Landslide Susceptibility Mapping Considering Time-Varying Factors Based on Different Models

Abstract

The selection of hazard factors is an important factor affecting the accuracy of landslide susceptibility mapping (LSM). The systematic development of an integrated input framework, incorporating both static and time-varying factors, as well as comparative studies of different input frameworks, remains at a preliminary stage. The degree of fit between each data-driven method and landslide-prone environment cannot be known in advance, so the best modeling method can only be determined through comparative studies. Therefore, the Pearson correlation coefficient method and collinearity diagnostics were used to screen the hazard factors, and three hazard factor combinations, considering both static and time-varying factors, were established. A total of 4498 landslide grids and 4498 non-landslide grids were determined, among which 70% (3149 landslide grids and 3149 non-landslide grids) were training samples, and the remaining 30% (1349 landslide grids and 1349 non-landslide grids) were verification samples. The three combinations were input to five models (Support Vector Machine, Random Forest, Convolutional Neural Network-Random Forest, Convolutional Neural Network-Support Vector Machine and Deep Belief Network-Multilayer Perceptron). The results show that the LSM results of different combinations and models are quite varied, and the combination No.3 and the Deep Belief Network-Multilayer Perceptron are the best. The study area is divided into extremely low susceptible areas, low susceptible areas, medium susceptible areas, high susceptible areas and extremely high susceptible areas, and the extremely high susceptible areas mainly distribute in the northwest, south and east. The other models overestimate the distance from the fault and underestimate the distance from the road. The extreme tendency of LSM results of the combinations No.1 and No.2 are strong, and they are easy to produce error estimation areas, which overestimate the elevation and underestimate the distance from the river. The LSM results of the Convolutional Neural Network-Support Vector Machine are closer to those of the benchmark, which underestimates the distance from the road and overestimates the distance from the fault. This study selected the best combination and model through comparative studies and revealed the degree of influence of each hazard factor on landslide susceptibility, greatly improving LSM accuracy, which can provide a scientific basis for land use planning.

1. Introduction

Landslides are defined as the downward movement of rock and soil masses, either intact or disrupted, along a weak surface or zone under gravitational influence [1]. According to the China Institute for Geo-Environmental Monitoring, 5659 geological disasters were recorded in 2022, causing more than 140 casualties and economic losses exceeding 1.5 billion yuan. Among these, landslides numbered 3919, accounting for 69.25% of the total occurrences [2]. Landslide susceptibility mapping (LSM) quantifies the spatial probability of landslide occurrence and classifies the study area into different susceptible levels, thereby providing a scientific basis for land-use planning and landslide risk mitigation policies [3,4].

The factors governing landslide susceptibility encompass both static and time-varying (dynamic) elements, with the latter inducing dynamic spatial-temporal shifts in susceptibility distributions [5]. Some studies in LSM consider only static factors or treat time-varying factors as constants, while other studies have analyzed the relationship between time-varying factors and landslide susceptibility [6]. However, due to the highly complex mechanisms through which time-varying factors influence landslide susceptibility, the systematic development of an input framework for landslide susceptibility assessment that incorporates both static and time-varying factors, as well as comparative studies of different input frameworks, remains in its early stages [7]. Soma and Kubota [8] applied frequency ratio and Logistic regression methods to demonstrate that land-use changes reduce slope stability and elevate landslide likelihood. Alberto et al. [9] integrated land-use change and Normalized Difference Vegetative Index (NDVI) variation to assess landslide susceptibility, reporting peak landslide probability 5–7 years after human disturbances such as deforestation. Jin et al. [10] combined static and dynamic factors to produce time-sensitive susceptibility maps, noting improved predictive performance and enhanced spatial alignment with observed landslide patterns when dynamic variables were incorporated. Francis and Bryson [11] introduced a novel workflow for dynamic susceptibility and forecastable hazard analysis in eastern Kentucky, integrating static geomorphic parameters with temporally varying vegetation data. Lamichhane et al. [12] generated multi-temporal susceptibility maps (1995–2020) that accounted for urbanization trends and climatic variations, highlighting the combined influence of static and dynamic factors on landslide prediction. Jia et al. [13] developed input datasets using twelve continuous and three discrete factors, combined through two distinct connection methods. Their findings emphasized the importance of accounting for the varying data characteristics and selecting suitable environmental factor integration strategies to enhance the accuracy of LSM. Similarly, He et al. [14] constructed an interpretable machine learning model to examine changes in landslide susceptibility and their underlying driving mechanisms amid urbanization between 2000 and 2020. The results demonstrated that urbanization elevated landslide susceptibility and underscored the value of employing interpretable machine-learning approaches to elucidate this relationship.

LSM approaches can be broadly categorized into two groups: deterministic and data-driven methods, the latter of which includes statistical, shallow learning and deep learning models [15,16]. A defining strength of deep learning models lies in their capacity for automated feature extraction. These automatically learned features generally offer greater representational power and robustness compared to manually engineered ones, underscoring that feature learning is central to deep learning methodologies [17,18]. Deep neural networks, constructed through stacked layers of nonlinear transformations, provide the foundational architecture for deep learning and have shown significant promise for LSM [19]. Youssef et al. [20] applied Support Vector Machine (SVM), 1D-Convolutional Neural Network (1D-CNN) and 2D-CNN to LSM in Saudi Arabia’s Asir Region. Their results indicated that the CNN-based models outperformed SVM, with 1D-CNN and 2D-CNN achieving accuracy improvements of 4.9% and 7.9%, respectively, while 2D-CNN surpassed 1D-CNN by 3.5%. Ge et al. [21] compared five deep learning architectures (AlexNet, Inception-v3, Xception, ResNet-101 and DenseNet-201) with two conventional models (SVM and Artificial Neural Network (ANN)) in a study along a transmission line corridor. Deep learning models attained high area-under-the-curve (AUC) values and demonstrated superior predictive accuracy and capability for deep feature extraction. Wang et al. [22] introduced a CNN model for LSM and assessed it against the Classification and Regression Trees (CART) and Multilayer Perceptron (MLP) using the Receiver Operating Characteristic (ROC) analysis. The CNN consistently outperformed both traditional models, with MLP ranking second and CART least effective. Bhattacharya et al. [23] also reported the advantage of deep learning in the Chamoli District of India, where the Deep Learning Neural Network (DLNN) achieved higher predictive performance compared to Random Forest (RF) and ANN. Similarly, Zhang et al. [24] introduced a novel multi-classification machine learning framework for LSM, designed to address the limitations inherent in conventional binary classification models. Experiments conducted in Lvliang City, Shanxi Province, employing eight machine learning algorithms, showed that the multi-classification approach achieved superior performance compared to binary modeling, with an average improvement of 6.71% in predictive accuracy.

Different regions are characterized by distinct geological, topographic and hydrological conditions, leading to variations in landslide types, triggering mechanisms and evolutionary processes [25,26]. LSM methods also differ substantially in their logical frameworks and mathematical underpinnings. The compatibility between a landslide-prone environment and a specific modeling approach cannot be predetermined and must be evaluated through comparative analysis [27,28]. Owing to the complex mechanisms by which time-varying factors influence landslide susceptibility, the systematic development of an integrated input framework, incorporating both static and time-varying factors, as well as comparative studies of different input frameworks, remains at a preliminary stage [29]. In this study, landslide hazard factors were selected by correlation analysis and collinearity diagnostics. A total of 4498 landslide grids and 4498 non-landslide grids were used to construct training and verification datasets. Three hazard factor combinations were formulated based on the information value method: (1) static factors + values of time-varying factors in 2021, (2) static factors + annual values of time-varying factors, (3) static factors + interannual variation values of time-varying factors. These combinations were fed into five predictive models: SVM, RF, CNN-RF, CNN-SVM and Deep Belief Network (DBN)-MLP. The combination and model yielding the highest accuracy were identified, and the study area was classified into five susceptible levels. The resulting LSM outputs from different combinations and models were compared, and the influence of selected hazard factors on landslide susceptibility was examined. The methodological workflow is shown in Figure 1.

2. Study Area and Data

2.1. Overview of the Study Area

The study area is Boshan District, Zibo City, Shandong Province, China, ranging from 117°43′ E to 118°42′ E and 36°16′ N to 36°31′ N. It extends approximately 20.0 km from east to west and 49.4 km from north to south, covering a total area of 698.2 km², as shown in Figure 2. Boshan District experiences a typical warm temperate semi-humid continental monsoon climate. From 1951 to 2023, precipitation ranged from 304.6 mm to 1853.1 mm, with a mean of 726.5 mm. Precipitation is unevenly distributed throughout the year, with 60%–70% concentrated between June and August. Intense summer rainfall serves as a major triggering factor for landslides, debris flows, and flash floods [30].

Boshan District lies on the southeastern margin of the North China Plate (Craton), specifically on the northern flank of the Luxi Uplift (Central Shandong Uplift), adjacent to the western side of the prominent Yishu Fault Zone (the Shandong segment of the Tanlu Fault Zone) [31], characterized by typical tectonic-erosion low mountain and hilly terrain. The topography slopes from higher elevations in the south to lower elevations in the north. Major geomorphological units include [32]:

(1)

Southern low-middle mountain area: the northern extension of the Lu Mountain range, featuring steep slopes and deeply incised valleys dominated by tectonic erosion landforms and Karst topography.

