Characteristics of a Debris Flow Disaster and Its Mitigation Countermeasures in Zechawa Gully, Jiuzhaigou Valley, China

: On 8 August 2017, an Ms 7.0 earthquake struck Jiuzhaigou Valley, triggering abundant landslides and providing a huge source of material for potential debris ﬂows. After the earthquake debris ﬂows were triggered by heavy rainfall, causing tra ﬃ c disruption and serious property losses. This study aims to describe the debris ﬂow events in Zechawa Gully, calculate the peak discharges of the debris ﬂows, characterize the debris ﬂow disasters, propose mitigation countermeasures to control these disasters and analyse the e ﬀ ectiveness of countermeasures that were implemented in May 2019. The results showed the following: (1) The frequency of the debris ﬂows in Zechawa Gully with small- and medium-scale will increase due to the inﬂuence of the Ms 7.0 Jiuzhaigou earthquake. (2) An accurate debris ﬂow peak discharge can be obtained by comparing the calculated results of four di ﬀ erent methods. (3) The failure of a check dam in the channel had an ampliﬁcation e ﬀ ect on the peak discharge, resulting in a destructive debris ﬂow event on 4 August 2016. Due to the disaster risk posed by dam failure, both blocking and deposit stopping measures should be adopted for debris ﬂow mitigation. (4) Optimized engineering countermeasures with blocking and deposit stopping measures were proposed and implemented in May 2019 based on the debris ﬂow disaster characteristics of Zechawa Gully, and the reconstructed engineering projects were e ﬀ ective in controlling a post-earthquake debris ﬂow disaster on 21 June 2019.


Introduction
A debris flow-a very to extremely rapid surging flow of saturated debris in a steep channel-is a widespread hazardous phenomenon in mountainous areas [1][2][3]. Because of their characteristics of high flow velocities, high impact forces and long run-out distances, debris flows pose a great threat to the safety of people, can cause catastrophic damage to infrastructure elements (such as roads and houses), and can even block rivers, leading to fatalities and property damage downstream [4][5][6][7][8][9][10]. In recent years, post-earthquake debris flow hazards have been widely investigated due to their long activity duration, high occurrence frequency and catastrophic damage [11][12][13][14]. Numerous studies have focused on rainfall thresholds and sediment supply to characterize the occurrence of post-earthquake debris flows. In the areas affected by the 1999 Chi-Chi earthquake and the 2008 Wenchuan earthquake, the thresholds for rainfall triggering post-earthquake debris flows were analysed, and it was recognized that the rainfall threshold in periods shortly after the earthquakes was markedly lower than that before the earthquake and gradually recovered over time [14][15][16][17][18][19][20]. In fact, a devastating earthquake generates a large sediment supply in the form of co-seismic collapses and landslides and changes the grain size of the material and the watershed permeability characteristics, thereby indirectly reducing the debris flow-triggering rainfall thresholds [18,21]. Because earthquakes tend to produce abundant loose material, if sufficient rainfall occurs soon after an earthquake, a catastrophic debris flow can be triggered. For example, influenced by the Wenchuan earthquake on 12 May 2008, a catastrophic debris flow event was triggered on 14 August 2010 in Hongchun Gully, claiming the lives of 32 people [8]. Similarly, five debris flow events were triggered in Wenjia Gully in the three rainy seasons after the Wenchuan earthquake, including a giant debris flow event on 13 August 2010 [9,13].
As an effective way to mitigate debris flow hazards, engineering countermeasures have attracted widespread attention [22][23][24][25][26][27][28][29][30][31][32][33], and the mitigation of debris flows is usually carried out by stabilizing, blocking, drainage and deposit stopping measures [11,23]. Check dams, which act to stabilize the bed, consolidate hillslopes, decrease the slope, and retain and control the transport of sediment, are commonly used engineering structures for controlling debris flows and can generally be divided into solid-body dams and open dams [25,28,29]. Because solid-body dams are associated with many drawbacks, such as the erosion of the dam foundation and changes in the hillslope-to-channel connectivity [26,27], open dams are more efficient at controlling debris flows [28,29]. After the Wenchuan earthquake, to protect people's lives and property and ensure smooth traffic, a large number of debris flow engineering structures, especially check dams, were built. However, due to the insufficient realization on the characteristics and formation mechanisms of post-earthquake debris flows, many newly-built engineering structures have failed to mitigate debris flows and have instead caused catastrophic damage. For example, due to the failure of check dams in Sanyanyu Valley on 8 August 2010, more than 200 buildings were damaged, and approximately 1700 people died [34]. Similarly, during the "8.13" Wenjiagou debris flow event, engineering structures failed, causing seven deaths and the burial of more than 497 houses [9,35]. Therefore, further research should be carried out to propose appropriate mitigation countermeasures for post-earthquake debris flows.
Recently, an Ms 7.0 earthquake struck Jiuzhaigou Valley on 8 August 2017, triggering abundant landslides and providing a vast source of material for debris flows. Due to the influence of heavy rainfall, post-earthquake debris flows were triggered in Jiuzhaigou Valley and heavily damaged infrastructure elements, such as pedestrian walkways and scenic roads, causing traffic disruption and serious property losses [36][37][38]. It is necessary to evaluate the characteristics of post-earthquake debris flows in Jiuzhaigou Valley, and to propose appropriate mitigation countermeasures to avoid catastrophic events, but only a few studies related to post-earthquake debris flow mitigation in this area have been published to date. In this paper, Zechawa Gully is taken as a case study to characterize a debris flow disaster and then discuss mitigation countermeasures. To improve the accuracy of parameter calculation, four different methods were used to calculate the debris flow peak discharge and quantify the debris flow magnitude. According to the survey and analysis, the destructive debris flow event in 2016 was caused by a dam breach. After the Ms 7.0 Jiuzhaigou earthquake on 8 August 2017, abundant loose solid material was available for debris flow activity, and at least one post-earthquake debris flow occurred in September 2017. The risk of dam breaches led to the implementation of engineering countermeasures with blocking and deposit stopping measures. Such works were finished on May 2019. On 21 June 2019, a post-earthquake debris flow was triggered by heavy rainfall, and the engineering countermeasures played a useful role in controlling the debris flow disaster even though the debris flow magnitude was greater than the design standard of the reconstruction engineering projects.

