The existence of debris flows not only destroys the facilities but also seriously threatens human lives, especially in scenic areas. Therefore, the classification and susceptibility analysis of debris flow are particularly important. In this paper, 21 debris flow catchments located in Huangsongyu Township, Pinggu District, Beijing, China, were investigated. Besides field investigation, a geographic information system, a global positioning system and remote-sensing technology were applied to determine the characteristics of debris flows. This article introduced a clustering validity index to determine the clustering number, and the fuzzy

Debris flow is a common geological disaster widely distributed across the
world. Due to its sudden occurrence, it is often difficult to give real-time
warning. Debris flow usually flows at a speed of 2.88–

Debris flow susceptibility analysis (DFS), which expresses the likelihood of a debris flow occurring in an area with respect to its geomorphologic characteristics (Blais-Stevens and Behnia, 2016), is very important for mitigating, evaluating and controlling debris flow disasters (Chiou et al., 2015). Physical, empirical and statistical approaches are used to analyse debris flow, which expresses the presumption of a debris flow occurring in an area with respect to its geomorphologic characteristics (Blais-Stevens and Behnia, 2016). Physically based approaches (Carrara et al., 2008; Burton and Bathurst, 1998) are more applicable to analysing physical and mechanical factors in independent catchments. The empirical model belongs to qualitative evaluation and is too subjective to be convincing. Statistical analyses which are usually applied to the research of regional debris flow belong to quantitative evaluation and depend on the completeness and accuracy of data. For a study area with a limited number of debris flows, a semi-quantitative evaluation method is more appropriate. This analysis includes the extraction of evaluation factors, the determination of weight factors and the establishment of an evaluation model. Considering that the influencing factors of debris flow are complex, multiple evaluation indices are generally involved, and linear correlations between different factors further complicate debris flow susceptibility analysis (Benda and Cundy, 1990). However, the unreasonable selection of factors may cause the loss of important information and failure to obtain accurate evaluation results. One way to alleviate these problems is dimension reduction through factor analysis (FA) (Aguilar and West, 2000). Some researchers (Peggy et al., 1991; Shi et al., 2015) have used the principal-component analysis method to conduct effective dimensionality reduction for selected factors and eliminate the correlation between factors. However, the coefficient of the principal component after dimensionality reduction can be positive or negative, which is not ideal for the occurrence of debris flow. Factor analysis, in which the coefficients of the common factors are all positive and the variables are more resolvable by rotation technology, is applied in the current study.

To determine the influence of different factors on debris flow susceptibility, the weights of these factors should be assigned first. The combined weighting method, which has the advantages of subjective and objective weighting methods, was applied to assign factors with logical weights.

The efficiency coefficient method (ECM) is a comprehensive evaluation method based on multiple factors and is suitable for complex research objects, such as debris flow. The factors can be converted into measurable scores through the appropriate function and objectively reflect the situation of the evaluation object in the case of a large difference in the factor value. This research primarily focuses on the method, which is applied to the debris flow susceptibility evaluation based on the results of the weight analysis.

Debris flow classification plays a direct guiding role in disaster prevention and mitigation, and mature classification methods have been developed (Iverson et al., 1997; Brayshaw and Hassan, 2009). However, a single classification standard cannot fully and accurately reflect the
comprehensive characteristics of debris flow ditches, and based on different
classification criteria, the same debris flow will belong to different types
at the same time. The fuzzy

In recent years, with the improvement of computer performance and the advanced features in geographic information systems (GISs), global positioning systems (GPSs) and remote-sensing (RS) techniques, these systems, also known as “3S technology”, have become very effective and useful especially to debris flow research (Gómez and Kavzoglu, 2004; Glade, 2005; Conway et al., 2010). In particular, the application of GISs has greatly improved the ability of spatial data processing and analysis, such as slope direction analysis and flow direction calculation (Mhaske and Choudhury, 2010; Xu et al., 2013; Kritikos and Davies, 2015). Therefore, the FA, FCM and ECM were used to classify and evaluate the susceptibility of debris flow in the current study, being combined with 3S technology and field investigation.

