the forecast model. The test with 4 debris flow events in 2006 shows that the model of debris flow forecast based on the water-soil coupling mechanism is effec- tive and most of debris flow events coincide to the forecast result.