Assessing the Susceptibility of the Xiangka Debris Flow Using Analytic Hierarchy Process, Fuzzy Comprehensive Evaluation Method, and Cloud Model

Abstract

The seasonal Xiangka debris flow, breaking out frequently in Xinghai County, Qinghai Province, poses a serious threat to resident safety, has significant potential economic impacts, and inflicts severe damage on the geological environment, vegetation, and land resources in the area. Therefore, a susceptibility assessment is crucial. Utilizing data from field investigations, meteorology, and remote sensing, this study devised an assessment system using 10 evaluation factors with pronounced regional characteristics as susceptibility indices. Based on data processing using ArcGIS 10.7 and MATLAB R2016B, this study assessed the susceptibility of the Xiangka debris flow using AHP, the fuzzy comprehensive evaluation method, and a cloud model. The analysis results show that, based on AHP, the primary index affecting the occurrence of Xiangka debris flow is mainly source factor (0.447). The secondary indices are mainly the length ratio of the mud sand supply section (0.219), fractional vegetation cover (FVC, 0.208), and watershed area (0.192). Combined with the actual characteristics, it can be seen that the formation conditions of the Xiangka debris flow primarily encompass the following: sources such as slope erosion and accumulation at gully exits, challenging topography and terrain conducive to the accumulation of water and solid materials, and water source aspects like surface runoff from intense rainfall. Based on the fuzzy mathematical method—fuzzy coordinate method—cloud model, it is concluded that the degree of susceptibility is mild-to-moderate. The combination of these methods provides a new idea for the evaluation of debris flow susceptibility. This study can provide a theoretical basis for the layout of treatment engineering and geological disaster prevention in this area and promote the sustainable development of the ecological environment.

1. Introduction

In recent years, natural and human factors have jointly led to frequent debris flows in Qinghai Province. The statistics made by the Geological Environment Monitoring Station of Qinghai Province indicate that, over the past three decades (1990–2019), 120 debris flow incidents occurred, resulting in severe casualties and over 400 million in direct economic damages [1]. The province’s geology, characterized by widely distributed loess, gravelly, sandy, viscous, and salinized soils with disordered, loose, and fragile structures, is particularly susceptible to rainfall-induced surface instability and subsequent debris flow formation [2]. Field investigations and data analysis revealed that the seasonal Xiangka debris flow in Xinghai County poses a certain threat to the residents. The debris flow seriously threatens 50 people including 15 villagers, the rural hardened road is about 500 m, the farmland is 13,333 m², and the potential economic loss is of about CNY 1.6 million. At the same time, the occurrence of debris flow geological disasters also caused serious damage to the geological environment, vegetation, and land resources in this area. At present, no one has studied the susceptibility evaluation of the debris flow and put forward reasonable measures to control it. Consequently, assessing the susceptibility of the Xiangka debris flow is crucial for developing effective prevention and control strategies to safeguard the lives and property of inhabitants in the area.

At present, a large number of domestic and foreign scholars have systematically studied the zonal assessment of the vulnerability of single-gully debris flow and the zonal assessment of regional debris flow, and the assessment methods tend to be diversified and can be a more objective and scientific evaluation of the vulnerability of debris flow. For the assessment method of debris flow susceptibility, the qualitative assessment method was first adopted, and the main object was the single ditch debris flow. This method was developed from practice. For example, Tan Bingyan first put forward the comprehensive assessment of debris flow severity in 1986 and adopted a qualitative assessment method for the judgment of debris flow gully and its activity intensity, which provided a basis for future research [3,4,5]. Subsequently, many scholars devoted themselves to the research of debris flow susceptibility, introduced various mathematical methods to the identification of debris flow susceptibility, and expressed its development process with mathematical language. The research on zoning assessment of debris flow susceptibility gradually changed from qualitative assessment to semi-qualitative and semi-quantitative assessment [6,7,8,9,10,11]. With the deepening of the research, more and more mathematical methods such as fuzzy evaluation and regression analysis have been applied to the assessment of debris flow susceptibility and gradually moved toward the quantitative assessment of debris flow susceptibility. The aim is to identify the main influencing factors of induced debris flow and use various mathematical methods to determine the importance and weight of each influencing factor, to build a mathematical model to assess the susceptibility of debris flow [12,13,14,15,16]. Nowadays, there are more widely used and mature methods in China, such as the fuzzy mathematics evaluation method, regression analysis method, gray system evaluation method, etc. [17,18,19].