(2)

Central hilly valley area: Centered on the belt-shaped valley formed by the Xiaofu River and its tributaries, consisting of river terraces, alluvial fans, and denudational hills.

(3)

Northern gentle hill-plain area: Composed mainly of denudation-accumulation hills and piedmont alluvial-proluvial plains, with elevations generally below 200 m.

The stratigraphic sequence in Boshan District is relatively complete, ranging from ancient basement rocks to Cenozoic unconsolidated sediments [33], as shown in

Table 1. Geological and lithological characteristics of the study area.

Eon	Era	Period	Lithology
Archean			Taishan group: composed of high-grade metamorphic rocks such as gneiss and amphibolite.
Phanerozoic	Paleozoic	Cambrian	Lower part: purple-red shale and sandstone (Mantou formation); Middle to upper part: thick-bedded oolitic limestone, edgewise limestone and shale (Zhangxia formation, Chaomidian formation).
		Ordovician	Majiagou formation: thick-bedded pure limestone and dolomitic limestone, interbedded with thin layers of shale.
		Carboniferous-Permian	Benxi formation/Taiyuan formation: a paralic coal-bearing sequence consisting of sandstone, shale, limestone and multiple coal seams; Shanxi formation/Shihezi formation: continental sandstone and shale containing coal seams.
	Mesozoic		Jurassic sandstone and shale (Fangzi formation).
	Cenozoic	Paleogene	Conglomerate and sandstone (Guanzhuang group).
		Quaternary	Loess, fluvial gravels and alluvial-proluvial clay.

.

Key structural features in Boshan District include folds and faults. The fold axes are generally oriented NNE, with the core structure being the Boshan Syncline, whose axis roughly follows the Xiaofu River valley. The western branch of the Yishu Fault Zone is a regional-scale fracture whose intense activity profoundly influences crustal stability, seismic activity and modern geomorphic patterns. The Boshan Fault and other secondary faults form a system of NNE- and NW-trending fractures that control the orientation of mountain ranges and valleys [34].

2.2. Data Sources

The sources and download links of the data used for landslide susceptibility modeling are shown in

Table 2. Data used for landslide susceptibility modeling.

Data	Source and Download Link
Fault data of Shandong Province	Geological Professional Knowledge Service System (http://103.85.177.213:9080/mlr)
Landsat image and GDEMV3 of Boshan District	Geospatial Data Cloud (http://www.gscloud.cn/)
Road data of Boshan District	Open Street Map (OSM) (https://www.openstreetmap.org)
River data, geologic map and population density distribution of Shandong Province	Institute of Geographic Science and Natural Resource, Chinese Academy of Sciences (http://www.resdc.cn/)
Geological disaster control census data of Boshan District	Zibo Natural Resource and Plan Bureau (https://gtj.zibo.gov.cn/)

.

According to the geological disaster control census data of Boshan District released by Zibo Natural Resource and Plan Bureau, combined with the remote sensing interpretation and on-site investigation, 99 landslides were determined in the study area. On satellite imagery, notable distinctions between landslide and non-landslide areas include [35,36]:

(1)

Landform signs: incoordination between the local landform and the overall landform, sudden destruction of the continuous landform.

(2)

Morphological signs: shape and boundary of the landslide can be clearly seen, and usually manifested as a special plane shape such as ring chair type, oval type and arc type.

(3)

Tone and color signs: the color of the surface coverage changes continually. The plant coverage is bad; the color is light, and the sliding mass is well preserved.

The results show that the total volume of the landslides is 2,732,400 m³ and the total area is 0.442 km². The largest landslide is in Boshan Town, with a volume of 74,160 m³ and an area of 0.021 km². Chishang Town has the largest number of landslides (19). The landslides are shown in Figure 2 and

Table 3. Landslide overview in Boshan District.

No.	Location	Volume	Area	No.	Location	Volume	Area	No.	Location	Volume	Area	No.	Location	Volume	Area
1	Chishang Town	15,321 m3	2927 m2	26	Boshan Town	74,160 m3	21,343 m2	51	Shima Town	16,934 m3	2244 m2	76	Baita Town	34,783 m3	6375 m2
2	Chishang Town	58,763 m3	8123 m2	27	Boshan Town	27,689 m3	4522 m2	52	Shima Town	33,284 m3	5435 m2	77	Baita Town	12,093 m3	1671 m2
3	Chishang Town	37,145 m3	5390 m2	28	Boshan Town	31,543 m3	4820 m2	53	Shima Town	53,521 m3	9245 m2	78	Baita Town	26,387 m3	3886 m2
4	Chishang Town	29,542 m3	5414 m2	29	Boshan Town	15,231 m3	2803 m2	54	Shima Town	10,162 m3	1404 m2	79	Baita Town	25,896 m3	5054 m2
5	Chishang Town	16,378 m3	2075 m2	30	Boshan Town	28,347 m3	5796 m2	55	Shima Town	16,745 m3	2593 m2	80	Yucheng Town	35,027 m3	4697 m2
6	Chishang Town	18,451 m3	2857 m2	31	Boshan Town	47,965 m3	7103 m2	56	Shima Town	40,527 m3	7137 m2	81	Yucheng Town	26,765 m3	7501 m2
7	Chishang Town	26,987 m3	4661 m2	32	Boshan Town	31,876 m3	6222 m2	57	Shima Town	13,376 m3	1695 m2	82	Yucheng Town	6271 m3	1024 m2
8	Chishang Town	39,874 m3	5347 m2	33	Boshan Town	14,765 m3	1980 m2	58	Shima Town	17,031 m3	2781 m2	83	Yucheng Town	35,294 m3	6083 m2
9	Chishang Town	45,789 m3	6744 m2	34	Boshan Town	28,129 m3	4512 m2	59	Shima Town	6578 m3	1055 m2	84	Yucheng Town	11,548 m3	2011 m2
10	Chishang Town	9123 m3	1672 m2	35	Yuanquan Town	47,754 m3	8249 m2	60	Shima Town	43,796 m3	7565 m2	85	Yucheng Town	26,158 m3	3852 m2
11	Chishang Town	36,654 m3	5066 m2	36	Yuanquan Town	32,189 m3	4519 m2	61	Shima Town	22,891 m3	3213 m2	86	Yucheng Town	15,693 m3	3063 m2
12	Chishang Town	30,215 m3	4450 m2	37	Yuanquan Town	14,432 m3	2235 m2	62	Badou Town	26,897 m3	3961 m2	87	Shantou Town	5518 m3	740 m2
13	Chishang Town	15,983 m3	3119 m2	38	Yuanquan Town	7891 m3	1389 m2	63	Badou Town	26,432 m3	6525 m2	88	Shantou Town	51,327 m3	8233 m2
14	Chishang Town	48,876 m3	6555 m2	39	Yuanquan Town	17,543 m3	2223 m2	64	Badou Town	34,018 m3	4311 m2	89	Shantou Town	46,047 m3	7954 m2
15	Chishang Town	17,231 m3	2764 m2	40	Yuanquan Town	42,457 m3	6934 m2	65	Badou Town	22,654 m3	3508 m2	90	Shantou Town	25,532 m3	3022 m2
16	Chishang Town	30,678 m3	5299 m2	41	Yuanquan Town	34,198 m3	5485 m2	66	Badou Town	26,765 m3	4623 m2	91	Shantou Town	45,763 m3	6424 m2
17	Chishang Town	10,999 m3	1544 m2	42	Yuanquan Town	47,632 m3	8228 m2	67	Badou Town	16,287 m3	2286 m2	92	Shantou Town	25,936 m3	4017 m2
18	Chishang Town	39,321 m3	5435 m2	43	Yuanquan Town	17,328 m3	2432 m2	68	Badou Town	34,275 m3	5498 m2	93	Chengxi Town	35,984 m3	6337 m2
19	Chishang Town	26,897 m3	3961 m2	44	Yuanquan Town	42,768 m3	6624 m2	69	Badou Town	22,437 m3	4112 m2	94	Chengxi Town	20,432 m3	2589 m2
20	Boshan Town	30,984 m3	3926 m2	45	Yuanquan Town	23,987 m3	4224 m2	70	Badou Town	26,634 m3	3468 m2	95	Chengxi Town	25,815 m3	4216 m2
21	Boshan Town	5543 m3	1081 m2	46	Yuanquan Town	17,465 m3	2213 m2	71	Badou Town	11,145 m3	1726 m2	96	Chengxi Town	25,178 m3	5714 m2
22	Boshan Town	18,569 m3	4065 m2	47	Yuanquan Town	17,129 m3	2797 m2	72	Baita Town	14,512 m3	2555 m2	97	Chengdong Town	36,195 m3	5003 m2
23	Boshan Town	27,432 m3	3679 m2	48	Yuanquan Town	33,015 m3	6051 m2	73	Baita Town	10,218 m3	1799 m2	98	Chengdong Town	20,217 m3	2977 m2
24	Boshan Town	31,127 m3	4584 m2	49	Yuanquan Town	13,754 m3	1901 m2	74	Baita Town	38,508 m3	4880 m2	99	Chengdong Town	15,697 m3	3064 m2
25	Boshan Town	15,876 m3	2796 m2	50	Shima Town	27,298 m3	5215 m2	75	Baita Town	56,014 m3	9148 m2

.