Formation Conditions of the Zechawa Gully Debris Flow
Zechawa Gully, with gully mouth coordinates of 103 • 55 22.8" E, 33 • 08 34.8" N, is located in Jiuzhaigou Valley, Sichuan Province, China, and lies approximately 13.9 km from a scenic entrance (Figure 1a,b). The outlet of the Zechawa Gully debris flow coincides with the location of the only scenic road from Nuorilang Waterfall to Long Lake (Figure 1c). The study area is the transition zone from the Qinghai-Tibet Plateau to the Sichuan Basin and belongs to the peripheral mountainous area of the Sichuan Basin. The watershed covers an area of 1.96 km 2 and features five tributaries; the main channel is 2.57 km long and has a 61.1% longitudinal slope. The elevation difference of Zechawa Gully is approximately 1601 m, with a maximum elevation of 4040 m in the southwest of the watershed and a minimum elevation of 2439 m at the gully mouth near the scenic road. The topography of Zechawa Gully is steep, with 86.9% of the total area of the watershed having a slope exceeding 25 • . The flow path of debris flow along Zechawa Gully can be divided into a formation zone, transport zone and deposition zone ( Table 1). The formation zone is located in the upper reaches of Zechawa Gully (elevation above 3620 m), with an area of 0.26 km 2 and a channel length of 470 m. The transport zone is situated in the middle reaches, with the elevations ranging from 3620 m to 2600 m. The area of the transport zone is approximately 1.47 km 2 , and the channel length is approximately 1530 m. The deposition zone, with an area of 0.23 km 2 and a channel length of approximately 570 m, is located in the area below an elevation of 2600 m.  Compared with the characteristics of the formation zone and transport zone, the topography of the deposition zone is gentle, with no collapses and landslides, and debris flow material tends to be deposited in this area, forming a large debris flow fan. Zechawa Gully is generally a "v"-shaped channel with the characteristics of a narrow gully bed, steep lateral slopes and a high longitudinal slope, providing favourable topographic conditions for the formation of debris flows.
The study area is located in the Songpan-Ganzi Block, and the outcropping strata are mainly Quaternary and Mesozoic (Figure 2a). The lithology consists mainly of limestone and slate with a small amount of sandstone, which were intensely deformed by folding and thrusting during the Late Triassic and Early Jurassic [39,40]. In addition, since the Quaternary, the geological tectonic movement in this area has been intense due to the influence of the Tazang fault (the eastern part of the East Kunlun Fault Zone), Minjiang fault and Huya fault [41][42][43][44][45] (Figure 2b). Historically, seismicity has occurred on the Minjiang fault and Huya fault, including the 1960 Zhangla Ms 6.7 earthquake, the 1973 Huanglong Ms 6.5 earthquake, and the 1976 Songpan-Pingwu earthquake swarm (Ms = 7.2, 6.7, and 7.2). A recent earthquake was the Jiuzhaigou 7.0 earthquake, which occurred on 8 August 2017 on the north-western extension of the Huya fault; the rupture was dominated by left-lateral strike-slip motion [41,[46][47][48]. On the whole, seismicity is frequent in the study area due to the geological conditions of the region, resulting in the fracture of the rock mass in the study area and triggering abundant collapses and landslides, which provide a rich source of loose material for incorporation into debris flows. The study area features a plateau cold temperate-subarctic monsoon climate. Due to the blocking effect of the Longmen Mountains to the southeast of the study area, most of the warm and humid air currents from the Pacific Ocean stay to the east of the Longmen Mountains. Therefore, the rainfall in Jiuzhaigou Valley west of the Longmen Mountains is relatively low, and the annual average precipitation is only 761.8 mm. The impact of cold air and high-pressure cold air currents from Mongolia in the winter is greatly weakened by the blocking of the Qinling Mountains to the north of the study area, causing this region to exhibit a mild climate, moderate precipitation and an annual average temperature of 7.3 • C [49]. There are more than 150 rainfall days annually in the study area, and the rainfall is concentrated mainly in May to September in the form of rainstorms. According to the rainfall data from the Jiuzhaigou Administration Bureau, the maximum rainfall over 24 h in Jiuzhaigou Valley is greater than 50 mm, and the precipitation increases with increasing elevation. The lowest average annual precipitation, at 696.6 mm, is found at the outlet of Jiuzhaigou Valley at an elevation of 1996 m. The highest annual average precipitation, at 957.5 mm, is found at Long Lake at an elevation of 3100 m. The snowpack period is from October to April, and the largest recorded snowpack depth exceeded 150 mm. The rainfall conditions of the study area are characterized by concentrated heavy rainfall, which is favourable for the formation of debris flows. Additional material with a volume of 0.5 × 10 4 m 3 was transported to the scenic road. During this debris flow event, the pedestrian walkways were buried again, and the only scenic road from Nuorilang Waterfall to Long Lake was blocked, causing traffic disruption and serious property loss [37,51].