However, the result of the traditional AHP–fuzzy comprehensive evaluation model is a simple value, which can only reflect the size of the risk, but cannot show the specific characteristics of a certain debris flow risk, to provide more detailed information for disaster prevention and reduction decision-making. To solve this problem, this paper combines the AHP–fuzzy comprehensive evaluation method with spatial coordinates. The three axes of spatial coordinates are defined as topographic and geomorphological factors (X-axis), source factors (Y-axis), and meteorological, hydrological, and vegetation factors (Z-axis). Fuzzy comprehensive evaluation is carried out on the susceptibility of debris flow, and spatial coordinates are composed of evaluation results. The distance from the coordinate point to the origin is defined as the size of the susceptibility. By using the three-dimensional attribute of spatial coordinates, the evaluation results can not only show the vulnerability but also express the specific characteristics of debris flow risk. At the same time, because the influence of fuzziness and randomness in the evaluation process is rarely considered in previous evaluation methods, this paper uses cloud model theory to propose an assessment model of debris flow susceptibility based on the AHP–fuzzy synthesis method and cloud model, which fully considers the characteristics of fuzziness and randomness of evaluation indices and data. At the same time, the feasibility and accuracy of the model are tested by combining it with the score table of the Xiangka debris flow field, which provides a scientific basis for the treatment of Xiangka debris flow and a new idea for the susceptibility evaluation of single ditch debris flow.

2. Overview of the Study Area

2.1. Topography

The study area, situated on the southern flank of the Daheba River in southwest Xinghai County, Qinghai Province, spans high-terrace and river valley plains, characterized by significant elevation differences and steep topographic slopes. The river’s intense cutting has sculpted deep gullies and ravines on either side of the river valley, fostering an environment where debris flows are notably prevalent. The terrain of the study area ascends from northeast to southwest, with slopes varying from 10° to 50°. The area’s apex, at an elevation of 3418 m, is located on the Gaotai Plain’s rear boundary, while its nadir, at 3010 m, lies along the Daheba River. The geomorphic units in the study area are categorized into high-terrace and river valley plains. The high-terrace plain, composed of Upper Pleistocene gravels, pebbles, and clays, is open and flat. Due to Daheba River’s erosive action, a high terrace has been formed at the forefront of the high-terrace plain, standing out at elevations ranging between 100 and 500 m and consisting predominantly of loosely consolidated Quaternary gravelly pebbles, making the area susceptible to frequent collapses and debris flows. Conversely, in the river valley plain, resembling a ribbon stretched along the Daheba River’s banks, the river channels meander deeply, cutting 400 to 500 m into the landscape, and the river valley’s breadth spans from 200 to 2000 m. At the river valley plain’s rear, the deposition zones of debris flow and collapses are commonly afflicted by disasters, suggesting elevated risks associated with geological hazards in the study area (Figure 1).

2.2. Stratigraphic Lithology

Outcrops in the study area predominantly consist of Carboniferous, Triassic, Neoproterozoic, and Quaternary strata, distributed along the NW–SE distribution. The surface geology mainly features Quaternary loose deposits, including Lower Pleistocene alluvial–lacustrine, Upper Pleistocene alluvial–proluvial, and Holocene proluvial and debris flow deposits from ancient to recent [20]. The Lower Pleistocene alluvial–lacustrine strata (${\mathrm{Q}}_1^{\mathrm{al}}$), found at the transition from high-terrace to river valley plains near the Daheba River, consist of light-yellow to yellowish-brown alluvial–lacustrine sand and gravelly pebbles embedded in calcareous and semi-colloidal mud. The Upper Pleistocene alluvial–proluvial deposits (${\mathrm{Q}}_3^{\mathrm{pal}}$), prevalent in the sloping plain areas adjacent to the Daheba River’s mountainous regions, are characterized by yellowish-gray to gray argillaceous gravels and pebbles, predominantly composed of granite and volcanic clastics. The Holocene proluvial deposits (${\mathrm{Q}}_4^{\mathrm{pl}}$) are distributed within the Daheba River valley and its large tributary gullies, featuring a mix of gravels, pebbles, and clay. The Holocene debris flow deposits (${\mathrm{Q}}_4^{\mathrm{set}}$) occupy the zones of debris flow accumulation, mainly comprising layers of sand and pebbles. Quaternary loose deposits, especially Holocene debris flow deposits, provide abundant solid material sources for debris flow.

2.3. Geotectonics and Earthquakes

The study area features a folded basement composed of Triassic strata, evolving into a Meso-Cenozoic faulted basin—the Xinghai Basin, with the surrounding fault structures dominated by EW-, NNW-, NWW-trending, and arc-shaped faults. The study area experienced intermittent vertical uplift and subsidence, leading to the elevation of the surrounding mountains and the relative depression of the basin. As a result, sharply inclined slopes formed. This topography plunges the valleys of the Yellow River, the Daheba River, and the Qushian River to depths of several hundred meters, fostering conditions conducive to collapses and debris flows. Geographically, the area is part of the northern Tibetan Plateau seismic region and the Tongde seismic sub-region. Historical data indicate that the study area and its vicinity have experienced multiple earthquakes, with a peak ground acceleration of 0.10 g and a magnitude of VII [21]. The seismic force will change the inertia force of the slope body, trigger sliding and flow, and then promote the formation of debris flow. Earthquake-triggered landslides and other geological disasters provide a significant amount of loose solid materials for debris flow. In the rainy season after the earthquake, these loose materials are easily washed and transported by rain, forming large-scale debris flows. Therefore, seismic activity not only increases the possibility of debris flow but also expands the scale of the debris flow.