The 30 m resolution GDEMV3 data (Source: Geospatial Data Cloud; Download link: http://www.gscloud.cn/) was first reprojected into a projected coordinate system using ArcGIS 10.2. Subsequently, a 10 m resolution dataset was generated by applying the “Resample” tool with the bilinear interpolation method. Based on this enhanced DEM, a total of 6,983,061 grids and 4498 landslide grids, each measuring 10 m × 10 m, were delineated, corresponding to a total area of 698.2 km² and landslide area of 0.442 km² across 99 identified landslides in the study area. It should be noted that this “upsampling” operation of the original DEM, while increasing the spatial resolution from 30 m to 10 m, does not introduce any additional genuine topographic detail. All newly generated details are mathematical estimates and do not represent actual measurement accuracy. Landslide susceptibility modeling requires both positive and negative samples; an additional 4498 grids were randomly selected from non-landslide areas to serve as negative samples. The method for selecting non-landslide grids was as follows:

(1)

4498 landslide grids and those located within a 50 m buffer distance from landslide grids were removed, resulting in 514,673 remaining grids.

(2)

Using the reclassification tool in ArcGIS 10.2, the 514,673 grids were categorized into 4499 groups. The first 4498 groups each contained 114 spatially adjacent grids, while the last group contained the remaining 1901 grids.

(3)

From each of the first 4498 groups, one grid was randomly selected to form the negative samples.

2.3. Typical Landslide

Liujiadayu landslide (No.26) is a typical accumulation layer-bedrock contact surface landslide. After a sliding event in July 1998, cracks appeared at the rear part, and the leading edge blocked the road. No significant changes have been observed in recent years.

The exposed stratum is the Cambrian Mantou formation, consisting mainly of limestone, mudstone and shale. The primary groundwater type is carbonate rock fissure-karst water. Its water abundance is related to lithology, with precipitation as the main recharge source. It generally exhibits short runoff paths and discharges over short distances; no stable groundwater table was observed. The landslide body has a semi-circular planform with a slope angle of 25°. It is 156 m long longitudinally and 140 m wide transversely, with a main sliding direction of N26° E. The landslide boundary is clear: the rear is bounded by a detachment surface formed by tensile cracks, and the sides are defined by gullies. The elevation of the rear scarp ranges from 400 to 410 m, while the leading edge features a free face, 2–10 m high, created by road construction, with a toe elevation between 359 and 366 m. The thickness of the landslide mass varies: 1.0–6.7 m in the front part, 2.2–5.3 m in the middle part and 3.3–7.5 m in the rear part, with an average thickness of 3.47 m. It covers a plan area of approximately 21,343 m² and has an estimated volume of about 74,160 m³, classifying it as a small-scale retrogressive landslide.

According to borehole data, the landslide body consists of silty clay containing rock fragments, which is a common colluvium in Shandong Province. The soil is in a plastic to hard plastic state, yellowish-brown in color, with a non-uniform texture containing a small amount of fine-grained rock fragments measuring 0.5–5 cm in diameter, comprising 10%–20% of the total volume. Beneath the colluvium is moderately weathered limestone, with a bedding dip angle of 13°. The limestone is relatively dense and has high strength; it was encountered in all boreholes, but its base was not reached. Investigation revealed that several days of continuous rainfall in July 1998 increased the water content within the accumulation layer, triggering a slide with a movement distance of about 20 m, which blocked the road at the landslide’s toe. Currently, sliding cracks approximately 2–4 m deep and 1–3 m wide are still visible in the middle and rear parts of the landslide body. Multiple tensile cracks have developed in the front part, generally linear in distribution, with a trend of about 10°, widths of about 0.5 m, depths of about 1.0 m, and extensions of 8–20 m in length, as shown in Figure 3.

3. Landslide Hazard Factor Selection and Classification

3.1. Landslide-Prone Environment

Landslide-prone environment involves topographic and geological factors (elevation, gradient, slope aspect, plane curvature, profile curvature, lithology, distance from fault), hydrological and vegetation factors (distance from river, topographic wetness index (TWI), sediment transport index (STI), stream power index (SPI), NDVI) and human activity factors (distance from road, land use, population density) [37]. Among them, TWI quantifies the control of terrain on the basic hydrological process, which is used to describe the degree of surface saturated runoff [38]. STI is a comprehensive topographic variable, which indicates the extent of surface sand and other materials carried with water flow [39]. SPI is a parameter to quantify the erosion capacity of surface water flow, which is used to identify the areas susceptible to gully erosion and the strong water flow path [40]. NDVI measures the extent of vegetation coverage, which ranges from −1.0–1.0 [41]. TWI, STI, SPI and NDVI are shown in Equations (1)–(4).

$$\mathrm{TWI}=\ln \left({\displaystyle \frac{A_s}{\tan \beta }}\right)$$

(1)

$$\mathrm{STI}={\left({\displaystyle \frac{A_s}{22.13}}\right)}^{0.6}\cdot {\left({\displaystyle \frac{\sin \beta }{0.0896}}\right)}^{1.3}$$

(2)

$$\mathrm{SPI}=A_s\cdot \tan \beta$$

(3)

$$\mathrm{NDVI}={\displaystyle \frac{NIR-R}{NIR+R}}$$

(4)

where: A_s is the upstream area of surface water flowing on the contour length, which is calculated by the cumulative confluence area and length of the upstream water flow; β is the terrain gradient; NIR is the reflecting value of the near-infrared band; R is the reflecting value of the red band.

3.2. Hazard Factor Screening

Too many hazard factors may exacerbate the collinearity problem, resulting in redundant information and unreliable results. Too few hazard factors may ignore important factors. Therefore, it is necessary to carry out correlation analysis and collinearity test on the hazard factors [42].

3.2.1. Correlation Analysis

The correlation between two variables can be measured using the Pearson correlation coefficient method [43], with values ranging from −1.0–1.0, as shown in Equation (5).

$${\rho }_{x,y}={\displaystyle \frac{\mathrm{cov}\left(x,y\right)}{{\sigma }_x\cdot {\sigma }_y}}={\displaystyle \frac{E\left[\left(x-{\mu }_x\right)\cdot \left(y-{\mu }_y\right)\right]}{{\sigma }_x\cdot {\sigma }_y}}$$

(5)

where: ρ_x,y is the Pearson correlation coefficient of x and y; μ_x, μ_y are the mean values of x and y; σ_x, σ_y are the variances of x and y; E is the expectation. ρ_x,y = 1.0 means x and y fall on a straight line, and y increases with the increase of x. ρ_x,y = −1.0 also means x and y fall on a straight line, but y decreases with the increase of x. ρ_x,y = 0 means no linear relationship between x and y, while |ρ_x,y| > 0.4 means strong correlation.

The Pearson correlation coefficients of the fifteen hazard factors (elevation, gradient, slope aspect, plane curvature, profile curvature, lithology, distance from fault, distance from river, TWI, STI, SPI, NDVI, distance from road, land use, population density) were calculated by SPSS23.0, as shown in Figure 4.

Among them, the coefficient between plane curvature and profile curvature is −0.599, and between SPI and STI is 0.816. The coefficients of other hazard factors are between −0.4–0.4, and the independence is strong. Therefore, profile curvature and SPI were excluded.

3.2.2. Collinearity Diagnostic

Variance inflation factor (VIF) is a measure of the severity of complex collinearity in multiple linear regression models [44]. It represents the ratio of the variance of the regression coefficient estimator to the variance when the independent variables are assumed not to be linearly correlated. When the correlation between independent variables is very low, VIF is close to 1. The larger the VIF, the larger the collinearity [45]. VIF > 10 means there is a serious collinearity problem in the variables, and VIF is shown in Equation (6).

$${\mathrm{VIF}}_i={\displaystyle \frac{1}{1-R_i^2}}$$

(6)

where: R_i² is the correlation coefficient of x_i for regression analysis of the other variables.

SPSS23.0 was used to test the collinearities of the thirteen hazard factors, and the results are shown in

Table 4. Collinearity diagnostic results.

Hazard Factor	Elevation	Gradient	Slope Aspect	Plane Curvature	Lithology	Distance from Fault	Distance from River
VIF	3.337	1.940	1.050	1.124	1.815	1.224	1.633
Hazard Factor	TWI	STI	NDVI	Distance from Road	Land Use	Population Density
VIF	1.855	1.406	2.452	1.904	1.024	1.174

.

The VIF of each hazard factor is <10, and the collinearity is low, indicating the hazard factors can be used for the establishment of hazard factor combinations.