The research area is located around several scenic spots in Huangsongyu Township, Pinggu District, Beijing. The village covers an area of 12.83 km

The study area is located in the northwest of the North China Plain, which belongs to the Yanshan. Surrounded by high terrain, the central part
is flat, the highest elevation of the territory is 1188 m and the lowest
elevation is 174 m. The Yanshanian and Indosinian periods in the study area were characterised by strong tectonic activity, which resulted in a series of
large fold and fault structures. Due to long-term geological processes, the
structure in the area is relatively complex. But the strata are relatively
simple, except for a few Archean metamorphic rocks; the exposed strata are
middle Proterozoic sedimentary strata and Quaternary sediments. The main
lithology of the Archean age (Ar) is amphibious plagiarise gneiss and biotite gneiss. The Great Wall System (Ch) is the broadest strata in this area, and the main lithology is dark gray ferric dolomite, silicalite micritic dolomite and dolomite sandstone. The main lithology of the Jixian System (

Average monthly rainfall data (from 1959 to 2017) for Pinggu District.

Geographical positions of the Huangsongyu scenic region and the investigated 21 debris flow catchments.

The study area is characterised by a northern temperate continental climate,
with four distinct seasons and large annual temperature variation. The
coldest average January temperature is 6–8

Shilin Gorge scenic spot.

Huangsongyu National Mining Park.

Lishu scenic spot.

The fuzzy

The membership matrix

For calculating clustering centres

For determining the number of clustering centres, the clustering number

Based on this, the clustering effectiveness

Calculating the value function

The operation is stopped when

Calculating the new matrix

A flowchart of FCM.

FA is a multivariate statistical analysis method which studies the internal dependence of variables and reduces some variables with intricate relations to a few comprehensive factors (Li et al., 2016). FA is the
inferred decomposition of observed data into two matrices. One matrix represents a set of underlying unobserved characteristics of the subject which give rise to the observed characteristics and the other explains the
relationship between the unobserved and observed characteristics (Tolkoff et al., 2018). The mathematical formula can be expressed as follows:

The main calculation steps of the factor analysis method can be divided into six steps (Fig. 7).

A flowchart of FA.

Considering the defects of the current method for determining the weight of factors, the combination of a analytic hierarchy process and factor analysis method is used to determine the weight of each influencing factor of debris flow.

The random average consistency index.

Definition of comparative importance.

The AHP was first proposed by Saaty (1978), a famous American mathematician. It decomposes the factors related to decision-making into multiple layers, such as the target layer, criterion layer and scheme layer. The AHP is a subjective weighting method and has obvious advantages in determining the weight of each factor. The
specific steps are as follows.

Factors frequently used in susceptibility analysis of debris flow.

The weight value obtained by the AHP is set as

Based on the principle of multi-objective programming, the efficiency
coefficient method transforms each factor into a measurable evaluation score
through the efficiency function and combines the weight of factors to make
a comprehensive evaluation. The specific steps are as follows.

Select the evaluation factors.

Determine the satisfactory value and the unallowable value: the satisfactory value is a value based on years of experience, while the unallowable value is the lowest or highest acceptable value of the evaluation index.

Calculate the single efficacy coefficient. The single efficacy coefficient was calculated by the corresponding efficacy function based on the sensitivity of each factor. It is mainly divided into three variables: the extremely large variable (the higher the factor, the higher the efficiency coefficient), the infinitesimal variable (the smaller the index value, the larger the efficiency coefficient value) and the interval variable (the value reaches its highest in a certain interval). The specific formula is as follows:

The infinitesimal variable is calculated as follows:

Calculating the total efficiency coefficient,

The flowchart for the method used for our classification and susceptibility analysis is shown in Fig. 8.

Flowchart used for classification and susceptibility assessment.

The values for the 13 factors of the 21 debris flow catchments.

The topographical, geological and climatic factors play a critical role in
the distribution and activities of debris flows (Di et al., 2008). Table 3 shows the influencing factors selected by research in debris flow susceptibility assessment in recent years. Rainfall is one of the most pivotal external factors inducing debris flow disasters, but the
meteorological data in our area are all from the same station, which cannot
reflect the differences between each catchment. Therefore, rainfall was not
included in this study. In addition, the frequency of debris flow and the
size of soil particles are difficult to obtain accurately. The loose-material volume reflects the lithological characteristics and fault length
to some extent, so lithology and fault length were not taken into account.
The basin area, main channel length, drainage density, average slope angle,
average gradient of the main channel, vegetation coverage, maximum elevation
difference and curvature of the main channel, which were cited and available, were selected in this paper. As source conditions, the loose-material volume and the loose-material supply length ratio were also considered. As the study area is located in a tourist area with a relatively dense population, population density is selected as the factor of human activities. A total of 13 influencing factors were selected based on the previous research findings to reflect the characteristics of the watershed. All these factors were acquired in our field survey or calculated in ArcGIS, as described below.

