A theoretical model for the initiation of debris flow in unconsolidated soil under hydrodynamic conditions

C.-X. Guo, J.-W. Zhou, P. Cui, M.-H. Hao, and F.-G. Xu Key Laboratory of Mountain Hazards and Surface Process, Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, Sichuan 610044, China University of Chinese Academy of Science, Beijing, 100049, China State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, Sichuan 610065, China College of Water Resources & Hydropower, Sichuan University, Chengdu, Sichuan 610065, China

model to be more in-depth. However, these authors ignored the influence of the pore water pressure on the shearing strength and those parameters that could change with time. Some researchers considered the debris flow to be generated from a landslide and established a 1-D infinite slope failure model to describe the problem (Iverson et al., 1997;Gabet and Mudd, 2006;Huang et al., 2009). Moreover, some statistical 20 models are presented based on many indoor and field experiments (Cui, 1992;Gregoretti and Fontana, 2008;Tognacca et al., 2000). The results from these models could have experimental and regional limitations due to the difficulty of their application.
As concerns research about the debris flow initiation mechanism from an unconsolidated soil or loose deposit, the current understanding is still at the level of superficial 25 phenomena, and it is difficult to perform the corresponding numerical analysis. Zhou (2013b) considers the surface runoff and seepage process in the slope stability analysis to achieve the dynamic process of debris flow formation. Zhuang et al. (2012) simplified the debris flow initiation under runoff into three patterns and analyzed the 4489 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mechanisms and process. Fang et al. (2012) found that the debris flow initiation process can be summarized into the appearance of surface runoff, fine particles moving, large particles falling, the whole slope moving and the debris flow forming. These analyses show that the surface runoff and internal seepage mainly contribute to the tumbling and moving of particles and shallow slope failure with loose deposits. Therefore, con-5 sidering the surface runoff and internal water pressure, which are affected by seepage into the debris flow, an initiation model is feasible and is a significant achievement.
Based on several indoor experiments and field investigations, we determine that the surface runoff is a key factor for the debris flow that is generated from unconsolidated soil. After comparative analysis of the previous initiation model for debris flow, a new 10 theoretical model for studying the initiation of debris flow in unconsolidated soil under hydrodynamic conditions is presented. This model is validated by a laboratory test and is applied to study the initiation of the debris flow in the Wenjiagou Gully in Sichuan, China. 15 Previous initiation models for debris flow can be organized into four types: (1) debris flow mobilization from landslides, which was first presented by Iverson et al. (1997), (2) coupling models of hydraulics and soil mechanics, first presented by Takahashi (1978); (3) statistical models from field investigations and indoor tests (Cui, 1992); and (4) surface runoff models, which are presented by Berti and Simoni (2005).  Iverson et al. (1997) indicated that landslides that mobilize to form debris flows can be divided into three processes: (a) widespread Coulomb failure within a sloping soil, rock, or sediment mass, (b) partial or complete liquefaction of the mass by high porefluid pressure and (c) conversion of landslide translational energy to internal vibration 25 4490 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | energy (i.e., granular temperature). The main reasons for soil failure are considered to be the increase in internal excessive pore water pressure that is caused by ground water and the local Coulomb failure and decreasing cohesion that results from particle liquefaction. The safety factor of soil can be determined by three parts:

Debris flow mobilization from landslides
(1) 5 where T f describes the ratio of frictional resistance strength to gravitational driving stress; T w describes the ratio of strength modification by groundwater to the gravitational driving stress, and T c describes the ratio of cohesive strength to gravitational driving stress. These three parts can be computed as follows: where c and ϕ are the cohesive and friction angle of the soil; θ is the inclination of the soil slope; Y is the slope failure depth; y is the direction perpendicular to the slope surface; d is the depth of the water table where the water pressure p = 0; the water table necessarily parallels the ground surface, as do all surfaces with constant p in infinite slopes; and γ t is the depth-averaged total unit weight of the saturated and unsaturated 15 soil below and above the water table. This model must analyze the pore water pressure in unconsolidated soil when considering the liquefaction and dynamics of the sliding. However, owing to a relative lack of data for rigorous model tests, liquefaction and slide dynamics models remain immature compared to slope failure models.