3.3. Landslide Hazard Factor Classification

Elevation, gradient, plane curvature, distance from fault, distance from river, TWI, STI, NDVI, distance from road and population density were classified by the natural breakpoint method. Taking elevation as an example, the principle of the natural breakpoint method is explained as follows [46,47]:

(1)

The elevation of the 6,983,061 grids was determined, with a minimum elevation of 102 m and a maximum elevation of 1066 m.

(2)

The classification number (c_n) and breakpoints were set, and all grids were classified in ascending order of elevation.

(3)

The mean and variance of elevations within each class were calculated, followed by the computation of the sum of variances (Var_a) across all c_n classes.

(4)

Global searches for c_n and the breakpoints were conducted using MATLAB R2024b software to identify the combination that resulted in the smallest Var_a.

This study set the initial c_n = 5, with initial breakpoints at 295 m, 490 m, 695 m, and 825 m. The results showed that Var_a was minimized when c_n = 8 and the breakpoints were 240 m, 329 m, 402 m, 475 m, 555 m, 645 m and 769 m, representing the optimal classification number and breakpoints. Besides, slope aspect, lithology and land use were divided into 9, 16 and 6 categories respectively, as shown in

Table 5. Landslide hazard factor classifications.

Hazard Factor	Classification
Elevation (m)	0–240; 240–329; 329–402; 402–475; 475–555; 555–645; 645–769; 769–1066.
Gradient (°)	0–5.9328; 5.9328–10.4418; 10.4418–15.1881; 15.1881–19.9344; 19.9344–24.6806; 24.6806–29.9016; 29.9016–36.5463; 36.5463–60.5150.
Plane curvature	−7.9765–−2.0350; −2.0350–−1.1948; −1.1948–−0.5946; −0.5946–−0.1145; −0.1145–0.3056; 0.3056–0.8457; 0.8457–1.6259; 1.6259–7.3274.
Distance from fault (m)	0–791.53; 791.53–1686.30; 1686.30–2546.65; 2546.65–3407.01; 3407.01–4267.37; 4267.37–5196.55; 5196.55–6435.46; 6435.46–8775.63.
Distance from river (m)	0–214.9345; 214.9345–470.1691; 470.1691–711.9704; 711.9704–953.7717; 953.7717–1209.0063; 1209.0063–1504.5412; 1504.5412–1920.9767; 1920.9767–3425.5180.
TWI	3.0010–5.1384; 5.1384–6.1674; 6.1674–7.4341; 7.4341–9.0965; 9.0965–11.0755; 11.0755–13.4504; 13.4504–16.6960; 16.6960–23.1873.
STI	0–1.0421; 1.0421–2.1134; 2.1134–12.9532; 12.9532–24.2145; 24.2145–42.7421; 42.7421–61.5125; 61.5125–101.0528; 101.0528–182.0463.
NDVI	−1–−0.0270; −0.0270–0.0844; 0.0844–0.1444; 0.1444–0.1823; 0.1823–0.2561; 0.2561–0.3720; 0.3720–0.4501; 0.4501–0.7202.
Distance from road (m)	0–206.8845; 206.8845–524.1073; 524.1073–855.1225; 855.1225–1186.1376; 1186.1376–1558.5296; 1558.5296–1972.2986; 1972.2986–2510.1982; 2510.1982–3503.2436.
Population density (p/km2)	23.1670–544.5703; 544.5703–646.6793; 646.6793–737.5949; 737.5949–764.0146; 764.0146–1100.3417; 1100.3417–1145.4753; 1145.4753–1201.6171; 1201.6171–1280.8762.
Slope aspect	Plane; North; Northeast; East; Southeast; South; Southwest; West; Northwest.
Lithology	Silty sand, sandy clay; Thick limestone, medium-thickness dolomite; Mudstone, shale with sandstone; Arkose; Yellowish·green sandstone; Edgewise limestone; Silty mudstone; Gabbro; Dolomitic limestone; Mudstone, shale with limestone; Gneissie monzogranite; Weak gneissic orthogranite; Tonalitic gneiss; Homblendite; Fine-grined granite; Micrite, micritic limestone.
Land use	Water area; Garden plot; Cultivated land; Reclaimed land; Bare land; Forest land.

and Figure 5.

4. Landslide Hazard Factor Combination and Quantification

4.1. Hazard Factor Combination

The thirteen hazard factors were divided into ten static factors (elevation, gradient, slope aspect, plane curvature, distance from fault, lithology, TWI, STI, distance from river, distance from road) and three time-varying factors (NDVI, land use, population density). The selection of NDVI, land use and population density as time-varying factors was based on long-term monitoring and tracking of the landslide-prone environment in the study area. We have observed that, with intensified engineering activities and accelerated urbanization, NDVI, land use and population density in the study area have undergone significant changes over the past two decades, which constitutes a major reason for the frequent occurrence of landslides in this region. The combinations were established, as shown in

Table 6. Hazard factor combinations.

No.	Static Factor	Time-Varying Factor
1	Elevation, gradient, slope aspect, plane curvature, distance from fault, lithology, TWI, STI, distance from river, distance from road	Values of NDVI, land use and population density in 2021.
2		Annual values of NDVI, land use and population density.
3		Interannual variation values of NDVI, land use and population density.

.

Combination No.1 represents the conventional approach commonly used in LSM, treating time-varying factors as constants. The values for the year 2021 were selected because that year recorded the highest number of landslides (12 events) in Boshan District. Combination No.2 assigns to each of the 4498 landslide grids the values of time-varying factors corresponding to the year in which the landslide occurred. This enables a precise match between the landslide-prone environment and the susceptibility conditions at the time of failure. Combination No.3 further refines combination No.2 by using the interannual variation values (i.e., changes relative to the previous year) of the time-varying factors for each landslide grid cell in the year of occurrence. These variation values better capture the intensity of human engineering activities and the degree of change in the landslide-prone environment, thereby offering higher interpretability for landslide susceptibility. By incorporating such temporal dynamics, combination No.3 provides a more comprehensive representation of the combined effects of internal and external driving forces that contribute to landslide initiation.

4.2. Hazard Factor Quantification

The information value (IV) method was used to quantify the hazard factors [48], and the IV calculation method for combination No.1 is shown in Equation (7).

$${\mathrm{IV}}_i=\ln \left({\displaystyle \frac{N_i/N}{S_i/S}}\right)$$

(7)

where: N_i is the number of landslide grids in the i-th interval, N is the total number of landslide grids and N = 4498, S_i is the number of grids in the i-th interval, S is the total number of grids and S = 6,983,061.

IV_i reflects the favorable degree of landslide occurrence of the i-th interval. The larger the IV_i, the larger the landslide susceptible probability. IV_i > 0 indicates that the i-th interval is conducive to landslide, while IV_i < 0 indicates not conducive to landslide, and IV_i = 0 indicates the impact of the i-th interval on landslide is not obvious.

When adding j to Equation (7), the IV calculation method is shown in Equation (8).

$${\mathrm{IV}}_{ij}=\ln \left({\displaystyle \frac{N_{ij}/N_j}{S_{ij}/S}}\right)$$

(8)

where: N_ij is the number of landslide grids in the i-th interval and j-th year, N_j is the number of landslide grids in the j-th year, S_ij is the number of grids in the i-th interval and j-th year.

(1)

Static factor quantification

The IVs of the static factors were calculated according to Equation (7), as shown in

Table 7. IVs of the static factors.