Calculation of the Debris Flow Peak Discharge
In the mountainous areas of China, due to the lack of observation data, the rain-flood method and cross-section survey method have been widely used to calculate the debris flow peak discharge [52]. Under the assumption that the occurrence frequencies of rainstorms, floods and debris flows are the same, the rain-flood method is widely employed to calculate the debris flow peak discharge under different occurrence frequencies [53,54]. The cross-section survey method calculates the peak discharge of a debris flow that has occurred based on the mud mark and cross-sectional morphology of the channel [7,55].
For the debris flow event that occurred on 4 August 2016, two obvious typical cross-sections downstream of the stone masonry check dam are available for the calculation of the debris flow discharge through the cross-section survey method. Moreover, the pedestrian walkways were buried, and the scenic roads were blocked, and the stone masonry check dam in the channel was broken during this debris flow event. According to previous research, the amplification effect caused by dam breakage can contribute to debris flow damage in downstream towns [9,56]. Therefore, to characterize the relationship between dam failure and the occurrence of the debris flow on 4 August 2016, the dam-breaking peak discharges were estimated through the dam-breaking calculation method.
During the debris flow event that occurred in September 2017, the cross-section survey method was unavailable due to the lack of an available cross-section. A coarse boulder with dimensions of 1.3 m, 1.1 m and 0.7 m was transported 20 m downstream of the check dam by the debris flow in September 2017. According to previous studies, the largest transported particle reflects the maximum kinetic energy of flooding in mountain streams, and the maximum particle size parameters are widely used to reconstruct the velocity, depth and peak discharge of floods [57]. Thus, in this study, based on the assumption that the rainstorm, flood and debris flow frequencies were the same, the maximum particle size parameters were used to calculate the flood peak discharge, and the peak discharge of the debris flow in September 2017 was then estimated by using the methodology proposed by Lanzoni [58] according to the calculated flood peak discharge.