Coupling models of hydraulics and soil mechanics
Coupling models of hydraulics and soil mechanics were presented by Takahashi (1978); this type of model is a Coulomb failure model. In this model, the shear stress 4491 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | τ and resisting stress τ r at the depth a are measured from the surface of the sediment layer, which can be computed as follows: where g is the acceleration of gravity; σ, c and ϕ are the density, cohesive strength and friction angle of the soil, respectively; θ is the inclination of the soil slope; h 0 is the depth of the flowing water above the slope surface; ρ is the fluid density; and C * is the concentration of the solids when packed.
The stability of the soil slope is determined by the following equations: Additionally, when the shear stress is greater than the cohesion of the soil on the slope surface (a = 0), and shear failure of the slope will occur. If considering the surface runoff, we must add the gravity component in the shear stress direction and in the resisting stress direction to the shear stress and resisting stress separately. Here, the water above the slope is expected to be parallel to the 20 slope surface. This model considers the surface runoff to be in a static condition and ignores its dynamic effects.

Empirical statistical model
There are several empirical statistical models for studying the initiation of debris flow. For example, Cui (1992) defined the concept of a quasi-debris flow body and presented 25 4492 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | an initiation model by fitting the experiment results. The soil failure criterion is that when the shearing stress τ f is equal to the resisting stress τ r , the soil begins to fail. This model considered the fine-grain content C (< 1 mm), the soil saturation S r (which equals the volume of the water divided by the volume of the pores in the material) and the bed slope θ to be the factors that impact the initiation of the debris flow: By the use of Eq. (7), we can be drawn into the space of θ, S r and C, and this curved surface is called S. For every quasi-debris flow body, there is a point P (θ, S r , C) in the space of θ, S r and C. When the point P is on the curved surface S, the quasi-debris flow body is in the critical start-up state. When the point P is below or above the surface S, the quasi-debris flow body is stable or unstable, respectively. Empirical statistical models are determined from indoor tests; because of the special soil samples and test conditions, these models are subject to significant soil type influences.

Surface runoff model 15
Debris flows can be initiated by the surface runoff in unconsolidated soil. This phenomenon is best described in terms of the equilibrium of single particles with the hydrodynamic forces rather than using the classical limit equilibrium analysis of a Mohr-Coulomb material employed for shallow slope stability (Chiew and Parker, 1994;Buffington and Montgomery, 1997;Armanini and Gregoretti, 2000). Although poorly sorted, 20 such debris contains a low fine fraction (less than 10-20 % silt and clay) compared to soils that are involved in landslide-induced debris flows, and it has a much higher hydraulic conductivity. Because of their ability to drain the rain water that infiltrates from the surface, the moisture content of these materials is always far from saturation; therefore, failure is very unlikely unless it occurs as a result of surface flow. 25

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Through direct observations and real-time data collection, Berti and Simoni (2005) found the relationship between the debris flow initiation and runoff discharge and developed a simple model that is based on kinematic wave theory to compute the hydraulic condition.
where Q R is the surface discharge; q is the flow per unit length of the channel (which is lost by infiltration into the bed); and c is the kinematic wave celerity. This equation can obtain the surface flow charge at an arbitrary length and time through the discrete length of the channel x and time t. Compared with the empirical models presented by Cui (1992), Tognacca et al. (2000) 10 or Gregoretti and Fontana (2001), this model has fewer empirical parameters and has been verified by field observations.

Comparative analysis
The main feature, critical condition and application range of the above four initiation models for debris flow are summarized in Table 1.

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The four kinds of debris flow initiation model have different application ranges with various methods. As shown in Table 1, before we fully get the debris flow initiation mechanism, the ESM can strengthen the understanding of the initiation mechanism of geotechnical debris flows. Then CM and DFMFL achieved some progress in understanding the failure process with water flow and debris flow transforming from land-20 slides. Moreover, the SRM helped us to realize that unconsolidated materials can also form a debris flow in a small gradient channel.
However, the debris flow initiation is still not widely accepted by the researchers despite its achievement in hazard area. The main reason is that the soil properties have complex effects influencing debris flow initiation which have not been clearly under-ESM provides a clear physical concept of debris flow initiation by focusing on the governable parameters (slope, material composition and water in soil) but needs to be specifically refined with other external hydrodynamic conditions. The SRM model can consider the surface flow; however, the appearance of the runoff effect is obtained from statistical data rather than a mechanics mechanism, which may not apply in other re-5 gions. CM adds the weight of runoff on the slope in the model, regarding it as a stable stage and ignoring the real dynamic effect.
Hence, to sum up, though the hydrodynamics condition of the surface runoff, which is very important for the initiation of debris flow in unconsolidated soil, has now begun to be taken into account, the particular mechanism and process inducing debris flow 10 from surface runoff should be studied in greater depth.