Static Factor	Classification	Number of Grids	Proportion of Grids	Number of Landslide Grids	Proportion of Landslide Grids	IV
Elevation (m)	0–240	85,557	0.110	74	0.051	−0.7687
	240–329	108,070	0.140	236	0.162	0.1460
	329–402	165,856	0.214	339	0.232	0.0808
	402–475	141,223	0.182	295	0.202	0.1043
	475–555	114,264	0.148	221	0.151	0.0201
	555–645	92,237	0.119	162	0.111	−0.0696
	645–769	54,820	0.071	89	0.061	−0.1518
	769–1066	12,543	0.016	44	0.030	0.6286
Gradient (°)	0–5.9328	148,948	0.192	142	0.097	−0.6828
	5.9328–10.4418	168,743	0.218	210	0.144	−0.4147
	10.4418–15.1881	141,830	0.183	221	0.151	−0.1922
	15.1881–19.9344	112,992	0.147	256	0.175	0.1744
	19.9344–24.6806	84,716	0.109	203	0.140	0.2503
	24.6806–29.9016	62,658	0.081	196	0.134	0.5034
	29.9016–36.5463	39,853	0.051	161	0.110	0.7687
	36.5463–60.5150	14,830	0.019	71	0.049	0.9474
Slope aspect	Plane	4893	0.006	0	0	0
	North	120,794	0.156	237	0.162	0.0377
	Northeast	101,005	0.130	234	0.160	0.2076
	East	78,792	0.102	161	0.110	0.0755
	Southeast	91,177	0.118	219	0.150	0.2400
	South	106,066	0.137	199	0.136	−0.0073
	Southwest	92,830	0.120	161	0.110	−0.0870
	West	76,958	0.099	94	0.064	−0.4362
	Northwest	102,054	0.132	155	0.106	−0.2194
Plane curvature	−7.9765–−2.0350	7311	0.009	15	0.010	0.1054
	−2.0350–−1.1948	37,545	0.048	85	0.058	0.1892
	−1.1948–−0.5946	99,773	0.129	161	0.110	−0.1593
	−0.5946–−0.1145	183,022	0.236	339	0.232	−0.0171
	−0.1145–0.3056	199,852	0.258	432	0.296	0.1374
	0.3056–0.8457	150,018	0.195	263	0.180	−0.0800
	0.8457–1.6259	75,910	0.098	108	0.074	−0.2809
	1.6259–7.3274	21,140	0.027	58	0.040	0.3930
Lithology	Silty sand, sandy clay	11,696	0.015	89	0.061	1.4028
	Thick limestone, medium thickness dolomite	146,576	0.188	192	0.132	−0.3536
	Mudstone, shale with sandstone	46,060	0.059	324	0.222	1.3083
	Arkose	1228	0.002	9	0.006	1.0986
	Yellowish·green sandstone	6895	0.009	46	0.032	1.2685
	Edgewise limestone	74,976	0.097	225	0.154	0.4622
	Silty mudstone	8221	0.011	35	0.024	0.7802
	Gabbro	88	0.001	0	0	0
	Dolomitic limestone	372,558	0.481	348	0.238	−0.7036
	Mudstone, shale with limestone	833	0.001	23	0.016	2.7726
	Gneissie monzogranite	85,193	0.110	127	0.087	−0.2346
	Weak gneissic orthogranite	7180	0.009	11	0.007	−0.2513
	Tonalitic gneiss	8660	0.011	29	0.02	0.5978
	Homblendite	1885	0.001	0	0	0
	Fine-grined granite	2137	0.003	2	0.001	−1.0986
	Micrite, micritic limestone	384	0.001	0	0	0
Distance from fault (m)	0–791.53	138,669	0.178	361	0.247	0.3276
	791.53–1686.30	141,261	0.182	342	0.234	0.2513
	1686.30–2546.65	128,384	0.166	208	0.142	−0.1562
	2546.65–3407.01	115,321	0.149	199	0.136	−0.0913
	3407.01–4267.37	107,743	0.139	169	0.116	−0.1809
	4267.37–5196.55	77,871	0.101	106	0.073	−0.3247
	5196.55–6435.46	48,623	0.063	61	0.042	−0.4055
	6435.46–8775.63	16,697	0.022	14	0.010	−0.7885
TWI	3.0010–5.1384	205,825	0.266	350	0.240	−0.1029
	5.1384–6.1674	257,617	0.333	467	0.320	−0.0398
	6.1674–7.4341	154,815	0.200	257	0.176	−0.1278
	7.4341–9.0965	70,567	0.091	164	0.112	0.2076
	9.0965–11.0755	41,059	0.053	91	0.062	0.1568
	11.0755–13.4504	28,852	0.037	82	0.056	0.4144
	13.4504–16.6960	11,951	0.015	38	0.026	0.5500
	16.6960–23.1873	3884	0.005	12	0.008	0.4700
STI	0–1.0421	70,660	0.091	117	0.080	−0.1288
	1.0421–2.1134	75,635	0.098	107	0.073	−0.2945
	2.1134–12.9532	320,212	0.413	622	0.426	0.0310
	12.9532–24.2145	159,093	0.205	304	0.208	0.0145
	24.2145–42.7421	98,176	0.127	204	0.140	0.0975
	42.7421–61.5125	23,917	0.031	44	0.030	−0.0328
	61.5125–101.0528	14,535	0.019	35	0.024	0.2336
	101.0528–+∞	12,341	0.016	28	0.019	0.1719
Distance from river (m)	0–214.9345	179,016	0.231	480	0.329	0.3536
	214.9345–470.1691	176,585	0.228	388	0.266	0.1542
	470.1691–711.9704	138,670	0.179	286	0.196	0.0907
	711.9704–953.7717	116,996	0.151	169	0.116	−0.2637
	953.7717–1209.0064	82,748	0.107	98	0.067	−0.4681
	1209.0064–1504.5413	50,404	0.065	24	0.016	−1.4018
	1504.5413–1920.9768	24,358	0.031	12	0.008	−1.3545
	1920.9768–3425.5181	5793	0.008	3	0.002	−1.3863
Distance from road (m)	0–206.8845	275,173	0.355	690	0.472	0.2849
	206.8845–524.1073	186,514	0.241	420	0.288	0.1782
	524.1073–855.1225	126,167	0.163	226	0.155	−0.0503
	855.1225–1186.1376	83,471	0.108	58	0.040	−0.9933
	1186.1376–1558.5296	51,968	0.067	38	0.026	−0.9466
	1558.5296–1972.2986	31,294	0.040	18	0.012	−1.2040
	1972.2986–2510.1982	14,583	0.019	7	0.005	−1.3350
	2510.1982–3503.2436	5401	0.007	3	0.002	−1.2528

.

(2)

Time-varying factor quantification for combination No.1

The IVs of the time-varying factors for combination No.1 were calculated according to Equation (7), as shown in

Table 8. IVs of the time-varying factors for combination No.1.

Time-Varying Factor	Classification	Number of Grids	Proportion of Grids	Number of Landslide Grids	Proportion of Landslide Grids	IV
NDVI	−1–−0.0270	1897	0.002	3	0.002	0
	−0.0270–0.0844	34,037	0.044	69	0.047	0.0660
	0.0844–0.1444	53,816	0.069	153	0.105	0.4199
	0.1444–0.1823	84,993	0.110	203	0.139	0.2340
	0.1823–0.2561	161,857	0.209	289	0.198	−0.0541
	0.2561–0.3720	190,692	0.246	336	0.230	−0.0673
	0.3720–0.4501	167,148	0.216	287	0.197	−0.0921
	0.4501–0.7202	80,129	0.103	120	0.082	−0.2280
land use	Cultivated land	77,374	0.0999	63	0.043	−0.8430
	Forest land	498,863	0.6441	839	0.574	−0.1152
	Garden plot	39,280	0.0507	255	0.175	1.2390
	Water area	4763	0.0061	8	0.006	−0.0165
	Reclaimed land	153,664	0.1984	295	0.202	0.0180
	Bare land	626	0.0008	0	0	0
Population density (p/km2)	23.1670–544.5703	619,476	0.7998	1185	0.8116	0.0146
	544.5703–646.6793	106,265	0.1372	202	0.1384	0.0087
	646.6793–737.5949	27,770	0.0358	36	0.0247	−0.3711
	737.5949–764.0146	12,023	0.0155	22	0.0151	−0.0261
	764.0146–1100.3417	5351	0.0069	9	0.0061	−0.1232
	1100.3417–1145.4753	2475	0.0032	4	0.0027	−0.1699
	1145.4753–1201.6171	1053	0.0014	2	0.0014	0
	1201.6171–1280.8762	157	0.0002	0	0	0

.

(3)

Time-varying factor quantification for combination No.2

The IVs of the time-varying factors for combination No.2 were calculated according to Equation (8), and the calculation results of NDVI during 2014–2021 are shown in

Table 9. IVs of NDVI during 2014–2021 for combination No.2.

