This phenomenon denotes a kind of debris flow process formed and moving on a slope, including small-scale gullies and so-called colluvium deposits in hollow region (CDHs from Zhang et al., 2020). It is usually driven by external forces such as continuous rainfall, rainstorm, melted ice, and snow. A large number of experiments and witness evidences have shown that slope debris flow generally begins with the process chain of softening, cracking, creep of the loose material, as well as footslope failure. After that, the slope failure proceeds into local collapse and liquefaction under continuous shear stress. Subsequently, the processes can be extended to the surrounding areas, and eventually lead to the overall initiation of debris flow (Morton and Cambell, 1974; Gabet and Mudd, 2006; Li et al., 2010; Zhou et al., 2017; Liao et al., 2017; Pan et al., 2017; Qiao et al., 2018; Li et al., 2019). Some other reports also indicated that slope materials could be transformed into debris flow directly without collapse or slide processes (Williams and Guy, 1973; Iverson, 1997b; Hu et al., 2015; Chen, 2016).

Generally, it is believed that the initiation of debris flow is mainly determined by water supply, landform, physical properties of potential loose materials, and corresponding stress states. Takahashi (1978), Takahashi (2007) calculated that the critical slope for debris flow occurring was only about 14.5° based on mechanical equilibrium. Many event-based cases also showed that in some areas, rainfall intensity of 10 mm/h or even lower could trigger landslides and debris flows (Wang et al., 1997; Cannon et al., 2008; Guzzetti et al., 2008; Zhou and Tang, 2013). Therefore, it seems that for most slope debris flows, precipitation and slope can hardly be the bottleneck or restricting factors for initiation. The initial mechanism is mainly related to internal properties and corresponding stress state of slope materials.

Grain composition and porosity of loose materials are two crucial properties that affect the initiation of debris flow. Grain composition determines porosity and permeability of soil layer to some extent. According to Cui (1991), the content of fine particles less than 1 mm was a useful indicator to reflect the structure and strength of loose materials, and it had a negative correlation with the critical slope of debris flow initiation. This was because the quantity increase of fine content could significantly reduce the porosity of soil, thereby decreasing the permeability coefficient or hydraulic conductivity of soil layer (Chen et al., 2006; Zhou et al., 2012; Yang et al., 2016). That means lower intensity of rainfall can also exceed the critical point for soil saturation and cause a series of chain reactions, such as increase in pore water pressure and reduction in effective stress (Wang et al., 1997; Gao et al., 2011). In recent years, some scholars have also proved that higher volume of fine particles did not necessarily cause initiation of debris flow. Rather, once a critical point was reached, erosion occurred (Zhou et al., 2017). In addition, the content of clay or sand can also contribute to the efficiency of debris flow initiation. Sandy soil has higher water permeability, which helps to reach the critical point more quickly (Gabet and Mudd, 2006).

According to the critical state theory of soil mass (Casagrande, 1936), under the action of continuous shear stress, soil mass can reach a critical porosity through dilation or contraction, regardless of its original state being compacted or loose. If the original state of soil is loose, high porosity may lead to massive positive pore pressure in the process of contraction, and the probability of debris flow initiation will increase sharply (Hutchinson, 1986; Fleming et al., 1989; Gabet and Mudd, 2006). In fact, during the whole process of soil deformation, continuous dilation and contraction may occur frequently, resulting in dynamic change of soil porosity, which in turn will affect water content and pore pressure of the soil. Therefore, the importance of porosity is more reflected in its water storage and pressure conduction, as well as the resulting changes in soil stress state.

The effective stress and cohesion determine the shear strength of soil mass based on Mohr–Coulomb criterion. This criterion can also be used to interpret the processes of slope instability and debris flow initiation. The limit equilibrium or safety factor method based on this criterion has been used widely in the field of engineering consultation. By further introducing the theory of unsaturated soil mechanics (Fredlund et al., 1978), Qi and Huang (2003) added the influences of pore water pressure and pore air pressure to the traditional formula of shear strength and proposed a discriminant formula to judge whether the loose material was started or not (Table 1, Formula 1). The basic idea of this formula is that with the continuous rainfall input, matrix suction of loose material decreases significantly with the increase of water content, resulting in reduction of shear strength. When the loose material is saturated and the shear strength is less than the tangential stress produced by flow and gravity, debris flow will occur.