2.4. Meteorology and Hydrology

The study area is distinguished by a continental semi-arid alpine steppe climate, featuring significant daily temperature fluctuations and high evaporation. The majority of annual rainfall occurs from May to September, representing over 80% of the total yearly precipitation. Xinghai County’s terrain is complex, marked by substantial elevation differences and pronounced vertical climate zoning [22]. Temperatures in the area are relatively elevated, with average multiyear temperatures ranging between 5 °C and 6.1 °C. Precipitation levels vary between 250 mm and 300 mm, while evaporations span from 900 mm to 1100 mm. The Daheba River, originating from the Baiga Source at the northwestern base of Suigenergang, begins at an elevation of 4720 m. From tributaries such as Qiemaolongwa in its upper reaches to Tangnaihai River, where it meets the Yellow River, the Daheba River covers a distance of 60.3 km and a watershed area of 3921.5 km², with average multiyear runoff of 2.991 × 10⁸ m³/a. The debris flow gullies within the study area are identified as seasonal flood gullies.

3. Assessment Method

According to the conditions of the catchment, stratigraphic lithology, disaster development, and reserves of possible debris flow in the Xiangka debris flow, Ditch, the susceptibility degree of debris flow is analyzed by the AHP–fuzzy synthesis method and cloud model. The technology roadmap is shown in Figure 2 below.

3.1. Construction of an Evaluation Index System

The choice of susceptibility evaluation indices is directly related to the accuracy of the evaluation results. Through field investigations in the study area, data collection, and review of the pertinent literature [20,23,24,25,26,27], and informed by the frequency of influencing factors cited by scholars in debris flow risk assessments [28,29,30,31], this study determined 10 evaluation indices reflecting significant regional traits to formulate the Xiangka debris flow evaluation index system. This system comprises three primary evaluation indices: topographic and meteorological factors (A), source factors (B), and hydrological and vegetation factors (C), along with ten secondary evaluation indices (Figure 3). The grading scales for each evaluation index were established according to the specification (

Table 1. Evaluation factors grading scale.

Norm	Extreme Susceptibility	High Susceptibility	Moderate Susceptibility	Mild Susceptibility
Relative height difference of watershed A11/m	>500	300–500	100–300	<100
Gully bank slope A12/°	>32	25–32	15–25	<15
Longitudinal gradation A13	>0.35	0.20–0.35	0.10–0.20	<0.10
Watershed area A14/km2	0.2–5	5–10	<0.2, 10–100	>100
Degree of gully blockage B11	Serious	Moderate	Mild	None
Volume of sources per unit area B12/(×104 m3/km2)	>1000	100–1000	30–100	30
Length ratio of the mud–sand supply section B13/%	>60	30–60	10–30	<10
24 h maximum rainfall C11/mm	>100	50–100	25–50	10–25
Vegetation coverage C12/%	<10	10–30	30–60	>60
Land use type C13	Bare ground, cultivated land	Townland	Grassland	Woodland

).

(1) Topographic and geomorphological factors: (1) Relative height difference of watershed. As shown in Figure 4a, the study area exhibits a significant relative height difference, providing substantial potential energy for debris flow movement, thereby greatly influencing debris flow activity; (2) Gully bank slope: In the study area, the gully bank slopes predominantly range from 30° to 50°, effectively capturing rainfall and thereby enhancing runoff (Figure 4b); (3) Longitudinal gradation: With an average longitudinal gradient of 313‰ in the study area, conditions are conducive to debris flow formation due to the steep gradient; (4) Watershed area: The 0.3 km² watershed area offers ample space for the origin and development of debris flows.

(2) Source factors: (1) Degree of gully blockage: The study area exhibits low-degree gully blockage, preventing sudden flow surges during debris flow events; (2) Volume of sources per unit area: The area’s high volume of sources per unit area ensures abundant materials for debris flow formation; (3) Length ratio of the mud–sand supply section: The mud–sand supply section, constituting about 40% of the area, significantly impacts debris flow magnitude.

(3) Meteorological, hydrological, and vegetation factors: (1) 24 h maximum rainfall: The area’s maximum 24 h rainfall is 50.6 mm, indicating that heavy rainfall and strong hydrodynamic forces increase the likelihood and scale of debris flow events (Figure 4d); (2) Vegetation coverage: With 30% vegetation cover in the watershed, high soil erosion rates and intense human activity heighten debris flow susceptibility (Figure 4c); (3) Land use type: The presence of extensive woodlands, cultivated lands, and unused lands in the area can somewhat mitigate debris flow development (Figure 4e).

3.2. Analytic Hierarchy Process (AHP)

AHP breaks down a specific problem into its various components, establishes a multi-tiered analytical structure based on the relationships among these elements, and employs a scaling method to determine the relative importance of each component for the benefit of decision-makers [32,33]. As a systematic quantitative evaluation tool, AHP holds considerable value in assessing debris flow susceptibility [34,35,36,37].

