Keywords

1 Introduction

As a result of the rapid urbanization occurring in the northern mountainous regions of Vietnam, long-term territorial planning and sustainable development of residential areas are essential tasks. The expansion of urban areas and agricultural land coincides with the decrease in natural forest areas, resulting in an increase in the probability of natural disasters (Nguyen et al. 2019). Sediment-related disasters, such as landslides, have attracted a great deal of attention from researchers in Vietnam and worldwide due to their diversity in magnitude, morphological characteristics, and severity of damage (Biswas et al. 2022; Sim et al. 2022).

Numerous qualitative (Dahl et al. 2010; Wang et al. 2013), quantitative (Ma et al. 2020; Ou et al. 2021), and semi-quantitative (Guillen et al. 2022) landslide susceptibility assessments have been conducted at various spatial scales. The main goal of landslide susceptibility assessments is to identify areas with the highest landslide potential based on an inventory of past landslide events and associated factors. When identifying landslide susceptibility zones, statistical models have demonstrated their simplicity and prediction efficiency, and consequently, they have been extensively utilized worldwide (Juliev et al. 2019; Ram et al. 2020).

Using the Statistical Index (SI) and Fractal-Statistical Index (FSI) models, landslide susceptibility assessments were conducted in Muong Khoa commune, Bac Yen district, Son La province, Vietnam. The analysis results demonstrated that the FSI model provided greater prediction efficacy, and this model is prospective for use in landslide studies in other regions of Vietnam.

2 Study Area

Similar to other “hot spots” for landslides in the Northwest area of Vietnam (Thanh Thi Pham et al. 2020), the mountainous terrain, tropical climate, geological conditions, and human activity in Son La province have all contributed to the significant number of landslides (1689 events) (Bui et al. 2022). Bac Yen district, located in the eastern portion of Son La province, is distinguished by highly complicated topographical characteristics. In the Bac Yen district, a high frequency of landslide and debris flow occurrences has been documented, accompanied by severe consequences. The results of a field survey and statistical analysis in the Bac Yen district have identified seven areas with a high density of landslides, including Muong Khoa commune (VIGMR 2014). Muong Khoa (84.16 km2) is a mountainous commune in the western portion of the Bac Yen district with elevations between 115 and 1563 m (Fig. 1). The landslide process that was documented in this area mostly developed in the weathering crust formed from the rocks of the Ban Cai Formation (D3bc), the Da Nieng Formation (C1đn), and the Vien Nam Formation (T1vn). Rainfall is the main trigger of landslide events, while human activity, weathering crust, vegetation cover, etc. are considered conditioning factors.

Fig. 1
Three maps. 1. The map marks Muong Khoa in the northern part of Vietnam. Laos and China are also marked. 2. A map marks the Muong Khoa Commune and the Bac Yen district. 3. A heat map marks landslides and elevation in meters. Landslides are more in the northern areas.

Location of study area

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The landslide event (Fig. 2) occurred on Highway 37 near the Muong Khoa market in the Muong Khoa commune of the Bac Yen district. There were no fatalities caused by the landslide, but three houses were completely devastated. The sliding mass has an estimated size of 80 by 160 m and occurred in a 10- to 15-meter-thick weathering crust. The landslide was first triggered in early 2020 and reactivated in September 2022 due to a prolonged rain event. The field survey results determined that the landslide was triggered by heavy accumulated rainfall and formed in a thick weathering crust on terrain with a high slope gradient caused by human construction activities.

Fig. 2
Two photos banking one side of a road, each of which depicts a stretch of a mound with vegetation growing on it, . The lower portions of the mounds are slightly caved in.

Photos of landslide event in the study area. Photo by T. K. Nguyen

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3 Landslide Susceptibility Assessment Using the Statistical Index and Fractal-Statistical Index Methods

3.1 Methods

Developed by Van Westen (1997), the statistical index model has proven effective for quantitatively assessing the potential for landslides in various regions around the globe (Rai et al. 2022; Wang et al. 2016). The class weight (WSI) values of causative factors are determined using the following formula based on the distribution of landslides within the factor classes:

$$ {W}_{SI}= Ln\left(\raisebox{1ex}{${D}_{LS i}$}\!\left/ \!\raisebox{-1ex}{${D}_{LS}$}\right.\right) $$
(1)

where: DLSi is the landslide density in the ith factor class and DLS is the landslide density in the study area. Positive WSI values represent areas with significant landslide potential, while negative WSI values represent areas with low landslide density. The value WSI = −1 is assigned to the factor class due to the lack of landslide distribution (Zhang et al. 2016).