Although the probability of slope material liquefaction and transformation into debris flow increases sharply after saturated, soil saturation is not a necessary condition for the development of debris flow (Iverson and Vallance, 2001; Chen et al., 2006). Thus, the applicability of above theories has limitations to some extent. Besides, there is no further analysis on the liquefaction mechanism and the transformation process from solid to fluid. In view of this, some researchers put forward the so-called slurry making theory and soft base effect of landslide transforming into debris flow based on case investigation and ring shear test (Chen, 1992; Zhang et al., 2009). However, physical description had not been described in details. Iverson of USGS had made a more beneficial exploration on this issue.

Based on theoretical derivation and large-scale solid model experiments, two liquefaction mechanisms of landslide transforming into debris flow were proposed by Iverson et al. (1997a); Iverson (1997b); Iverson and Vallance (2001). One was that for the soil mass with negligible cohesion, liquefaction occurred when the pore water pressure increased to the value of total normal stress, that is, the effective stress dropped to 0. The other was that for the cohesive soil mass, in addition to maintaining a high level of pore water pressure, it was necessary to reduce the cohesive force by vibration before liquefaction. The increase of pore water pressure, mainly caused by soil contraction and continuous water supply, was the main cause for landslide transforming into debris flow. While the vibration of soil mass was mainly realized by earthquake or movement on a rough slope, that is, converting kinetic energy into heat energy of soil particles. Combined with the Coulomb grain flow equation (Iverson, 1997b), the author realized the mathematical simulation of the whole process of landslide debris flow and reproduced the initial processes under the two liquefaction mechanisms in solid model experiments (Iverson et al., 1997a).

Iverson’s work indicated the critical influence of pore water pressure on the formation of landslide debris flow in different mechanisms and soil types on mathematical and physical level and strongly promoted the application of relevant indicators in debris flow prediction and early warning research. Additionally, the work provided a more systematic, coherent, and dialectical understanding of the connections among the Mohr–Coulomb criterion, the unsaturated soil mechanics theory, the critical state theory of soil mass, and the vibration of liquefaction. However, some process details, especially the issues on soil liquefaction, are still needed to be addressed, such as how to establish the mathematical relationship between vibration energy and soil cohesion, the relationships between different soil properties and liquefaction vibration, and the corresponding critical phenomena. If these issues cannot be discussed sufficiently, it is difficult to break through the framework of safety factor method on slope debris flow initiation.

This phenomenon means that the initiation and movement of debris flow mainly occur on the gully or channel bed. It can be formed by the erosion of bed basal materials or by the entrainment of bank collapse materials caused by continuous lateral erosion. Compared with slope debris flow, gully debris flow has more diversity in material sources and development forms. Besides, the development environment of gully debris flows usually presents lower requirement on channel gradient because of the dramatic influence from water flow, that is, the initiation of gully debris flow is more sensitive to the channel gradient. Therefore, the traditional research on the initiation of gully debris flow mainly focuses on the relationships among discharge, channel gradient, and the grain composition of loose materials.

Being the most direct triggering factor of gully debris flow, the influence of discharge is the first concern. It is generally believed that the critical discharge for gully debris flow always increases with the increase of particle size (Table 1, Formula 2). However, some studies have pointed out that the potential energy provided by channel slope should also be considered. If the channel slope is very small and the particle size is large enough concurrently, it can only develop bed load movement even if the discharge is very large (Wang, 2001). Based on a great number of experiments, Wang (2001) established the empirical relationship between the critical slope and the median diameter of loose materials in the process of debris flow formed by flow scouring (Table 1, Formula 3). By laying nearly homogeneous gravel layer in the flume with gradient from 12 to 20°, Gregoretti and Fontana (2008) carried out an experiment and summarized the rule of critical discharge of gully debris flow initiation under different particle size and slope conditions (Table 1, Formula 4). The outcome was used to estimate the critical discharges of erosion-induced debris flow events in 6 catchments in Dolomites of Italy. The author believed that the formula was competent for general sensitivity analysis.

In addition to the process research represented by the above achievements, that is, summarizing empirical or semiempirical relationships through solid model experiments, researchers also tried to further expand their knowledge from mechanical or energy level (Table 1, Formula 5, 6).