Rain-Flood Method
The debris flow peak discharges under different occurrence frequencies are computed by Ref. [54]: where D df is the blockage coefficient, whose value varies with the degree of blockage, namely, very serious blockage (D df = 3.0-2.6), serious blockage (D df = 2.5-2.0), normal blockage (D df = 1.9-1.5) and minor blockage (D df = 1.4-1.1); ψ df is the amplification coefficient of the debris flow peak discharge; γ df is the density of the debris flow (t/m 3 ); γ w is the density of water (t/m 3 ), usually taken as 1.00 t/m 3 ; γ s is the density of the solid material (t/m 3 ), usually taken as 2.65 t/m 3 ; and Q f is the flood peak discharge under different return periods (m 3 /s), which is calculated by: where ϕ is the runoff coefficient of the flood peak, which is related to the convergence of runoff; S is the rainfall intensity (mm); t is the runoff confluence time of the rainstorm (h); n is the attenuation index of the rainstorm; and F is the watershed area (m 2 ). Here, ϕ, S, t and n are calculated by the following empirical equations: where H 1 and H 6 are the 1-hour average rainfall and 6-hour average rainfall, respectively (mm), which are obtained from "The Rainstorm and Flood Calculation Manual of Medium and Small Basins in Sichuan Province" (published in 2010, with rainfall data from 1978 to 2004); K 1 and K 6 are the modulus coefficients corresponding to H 1 and H 6 under different return periods, respectively, which can be obtained from a Pearson type III distribution table; η is the runoff yield parameter, which reflects the average infiltration intensity (mm/h); t 0 is the runoff confluence time of the rainstorm when ϕ equals 1, which can be calculated by: where K p is the modulus coefficient when the variation coefficient is equal to 0.23, which is obtained from the Pearson type III distribution table; m is the runoff confluence parameter; and θ is the watershed characteristic parameter, which is obtained from: where L is the main channel length and J is the longitudinal slope of the channel.

Cross-Section Survey Method
Because natural channels have irregular channel bottoms, information on the channel roughness is not easy to obtain and measure. Therefore, an empirical formulation (Manning formula) was developed for turbulent flows in rough channels. It can be applied to calculate the discharge for fully rough turbulent flows and water flows. Although it is an empirical relationship, it has been found to be reasonably reliable [59,60]. Thus, the Manning formula was employed to obtain debris flow peak discharge when computing by the cross-section survey method. Based on the mud marks and cross-section morphology of the channel, the debris flow peak discharge Q df (m 3 /s) can be obtained by Ref. [54]: where A df is the area of the cross-section (m 2 ), and V df is the average velocity of the debris flow (m/s), which can be calculated by: where n df is the roughness coefficient of the debris flow gully, R df is the hydraulic radius of the debris flow (m), and I df is the longitudinal slope gradient of the channel bed (m/m).

Dam-Breaking Calculation Method
Considering the scarcity of observational data in this study, three commonly used semi-empirical methods are employed to obtain the dam-breaking peak discharge during the debris flow event on 4 August 2016. The semi-empirical method of the Ministry of Water Resources of the People's Republic of China (MWR) [61] estimates the debris flow peak discharge Q df through: where g is acceleration due to gravity (9.8 m 2 /s); B 0 is the debris flow width before breakage (m); h 0 is the debris flow depth before breakage (m); B m is the breach width (m), and h d is the residual height of the dam. The semi-empirical method of Dai and Wang [62] calculates the debris flow peak discharge Q df by: where L b is the deposit length of the debris flow material behind the check dam (m); κ is the influence factor that accounts for residual height, which is obtained by:

Maximum Boulder Size Method
Based on the particle size parameters of the maximum-sized boulder, the debris flow peak discharge can be obtained through Ref. [58]: where C is the transported sediment concentration; ρ f is the fluid density (kg/m 3 ); ρ s is the sediment density; β is the bed slope angle (degrees), and the value of β is usually between 15 • to 25 • when using Equation (19) [63]; ϕ df is the quasi-static friction angle (degrees); and Q f is the flood peak discharge (m 3 /s), which was estimated by the methods of Schoklitsch, Helley, Williams and Clarke.

Method of Schoklitsch
This method estimates the flood peak discharge Q f (m 3 /s) by computing the unit width flux by Ref. [64,65]: where q f is the unit width flux; d I is the diameter of the boulder intermediate axis (m), and B f is the channel width (m).

Method of Helley
This method computes the "bed velocity" for incipient motion (overturning) by equating the turning moments for fluid, drag, and lift with the resisting moment of the submerged particle weight.
The critical velocity V f (bed velocity) can be calculated by Ref. [66]: where ρ b is the maximum boulder density (kg/m 3 ); d L is the diameter of the boulder long axis (m); d S is the diameter of the boulder short axis (m); C' D is the drag coefficient; MR D and MR L are the drag turning arm and lift turning arm, respectively; and α is the original imbrication angle of the deposited boulder. During the calculation process, Equation (22) uses English units of feet, and the units of critical velocity calculated by Equation (22) need to be converted into metres per second.
The critical velocity V f calculated by Equation (22) needs to be converted to the average velocity V avg [57]: The flood peak discharge Q f can then be calculated as the product of the average velocity, mean depth and channel width by: where h f is the mean flood depth (m). Given that the channel width was much larger than the mean depth of flooding, the hydraulic radius obtained by the Manning formula can estimate the average depth; thus, h f was obtained by the Manning formula: where n f is the roughness coefficient of a mountain stream.