(1)

Construction of judgment matrix

The process involved multiple consultations with 10 experts to rate the evaluation factors using the 1 to 9 scale discrimination method (

Table 2. 1–9 scale theory for the elements of a judgment matrix.

Scale Value	Comparative Rule
1	Both factors are equally important
3	Factor a is slightly more important than factor b
5	Factor a is more important than factor b
7	Factor a is much more important than factor b
9	Factor a is extremely more important than factor b
2, 4, 6, 8	30
Reciprocal of the above data	<10

) [38]. This is followed by the assessment of the significance of each factor and the construction of a judgment matrix. Subsequently, MATLAB was utilized to extract the eigenvalues and eigenvectors from this matrix. The next phase involved normalizing the judgment matrix and assigning weight values to each factor. Among them, the maximum eigenvalue (λ_max) was calculated using Equation (1).

$${\lambda }_{\max }=\sum _{i=1}^n\frac{\left(A{W}_{\mathrm{i}}\right)}{n{W}_{\mathrm{i}}}$$

(1)

where λ_max is the maximum eigenvalue of the judgment matrix, A is the constructed judgment matrix, and W is the weight value of an index.

(2)

Consistency test

This study conducted consistency tests on the constructed judgment matrix using the consistency index in Equation (2) and the consistency test index in Equation (3). The criteria for the consistency test index, namely consistency ratio (CR), are as follows: CR < 0.1 means excellent consistency of the judgment matrix and, accordingly, highly reliable evaluations; CR = 0.1 means good consistency of the matrix and comparatively sound judgments; and CR > 0.1 denotes that the matrix requires adjustment due to its poor consistency [39,40]

$$CI=({\lambda }_{\max }-n)/(n-1)$$

(2)

where CI is the consistency index and n is the order of the judgment matrix.

$$CR=CI/RI$$

(3)

where CR is the consistency test index and RI is a random consistency index, the reference value of which refers to [41].

3.3. Fuzzy Mathematics Method

The fuzzy mathematics method employs the principles of fuzzy mathematics and the principle of maximum membership to assess entities influenced by various factors [42,43,44]. Based on the comprehensive evaluation index system for the Xiangka debris flow depicted in Figure 2, a fuzzy set was established, encompassing both the evaluation factors and the evaluation criteria.

(1)

Construction of evaluation factor set U

$$U=\{U_1,U_2,U_3\}$$

(4)

$$U_1=\left\{A_{11},A_{12},A_{13},A_{14}\right\}$$

(5)

$$U_2=\left\{B_{11},B_{12},B_{13}\right\}$$

(6)

$$U_3=\left\{C_{11},C_{12},C_{13}\right\}$$

(7)

In Equations (4)–(7), U₁ is the set of topographic and geomorphologic factors, U₂ is the set of source factors, and U₃ is the set of meteorological, hydrological, and vegetation factors; A₁₁ is the relative height difference of watershed; A₁₂ is longitudinal gradient, A₁₃ is the gully bank slope; A₁₄ is the watershed area; B₁₁ is the degree of gully blockage; B₁₂ is the volume of provenances per unit area; B₁₃ refers to the length ratio of mud–sand supply section; C₁₁ is 24-h maximum rainfall; C₁₂ is the vegetation coverage; and C₁₃ is the land use type.

(2)

Construction of evaluation set V

Based on the classification criteria for debris flow geological hazards, the susceptibility of the Xiangka debris flow was categorized into four grades: no, mild, moderate, and extreme, as outlined in Equation (8).

$$V=\left\{\mathrm{no} \mathrm{susceptibility}\right(\mathrm{I}\left), \mathrm{mild} \mathrm{susceptibility}\right(\mathrm{II}\left), \mathrm{moderate} \mathrm{susceptibility}\right(\mathrm{III}\left), \mathrm{extreme} \mathrm{susceptibility}\right(\mathrm{IV}\left)\right\}$$

(8)

(3)

Determination of membership function

Determining the membership degree is crucial in the fuzzy comprehensive evaluation method. The membership degree can be derived using a membership function. In this study, the trapezoidal distribution function was employed to ascertain the membership degrees for various factors.

$$R_1=\left\{\begin{array}{c}1,x<s_1;\\ \frac{3s_1+s_2-4x}{s_2-s_1},s_1\le x\le \frac{3s_1+s_2}{4};\\ 0,x>\frac{3s_1+s_2}{4}.\end{array}\right.$$

(9)

$$R_2=\left\{\begin{array}{c}0,x<s_1,x>\frac{3s_2+s_3}{4};\\ \frac{4x-4s_1}{s_2-s_1},s_1\le x\le \frac{3s_1+s_2}{4};\\ 1,\frac{3s_1+s_2}{4}\le x\le \frac{ s_1+3s_2}{4};\\ \frac{3s_1+s_2-4x}{s_2-s_1},\frac{s_1+3s_2 }{4}\le x\le \frac{{3s}_2+s_3}{4}.\end{array}\right.$$