Takahashi (1978) constructed a model for critical slope calculation of gully debris flow from the perspective of mechanical equilibrium based on Bagnold’s theory of granular flow. The model assumed a scenario that in an infinite gully slope, the loose material reached the state of saturation after being soaked by flow water, and then failure and debris flow occurred due to the excess shear stress. Blijenberg (2007) provided the safety factor version of the model and applied it to the Alps in southern France. It was found that the results of the model were too conservative, that is, even in cases where only extreme rainstorms could induce debris flows, the cases would still be considered unsafe. The author believed that one of the important reasons for this was that the loose materials in the channel were difficult to reach the state of saturation under the flow scouring, which had also been confirmed by some recent experimental studies (Pan et al., 2017; Li et al., 2019). On one hand, the flow at the beginning would take away the fine particles to form enough pores in loose materials; on the other hand, the water carrying a large amount of sand and stone was likely to bypass these pores and flow through the surface of loose materials directly during the flood process.

Besides, Wang (2001) pointed out that the loose materials in Takahashi’s model might be washed away by water flow before failure; thus, the critical slope obtained from this model was overestimated to some extent. Iverson and Ouyang (2015) also believed that such models based on granular flow theory were not suitable for gully debris flows because these debris flow processes were far away from equilibrium, commonly.

Gully debris flow may present wave-like discontinuous characteristic due to the erosion and entrainment of loose materials (Iverson and Ouyang, 2015). The eroded materials continuously concentrated to the front and provided energy through particle collision, so that the front could move in the channel with gentle or even reverse slope (Wang, 2001; Lyu et al., 2017; Gregoretti et al., 2018). Therefore, erosion and entrainment are an important mechanism for gully debris flow development. Case analyses and experimental studies showed that most of the erosion and entrainment occurred at the stage of front passing (Haas and Woerkom, 2016; McArdell, 2016). The scouring depth of riverbed usually increased with the increase of channel gradient, flow depth, discharge, basal shear stress, front water content, and particle size (Theule et al., 2015; Haas and Woerkom, 2016; Vázquez et al., 2016; Frank et al., 2017).

Furthermore, theoretical analysis indicated that when the density of mixed layer was distinctive with that of riverbed layer, the changes of eroded material volume and pore water pressure during the entrainment process might affect entrainment rate as a feedback effect (Iverson, 2005). Compared with the undisturbed bed material, the eroded material was more likely to be entrained by runoff due to the decrease of cohesion (McGuire et al., 2017). Some researchers believed that when the debris flow passed through the riverbed, it would rapidly infiltrate and saturate the bed material with a certain thickness, that is, forming a moist layer. Consequently, the layer would be eroded completely when the safety factor was less than 1 (Huang and Tang, 2017).

Before being transformed into debris flow, the riverbed materials must undergo complex mechanisms such as material exchange, energy transfer, and rheology during the processes of erosion, deposition, and entrainment, among which the problems of erosion and entrainment have aroused widespread concern in the academic community. However, although the physical senses of these two phenomena are different (Iverson and Ouyang, 2015), they are generally considered to be uniform when calculating the erosion or entrainment rate.

Many studies have established the relationship between the entrainment rate and the process of hyperconcentrated flow transforming into debris flow by using numerical models. Based on the specific rheological law and continuum theory, these models were usually presented in the form of single-/two-phase depth-average/integral model coupling the formula of entrainment rate (Stancanelli et al., 2015; McGuire et al., 2017; Mergili et al., 2017; Vagnon et al., 2018; Gregoretti et al., 2018, 2019; Liu and He, 2020; Zhou et al., 2019). Among these entrainment formulas, there were not only empirical formulas established by the parameters of sediment concentration and slope gradient before and after scouring (Table 1, Formula 7; Takahashi, 1978; Frank et al., 2017) but also mechanism or semi-mechanism formulas based on the physical relationships among riverbed morphology, velocity, and basal shear stress (Table 1, Formula 8, 9). The motion state of mixed flow in these models was basically determined by the volumetric proportion of solid and liquid factions, for example, the empirical threshold value from the apparent viscosity or the volumetric sediment concentration (McGuire et al., 2017; Bout et al., 2018; Liu and He, 2020).

The above numerical simulation originated from depth-average/integral model coupling entrainment rate formula could restore the evolution characteristics of some typical debris flow events to some extent, especially the characteristic of rheology and the amplification effect. However, there are yet some problems to be solved in theory (Iverson and Ouyang, 2015; Garres-Díaz et al., 2020).