Because the statistical index method only provides information on the class weight values of the causative factors, fractal analysis was utilized to quantify the contribution of each causative factor in the development of the landslide process in the study area. Since being introduced by Mandelbrot (1967), the fractal theory has been successfully used in studies to determine the geometrical features of landslides (Pourghasemi et al. 2014) and predict the spatial distribution of landslides (Liu et al. 2019; Zhao et al. 2021). The fractal theory expresses the variation in fractal dimension D as a function of the linear scale (r) (Liu et al. 2019):

$$ D=f(r) $$
(2)

Rouai and Jaaidi (2003), based on their analysis, concluded that the distribution of landslides is characterized by a heterogeneous fractal structure. Therefore, the variable dimension fractal method (VDFM) was utilized to determine the D value for the causative factors based on the relative density of landslides (Hu et al. 2020). The factor weight (Wi) value of each causative factor is calculated using the following formula:

$$ {W}_i=\raisebox{1ex}{${D}_i$}\!\left/ \!\raisebox{-1ex}{${\sum}_{i=1}^n{D}_i$}\right. $$
(3)

Finally, the formula [4] is used to determine the landslide susceptibility index (LSI) value:

$$ LSI=\sum {W}_{SI}\times {W}_i $$
(4)

3.2 Spatial Relationship Between Conditioning Factors and Landslide Distribution

The landslide inventory map in this study was established using aerial photography and field survey data. A total of sixty landslide sites were identified, with estimated volumes ranging from 8.75 m3 to 21,000 m3 (Fig. 3). According to statistical analysis results, 34 landslides have a mass volume of less than 200 m3, 22 sliding masses have a mass volume between 200 and 1000 m3, and the remaining four landslides range in mass volume from 1000 to 21,000 m3. The volume of small sliding masses accounts for only 7.74% of the total landslide volume in the study area, while the remaining 22 and four landslides account for 20.74 and 71.52%, respectively. All sixty landslides were used to build landslide susceptibility models for the study area.

Fig. 3
A graph presents the landslide volume statistics. The data are as follows. Number of landslides 60, average 647.81 cubic meters, standard deviation 2727.16 cubic meters, minimum 8.75 cubic meters, maximum 21000 cubic meters, and sum 38868.5 cubic meters.

Landslide volume statistics in the study area

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For mapping landslide susceptibility in the study area, eight causative factors, including elevation, distance to roads, slope, distance to geological boundaries, distance to faults, land use, slope aspect, and distance to drainage, were selected in this study. The EarthData database (https://www.earthdata.nasa.gov) was first accessed to download the open-access global ASTER DEM (30-meter resolution). Afterward, DEM-derived factor maps, including elevation (Fig. 4a), slope (Fig. 5a), slope aspect (Fig. 7a), and distance to drainage (Fig. 7b), were prepared in ArcGIS 10.5. The relationship between these factor maps and past landslides was then analyzed by subdividing them into subclasses. The map of distance to roads (Fig. 4b) was produced in ArcGIS using OpenStreetMap data downloaded from the Geofabrik database (https://download.geofabrik.de) and then divided into six subclasses. The Vietnam Institute of Geosciences and Mineral Resources (VIGMR) provided the data employed to prepare maps displaying the distance to geological boundaries (Fig. 5b) and faults (Fig. 6a). In this study, land use classification was performed in ERDAS 2015 using Landsat 8 Operational Land Imager (OLI) (Date Acquired: 10/15/2022, Path 128, Row 45), and the study territory was divided into water, urban area, forest, shrubland, agricultural land, bare land, and river bed (Fig. 6b). The results of the analysis of the relationship between landslide distribution and causative factors using the SI method are shown in Table 1.

Fig. 4
Two heat maps of Muong Khoa a and b. Map A marks the elevation in meters from less than 300 to more than 1100, and landslides. The western regions depict an elevation greater than 1100, and a high occurrence of landslides. Map b marks the distance to roads in meters from 0 to greater than 500.

(a) Elevation map and (b) map of distance to roads

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Fig. 5
Two maps. A marks the slope in degrees from 0 to greater than 45, and landslides. The northeastern border depicts 0 to 10. Map b marks the distance to geological boundaries in meters from 0 to greater than 500, and landslides. Most of the regions depict greater than 500.

(a) Slope map and (b) map of distance to geological boundaries

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Fig. 6
Two maps. Map A marks the distance to faults in meters from 0 to greater than 2500, and landslides. Most of western regions depict greater than 2500 meters. Map B marks the landslide, forest, water, bare land, river bed, shrubland, urban area, and agricultural land.