(10)

$$R_3=\left\{\begin{array}{c}0,x<\frac{s_1+3s_2}{4},x>s_3;\\ \frac{4x-s_1-3s_2}{s_3-s_1},\frac{s_1+3s_2 }{4}\le x<\frac{3s_2+s_3}{4};\\ 1,\frac{3s_2+s_3}{4}\le x<\frac{s_2+3s_3}{4};\\ \frac{4s_3-4x}{s_3-s_2},\frac{s_2+3s_3}{4}<x\le s_3.\end{array}\right.$$

(11)

$$R_4=\left\{\begin{array}{c}0,x<\frac{s_2+3s_3}{4};\\ \frac{4x-s_2-3s_3}{s_3-s_2},\frac{s_2+3s_3}{4}\le x\le s_3;\\ 1,x>s_3.\end{array}\right.$$

(12)

In the above Equations (9)–(12), x is the measured value of an evaluation factor; s₁, s_2, and s₃ are the boundary values of various factors; R₁, R₂, R₃, and R₄ are the membership degrees of a factor of various evaluation grades.

U_i was evaluated separately, and the membership degrees of each factor relative to the evaluation grades were determined according to the above-mentioned “trapezoidal distribution” function [45]. Then, fuzzy matrices R_A, R_B, and R_C of each factor set were obtained through calculation. For each secondary index, according to the weights obtained by the fuzzy matrices and AHP, the fuzzy weighted averaging operators (*, +) are used for research, and B_A, B_B, and B_C are obtained, respectively. The total evaluation matrix R was a fuzzy matrix with B_A, B_B, and B_C as rows. The evaluation results of the susceptibility of Xiangka debris flow are obtained according to the formula B = W × R and the weight vector W of the primary index.

3.4. Fuzzy Coordinate Method

The calculation results of the fuzzy mathematics method can reflect the susceptibility of debris flow but fail to capture the specific characteristics of debris flow risks. To furnish decision-makers with more details, the fuzzy mathematics method was amalgamated with the coordinate method to assess the Xiangka debris flow. Initially, a spatial rectangular coordinate system was established, with the X axis designated for topographic and geomorphological factors, the Y axis for source factors, and the Z axis for meteorological, hydrological, and vegetation factors. Axis scales 1, 2, 3, and 4 correspond to susceptibility evaluation grades I, II, III, and IV. The unique coordinate point D can be determined from the evaluation results of the susceptibility of debris flow topographic and geomorphological factors, source factors, and meteorological, hydrological, and vegetation factors as shown in Equation (13). The distance from this coordinate point to the origin was defined as susceptibility R, leading to the derivation of the susceptibility calculation formula presented in Equation (14).

$$D\left(X, Y, Z\right)$$

(13)

where X is the evaluation result of topographic and geomorphological factors; Y is the evaluation result of source factors; and Z is the evaluation result of meteorological, hydrological, and vegetation factors.

$$R=\sqrt{X^2+Y^2+Z^2}$$

(14)

The susceptibility of debris flow was classified based on the distance from coordinate point D to the origin, with the classification criteria being: 0 < R< 1.732 indicating no susceptibility, 1.732 < R< 3.464 denoting mild susceptibility, 3.464 < R< 5.196 representing moderate susceptibility, and R> 5.196 denoting extreme susceptibility. Following these criteria, based on the membership degree of each factor obtained by fuzzy mathematics, the susceptibility of Xiangka debris flow was evaluated by the fuzzy coordinate method.

3.5. Cloud Model

The cloud model is a decision-making tool adept at facilitating the conversion between qualitative descriptions and quantitative values. This technique is characterized by the normal cloud model, which is defined by three parameters: expected value (Ex), entropy (En), and hyper-entropy (He) [46,47].

(1)

Building of a standard cloud

Following the susceptibility classification criteria of the fuzzy coordinate method, the standard cloud parameters for various evaluation intervals were determined using Equation (15) [48]. Subsequently, MATLAB R2016B software was employed to program and plot the cloud model of the comment set, as depicted in Figure 5, where blue scatters represent the range of the comment set. During the development of the cloud model of evaluation indices, to encapsulate the uncertainty of an evaluation index exceeding the defined boundaries, half-descending and half-ascending normal cloud models were utilized for susceptibility levels at the boundaries of the comment set [49,50].

$$\left\{\begin{array}{c}Ex={(Q}_{\min }+Q_{\max })/2\\ Ex-\sqrt{\ln 8}En=Q_{\min }\\ He=0.02\end{array}\right.$$

(15)

where Q_min and Q_max represent the upper and lower limits of the evaluation interval.

(2)

Cloud parameters of evaluation index

Based on the scoring results of various evaluation indices provided by numerous experts, three characteristic parameters for each evaluation index were derived using the reverse cloud model. The relevant formula is presented in Equation (16), with the calculation results shown in

Table 3. Characteristic parameters of cloud models for various evaluation factors.