Flume experiment for unconsolidated soil
Here, we design an artificial rainfall test for unconsolidated soil to study the failure mechanism and initiation condition of debris flow. 15 We took the unconsolidated soil from the Wenjiagou Gully in China as the study soil, with conditions of rainfall intensity of 140 mm h −1 (the rainfall intensity that occurs every 5 years in this area is 70 mm h −1 ), slope angle 39.1 • , bed gradient 5 % and 10 %, and rainfall duration of 3 h. An artificial rainfall system and flume and monitoring sensors are shown in Fig. 1. A total of 12 sets of pore water pressure and volumetric water 20 content sensors were arranged in the slope. Table 2 shows the particle size distribution of the soil samples that are used in the artificial rainfall tests (maximum particle size is 60 mm, and particles larger than 60 mm are first excluded).

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | In addition to rainfall condition, water flow of approximately 1.70 m s −1 and 0.05 m depth is used to simulate surface runoff in the field. And a new flume is designed for separating surface runoff and seepage, as shown in Fig. 1.

Flume experiment with rainfall
When the unconsolidated slope is under the rainfall condition, only small shallow slope 5 failures occur, such as particle tumbling, small slides or collapse in the whole rainfall process (see Fig. 2). Here, the rainfall intensity is 140 mm h −1 , which is sufficiently large, but no large slope failure or debris flow happens.
To find the reason why large slope failure and debris flow are not forming, variations of the pore water pressure (PWP) and volumetric water content (VWC) at the slope toe are tested, as illustrated in Fig. 3.
As shown in Fig. 3, PWP and VWC variations can be summarized into three stages during rainfall of 2 h: (1) the initial steady stage, (2) a rapidly increasing stage and (3) steady again stage. The rapidly increasing and steady again stages are ahead of the time at a high gradient of 10 %, which can reach a maximum value at 50 min. With 15 the gradient increasing, the water-holding capacity of the loose deposit decreases, and water flows out more rapidly, which leads to the water content increasing (reaching 34.5 % with a 10 % gradient at T = 180 min), and the surface soil of the slope is almost saturated. However, the pore water pressure at the slope toe is approximately 0.8 kPa, and might not be large enough to induce slope toe failure or regressive failure. Compar-20 ing the large-scale debris flow triggered in the field of Wenjiagou Gully with the same conditions, it is found that failure of the large loose deposit may depend on not only the increasing internal pore water pressure but also the external hydrodynamic effect of surface runoff.

Flume experiment with runoff
In order to reproduce the initiation process of the Wenjiagou Gully debris flow, water flow at 1.7 m s −1 and a depth of 5 cm is applied in addition to the artificial rainfall condition above.
It is found that the deeper sensors (PWP and VWC) show fluctuations while the soil 5 failure happens, which corresponds with the previous findings (Iverson, 2000;Chen, 2006). Experimental tests shown in Fig. 4 indicate that the soil failure is occurring at the shallow layer, about 5 cm. This failure is so minor that it is usually regarded as a type of erosion (Bryan, 2000). In fact, erosion is the process of a small amount of particles slowly moving, and may last for a few minutes or even a few years, such as 10 sheet wash, rill erosion, piping erosion, etc. But, in our tests, the slope failure is happing at a shallow position on a small scale. When the runoff flows across the slope, fine particles are first to detach and liquefy (the maximum flow concentration reaches about 1.8 g cm −3 ). At the same time, the runoff entrains surface particles, even leading to shallow landslide. Then debris flow is easily triggered along the slope surface, with 15 abundant loose particle material and water flow. This process also indicates that initiation of the debris flow is not a simple erosion failure but a complex disaster chain with various transformations. In addition, debris flow initiation forms instantaneously and is difficult to catch even with a video camera (20 fps). Moreover, the soil failures are of several types, such as 20 shallow landslide, flowslide, and particles migration, which are difficult to differentiate in the current research (Hungr et al., 2001(Hungr et al., , 2014Wang, 2003;Take, 2004;Klubertanz, 2009).
In a word, in the runoff condition, the unconsolidated soil forms failures, especially the shallow landslide, flowslide, and even debris flow, more easily than with rainfall 25 only. At the process of debris flow initiation, fine particles migrate with hydrodynamic force vertically apart from along the slope surface, which can be verified by grading analysis of the slope after the experiment. From the grading curve, we find that the fine 4497 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | particles (< 2 mm) increase from 18 to 23 %, which shows their great influence on the slope failure and debris flow initiation. A similar conclusion can also be found in flume tests with rainfall (Cui et al., 2014). 5 From the flume experiment with no runoff being generated, the slope stays in a stable state with strong rainfall. Comparing the slope physics properties before and after the tests, the resisting strength decreases only a little, as shown in Table 3, and the slope is still stable even with a peak pore water pressure of about 0.9 kPa (upper soil). And considering debris flow occurring in the field situation, it indicates that the factors trig-10 gering debris flow involve the hydrodynamic condition, like huge runoff or flood besides rainfall.