The first one is the conservation of momentum of the mixture fluid after entraining new loose material, that is, whether the energy of the debris front is increased or decreased after the loose material is absorbed, which needs to be further analyzed in different scenarios. The second one is the changes of volume and excess pore water pressure of entraining front caused by the density difference between mixture fluid and loose material, as well as the corresponding feedback effects on erosion, deposition, and rheological processes, which call for more experimental and simulation studies. The third one is that the existing entrainment rate formulas rarely considered the material supplement caused by lateral erosion and bank collapse, which may play a greater role in the formation of debris flow (Lyu et al., 2017).

In addition, although the existing technology of numerical simulation can provide some support for the estimation of critical rainfall or discharge, its calculation time is too long to meet the requirements of monitoring and early warning in terms of timeliness. This technology is more suitable for scenario analysis and risk or hazard assessment. Therefore, the relatively simple discrimination method for debris flow initiation has gradually become a research hotspot. For instance, Berti and Simoni (2005) established a runoff yield model for initial area of debris flow in Dolomites area of Italy based on kinematic wave equation. It was found that the critical discharge for the initiation of loose materials was so small that the interval of threshold values between the generation of surface runoff and the debris flow initiation could be ignored. Hence, the author believed that the study and simulation of runoff generation process was an alternative and relatively convenient way to identify the initiation of debris flow.

Shu et al. (2017) proposed a discriminant for particle initiation of nonhomogeneous debris flow by using the Shields number based on sediment movement mechanics, that is, when the ratio of flow shear stress to critical particle starting stress was larger than 1, the particle initiation occurred. This idea was similar to Berti’s and Simoni’s hypothesis and was supported by Tillery and Rengers (2020). However, since the initiation of sediment particles or the formation of surface runoff is not a sufficient condition for debris flow initiation, there are limitations to use these methods for discrimination.

Taking the bulk density >1,300 kg/m³ as the basis of gully debris flow formation, Dang et al. (2014) and Wang et al. (2018) built another type of discrimination indicator based on the same formula framework by using the parameters such as flow power and dimensionless shear stress. However, the threshold of these indicators would change with the variation of volumetric solid concentration. Thus, a range of tests are needed to calibrate the parameters before being applicated. Moreover, the relevant monitoring indicators are not easy to accurately measure when disasters occur, so it is difficult to promote.

In a word, although people have gained some knowledge on the initiation of gully debris flow, there is still room for further development and improvement in terms of erosion or entrainment mechanism of loose materials from different sources, the boundary tractions and materials exchange, and the construction and application of rapid discrimination method.

The rainfall is an indispensable condition of external force for most debris flow events. Due to the relatively lower technical threshold and system maintenance cost, it is the most popular method in the world to use rainfall index for debris flow monitoring and early warning (Table 2), and its representative method is the power law equation (I-D method) proposed by Caine (1980) I   =   a D β , (1) where I is the critical rainfall intensity per unit time, which can be the peak intensity (Cannon et al., 2008) or the average intensity (Brunetti et al., 2010); D is the rainfall duration; and α and β are the empirical calibration parameters, respectively.

The method assumes that there is a nonlinear relationship between the critical rainfall intensity and the rainfall duration, and the former decreases with the increase of the latter. In practice, two strategies of the method, that is, the upper limit method and the lower limit method are used commonly. The former takes the maximum rainfall intensity that cannot cause debris flow events at a specific time and space as the critical point, while the latter takes the minimum rainfall intensity that can induce debris flow events as the point (Guzzetti et al., 2008). Obviously, the lower limit method is more conservative and prone to false alarm, while the upper limit method is loose and prone to fail alarm. If any interval value is taken as the critical point, it mainly depends on the empirical judgment and has strong subjectivity.

In conjunction with USGS, the National Oceanic and Atmospheric Administration (NOAA) started the work of monitoring and early warning for wildfire-induced debris flow in mountainous areas of Southern California since 2005 (Restrepo et al., 2008). A determination method of critical rainfall intensity based on the I-D idea was proposed during the project. The method, providing a path for the objective selection of the I-D curve, used receiver operating characteristic curve (ROC) to find the equilibrium solution under the conditions of minimum false/fail alarm rate and maximum accuracy rate based on the outputs from the upper limit method and the lower limit method (Staley et al., 2013). Besides, as an empirical statistical method, the same purpose, that is, objectively setting the critical point, can also be realized by using trial and error or multi-objective optimization algorithms (Wu et al., 2018; Yan et al., 2020).