Secondary Index	Weight	Ex	En	He
A11	0.097	3.20	0.80	0.39
A12	0.027	1.60	0.48	0.27
A13	0.018	1.20	0.22	0.39
A14	0.192	5.80	0.39	0.67
B11	0.027	1.40	0.48	0.27
B12	0.088	4.80	0.42	0.75
B13	0.219	7.00	0.48	0.27
C11	0.080	2.80	0.80	0.39
C12	0.208	6.00	0.39	0.67
C13	0.046	2.40	0.25	0.36

.

$$\left\{\begin{array}{c}Ex=\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^n}{x}_i\\ En=\sqrt{\frac{\mathsf{\pi }}{2}}\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left|x_i-Ex\right|\\ He=\sqrt{S^2-{En}^2}=\sqrt{\frac{1}{n-1}{\displaystyle \sum _{i=1}^n}{\left(x_i-\overline{x}\right)}^2-{En}^2}\end{array}\right.$$

(16)

(3)

Parameters of the comprehensive cloud

Building on the cloud models of the comment set, as well as the weights of various evaluation indices obtained using AHP, this study carried out a cloud model-based comprehensive assessment of the Xiangka debris flow’s susceptibility using Equation (17).

$$\left\{\begin{array}{c}Ex={\displaystyle \sum _{i=1}^n}{Ex}_i{z}_i\\ En=\sqrt{{\displaystyle \sum _{i=1}^n}{En}_i^2{z}_i}\\ He={\displaystyle \sum _{i=1}^n}{He}_i{z}_i\end{array}\right.$$

(17)

where z_i is the weight of an evaluation index.

4. Result Analysis

By performing calculations, the weight values for both primary and secondary indices can be ascertained. The results reveal that the source factors carried the highest weight among the primary indices, indicating their paramount importance in influencing the debris flow. These factors are followed by the meteorological, hydrological, and vegetation factors, and lastly, the topographic and geomorphological factors. Normalizing the weights of the secondary indicators yielded the composite weights of the 10 evaluation factors for the Xiangka debris flow, expressed as W = [0.097, 0.027, 0.018, 0.192, 0.027, 0.088, 0.219, 0.080, 0.208, 0.046]. Analysis of these composite weights highlights that the length ratio of the mud–sand supply section (0.219), vegetation cover (0.208), and watershed area (0.192) serve as predominant secondary indices affecting the Xiangka debris flow. Furthermore, consistency tests confirm the reliability of the judgment matrix, suggesting that the derived results are accurate (

Table 4. Weights of factors at various levels for the susceptibility evaluation of the Xiangka debris flow.

Primary Index	Primary Index Weight	Secondary Index	Secondary Index Weight	Consistency Test
Topographic and geomorphologic factors A	0.256	Relative height difference of watershed A11/m	0.290	0.0433 pass
		Gully bank slope A12/°	0.082
		Longitudinal gradation A13	0.053
		Watershed area A14/km2	0.575
Source factors B	0.447	Degree of gully blockage B11	0.080	0.0313 pass
		Volume of sources per unit area B12/(×104 m3/km2)	0.265
		Length ratio of mud-sand supply section B13/%	0.656
Meteorological, hydrological, and vegetation factors C	0.297	24 h maximum rainfall C11/mm	0.239	0.0176 pass
		Vegetation coverage C12/%	0.623
		Land use type C13	0.137

).

Each factor Ui was evaluated based on fuzzy mathematics, and the fuzzy matrices R_A, R_B, and R_C of each factor subset were obtained through calculation, as shown in Equations (18)–(20).

$$R_{\mathrm{A}}=\left[\begin{array}{c}0.114 0.127 0.331 0.428\\ 0.106 0.420 0.312 0.162\\ 0.121 0.441 0.303 0.135\\ 0.109 0.224 0.338 0.329\end{array}\right]$$

(18)

$$R_{\mathrm{B}}=\left[\begin{array}{c}0.541 0.325 0.131 0.003\\ 0.304 0.446 0.123 0.127\\ 0.111 0.323 0.338 0.228\end{array}\right]$$

(19)

$$R_{\mathrm{C}}=\left[\begin{array}{c}0.127 0.349 0.303 0.221\\ 0.211 0.464 0.323 0.002\\ 0.206 0.459 0.237 0.098\end{array}\right]$$

(20)

The total evaluation matrix R was a fuzzy matrix with B_A, B_B, and B_C as rows, as shown in Equations (21)–(23). According to the weight vector W of the primary indices, the susceptibility assessment result was calculated, as shown in Equation (24).

$$B_{\mathrm{A}}=W_{\mathrm{A}}{R}_{\mathrm{A}}=\left[0.111,0.223,0.332,0.334\right]$$

(21)

$$B_{\mathrm{B}}=W_{\mathrm{B}}{R}_{\mathrm{B}}=\left[0.359,0.418,0.125,0.098\right]$$

(22)

$$B_{\mathrm{C}}=W_{\mathrm{C}}{R}_{\mathrm{C}}=\left[0.190,0.436,0.306,0.068\right]$$

(23)

$$\mathrm{B}=WR=\left[0.256,0.447,0.297\right]\times \left[\begin{array}{c}0.111 0.223 0.332 0.334\\ 0.359 0.418 0.125 0.098\\ 0.190 0.436 0.306 0.068\end{array}\right]=\left[0.245,0.373,0.232,0.150\right]$$

(24)

where B is the evaluation result, and the final evaluation grade was determined by obtaining the maximum value according to the principle of maximum membership.