Debris flow initiation mechanism
For the flume experiment under runoff, an obvious soil failure and debris flow appears. In fact, when the runoff flows through the slope surface, there are two effects: on the one hand, fine particles (less than 2 mm) migration leads to a coarse layer (the 15 surface soil is in a saturated state and its cohesion is close to zero); on the other hand, the moving fine particles block the soil pores and cause saturation of the top soil, increased pore water pressure and uplift pressure, and decreased soil shear strength. Moreover, the fine particles liquefying and integrating into water flow will increase the viscosity and enlarge the hydrodynamic effect. However, this effect is usually ignored 20 in our research.
Besides the hydrodynamic effect, soil shear strength will be reduced by the coarse particle gradation. And a perched water table and water film will form with the pores blocked, and then provide lubrication Lu et al., 2010). In addition to the detachment of fine particles by erosion and scour, the soil failure will happen During the process of soil failure with the runoff, the failure soil will disintegrate in a moment, or integrate into the water flow (the liquidation and suspension effect), and/or move down to the slope toe with the run off, leading to the large particles aggregating at the slope toe. And with the fine particles integrating into the water flow and constantly increasing in concentration, it can build up greater power with the loose material joining, 5 and then form a destructive debris flow. In the field, with steep terrain, the requisite hydrodynamic conditions, and a long motion distance, the huge debris flow triggered in the channel will cause major disasters such as the Wenjiagou debris flow in 2010 (Zhou, 2013b).
To verify the important role of runoff, after the experiment with only rainfall, the shear 10 strength parameters of unconsolidated soil are tested by direct shear testing under four normal stress conditions (200, 400, 800 and 1200 kPa), as shown in Fig. 5. The sample is the original soil in the flume after rainfall, which has a density of 1.909 g cm −3 and water content of 4.5-6.5 % (approximately). The water content of natural soil is about 1.0-2.0 % and for saturated soil is about 15-17 %.

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Experimental results show that the cohesion and friction angle for unsaturated soil (water content 4.5-6.5 %) are 22.3 kPa and 37.6 • , respectively, and 42.5 kPa and 38.1 • for natural soil (water content 1.0-2.0 %). Laboratory tests indicate that the cohesion reduced sharply with both runoff and rainfall, but the friction angles changed less. For the saturated soil behind the surface runoff, the cohesion is assumed equal to 0, and 20 the friction angle is determined by the experimental test for unconsolidated soil when the water content is 15-17 %. Table 3 summarizes the shear strength parameter of unconsolidated soil in different water content conditions, which are used for numerical analysis.
The stability of the unconsolidated soil slope is influenced by three main factors: 25 a decrease in the shear strength of the unconsolidated soil, an increase in the pore water pressure in the slope and erosion of the surface runoff. Here, we apply the limit equilibrium method to the analysis of the stability of the unconsolidated slope under different shear strength parameters (Fig. 6). As shown in Fig. 6a, a shallow failure 4499 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | of the landslide slope will occur when the shear strength parameters are very low. Sensitivity analysis for the impact of the shear strength parameters on the safety factor of the slope is conducted based on a certain sliding surface (Fig. 6b). As shown in Fig. 6c, the safety factor decreases with a decrease in the cohesion and friction angle of the unconsolidated soil, which is a linear relationship. 5 As shown in Fig. 6a and c, in most cases, the safety factor of the unconsolidated slope is larger than 1.0; decreasing the shear strength of the unconsolidated soil is only one factor that has an impact on the failure of the slope. The hydrodynamic effect of the surface runoff is another key factor in the failure of the slope, especially for the initiation of the debris flow. For unconsolidated soil with wide grading and loose structure, the 10 triggering factors for the debris flow are floods or large runoff besides a strong rainfall even in a long period.
Therefore, wide grading loose soil inducing debris flow is a process involving the interaction of its own and outside conditions. Especially in high mountain areas like those of West China and Italy, the runoff on the slope surface can be ignored. When 15 the slope stability is analyzed, hydraulic calculation of parameters such as peak discharge, flow velocity and depth should first be executed, and then coupled with the self-weight. Though Berti (2005) introduced experimental evidence and a numerical model for predicting debris flow initiation through hydraulic calculations, the author's prediction model still required the help of an empirical formula and is difficult to apply 20 in other areas.
In this paper, we regard the hydraulic calculation as a known condition, and add the hydrodynamic effect to the current model for a more widely applicable debris flow initiation model.