Method of Williams
This approach calculates either the bed shear stress or the stream power needed to entrain the boulder. First, the intermediate axis diameter of the largest boulder d I is obtained through field investigation, and then the empirical relationship between the unit stream power w, bed shear stress τ, average velocity V avg and d I is established by Ref. [67]: V avg , h f and Q f based on the shear stress can be determined by Equations (30)- (32), respectively: V avg and h f based on the stream power can be obtained by: The value of Q f in Equation (33) is obtained by Equation (32); then, Q f based on the stream power can be obtained by inserting the calculated values of V avg and h f from Equations (33) and (34), respectively, into Equation (26).

Method of Clarke
This method assumes that the critical force (i.e., the minimum force needed to move the boulder) is equal to the resisting force and that the critical force is equal to the sum of the lift force and drag force. The critical velocity V f (bed velocity) required to carry the maximum-sized boulder is solved by the following formula [68]: where C D is the lift coefficient of the boulder, which is dependent on the shape of the largest boulder, with C D = 1.18 for a cubic boulder and 0.20 for a spherical boulder; A B is the cross-sectional area of the largest boulder; and F D is the drag force, which is obtained by: where C L is the lift drag coefficient, which is dependent on the shape of the largest boulder, with C L = 0.178 for a cubic boulder and 0.20 for a spherical boulder; and F C is the critical force, which is calculated by: where µ is the shape coefficient, which is dependent on the shape of the largest boulder, with µ = 0.675 for a cubic boulder and 0.225 for a spherical boulder; and M B is the boulder mass (kg). M B can be obtained for a cubic boulder and a spherical boulder by Equations (39) and (40), respectively: where D is the nominal diameter of the boulder (m), which is solved by: The flood peak discharge Q f can be obtained by inserting the calculated value of V f into Equations (25)- (27).

The Calculated Debris Flow Peak Discharge in 2016
With the data collected during the field investigation, the peak discharge of the debris flow that occurred on 4 August 2016 was estimated by the cross-section survey method and dam-breaking calculation method. Table 2 shows the calculation results for the debris flow peak discharge. The permissible debris flow peak discharges at the two typical mud mark cross-sections estimated by the cross-section survey method were 33.29 m 3 /s and 36.69 m 3 /s. The values of A df , R df and I df were obtained through field investigation. The roughness coefficient of the debris flow gully (n df ) is related to the properties of the debris flow fluid and channel characteristics, and the value in this case is 0.1 according to a field survey [54]. Table 2. Calculation results of the debris flow peak discharge by using the cross-section survey method and dam-breaking calculation method.  According to the calculation results in Table 2, the permissible maximum debris flow peak discharges resulting from the breach in the check dam varied from 36.5 m 3 /s to 43.6 m 3 /s. The calculation result by Equation (14) was the lowest (36.5 m 3 /s), and the calculation result by Equation (15) was the highest (43.6 m 3 /s). The values of B 0 , h 0 , B m , h d , and L b were obtained by field investigation. Since the data inputs used in Equations (14)- (16) were the same, the differences among the results arose from the different combinations of data used for a given technique. The calculated values are reasonable and are similar to the debris flow peak discharge estimated by the cross-section survey method.

The Calculated Debris Flow Peak Discharge in 2017
With data collected during the field investigation, the peak discharge of the debris flow that occurred in September 2017 was calculated by the maximum boulder size method. Table 3 shows the calculation results. The calculated values of Q f vary from 0.58 m 3 /s to 6.05 m 3 /s, and the calculated values of Q df range from 1.76 m 3 /s and 18.33 m 3 /s. The minimum permissible debris flow peak discharge of 1.76 m 3 /s is estimated through the method of Schoklitsch, and the maximum discharge of 18.33 m 3 /s is estimated through the method of Helley. ρ f is usually taken as 1150 kg/m 3 considering the turbidity of the flood waters [68]. ρ s is usually taken as 2650 kg/m 3 . Owing to the absence of information, a value of 36.5 • was given for ϕ df based on previous studies [58]. The values of d L , d I , d S , ρ b , B f , β, and α were obtained through field investigation. The transported sediment concentration (C) is 0.67 by inserting the values of ρ f , ρ s , β and ϕ df into Equation (19). The roughness coefficient of a mountain stream (n f ) is related to the channel characteristics, and a value of 0.05 was used here according to a field survey [69].