Following the maximum membership principle, the evaluation outcomes exhibited a maximum of 0.373, corresponding to the mild susceptibility (II) level (

Table 5. Membership degrees of various evaluation indices.

	No Susceptibility (I)	Mild Susceptibility (II)	Moderate Susceptibility (III)	Extreme Susceptibility (IV)
Topographic and geomorphologic factors A	0.111	0.223	0.332	0.334
Source factor B	0.359	0.418	0.125	0.098
Meteorological, hydrological, and vegetation factors C	0.190	0.436	0.306	0.068
Comprehensive evaluation	0.245	0.373	0.232	0.150

). Consequently, it can be deduced that the Xiangka debris flow exhibits mild susceptibility, aligning with the findings from field investigations. Therefore, the evaluation results offer a theoretical foundation for subsequent control measures against debris flow geological hazards.

Based on the fuzzy coordinate method, the susceptibility of Xiangka debris flow was evaluated, and the calculation results are shown in

Table 6. Calculation results of fuzzy coordinate method.

Evaluation Factor	Membership Degree				Evaluation Result	Coordinate Value	Susceptibility
	I	II	III	IV
X	0.111	0.223	0.332	0.334	IV	(4, 2, 2)	4.899
Y	0.359	0.418	0.125	0.098	II
Z	0.190	0.436	0.306	0.068	II

. The unique coordinate point was projected into the spatial rectangular coordinate system, as shown in Figure 6. The coordinate value was (4, 2, 2), and the distance from the origin of the coordinate axis was 4.899, indicating that it fell within the medium susceptibility range.

The cloud model is used to comprehensively evaluate the susceptibility of Xiangka debris flow, and the results are expected to be Ex = 4.56, entropy En = 0.51, and hyper-entropy He = 0.50. Moreover, MATLAB software is used to draw a cloud model of the evaluation results of Xiangka debris flow susceptibility, which can directly judge the evaluation grade of the debris flow and the fuzziness of the results, as shown in Figure 7, where the red scatter points represent the normal distribution set of debris flow verification in the study area, and this distribution model is between the blue curve of mild susceptibility to moderate susceptibility.

Utilizing the cloud model, the susceptibility assessment of the Xiangka debris flow was conducted, circumventing the subjective bias inherent in manually determining membership degrees. The findings indicate a mild susceptibility for the Xiangka debris flow, aligning with results from the fuzzy coordinate method, and field observations. This consistency underscores the cloud model’s efficacy in assessing debris flow susceptibility, offering a valuable reference for evaluating other qualitative, fuzzy issues.

As shown in the quantitative assessment table of the debris flow susceptibility in specification [51], the susceptibility of the Xiangka debris flow scored 84 (

Table 7. Quantitative scores of debris flow susceptibility in the study area.

Influencing Factor	Susceptibility Evaluation	Score
Severity of collapse, landslide, and soil erosion	Sporadic collapses, landslides, and gullies will occur	12
Length ratio of mud–sand supply section/%	The length ratio of mud–sand supply section accounts for about 40%	12
Degree of debris flow accumulation activity at the gully exit	No changes in river morphology in the main river	1
Longitudinal gradation of gully/‰	Average 313‰	12
Degree of regional tectonic influence	Intensely uplifted area, basic intensity VII	9
Vegetation coverage of watershed/%	Vegetation coverage 30%	5
A recent changing amplitude of gully/m	Changing amplitude of siltation less than 0.2 m	1
Lithologic influence	Gravelly pebble	6
Loose material reserves along the gully/(×104 m3/km2)	3 × 104 m3/km2	4
Gully bank slope/‰	Slope mostly 30°–50°	6
Cross-section of gully in sand-producing area	”V” type	5
Average thickness of loose material in sand-producing areas/m	Thickness of loose material is about 3 m	3
Watershed area/km2	0.3 km2	5
Relative height difference of watershed/m	279 m	2
Gully blockage degree	None	1
Total		84

), categorizing it as mildly susceptible. Field surveys reveal that the area experiences debris flows of various magnitudes every year, corroborating the consistency of the quantitative evaluation table with both the real conditions of the study area and the outcomes from the fuzzy comprehensive evaluation method.