Model assumption and construction
In order to simplify this problem, we here consider the soil which is in a critical state with a failure shape of a rectangle; the cohesion in the top soil is regarded as zero because of the low clay content (in practice, the value should be adjusted for different soils). 4500 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | According to the experimental results, Fig. 7 shows the simplification of assumptions for the stress distribution of unconsolidated soil under hydrodynamic conditions. As shown in Fig. 7, three simplification assumptions are introduced: (1) the surface runoff is parallel to the slope surface, and the failure face is also parallel, (2) the superficial soil of the unconsolidated soil is in the saturated stage; and (3) underground water 5 is omitted here. The first assumption is applied in the model to reduce the complexity of this problem because the surface runoff shape does not have a large influence on the slope stability. Through the field investigation (Tang et al., 2012;Zhou et al., 2013b) and indoor experiments above, we find that the soil is almost completely saturated when shallow failures are occurring. For the second simplification assumption, 10 it is known that the failure of unconsolidated soil is always in the valley, which indicates that the main factor is not the increase in the underground water level; thus, the underground water can be omitted here.
To consider the unit length and width, as shown in Fig. 7, assuming that there is an unconsolidated soil failure with a slope failure depth of a, a surface runoff depth 15 h, a pore water pressure u w on the failure surface (details are in Sect. 4.3), a slope angle θ, a cohesion c, a frictional angle ϕ with saturated soil, and water unit weight r w , and the soil surface friction provided by the surface flow f (details are in Sect. 4.2) (and with the small buoyancy and seepage force omitted here), using the Fredlund soil strength theory (Fredlund and Rahardio, 1993) and the principle of effective stress, the 20 soil resisting stress at a depth of a can be expressed as follows: Combining the above, we can then obtain the resist stress of the unconsolidated soil, and the shear stress can be computed as follows:

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Considering the effect of surface runoff, if the shear stress is less than the resist stress of the unconsolidated soil, the slope is stable: Takahashi (1978) thinks that the cohesion of a saturated unconsolidated soil can be ignored, but in fact, this is an important parameter that cannot be ignored. If the shear 5 stress is greater than the resisting stress at a depth of a > 0, a failure of the unconsolidated slope will occur. Since the 1970s, many scholars have done a lot of research on the overland flow resistance with indoor or outdoor rainfall and erosion tests, by means of different concepts and expressions such as the Darcy-Weisbach, Chezy and Manning friction factor. Due 10 to the complexity of this problem, the Darcy-Weisbach friction factor is mainly used in their models because of its concise form and wide application, suitable for laminar flow and turbulent flow.
At present, it is broadly accepted that the overland flow resistance in different surfaces can be divided into four sources, namely the grain resistance f g , form resis-15 tance f f , wave resistance f w and rainfall resistance f r . Grain resistance is the resistance formed by soil particles and micro aggregate. The form resistance f f contains the dissipation of energy by microtopography, vegetation, gravel and so on. Wave resistance f w forms by vast scale surface deformation. And rainfall resistance is generated by the raindrop.