The Calculated Debris Flow Peak Discharge under Different Occurrence Frequencies
According to the magnitude of the debris flow, hazard degree and importance of the protection object, mitigation countermeasures in Zechawa Gully were required to resist a debris flow with a return period of 20-50 years [70]. Thus, the debris flow peak discharges under 10-, 20-and 50-year return periods were computed, and the calculated results of related parameters are listed in Table 4.  To better compare with the debris flow peak discharges calculated by the cross-section survey method, dam-breaking calculation method and maximum boulder size method, the calculation section located at the check dam site was selected to compute the debris flow peak discharges through the rain-flood method. The values of F, L and J were obtained from a topographic map with a scale of 1:5000. According to the results of the querying specification table and spot investigation, the average density of the debris flow was 1.8 t/m 3 . Under given conditions, the debris flow density is positively related to the debris flow peak discharge [54,71], thus the densities of the debris flows γ df under the three return periods (10-year, 20-year and 50-year) were 1.8 t/m 3 , 1.85 t/m 3 and 1.9 t/m 3 , respectively. According to the site investigation, the blockage degree of the channel was normal, and the values of D df were considered to be 1.8-1.9.

The Applicability and Limitations of the Calculated Debris Flow Peak Discharge
The debris flow peak discharge is an important parameter for debris flow disaster prevention and risk assessment. As debris flows occur in remote mountain areas, it is difficult to measure the peak discharge and other parameters of debris flow under the conditions of severe weather and traffic delays. At present, the debris flow peak discharge is usually calculated by the rain-flood method and cross-section survey method based on certain assumptions, resulting in calculation results with low credibility. In this study, under certain assumptions, the peak discharge of debris flow was estimated by the rain-flood method, the cross-section survey method, the dam-breaking calculation method and the maximum boulder size method, and comparative analysis of the calculation results was conducted to obtain an accurate peak discharge. The limitations of the calculation results are explained as follows: (1) Due to the complexity of debris flows and the measurement limitation, the values of relevant parameters are usually obtained by field surveys and querying the specifications. In this study, the roughness coefficient of the debris flow gully (n df ), the roughness coefficient of a mountain stream (n f ), the density of debris flow (γ df ) and the blockage coefficient (D df ) were obtained through field investigations and querying specifications. (2) Considering the complexity of the debris flow and the operability of the calculation method, it is necessary to make certain assumptions and simplifications to obtain the peak discharge of the debris flow in the calculation process. The rain-flood method assumes that the occurrence frequencies of rainstorms, floods and debris flows are the same and that the calculated flood peak discharge is completely converted into the peak discharge of the debris flow [54]. Under such assumptions, important parameters such as debris flow peak discharge and total volume of debris flow material under different occurrence frequencies can be obtained, which provide important references for the design of engineering countermeasures. In addition, the breach in the check dam was idealized as a trapezoidal shape, and the average width of the breach was taken as the calculated value of B m in the dam-breaking calculation. (3) Four methods were used to estimate the peak discharge of the debris flow based on the maximum particle size parameters (Table 3), and the related issues in the calculation are as follows: Both Clarke and Helley solved for the critical velocity required to move the largest boulder, obtained the flow depth through the Manning formula, and finally calculated the peak discharge. Differences in the critical velocity result in differences in the flow depth and peak discharge. The method of Clarke idealizes the largest boulder as either cubic or spherical for the shape-dependent parameters, and the calculated velocities are averaged to provide the critical velocity. By setting the critical force F C = 0, the downward gravitational component is balanced by the gravity-induced friction, and the extreme use condition of this method can be obtained. The limit bed slope angle (β) is equal to 34.1 • for a cubic boulder and 12.7 • for a spherical boulder when using the Clarke method; therefore, a spherical boulder is easier to move than the cubic boulder under the same conditions. According to the field investigation, β is equal to 19 • , which exceeds the limit bed slope angle for a spherical boulder. Therefore, the selected boulder in this study was considered a cubic boulder, resulting in a calculated critical velocity that is higher than the actual value.
Compared with the method of Clarke, the method of Helley neglects the bed slope, ignoring the downstream gravitational component. Generally, the bed slope of a stream is small; even for a stream with a channel longitudinal slope of 10%, the downstream gravitational component is negligibly small compared to the fluid drag and lift, so this component can be ignored [57]. However, the bed slope is 19 • in this study, and neglecting the gravitational component results in a calculated critical velocity that is much higher than the actual value, ultimately resulting in a higher calculated peak discharge. The methods of Schoklitsch and Williams estimate the peak discharge by establishing an empirical correlation based on boulder size parameters without considering the influence of the boulder shape on the calculation results. In addition, the values of w, τ and V avg in the method of Williams represent the lowest values, and the actual values are higher than the calculated value. (4) In summary, certain assumptions and simplifications were made in the calculation process, causing the peak discharge of the debris flow calculated by a single method to exhibit low accuracy. Thus, multiple methods should be used to comprehensively obtain the peak discharge, further quantifying the scale of debris flow disasters. It is worth noting that the method for calculating the debris flow peak discharge proposed in this study is mainly based on the specifications in China, especially the selection of some parameters. When calculating the debris flow peak discharge in other countries, local specifications should be considered.