Year	Classification	Number of Grids	Proportion of Grids	Number of Landslide Grids	Proportion of Landslide Grids	IV
2014	−0.3996–−0.0687	40,701	0.052	0	0	0
	−0.0687–0.0016	91,310	0.118	26	0.137	0.1493
	0.0016–0.0719	126,257	0.163	40	0.211	0.2581
	0.0719–0.1422	135,607	0.175	38	0.200	0.1335
	0.1422–0.2208	137,015	0.177	32	0.168	−0.0522
	0.2208–0.3118	116,312	0.150	28	0.147	−0.0202
	0.3118–0.4193	81,211	0.105	18	0.095	−0.1001
	0.4193–0.6551	46,157	0.060	8	0.042	−0.3567
2015	−0.5383–−0.2274	1044	0.001	0	0	0
	−0.2274–−0.0134	56,703	0.073	8	0.076	0.0403
	−0.0134–0.1088	93,448	0.121	20	0.191	0.4565
	0.1088–0.2210	112,590	0.145	18	0.171	0.1649
	0.2210–0.3331	134,557	0.174	19	0.181	0.0394
	0.3331–0.4452	137,682	0.178	16	0.152	−0.1579
	0.4452–0.5624	124,556	0.161	15	0.143	−0.1186
	0.5624–0.7612	113,990	0.147	9	0.086	−0.5361
2016	−0.2953–−0.0401	47,593	0.062	0	0	0
	−0.0401–0.0436	87,315	0.113	21	0.131	0.1478
	0.0436–0.1236	91,747	0.118	25	0.156	0.2792
	0.1236–0.2036	125,703	0.162	33	0.206	0.2403
	0.2036–0.2797	129,420	0.167	28	0.175	0.0468
	0.2797–0.3597	121,893	0.157	24	0.150	−0.0456
	0.3597–0.4435	103,774	0.134	19	0.119	−0.1187
	0.4435–0.6721	67,125	0.087	10	0.063	−0.3228
2017	−0.4567–−0.1691	2479	0.003	0	0	0
	−0.1691–−0.0041	64,557	0.083	19	0.092	0.1029
	−0.0041–0.1090	92,183	0.119	35	0.169	0.3508
	0.1090–0.2221	103,690	0.134	36	0.174	0.2612
	0.2221–0.3259	133,741	0.173	35	0.169	−0.0234
	0.3259–0.4296	143,714	0.186	35	0.169	−0.0958
	0.4296–0.5333	128,762	0.166	29	0.140	−0.1703
	0.5333–0.7455	105,444	0.136	18	0.087	−0.4467
2018	−0.3397–−0.0236	43,113	0.056	0	0	0
	−0.0236–0.0614	72,003	0.093	19	0.117	0.2296
	0.0614–0.1505	84,846	0.110	28	0.173	0.4528
	0.1505–0.2356	94,081	0.121	23	0.142	0.16
	0.2356–0.3207	128,899	0.166	27	0.167	0.006
	0.3207–0.4058	136,939	0.177	28	0.173	−0.0229
	0.4058–0.4990	118,750	0.153	21	0.130	−0.1629
	0.4990–0.6935	95,939	0.124	16	0.098	−0.2353
2019	−0.5500–−0.2012	2169	0.003	0	0	0
	−0.2012–−0.0242	62,839	0.081	8	0.029	−1.0272
	−0.0242–0.0818	94,569	0.122	36	0.131	0.0712
	0.0818–0.1880	113,783	0.147	59	0.215	0.3802
	0.1880–0.2941	133,347	0.172	47	0.171	−0.0058
	0.2941–0.4053	136,153	0.176	52	0.189	0.0713
	0.4053–0.5166	121,229	0.156	40	0.145	−0.0731
	0.5166–0.7390	110,481	0.143	33	0.120	−0.1754
2020	−0.2628–−0.0207	43,526	0.056	0	0	0
	−0.0207–0.0588	72,067	0.093	19	0.100	0.0726
	0.0588–0.1350	74,359	0.096	22	0.116	0.1892
	0.1350–0.2080	101,841	0.132	30	0.158	0.1798
	0.2080–0.2743	136,331	0.176	39	0.205	0.1525
	0.2743–0.3406	142,707	0.184	37	0.195	0.0581
	0.3406–0.4070	123,713	0.160	28	0.147	−0.0847
	0.4070–0.5827	80,026	0.103	15	0.079	−0.2653
2021	−0.3211–−0.0270	1897	0.002	0	0	0
	−0.0270–0.0844	34,037	0.044	8	0.047	0.0660
	0.0844–0.1444	53,816	0.070	15	0.088	0.2288
	0.1444–0.1823	84,993	0.110	24	0.14	0.2412
	0.1823–0.2561	161,857	0.209	34	0.199	−0.0490
	0.2561–0.3720	190,692	0.246	40	0.234	−0.0500
	0.3720–0.4501	167,148	0.216	34	0.199	−0.0820
	0.4501–0.7202	80,130	0.103	16	0.093	−0.1021

.

(4)

Time-varying factor quantification for combination No.3

The interannual variation values of NDVI, land use and population density during 2014–2021 were extracted. The variation values of NDVI and population density were divided into eight categories by the natural breakpoint method. The land use variation was divided into 36 categories. The distributions of interannual variation values of NDVI, land use and population density in 2016 are shown in Figure 6.

The IVs of the time-varying factors for combination No.3 were calculated according to Equation (8), and the calculation results of the land use variation in 2016 are shown in

Table 10. IVs of the land use variation in 2016.

Land Use Variation	Number of Grids	Proportion of Grids	Number of Landslide Grids	Proportion of Landslide Grids	IV
Cultivated land → Water area	345	0.00045	0	0	0
Cultivated land → Garden plot	775	0.001	0	0	0
Cultivated land → Cultivated land	103,524	0.13365	6	0.0375	1.2709
Cultivated land → Reclaimed land	6881	0.00888	2	0.0125	0.3419
Cultivated land → Bare land	0	0	0	0	0
Cultivated land → Forest land	16,155	0.02086	6	0.0375	0.5865
Forest land → Water area	379	0.00049	0	0	0
Forest land → Garden plot	5023	0.00649	1	0.00625	0.0377
Forest land → Garden plot	15,646	0.0202	2	0.0125	0.4799
Forest land → Reclaimed land	7507	0.00969	2	0.0125	0.2546
Forest land → Bare land	330	0.00042	0	0	0
Forest land → Forest land	418,614	0.54044	66	0.4125	0.2701
Garden plot → Water area	9	0.00001	0	0	0
Garden plot → Garden plot	54,135	0.06989	27	0.16875	0.8815
Garden plot → Garden plot	371	0.00048	0	0	0
Garden plot → Reclaimed land	294	0.00038	3	0.01875	3.8988
Garden plot → Bare land	0	0	0	0	0
Garden plot → Forest land	4692	0.00606	11	0.06875	2.4288
Water area → Water area	4056	0.00524	0	0	0
Water area → Garden plot	24	0.00003	0	0	0
Water area → Garden plot	72	0.00009	0	0	0
Water area → Reclaimed land	223	0.00029	0	0	0
Water area → Bare land	0	0	0	0	0
Water area → Forest land	583	0.00075	2	0.0125	2.8134
Reclaimed land → Water area	211	0.00027	0	0	0
Reclaimed land → Garden plot	118	0.00015	5	0.03125	5.3391
Reclaimed land → Garden plot	1772	0.00229	0	0	0
Reclaimed land → Reclaimed land	121,419	0.15676	23	0.14375	0.0866
Reclaimed land → Bare land	52	0.00007	0	0	0
Reclaimed land → Forest land	10,306	0.01331	3	0.01875	0.3427
Bare land → Water area	0	0	0	0	0
Bare land → Garden plot	0	0	0	0	0
Bare land → Garden plot	35	0.00005	0	0	0
Bare land → Reclaimed land	100	0.00013	0	0	0
Bare land → Bare land	662	0.00085	0	0	0
Bare land → Forest land	257	0.00033	1	0.00625	2.9412

.

5. Landslide Susceptibility Mapping

5.1. LSM Model Construction

SVM is a generalized linear classifier that performs binary classification on data through supervised learning, with its decision boundary being the maximum-margin hyperplane derived from the training samples [49]. RF is an ensemble machine learning algorithm employed for both classification and regression tasks. It operates by constructing a multitude of decision trees and aggregating their predictions to yield more accurate and stable results than those achievable by a single model. CNN leverages the structural advantages of parameter sharing and local connectivity, enabling efficient processing of grid-like data without relying on additional features [50]. CNN-RF integrates the spatial feature-extraction strengths of CNN with the high stability and strong robustness of RF, thereby enhancing the analysis of landslide features and the exploration of disaster-causing patterns. DBN-MLP provides a new technical pathway for LSM by combining the efficient feature pre-training capability of DBN and the powerful nonlinear classification ability of MLP [51]. This paper employed SVM, RF, CNN, CNN-RF, and DBN-MLP models to conduct LSM, respectively. The hardware environment for modeling was a CPU i7-6700 processor, 8G memory, GTX1050 Ti-8G graphics card. A total of 70% grids (3149 landslide grids and 3149 non-landslide grids) were selected as training samples, and the remaining 30% grids (1349 landslide grids and 1349 non-landslide grids) were selected as verification samples.

5.1.1. SVM

SVM separates data by finding the optimal maximum-margin hyperplane, demonstrating strong robustness against noise and outliers. The loss function employed by SVM not only considers classification accuracy but also maximizes the margin width, which prevents overfitting on training data while effectively mitigating computational burdens caused by the curse of dimensionality. This gives SVM distinct advantages in solving nonlinear problems. However, SVM has limitations in parameter selection, as critical parameters like the penalty coefficient and kernel functions significantly impact prediction results, and improper choices may reduce model accuracy [52].

When applied to LSM, SVM treats hazard factors as independent variables (x), and a binary dependent variable (Y), where −1 indicates a non-landslide, and 1 indicates a landslide. It distinguishes between a landslide and a non-landslide in n-dimensional space by constructing an n-1-dimensional hyperplane, as shown in Equation (9).

$$y_i\cdot \left({\omega }^T\cdot x_i+b\right)\ge 1$$

(9)

where: b is the bias term. For linearly inseparable cases, SVM introduces slack variables (ξ) to allow approximate classification with tolerable misclassification, as shown in Equation (10).

$$y_i\cdot \left({\omega }^T\cdot x_i+b\right)\ge 1-{\xi }_i$$

(10)

By incorporating Lagrange multipliers (λ_i), the Lagrangian function is derived, as shown in Equation (11).

$$L={\displaystyle \frac{1}{2}}\cdot {‖\omega ‖}^2+{\displaystyle \sum _{i=1}^n{\lambda }_i\left(1-y_i\cdot \left({\omega }^T\cdot x_i+b\right)\right)}$$

(11)

where: ‖ω‖ denotes the norm of the hyperplane’s normal vector. Taking partial derivatives with respect to ω and b yields an expression containing λ_i, as shown in Equation (12).

$${\displaystyle \sum _{i=1}^n{\lambda }_i\cdot y_i}=0,\hspace{1em}\hspace{1em}{\lambda }_i\ge 0$$

(12)

The SVM was constructed with key parameters listed in

Table 11. Key parameters of the SVM in this paper.