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However, these resistances are difficult to measure and quantify in experiments. And the factors may have an interaction effect. So, to simplify, the Darcy-Weisbach friction factor λ is chosen to indicate the overflow resistance.
According to hydraulics theory, the shear force F that is generated by the surface flow on the slope surface can be calculated as follows: where ρ is the density of water; l is the slope length; λ is the friction loss factor of the hydraulically open channel, and when the runoff is laminar flow (Re < 4502 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2000, Re is Reynolds number), λ = 64/Re; when it is turbulent flow (Re > 2000), λ = 1/[2l g(3.7R/∆) 2 ] (Nikuradse empirical formula). R = A/χ is the hydraulic radius of the cross-section; and ∆ is the roughness (slope surface sand diameter), which is usually close to 30-60 mm in a pebble river bed. 5 The physical model above shows that the slope stability condition (safety factor) is related to the grains' physical characteristics, the slope, runoff velocity, runoff depth, water flow unit weight, etc. For a specific type of soil, its physical characteristics are determinate. Therefore, for a physical model, it is important to find out which are the most sensitive factors for slope failure. Here, we assume that the fluid has a laminar 10 flow, and the safety factor is shown as follows:

Sensitivity analysis of the parameters
The values of the model parameters that are used for sensitivity analysis are shown in Table 4. Considering the safety factor F s to be a function of the sensitive factors, we can use 15 the usual form S i = ∆F s /∆x i to conduct sensitivity analysis (∆ represents a tiny variable; F si , x i respectively represent the i th safety factor and a sensitive factor influencing the F s . To compare all of the factors, which have different units, the common method is A high absolute value of I i stands for the high sensitivity of the i th factor. Through the relationships between ∆F s /F si and ∆x i /x i (Fig. 8), we 20 can find how the model parameter affects the initiation of the debris flow. As shown in Fig. 8, we can obtain that the sensitivity, from high to low, is as follows: slope angle, runoff depth, runoff velocity, failure depth, cohesion, water unit weight, surface roughness, viscosity and angle of internal friction. The cohesion, which has a negative correlation with the slope stability, makes a certain contribution and cannot 25

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | be ignored. Besides the slope angle, which is well known for its important effect, the following runoff depth and velocity indicate that the runoff that can produce the shear stress should also not be omitted in the model, especially as, when the runoff runs down the slope, it can carry fine particles away and decrease the cohesion, leading to slope instability. 5 This model is derived from soil mechanics and experimental results and is suitable for slopes where there is a low impervious surface angle and the debris flow is triggered by a large surface runoff.

Simulation of laboratory testing
In this section, we use the presented model to simulate laboratory testing. Accord-10 ing to the artificial rainfall test for the unconsolidated slopes, the values of the model parameters are shown in Table 3.
Because the slope failure did not occur with a strong rainfall condition (no runoff generated) and did occur with a large surface runoff condition, we simulate the slope stability under two stages (no runoff, non-uniform runoff). For the no-runoff condition, 15 the cohesion is found to be 22.3 kPa as measured by the shear tests after tests shown in Sect. 3.2. And it is zero under the runoff condition because of the surface runoff's sand-carrying effect, which leads to the soil coarsening, giving the cohesion c a value of nearly zero. This phenomenon is also observed in the tests shown in Fig. 8. Moreover, a shallow failure pattern for loose deposit under rainfall is usual. Here, the position 20 0.05 m below the slope surface is chosen for analyzing the slope stability. Through the formula Eq. (14), the safety factors under no-runoff and runoff conditions are respectively 32.51 (no-runoff, c = 22.3 × 10 3 kPa, h = 0 m, other parameters are the same as Table 3) and 0.19 (c = 0 kPa, with runoff, detailed parameters are shown in Table 5). Thus, the results show that the slope is stable under the no-runoff condition and fails 25 with the runoff condition, which is consistent with the experiment results and indicates the rationality of this hydrodynamic model.