The Scales of the Debris Flow Disasters in 2016 and 2017
To identify the disaster characteristics and the occurrences of debris flow events, the peak discharges of the debris flows occurring on 4 August 2016 and in September 2017 were estimated based on field investigations, and the calculation results were compared with the debris flow peak discharges under different occurrence frequencies to quantify the scale of the debris flow disasters. The related explanations are as follows: (1) The debris flow peak flow obtained by the cross-section survey method and dam-breaking calculation method are essentially the same and are generally equivalent to the peak discharge of the debris flow with a 20-year return period (Tables 2 and 4). In addition, the total volume of the debris flow material W df is estimated by Ref. [54]: where T df is the duration time of the debris flow (s), and its value is approximately 1500 s based on the reports of patrol personnel. The value of Q df is the average calculation result through the cross-section survey method and dam-breaking calculation method, and its value is 37.38 m 3 /s. The total volume of debris flow material from Equation (42) is 1.48 × 10 4 m 3 , which is consistent with the value of 1.39 × 10 4 m 3 based on the field investigation. Thus, it is reasonable that the scale of the debris flow on 4 August 2016 is equivalent to that of a debris flow with a 20-year return period. Moreover, based on the study above, the debris flow peak discharges calculated by Equations (14)- (16) were similar to the values obtained by the cross-section survey method. Thus, we conclude that the debris flow peak discharge on 4 August 2016 was amplified by the failure of the check dam, causing widespread damage, and this aspect also explains why the magnitude of the debris flow on 4 August 2016 was large even though the accumulated rainfall and rainfall intensity were extremely low. Similarly, check dam failures have led to catastrophic disasters in other regions, such as the "8.13" Wenjiagou debris flow event [72] and the "8.8" Zhouqu debris flow event [73,74]. (2) Based on the above analysis, the flood peak discharge estimated by the method of Helley is the largest, and is equivalent to that of a debris flow with a 10-year return period. Both of the peak discharges calculated by the methods of Clarke and Helley are larger than the actual value, while the value calculated by the method of Williams is smaller than the actual value.
In addition, compared with the extensive destruction of the 2016 debris flow event with a 20-year return period, the destruction of the 2017 debris flow event was smaller, according to the field investigation. Therefore, it is reasonable that the magnitude of the debris flow in September 2017 was less than that of a debris flow with a 10-year return period.
(3) In the remote mountain areas of China, rainfall data are difficult to obtain, and the rainfall throughout a whole catchment usually cannot be recorded by precipitation stations due to the influence of terrain, resulting in inconsistencies between the triggering rainfall and the scale of debris flow disasters. Thus, the relationships between the occurrence of debris flow disasters and the triggering rainfall are not researched in this paper.

Mitigation Countermeasures in Zechawa Gully
More than 23 × 10 4 m 3 of loose solid material was generated by the Ms 7.0 Jiuzhaigou earthquake and remains available as material for debris flows in Zechawa Gully in the near future [37,75]. Therefore, appropriate engineering countermeasures must be taken in a timely manner to mitigate post-earthquake debris flow disasters. According to the field investigation and calculation results above, the stone masonry check dam built in 2009 were broken, and the failure of the check dam amplified the debris flow peak discharge, resulting in a very large amount of damage during the debris flow event on 4 August 2016. Thus, the potential failure of a check dam should be fully taken into account during engineering design processes, and an integrated strategy including blocking measures and deposit stopping measures should be adopted for debris flow mitigation. On the one hand, the construction of deposit stopping structures (e.g., retaining walls) can increase the retention capacity of engineering structures; on the other hand, the debris flow material can be trapped by the deposit stopping structures even if the blocking structures (e.g., check dams) in the channel are damaged, thereby reducing the disaster risk downstream.
The engineering countermeasure taken in 2009 were designed to resist a debris flow with a 20-year return period but were damaged during the debris flow event in 2016. Considering the high-frequency and large-scale characteristics of post-earthquake debris flows, engineering countermeasures were designed to resist a debris flow with a 50-year return period after the Ms 7.0 Jiuzhaigou earthquake based on the scale, damage degree and threatened objects threatened by the subsequent debris flows. The total volume of debris flow material with a 50-year return period can be obtained by inserting the calculated value of Q df into Equation (42), and the resulting value is 1.91 × 10 4 m 3 (Table 4). Thus, the designed engineering structures are required to trap at least 1.91 × 10 4 m 3 of debris flow material. In addition, the control principles of prevention projects should not only control the debris flow itself but also operate in harmony with the landscape and reduce the harm to landscape resources, as required in Jiuzhaigou Valley [76]. Under the guidance of these principles, in conjunction with the specific characteristics of the Zechawa debris flows, a concrete check dam and a concrete auxiliary dam were constructed in the channel, and a concrete retaining wall was constructed on the debris flow fan. The concrete check dam, 42.6 m long and 6 m high, was built close to but downstream of the broken stone masonry check dam in order to reduce the peak discharge, stabilize the gully bed, minimize scouring along the bottom and sides of the gully, and stabilize the debris flow material trapped behind the broken check dam. The downstream concrete auxiliary dam, 38.1 m long and 3 m high, was constructed close to the concrete check dam to protect the latter's foundation ( Figure 5). Moreover, the reconstructed check dams were located somewhat upstream in the gully and were satisfactorily concealed. The retaining wall with a total length of 95.6 m was built 93 m away from the scenic road and is out of sight of tourists, and it can trap a volume of 2.27 × 10 4 m 3 of debris flow materials ( Figure 6). In May 2019, new control works (the reconstructed check dam and the retaining wall) were finished.