The curve of the clustering effectiveness index

Clustering validity function

Thus 21 debris flow catchments in the study area are divided into four categories. The data of each catchment belonging to the same category have a certain internal similarity and vary greatly among different categories. In other words, data of different influencing factors have different effects on different types of debris flows, which provide a favourable basis for us to analyse the main influencing factors of debris flows, and also point out the direction for monitoring and prevention of debris flows.

Based on the clustering results of 21 debris flow catchments, FA was used to analyse each type of debris flow. Tables 6–9 are the results of the first, second, third and fourth categories, respectively.

Clustering results of 21 debris flow catchments.

As shown in Table 2, in the first category, the accumulative contribution rate of the first three factors (C1–C3) reaches 86.40 %, which retains most information of the 13 original variables. For the first group, the load values of the main factors 1–3 are relatively large in the basin area, the highest volume of one flow, the maximum elevation difference, the main channel length and curvature of the main channel, and population density and drainage density. Similarly, in the second type, the load values of the main factors 1–3 are relatively large in the basin area, the main channel length and population density, loose-material volume and drainage density, and maximum elevation difference. In the third category, the load values of the main factors 1–3 are relatively large in the basin area, main channel length, the highest volume of one flow, loose-material volume, and the loose-material supply length ratio and vegetation coverage. In the fourth category, the load values of the main factors 1–3 are relatively large in main channel length, drainage density, loose-material volume, the highest volume of one flow, and the loose-material supply length ratio and population density.

The factor-loading matrix after rotation and contribution ratios for the first category.

Among the 13 factors, the basin area and the highest volume of one flow reflect the scale of debris flow eruption. The main channel length, drainage density, average gradient of the main channel, the average slope, maximum elevation difference, curvature of the main channel and roundness reflect the topographical condition. The loose-material volume and the loose-material supply length ratio are the material sources for debris flow. Vegetation coverage reflects the geomorphologic condition. Population density reflects the impact of human activities on nature to some extent. Therefore, four types of debris flows can be named according to the results of the FCM and FA.

The factor-loading matrix after rotation and contribution ratios for the second category.

The first category can be defined as debris flow closely related to scale–topography–human activities. Considering the situation, monitoring and control of basic material sources is recommended. Similarly, the second, third and fourth categories can be defined as topography–human activities–provenance, scale–provenance–topography and topography–scale–provenance–human activities, respectively. In the same way, corresponding prevention measures can be proposed according to the characteristics of each type of debris flow.

The factor-loading matrix after rotation and contribution ratios for the third category.

Based on the FA of each category of debris flow in the previous section, the main influencing factors were obtained. However, the repeatability of evaluation information should be reduced. Average slope angle and average gradient of the main channel are both indicators of potential energy, so the average gradient of the main channel is omitted. Similarly, curvature of the main channel, the loose-material supply length ratio and roundness were omitted. Thus nine factors, including basin area (F1), main channel length (F2), drainage density (F3), average slope angle (F5), maximum elevation difference (F6), the loose-material volume (F8), vegetation coverage (F10), population density (F11) and the highest volume of one flow (F13) were selected. On the other hand, a reduction in the number of indicators facilitates the allocation of weight values.

The factor-loading matrix after rotation and contribution ratios for the fourth category.

Hierarchical structure for debris flow susceptibility analysis.

The AHP was applied to calculate the subjective weight in this paper. The hierarchical structure (Fig. 10) was constructed,
and the 1–9 scale method was used to grade each factor. The judgement
matrices

Comparison matrix elements for geology condition.

CR

Comparison matrix elements of the criterion level factors.

CR

The weighted values of the factors obtained by AHP.

FA was applied to calculate the objective weight in this paper. The weight values of each factor are shown in Table 13.

Tree diagram obtained by hierarchical clustering.

The weighted values of the factors obtained by factor analysis.

The combined weighted values of the factors.

After the subjective weight and objective weight are obtained, the respective distribution coefficients are solved according to Eq. (1), and the final combined weight values of each factor are shown in Table 14:

Among the nine factors, basin area, main channel length, drainage density, maximum elevation difference, the loose-material volume, the highest volume of one flow and population density are all extremely large variables. Vegetation coverage is the infinitesimal variable. The average slope angle is an interval variable. Table 15 shows the efficacy coefficient scores of 21 debris flow catchments after being combined with the weight calculation.

The efficacy coefficient scores of 21 debris flow catchments.

Taking the total efficiency coefficient of each catchment as the evaluation standard (the larger the value, the higher the possibility of debris flow), the FCM was conducted for 21 debris flow catchments in the study area. The result showed that the susceptibility of debris flow was divided into three grades: high (H), moderate (m) and low (L). Combined with the classification of each debris flow mentioned above, the final results are shown in Table 16.