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | To be sure, with the runoff condition, the fluid is regarded as laminar flow (Re ≈ 1214). And generally, soil internal friction is less influenced by water content. So the soil parameter with no-runoff is the same as the runoff condition except for the cohesion.
When unconsolidated soil is in the saturated state, the cohesion and friction angle of the soils are decreased to a certain small value, but the loose unconsolidated soil is 5 still stable. This finding indicates that the decrease in the shear strength is a necessary condition for the soil failure, but the most necessary feature is the hydrodynamic effect of the surface runoff. Considering the variables slope angle θ, and runoff depth h, we can get the critical failure depth for the initiation of the debris flow through the formula Eq. (15) 10 a ≤ c − r w h sin θ − λρv 2 l 8 where the parameters are the same as Table 3 except for the variables slope angle θ, and runoff depth h. Then, we can use Eq. (15) to determine the initiation condition of the debris flow in the unconsolidated slope by the use of laboratory testing. Figure 9 shows the critical 15 failure depth of the initiation condition for the debris flow in the unconsolidated slope under laboratory testing conditions. The critical failure depth decreases with the increase in the slope and runoff depth. On the other hand, below a certain failure depth, it reflects the critical slope and surface runoff conditions, which have the same relationship as in Sect. 4.2. 20 To sum up, not only the shear force of runoff but also its sand-carrying effect is considered in the hydrodynamic model, which shows a conservative and safe method for slope safety analysis. Compared with the current method with the runoff effect neglected, this method can be applied in the analysis of loose deposit failure under rainfall or runoff in the future. If there is no runoff generated, the hydrodynamic parameters (such as runoff depth, runoff velocity, etc) can be omitted from the common slope safety analysis. 4505 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 6 Conclusion and discussion

Conclusion
To find the debris flow triggering mechanism, previous studies about the debris flow initiation model are first summarized. The current numerical models which almost all have specific application in their respective regions have all ignored the hydrodynamic effect 5 with fine particles and slope stability. With the experiments under rainfall and runoff, the important role of the hydrodynamic effect in the debris flow initiation has been found and clearly understood. For example, on the one hand, it carries away the fine particles which lead to the soil coarsening and soil strength decreasing; on the other hand, it increases the unit weight and viscosity of water flow, which will increase the shear 10 stress to the slope. However, these processes are sudden, invisible and always omitted in practice. Finally, a theoretical model for debris flow initiation considering the hydrodynamic effect is built and verified by test data. The simulation results show that this model is much more appropriate for unconsolidated soil failure analysis by considering the hydrodynamic condition and simplifying other soil properties.

Discussion
Debris flow initiation is usually classified into two types: the landslide transforming type and water erosion type. In fact, these initiation mechanisms exist widely and simultaneously in the field. Though the large water flow can lead to huge erosion and entrainment, the hydrodynamic effects which add the shear force along the slope and lead to 20 soil strength decreasing, with fine particles migrating and forming local relatively impermeable faces, have not been well known in the current literature (Iverson et al., 2010(Iverson et al., , 2011Huang et al., 2009Huang et al., , 2010Lade, 2010). The surface runoff resulting in soil failure in this way is usually regarded as an erosion effect. In practice, this process (soil failure, from sliding to flowing) is sudden and relatively complex in nature (Malet, 2005). incorporated by water flow and mistaken for erosion or entrainment. So the findings in this paper will provide a new view of the debris flow initiation and unconsolidated soil failure. Based on hydraulic theory, an unconsolidated soil failure model has been established that incorporates the hydrodynamics shear stress and pore water pressure. This model 5 has improved on a defect in the hydraulic and soil mechanics coupling model (Takahashi, 1978), which omits the hydrodynamics and has an insufficient surface runoff model (Berti and Simoni, 2005), in which the critical condition is not able to prevent the debris flow from forming when there is a low velocity surface runoff.
In classical slope analysis, the sliding face can always be fixed by geological analysis 10 such as the soft layer or stability computation. However, the sliding surface is random and shallow, existing in the wide grading loose soil and this needs to be analyzed and estimated by simulation experiments. Here, the sliding surface is assumed to be a plane at a depth of 5 cm. In the future, it will be studied in depth and defined using a precise numerical model rather than by estimation. Moreover, though our realization 15 of the debris flow initiation considering the hydrodynamic effect can provide a physical basis for understanding the debris flow triggering threshold, it must be admitted that the loose unconsolidated soil forming the debris flow is notably complex and other unknown factors should be considered in our model.       Table 2 shows the particle size distribution of the soil samples that are used in the artificial rainf 181 (maximum particle size is 60 mm, and particles larger than 60 mm are first excluded). 182

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With the gradient increasing, the water-holding capacity of the loose deposit decreases, and water flows out 203 more rapidly, which leads to the water content increasing (reaching 34.5% with a 10% gradient at T=180 min), 204 and the surface soil of the slope is almost saturated. However, the pore water pressure at the slope toe is 205 approximately 0.8 kPa, and might not be large enough to induce slope toe failure or regressive failure.