Effectiveness of Mitigation Countermeasures and Evaluation of Debris Flow Impact Force
On 21 June 2019, one post-earthquake debris flow was triggered by heavy rainfall, and a volume of 2.3 × 10 4 m 3 of debris flow material was transported; this value was greater than the calculated total volume of debris flow material with a 50-year return period in Table 4. A volume of 0.48 × 10 4 m 3 of debris flow sediment was trapped by the concrete check dam (Figure 5), which contributed to stabilizing the gully bed and preventing entrainment of additional material. Moreover, a volume of approximately 0.66 × 10 4 m 3 debris flow sediment was trapped by the retaining wall (Figure 6), and a portion of material with a volume of 1.16 × 10 4 m 3 emerged from the breach in the middle of the retaining wall and was transported downstream. During the debris flow event on 21 June 2019, the prevention projects played a satisfactory role in controlling the debris flow disaster even though the flow magnitude exceeded the design standard.
In addition, studying the damage mechanism of mitigation structures is significant for effective debris flow mitigation. According to previous studies, the huge impact force of a debris flow can contribute significantly to the destruction of mitigation structures [34,77], and numerous impact models have been established [77][78][79][80]. Through comprehensive analysis of the existing debris flow impact models, a modified hydro-static model with a good prediction capability was proposed by Vagnon [77]. Therefore, the impact force of debris flow on the retaining wall was evaluated to study the damage mechanism by Ref. [77]: where P peak is the peak impact pressure (kN/m 2 ); F r is the Froude number; and h df is the mean debris flow depth (m). Considering the large scale of the debris flow disaster on 21 June 2019, γ df is taken as 1.9 t/m 3 according to Table 4. Based on field investigation, the average velocity of the debris flow (V df ) near the retaining wall was calculated through Equation (13), and related parameters are shown in Table 5. Based on the related report, the designed resistance of the retaining wall is 51.34 KN/m 2 [75], which is far below the calculated value of the peak impact pressure (80.39 kN/m 2 ) in Table 5. The debris flow impact force was greater than the resistance of the retaining wall, causing partial failure of the retaining wall on 21 June 2019. Thus, the resistance of the retaining wall should be increased during the design processes. In general, considerable attention should be given to the post-earthquake debris flow disaster in Zechawa Gully in the future, and it is necessary to repair the broken retaining wall with a greater design resistance and remove the debris flow material deposited behind the retaining wall to prepare for the next post-earthquake debris flow in the near future.

Conclusions
This study is intended to describe the debris flow events in Zechawa Gully, characterize the debris flow disaster, propose appropriate mitigation countermeasures and analyse the effectiveness of mitigation countermeasures that were already implemented in May 2019. Field investigations were conducted in a timely manner to determine the debris flow peak discharge, and the disaster characteristics and occurrence of debris flows in 2016 were analysed. The following conclusions can be drawn: (1) In this study, the debris flow peak discharge was calculated using the rain-flood method, cross-section survey method, dam-breaking calculation method and maximum boulder size method. Based on our research, compared with previous results based on a single method, an accurate debris flow peak discharge can be obtained by comparing the results of each calculation method with each other, which increases the parameter accuracy for debris flow disaster prevention and risk assessment.  Density of the solid material γ w Density of the water θ Watershed characteristic parameter µ Shape coefficient, which is dependent on the shape of the largest boulder ρ b Maximum boulder density ρ f Fluid density ρ s Sediment density τ Bed shear stress η Runoff yield parameter, which reflects the average infiltration intensity φ Runoff coefficient of the flood peak, which is related to the convergence of runoff ϕ df Quasi-static friction angle ψ df Amplification coefficient of the debris flow peak discharge κ Influence factor that accounts for residual height

Conflicts of Interest:
The authors declare no conflict of interest.