The qualitative description and susceptibility class for each debris flow catchment.

As shown in Table 16, susceptibility for the 10th and 13th catchments was high, and both of them belong to the debris flow with a close relationship between topography, human activities and provenance. Susceptibility for six catchments, including the 1st, 4th, 6th, 17th, 20th and 21st, was medium. The other 13 had low susceptibility.

Normative scoring, the

Based on the field investigation, the 10th catchment is located in Huangsongyu National Mining Park, where a large amount of slag accumulated. With low vegetation coverage and steep terrain, the gully was in its prime, which directly threatened the safety of villagers and tourists. What is more, there are several warning boards for natural disasters and corresponding monitoring equipment in the scenic spot (as shown in Fig. 5). The 13th catchment is located in the Lishugou village scenic spot. Part of the pedestrian passageway was built, but a lot of stones were piled up in the trench and the road was broken and steep (as shown in Fig. 6). However, there is no obvious accumulation of loose materials in the catchments with low susceptibility. The gully was in its old stage, with high vegetation coverage and little human interference. The quantitative comprehensive evaluation results of debris flow susceptibility are shown in Table 17, which are divided into two levels: low (L) and moderate (M). Among them, the susceptibility levels of the 10th and the 13th catchments were moderate and the others were low.

Comparison of susceptibility analyses based on different algorithms.

The

The accuracy of the debris flow classification directly affects the development of prevention and control measures. Based on different criteria,
such as genetic classification, occurrence frequency and material composition, the same debris flow can belong to multiple categories at the same time, which does not reasonably reflect its multiple characteristics. In addition, the traditional classification standard has some hysteresis to prevent debris flow. Considering that different types of debris flow have different
main influencing factors, the FCM and FA were combined in this study to refine and summarise the importance of various factors to improve the accuracy of the classification. The FCM is different from traditional rigid
division, and it is based on the distance function to calculate the maximum
correlation between the same kind of data and the minimum correlation between different kinds of data (Eke et al., 2019). The clustering effectiveness

The reasonable selection of evaluation factors is the premise of accurate evaluation of debris flow susceptibility. In this paper, 13 factors were preliminarily selected based on previous experience and field investigation conditions. Secondary screening was carried out based on FA analysis results, which enhanced the rationality of the screening. The determination of the factor weight is crucial to accurately evaluating the susceptibility of the debris flow (Zhang et al., 2013). FA is a common objective evaluation method in statistical analysis that determines the weight of factors according to the internal correlation and patterns of data. However, the objective method cannot reflect the relative significance of each influencing factor and may create misleading information. The AHP can make full use of expert experience and achievements in the corresponding fields to evaluate the influencing factors, which is a subjective method. However, different researchers have different preferences for major factors, which have a negative impact on the results. Therefore, combination weighting, which combines the advantages of the FA and AHP, is superior to the other methods alone when trying to obtain a more scientific and reasonable evaluation result.

The efficiency coefficient method is different from other evaluation systems. By determining the satisfactory value of each factor as the upper limit and the unallowable value as the lower limit, the satisfaction degree is calculated through the corresponding efficiency function, and the final comprehensive score was obtained based on the weight evaluation. This method
not only considers the relative importance of different factors but also
determines the value based on the susceptibility to debris flow. Therefore,
the efficiency coefficient method can objectively evaluate complicated
research objects, such as debris flow, with this form of classification that
conforms to logical thinking. However, the evaluation method adopted in this paper also has limitations: (1) fuzzy

Classification and susceptibility analysis are of great significance for the early warning and prevention of debris flow. Based on field investigation and 3S technology, an improved FCM and FA method were used to establish the classification model and obtain the main influencing factors of different types of debris flow in the current study. The ECM was used for the susceptibility analysis based on the combination weights of major factors.

In this paper, 21 debris flow catchments in Beijing were divided into four categories. Nine major factors screened from the classification results were determined
for susceptibility analysis using both the ECM and combination weighting,
and the susceptibility assessment was divided into three levels, which have been
validated with normative scoring, the

The data used to support the findings of this study are included within the article.

ZL was responsible for the writing and graphic production of the paper. CW was responsible for the revision of the paper. SH was responsible for part of the calculations. KUJK was responsible for the translation. YL was responsible for the reference proofreading.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Resilience to risks in built environments”. It is not associated with a conference.

This work was supported by the National Natural Science Foundation of China (grant nos. 4197020250 and 41572257).

This research has been supported by the National Natural Science Foundation of China (grant nos. 41572257 and 4197020250).

This paper was edited by Mattia Leone and reviewed by Daniele Masi and one anonymous referee.