The traditional I-D method requires high spatial and temporal resolution on historical data, which is not in line with the reality that most mountainous areas lack or do not have data at all. What is more, it does not consider the impact of antecedent rainfall accumulation. Although this can be compensated partly by constructing I-D curves under different antecedent rainfall scenarios, the efficiency and convenience will decline. Therefore, scholars from different regions are constantly trying to develop or improve relevant methods. For example, Glade et al. (2000) proposed an initial discriminant for landslide by improving the antecedent precipitation index model (Bruce and Clark, 1966) in New Zealand (Table 2, Formula 1); a debris flow prediction model in Jiangjia gully in China was put forward by the Institute of Mountain Hazards and Environment, CAS, 2000 based on long-term observation and water balance principle (Table 2, Formula 2). These discrimination methods based on rainfall intensity–antecedent effective rainfall, that is, I-A method, have also been applied in many early warning cases of flash floods and debris flows (Clark et al., 2014; Deng et al., 2018), and it is especially suitable for those watersheds with better vegetation coverage and greater water storage potential. However, some findings reported that the early warning effect of I-D method was better than that of I-A method for the watersheds with sandy soil (Abancó et al., 2016), and the minimum duration of rainfall triggering debris flow should even be upgraded to the key indicator (Pastorello et al., 2020).

In view of the lack of data in mountainous areas, the conventional method is to use the data of nearby stations for analogy or interpolation. However, recent studies have shown that these methods were easy to overestimate or underestimate the rainfall threshold to some extent (Marra et al., 2016; Destro et al., 2017; Marra et al., 2017), especially for the convective weather events with small watershed scale. Even if the data of adjacent basins were used, they might lead to calculation errors. Fortunately, radar rainfall measurement could improve this situation to a certain extent (Abancó et al., 2016).

In addition, there are two indirect solutions: 1) according to the determined contour maps of maximum rainstorm and their coefficients of variation, the design rainstorms with different frequencies can be calculated, and then, the results consistent with the frequency of historical disaster events can be taken as the regional critical rainfall. This idea has been widely used in the field of prediction and early warning of regional flash floods and debris flows (Liang and Yao, 2008; Duan, 2009). 2) The threshold of the key index for debris flow initiation can be obtained by using various mechanism or semi-mechanism models (Huang and Tang, 2017; Bout et al., 2018; Zhou et al., 2019; Liu et al., 2020), and then, the critical rainfall value can be deduced according to the threshold. For example, Pan et al. (2018) first obtained the critical flow depth for debris flow based on Takahashi’s model and then deduced the rainfall threshold by using the water balance equation of stored-full runoff; Zhang et al. (2019) used the safety factor method and the excess infiltration–saturation runoff model to obtain the bulk density of mixed flow and then established the I-D curve according to whether the density reached the critical condition of debris flow formation. Although there is no requirement for historical data in this kind of scheme, the process model used here usually has certain theoretical assumptions. Therefore, the mechanism of runoff generation and the types of debris flow, that is, stony debris flow, viscous debris flow, or other types, should be clarified before its application. Besides, the scheme also needs to ensure the reliability of some key parameters such as the gully morphology and the infiltration rate, thus the workload in early stage is generally large.

There are a number of factors that affect the initiation of debris flow, and solely relying on rainfall indicators for discrimination and early warning will have many limitations. Especially for some small watersheds where environment changes rapidly, the comprehensive assessment method can achieve twice the result with half the effort. According to the number of elements considered and the difference of estimation means, the comprehensive assessment method can be roughly divided into the multielement method and the key-element method. The former has the similar technical process with the natural hazard assessment, but it emphasizes more on the input of dynamic factors, data fusion, and rapid response. The latter is more associated with hydraulic and soil mechanic tests or field observation, and the indices of investigation are more concentrated.

It should be noted that the boundaries of this classification are not always clear. Many methods integrate the advantages of each idea. For example, the US Flash Flood Guidance (FFG) system not only considered the results from hydrological forecast, which could be regarded as the combination of key-element method and rainfall indicator method, but also referred to the level of Flash Flood Potential Index (FFPI) of each watershed based on the multielement method (Clark et al., 2014). The similar examples also appeared in the works of Posner and Georgakakos (2015) and Berenguer et al. (2015).