Parameter	Kernel Function	γ	C	Gamma	Shrinking	Tol
Value	RBF	0.1	5	Scale	False	1 × 10−4

.

5.1.2. RF

RF is an ensemble learning model based on decision trees, used for regression and classification analysis. It employs the bootstrap method to randomly select n sample sets with replacement from the original training dataset, selects the optimal splitting attributes to construct CART decision trees, and integrates n decision trees through the Bagging algorithm to form a random forest. In essence, it is an improvement over the decision tree algorithm, combining multiple decision trees, with each tree’s construction relying on an independently sampled dataset. The CART decision tree algorithm performs binary splits (rather than multi-way splits) on the values of a specific feature each time, resulting in the construction of binary trees instead of multi-way trees. The CART decision tree uses the Gini index to select the optimal splitting attribute. The Gini index represents the impurity of the model: the lower the Gini index, the lower the impurity and the better the features [53]. The calculation methods of the Gini index are shown in Equations (13) and (14).

$$gini\left(A\right)=1-{\displaystyle \sum _{i=1}^n{p}_i^2}$$

(13)

$$gini\left(A,B\right)={\displaystyle \sum _{j=1}^m\frac{\left|A_j\right|}{\left|A\right|}}gini\left(A_j\right)$$

(14)

where: gini(A) is the Gini index of sample A, n is the number of categories of sample A, p_i is the proportion of the i-th category of sample A, gini(A, B) is the Gini index after splitting sample A using sample B, m is the number of samples, ∣A_j∣ is the size of the j-th subset.

The RF was constructed with key parameters listed in

Table 12. Key parameters of the RF in this paper.

Parameter	N_Estimators	Criterion	Bootstrap	Random_State
Value	77	Gine	Sampling with replacement	None
Parameter	Max_Features	Max_Depth	Min_Samples_Leaf	Min_Samples_Split
Value	3	4	4	3

.

5.1.3. CNN

CNN is a feed-forward neural network with deep structure, which can learn features from data and effectively identify characteristics like edges, textures and shapes through convolutional kernels, synthesizing this information to enhance data processing efficiency. CNN includes an input layer, a convolutional layer, a pooling layer, a fully connected layer and output layer. Convolutional layer parameters include the size, step size and filling method of the convolutional kernel. Pooling operation is divided into maximum pooling and average pooling. Maximum pooling selects the maximum value of the element as the value after pooling, while average pooling selects the average value. Fully connected layer nonlinearly combines the features extracted by convolution and pooling, and the feature matrix is expanded into a one-dimensional vector. The output layer uses the Logical function to output the classification label, and assesses the similarity between the predicted value and the actual value of the model by the loss function [54]. The convolutional operation is shown in Figure 7.

In the training process of CNN, the landslide grids are converted into a two-dimensional square matrix with equal rows and columns. The specific steps are as follows:

(1)

Comparing the number of factors in the three combinations and the number of grades of each factor, the larger one is selected as the size of the matrix.

(2)

Each column of the matrix represents the corresponding factor. If the attribute value of the m-th factor of a grid is in the n-th grade, the element of the m-th column and the n-th row is calibrated to 1, and the other elements of the n-th column are calibrated to 0. For example, the categories of lithology in combination No.1 and No.2 are the largest (16), so the matrix size is 16 × 16. The categories of the land use variation in combination No.3 are 36, and the size is 36 × 36.

Taking a landslide grid in 2015 as an example, the hazard factors in combination No.2 are as follows: elevation is 832 m, gradient is 32.0752°, slope aspect is northeast, plane curvature is 1.3528, distance from river is 232.4534 m, STI is 23.0425, TWI is 21.6551, distance from road is 455.4205 m, land use is forest land, distance from fault is 2813.95 m, lithology is dolomitic limestone, NDVI is 0.1856, and population density is 128.7560 p/km². The corresponding two-dimensional square matrix is shown in Figure 8.

The model structures of inputs are shown in

Table 13. CNN model structures.

No.	Layer	Model Size	Filter Size	Step	Zero Fill Way
1	Input	16 × 16/36 × 36	0	0	NONE
2	Conv-1	16 × 16/36 × 36	3 × 3 × 4/5 × 5 × 4	1	SAME/VALID
3	Pool-1	16 × 16 × 4/32 × 32 × 4	2 × 2	2	VALID
4	Conv-2	8 × 8 × 4/16 × 16 × 4	3 × 3 × 8/9 × 9 × 8	1	SAME/VALID
5	Pool-2	8 × 8 × 8/8 × 8 × 8	2 × 2	2	VALID
6	F-layer	128	NONE	NONE	NONE
7	Output	2	NONE	NONE	NONE

, including one input layer, two convolutional layers, two pooling layers, one fully connected layer and one output layer.

The CNN was constructed with key parameters listed in

Table 14. Key parameters of the CNN in this paper.

Parameter	Activation Function	Optimization Algorithm	Learning Rate	Learning Rate Scheduler
Value	Leaky ReLU	AdamW	3 × 10−4	Cosine annealing
Parameter	Max_Epoch	Batch Size	Patience	Dropout
Value	100	128	15	0.0 (convolutional layer); 0.5 (fully connected layer)

.

5.1.4. CNN-SVM

CNN-SVM is constructed by integrating CNN and SVM, combining the strengths of both. Its core workflow is as follows: CNN module processes input data through convolution and pooling operations, enabling multi-level deep feature extraction and generating high-dimensional feature vectors. This process not only preserves critical information but also mitigates the “curse of dimensionality”. Subsequently, the feature vectors are fed into SVM, where they are mapped to a higher-dimensional space via kernel functions, and precise classification is achieved by an optimal hyperplane. The training of CNN-SVM follows a two-stage logic of “feature extraction-classification optimization”. First, CNN undergoes independent pre-training. As the number of iterations increases, the model’s loss function declines, demonstrating continuous optimization in feature learning. After pre-training is completed, the CNN network parameters are fixed, and only the subsequent SVM classifier is trained. The selection of its kernel function and regularization parameters is based on the optimal configuration of an independent SVM model [55].

5.1.5. DBN-MLP

DBN-MLP is a hybrid neural network model constructed by integrating DBN and MLP. DBN consists of multiple stacked Restricted Boltzmann Machines (RBM) and relies on unsupervised learning to achieve hierarchical feature extraction. It can efficiently learn the implicit features of data and progressively optimize them. Its autoencoding capability enables the extraction of high-level abstract features, facilitating effective modeling of complex unlabeled data. MLP centers on supervised learning. It adjusts weights via the backpropagation algorithm and minimizes the loss function to achieve accurate predictions, demonstrating strong performance in complex pattern classification and regression tasks due to its powerful nonlinear mapping ability. The core workflow of DBN-MLP is as follows: DBN extracts deep features from input data in an unsupervised manner, encoding the intrinsic patterns across its layers. The extracted features are fed into the MLP, which optimizes its parameters through its multi-layer structure and backpropagation algorithm to accomplish classification or regression tasks [56].

The rational configuration of the number of RBM layers is crucial for balancing model complexity and generalization capability. Too few layers result in insufficient model expressiveness, failing to adequately learn the complex features of landslide data; too many layers increase model complexity, leading not only to higher computational costs and longer training cycles, but also making the model prone to overfitting. This paper adopted a three-layer RBM stacked structure, with neuron counts set to 256, 128 and 64. Each RBM layer aims to learn high-level feature representations of the data. Taking the first RBM layer as an example, its visible layer receives input data from the training set and performs feature transformation by adjusting the connection weights with the hidden layer neurons. The hidden-layer neurons then output abstract representations based on specific activation rules. After the first layer is trained, its hidden layer output is directly used as the input for the second RBM layer. This iterative process achieves gradual abstraction and deep extraction of features. The parameters of the DBN are shown in

Table 15. DBN model parameters in this paper.

Parameter	Learning Rate	Training Epochs	Layers	RBM Neuron Counts
				First Layer	Second Layer	Third Layer
Value	0.01	50	3	256	128	64

.

MLP comprises two hidden layers, each with the neuron count set to 128, and the output layer is set to five neurons. The ReLU function can effectively address the vanishing gradient problem and accelerate model convergence. When the input value is >0, the output is the input value itself; when the input value is ≤0, the output is 0 [57].