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Comparing the large-scale debris flow triggered in the field of Wenjiagou Gully with the same conditions, it is 207 found that failure of the large loose deposit may depend on not only the increasing internal pore water pressure 208 but also the external hydrodynamic effect of surface runoff. corresponds with the previous findings (Iverson, 2000;Chen, 2006). Experimental tests shown in Figure 4 217 indicate that the soil failure is occurring at the shallow layer, about 5cm. This failure is so minor that it is usually 218 regarded as a type of erosion (Bryan, 2000). In fact, erosion is the process of a small amount of particles slowly 219 moving, and may last for a few minutes or even a few years, such as sheet wash, rill erosion, piping erosion, etc.

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But, in our tests, the slope failure is happing at a shallow position on a small scale. When the runoff flows across 221 the slope, fine particles are first to detach and liquefy (the maximum flow concentration reaches about 1.8g/cm 3 ).

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At the same time, the runoff entrains surface particles, even leading to shallow landslide. Then debris flow is 223 easily triggered along the slope surface, with abundant loose particle material and water flow. This process also 224 indicates that initiation of the debris flow is not a simple erosion failure but a complex disaster chain with 225 various transformations.

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In addition, debris flow initiation forms instantaneously and is difficult to catch even with a video camera 227 (20fps). Moreover, the soil failures are of several types, such as shallow landslide, flowslide, and particles 228 migration, which are difficult to differentiate in the current research (Hungr et al., 2001(Hungr et al., , 2014Wang, 2003;229 Take, 2004;Klubertanz, 2009).

230
In a word, in the runoff condition, the unconsolidated soil forms failures, especially the shallow landslide,   runoff. Here, we apply the limit equilibrium method to the analysis of the stability of the unconsolidated slope 283 under different shear strength parameters ( Figure 6). As shown in Figure 6(a), a shallow failure of the landslide 284 slope will occur when the shear strength parameters are very low. Sensitivity analysis for the impact of the shear 285 strength parameters on the safety factor of the slope is conducted based on a certain sliding surface (Figure 6(b)).

286
As shown in Figure 6(c), the safety factor decreases with a decrease in the cohesion and friction angle of the 287 unconsolidated soil, which is a linear relationship.

288
As shown in Figure 6(a) and 6(c), in most cases, the safety factor of the unconsolidated slope is larger than 289 1.0; decreasing the shear strength of the unconsolidated soil is only one factor that has an impact on the failure 290 of the slope. The hydrodynamic effect of the surface runoff is another key factor in the failure of the slope, 291 especially for the initiation of the debris flow. For unconsolidated soil with wide grading and loose structure, the 292 triggering factors for the debris flow are floods or large runoff besides a strong rainfall even in a long period.

293
Therefore, wide grading loose soil inducing debris flow is a process involving the interaction of its own and 294 outside conditions. Especially in high mountain areas like those of West China and Italy, the runoff on the slope 295 surface can be ignored. When the slope stability is analyzed, hydraulic calculation of parameters such as peak 296 discharge, flow velocity and depth should first be executed, and then coupled with the self-weight. Though Berti 297 (2005) introduced experimental evidence and a numerical model for predicting debris flow initiation through 298 hydraulic calculations, the author's prediction model still required the help of an empirical formula and is 299 difficult to apply in other areas.

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In this paper, we regard the hydraulic calculation as a known condition, and add the hydrodynamic effect to  As shown in Figure 8, we can obtain that the sensitivity, from high to low, is as follows: slop 377 depth, runoff velocity, failure depth, cohesion, water unit weight, surface roughness, viscosity 378 internal friction. The cohesion, which has a negative correlation with the slope stability, m 379 contribution and cannot be ignored. Besides the slope angle, which is well known for its impor 380 following runoff depth and velocity indicate that the runoff that can produce the shear stress sho 381 omitted in the model, especially as, when the runoff runs down the slope, it can carry fine part 382 decrease the cohesion, leading to slope instability.

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This model is derived from soil mechanics and experimental results and is suitable for slopes w 384 low impervious surface angle and the debris flow is triggered by a large surface runoff.

Simulation of laboratory testing 386
In this section, we use the presented model to simulate laboratory testing. According to the ar 387 test for the unconsolidated slopes, the values of the model parameters are shown in Table 3.

388
Because the slope failure did not occur with a strong rainfall condition (no runoff generated 389 with a large surface runoff condition, we simulate the slope stability under two stages (no runof 390 runoff). For the no-runoff condition, the cohesion is found to be 22.3kPa as measured by the s