5. Discussion

Based on AHP, it is concluded that the primary index affecting the occurrence of debris flow in Xiangka is the source factor (0.447), which is the necessary material condition for the occurrence of debris flow. According to the field measurement, the source in the study area mainly includes slope erosion sources and accumulation sources at the gully exit. The slope erosion sources are distributed in the flow area of the debris flow gully, where vegetation is sparse and the slope surface is bare. The slope lithology is mainly the Lower Pleistocene alluvial–lacustrine sand and gravelly pebbles, which are embedded in calcareous and semi-colloidal mud, easy to weather, and easy to be eroded by precipitation. The sloping structure is relatively loose, and it participates in debris flow activities in the form of spallation and slope erosion under heavy rain. Based on the research area of 12.48 m² and the thickness of source material from 0.5 to 1.0 m, the total amount of slope erosion sources is calculated to be 9.36 × 10⁴ m³, and the product with the thickness of storm erosion once (0.01 m) is the slope erosion source dynamic reserve, that is, 0.12 × 10⁴ m³. These accumulation sources at the gully exit are dominated by gravelly pebbles, with sizes ranging from 5 to 40 mm, and engage in debris flow activities primarily through erosion and scouring by surface runoff. The zonation area of No. I–III fan is 14.5 m², 4.8 m², and 6.3 m², respectively, and the thickness of the loose solid source at the mouth of the gutter is 0.5~2.0 m. It is estimated that the static reserve of solid source in the debris flow trench is 36.0 × 10⁴ m³, the thickness of primary erosion by rainstorms is 0.03~0.05 m, and the dynamic reserve is 0.17 × 10⁴ m³. A large number of slope erosion sources and accumulation sources at the gully exit provide abundant source conditions for debris flow.

According to the evaluation of Xiangka debris flow by fuzzy mathematics, coordinate method, and cloud model, it is found that the degree of susceptibility is mild-to-moderate. First of all, topographic conditions are one of the important factors for the formation of debris flow. The Xiangka debris flow developed at the front of the high platform with steep terrain and the longitudinal gradient of the formation and conveyance zone reached 417‰. The main gully is in the shape of a “V”, and the slope of both sides is of 30°~50°. The vegetation in the area is sparse, the slope of the mountain is large, and the hydrodynamic force formed during rainfall is large, which will drive the loose accumulation bodies on both sides to participate in debris flow activities through landslides and lateral erosion processes. In addition, the abundant atmospheric precipitation and snowmelt water in the area provide conditions for groundwater recharge. Precipitation in the area is mainly concentrated from May to September, accounting for more than 80% of the annual precipitation, and there is more heavy rain and showers in the area, with heavy rain occurring mostly in the evening or at night. This means that, when it rains, a large amount of precipitation will rapidly gather on the hillside, which makes it easy to form a slope torrent, and then wash and transport loose materials. In addition, this feature makes the prone period of geological disasters highly coincide with the rainfall period. When the rainfall intensity exceeds the interception capacity of soil and vegetation, surface runoff is easy to form, which further affects the occurrence and intensity of debris flow.

The occurrence of debris flow is affected by many factors, and its susceptibility evaluation is a complex uncertainty problem. The evaluation based on fuzzy mathematics theory avoids the subjective influence of artificial determination of membership degree. In addition, this paper introduces the cloud model (which has obvious advantages in dealing with qualitative and quantitative transformation) to realize the quantitative description of debris flow susceptibility evaluation and comprehensively considers the randomness and fuzziness in the process of susceptibility evaluation, which makes up for the shortcomings of previous methods that cannot take both into account. Based on the comprehensive evaluation of Xiangka debris flow, it is found that Xiangka debris flow has mild-to-moderate susceptibility, and the application process of the model is simple, which can meet the needs of practical engineering and point out a clear direction for the later debris flow control. To better apply this, the construction of the evaluation index system and the professionalism of AHP expert scoring need to be further studied and improved.

6. Conclusions

(1) Based on AHP, it is concluded that the primary factor influencing the occurrence of Xiangka debris flows is identified as the source factor (0.447). Secondary factors include the length ratio of the mud–sand supply section (0.219), vegetation cover (0.208), and watershed area (0.192). The formation conditions of the Xiangka debris flow primarily encompass challenging topography and terrain conducive to the accumulation of water and solid materials; sources such as slope erosion and accumulation at gully exits; and water source aspects like surface runoff from intense rainfall. (2) Based on the AHP–fuzzy mathematical method–fuzzy coordinate method–cloud model, it is concluded that the degree of susceptibility is mild-to-medium, which is consistent with those derived from comprehensive quantitative analyses and field observations. (3) The fuzzy coordinate method enables the evaluation results to show both the susceptibility and characteristics of debris flow. The cloud model avoids the defects of subjective certainty, considers the fuzziness and randomness of evaluation indicators as a whole, and turns qualitative problems into quantitative analysis. The combination of these methods provides a new way of thinking for the assessment of debris flow susceptibility. Through comprehensive evaluation, a more accurate evaluation result of Xiangka debris flow susceptibility is obtained, which provides a reliable scientific basis for subsequent prevention and control work and promotes the sustainable development of the environment in the region.