(a) Map of distance to faults and (b) land use map

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Table 1 Analysis of the relationship between landslide distribution and causative factor using SI method
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3.3 Results of Landslide Susceptibility Assessment Using Statistical Index and Fractal-Statistical Index Methods

The analysis of the relationship between past landslides and causal factors (Table 1) revealed that 47% of landslides occurred in areas below 500 m in elevation. Less than 100 m from roads is associated with a significant frequency of landslides. This result indicates that construction activities in the study area have increased the likelihood of landslides. Therefore, landslides occurred frequently in areas with slopes between 10 and 30°. The highest WSI values were determined for urban areas, agricultural land, and bare land. This distribution highlights the significance of vegetation cover and the influence of human activities on the development of landslides in the study area. The highest frequency of landslides was recorded on the east, south, and southwest slope aspects. Due to the correlation between the drainage system and the degree of saturation of the slope material, landslides occurred frequently within 300 m of the drainage system. The landslide process in the study area is also related to the geological boundaries and fault system. According to Table 2, fractal analysis results showed that the distance to drainage is the most significant factor in the landslide process in the study area (Fig. 7).

Table 2 Calculated factor weights based on fractal analysis
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Fig. 7
Two maps. Map A marks the slope aspect and includes the north, east, south, west, northwest, northeast, southeast, and southwest, and landslides. Map B depicts the distance to drainage in meters from 0 to greater than 500, and landslides. Most of the regions are 0 to 100 meters.

(a) Slope aspect map and (b) map of distance to drainage

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Figures 8 and 9 show the LSZ maps and the distribution of susceptibility zones in the Muong Khoa commune. As depicted in Fig. 9a, 18.92% of the study area was predicted to be a very low (VL) susceptibility zone using the FSI model. Compared to the outcome predicted by the SI model (10.11%), this result is highly significant for land use planning and residential area development. The SI model predicted a higher percentage of low (L), moderate (M) and high (H) susceptibility zones, whereas the FSI model indicated that 19.42% of the study area was classified as a very high (VH) susceptibility zone, which is 6.32% larger than the SI model. The model efficiency is evaluated based on the number (area) of predicted landslides, especially in the VH zone. Figure 9b reveals that 58.33% of landslides were predicted in the VH zone, compared to 48.33% predicted by the SI model. This outcome proved the effectiveness of the FSI model in this study when compared to the SI model.

Fig. 8
Two maps. Maps A and B mark the landslide susceptibility zonation as low, high, very low, moderate, very high, and water and landslides using the S I model and the F S I model, respectively. The eastern boundary depicts water.

LSZ map using (a) SI and (b) FSI models

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Fig. 9
Two maps A and B. A, a dual bar graph presents the area percentage of landslide susceptibility zones for S I and F S I models. Moderate in S I reads the highest at 29.71, and high in F S I reads the highest at 22.94. B, presents the predicted landslide percentage for the S I and F S I models. Very high reads the highest under both.

(a) Area percentage of landslide susceptibility zones and (b) predicted landslide percentage using SI and FSI models

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The prediction model’s performance was evaluated using the ROC method (Swets 1986), and the ROC curves are displayed in Fig. 10. All the AUC values for the models are greater than 70%, indicating that the models have good performance and are suitable for assessing the spatial distribution of landslides in the study area. Because fractal analysis evaluated the role of each factor in the landslide process, the FSI model provided better performance. Future studies can improve the performance of the FSI model with improved input data quality and an up-to-date landslide inventory map.

Fig. 10
A graph of sensitivity versus 1 specificity plots two graphs for A U C S I equals 71.18%and A U C F S I equals 75.18%. Both curves depict increasing trends.

ROC curves of landslide susceptibility models

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4 Conclusions

Bivariate statistical methods have been extensively utilized in landslide studies because of their efficiency and simplicity. This study employed an integration (FSI) of the Fractal method and the Statistical Index method to enhance the efficacy of assessing the potential for landslide development in Muong Khoa commune, Bac Yen district, Son La province. Statistical analyses were conducted to determine the class weight of each causal factor, whereas the factor weight values were calculated using the fractal method. A higher AUC value indicates that the FSI model improved the accuracy of the landslide susceptibility zonation maps, as demonstrated by the conducted analyses. Simultaneously, the FSI model predicted a larger area with very low landslide susceptibility, providing a significant base for territorial planning and land use management. Consequently, the fractal method can be combined with other statistical methods to produce highly accurate prediction models. In addition, the methodologies and results of this study can be employed in landslide studies in other areas of Vietnam.