5.2. Accuracy Analysis

The five models were trained using training samples. The trained models were then applied to the verification samples (1349 landslide grids and 1349 non-landslide grids), and their performance was evaluated using Accuracy, Precision, Recall, F1-Score, ROC and AUC. The calculation methods are shown in Equations (15)–(19).

$$\mathrm{Accuracy}={\displaystyle \frac{TN+TP}{TN+TP+FP+FN}}$$

(15)

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}}$$

(16)

$$\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}}$$

(17)

$$\mathrm{F}1-\mathrm{Score}=2\cdot {\displaystyle \frac{\mathrm{Recall}\cdot \mathrm{Precision}}{\mathrm{Recall}+\mathrm{Precision}}}$$

(18)

$$\mathrm{FPR}={\displaystyle \frac{FP}{TN+FP}}$$

(19)

where: TP means the prediction and actual situation both indicate a landslide, FP means the prediction is a landslide, but the actual situation is a non-landslide, TN means the prediction and actual situation both indicate a non-landslide, FN means the prediction is a non-landslide, but the actual situation is a landslide.

The FPR is the abscissa, and the Recall (TPR) is the ordinate in the ROC, as shown in Figure 9. The calculation results of Accuracy, Precision, Recall, F1-Score and AUC are shown in

Table 16. The calculation results of Accuracy, Precision, Recall, F1-Score and AUC.

Model	Combination
	No.1					No.2					No.3
SVM	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC
	1124	225	254	1095	0.831	1138	211	241	1108	0.836	1191	158	163	1186	0.889
	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR
	0.822	0.815	0.833	0.824	0.188	0.832	0.825	0.843	0.834	0.178	0.881	0.879	0.882	0.881	0.120
RF	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC
	1129	220	250	1099	0.833	1152	197	207	1142	0.846	1203	146	154	1195	0.891
	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR
	0.825	0.818	0.836	0.827	0.185	0.850	0.847	0.853	0.850	0.153	0.888	0.886	0.891	0.889	0.114
CNN	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC
	1150	199	205	1144	0.846	1178	171	171	1178	0.871	1227	122	146	1203	0.900
	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR
	0.850	0.848	0.852	0.850	0.151	0.873	0.873	0.873	0.873	0.126	0.900	0.893	0.909	0.901	0.108
CNN-SVM	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC
	1161	188	184	1165	0.859	1215	134	146	1203	0.895	1251	98	107	1242	0.911
	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR
	0.862	0.863	0.860	0.861	0.136	0.896	0.892	0.900	0.896	0.108	0.924	0.921	0.927	0.924	0.079
DBN-MLP	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC	TP	FN	FP	TN	AUC
	1175	174	175	1174	0.869	1231	118	135	1214	0.908	1276	73	85	1264	0.920
	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR	Accuracy	Precision	Recall	F1-Score	FPR
	0.870	0.870	0.871	0.870	0.129	0.906	0.901	0.912	0.906	0.100	0.941	0.937	0.945	0.941	0.063

. By comprehensively considering Accuracy, Precision, Recall, F1-Score and AUC, the rankings of modeling effectiveness for various models and factor combinations are shown in

Table 17. Rankings of modeling effectiveness for various models and factor combinations.

Model and Combination	DBN-MLP + No.3	CNN-SVM + No.3	DBN-MLP + No.2	CNN + No.3	CNN-SVM + No.2
Ranking	No.1	No.2	No.3	No.4	No.5
Model and Combination	RF + No.3	SVM + No.3	CNN + No.2	DBN-MLP + No.1	DBN-SVM + No.1
Ranking	No.6	No.7	No.8	No.9	No.10
Model and Combination	CNN + No.1	RF + No.2	SVM + No.2	RF + No.1	SVM + No.1
Ranking	No.11	No.12	No.13	No.14	No.15

.

Among the five models, DBN-MLP yielded the best performance. This can be attributed to the hierarchical feature extraction enabled by its multi-layer network architecture. As network depth increases, the model progressively learns more abstract and global feature representations. In the context of LSM, multi-source data encompassing geological, topographic and meteorological information are inherently high-dimensional and complex. The stacked RBM structure in a DBN allows for progressive abstraction of such data, thereby uncovering deep-seated latent patterns and hazard-related regularities. Specifically, the three-layer RBM stacking employed in this study enables the DBN to gradually extract features from the training samples, from elementary to highly abstract levels, providing more informative and discriminative data representations for subsequent processing.

5.3. LSM Results

LSM results of the DBN-MLP model and combination No.3 were the best, and the landslide susceptible probabilities were divided into five levels: extremely low susceptible areas [0.000, 0.200), low susceptible areas [0.200, 0.400), medium susceptible areas [0.400, 0.600), high susceptible areas [0.600, 0.800) and extremely high susceptible areas [0.800, 1.000]. LSM results based on the DBN-MLP model are shown in Figure 10 and

Table 18. LSM results based on the DBN-MLP model.

Combination	No.1	No.2	No.3	No.1	No.2	No.3	No.1	No.2	No.3	No.1	No.2	No.3
LSM results	Number of partition grids			Proportion of partition grids (%)			Number of landslide grids			Proportion of landslide grids (%)
Extremely low susceptible areas	247,674	243,794	263,027	31.98	31.47	33.96	24	15	13	1.64	1.03	0.89
Low susceptible areas	164,564	124,699	113,539	21.25	16.10	14.66	27	23	17	1.85	1.58	1.16
Medium susceptible areas	185,914	253,151	233,292	24.00	32.68	30.12	114	71	55	7.81	4.86	3.77
High susceptible areas	124,564	102,652	117,799	16.08	13.25	15.21	268	279	277	18.36	19.11	18.97
Extremely high susceptible areas	51,854	50,274	46,913	6.69	6.50	6.05	1027	1072	1098	70.34	73.42	75.21

.

The grids of the extremely high susceptible areas account for 6.69%, 6.50% and 6.32% of the total when employing combination No.1, No.2 and No.3, respectively, mainly distributed in the northwest, south and east of Boshan District. The landslide grids distributed in the extremely high susceptible areas account for 70.34%, 73.42% and 75.21% of the total when employing combination No.1, No.2 and No.3, respectively. This indicates that compared with combinations No.1 and No.2, combination No.3 corresponds to the smallest extremely high-susceptibility areas and the highest proportion of landslide grids, which means it achieves the best modeling effect.

6. Discussions

6.1. LSM Results of Different Combinations

The combination No.3 and the DBN-MLP model were used as the benchmark. LSM results of the benchmark were compared with the results of the combinations No.1 and No.2, and the study area was divided into overestimation areas, underestimation areas and the same areas, as shown in Figure 11.

The LSM results of different combinations are quite varied. The overestimation areas are distributed in the south of Boshan District, while the underestimation areas are in the northwest for combination No.1. The overestimation areas are evenly distributed, while the underestimation areas are in the northwest of Boshan District for combination No.2. The error estimation areas were superimposed with some hazard factors, as shown in Figure 12 and Figure 13.

The coincidence rate between the overestimated areas and the high-elevation areas is high, and that between the underestimated areas and areas near rivers is also high, indicating that the DBN-MLP for the combinations No.1 and No.2 overestimates the elevation and underestimates the distance from rivers.

6.2. LSM Results Based on Different Models

LSM results of the benchmark were compared with the results of RF, CNN and CNN-SVM, as shown in Figure 14.

The error-estimation areas based on the CNN show a patchy distribution. The RF has the largest error-estimation areas, which are mostly overestimation and show a scattered distribution. The CNN-SVM has the smallest error estimation areas, which are basically within the error estimation areas of other models. The overestimation areas and underestimation areas of the CNN-SVM were superimposed with some hazard factors, as shown in Figure 15.

Underestimation areas are distributed in areas close to roads. The distribution of the overestimation areas is scattered, and the coincidence rate of the underestimation areas and the areas close to the faults is high. Compared with the DBN-MLP, the other models underestimate the distance from the road and overestimate the distance from the fault. In summary, the RF, CNN and CNN-SVM easily discard the feature information of some factors, missing the optimal accuracies of the models. It should be noted that the error estimation areas are primarily described in a descriptive manner. The underlying causes of these errors are likely related to the logical structure and intelligence level of the model, yet the specific error-inducing mechanisms have not yet been addressed by researchers. This could serve as a potential topic for future investigation.

7. Conclusions

This study selected the best combination and model through comparative studies and revealed the degree of influence of each hazard factor on landslide susceptibility, greatly improving LSM accuracy, which can provide a scientific basis for land use planning.

(1)

Three hazard factor combinations considering time-varying factors (No.1: static factors + values of time-varying factors in 2021; No.2: static factors + annual values of time-varying factors; No.3: static factors + interannual variation values of time-varying factors) were constructed. LSM was conducted based on the SVM, RF, CNN, CNN-SVM, and DBN-MLP. The results show that among the three combinations, the combination No.3 is the best, followed by the combination No.2; among the five models, the DBN-MLP is the best, followed by the CNN-SVM. The extremely high susceptible areas mainly distribute in the northwest, south and east of Boshan District.

(2)

The combination No.3 and DBN-MLP were used as the benchmark; the LSM results of different combinations and models were compared. The results show that the extreme tendency of the LSM results of the combinations No.1 and No.2 are strong, and they are easy to produce error estimation areas, which overestimate the elevation and underestimate the distance from river; the LSM results of the CNN-SVM are closer to those of the benchmark, which underestimates the distance from road and overestimates the distance from fault.

(3)

Although the DBN-MLP performs well in handling uncertainties, its results can still be influenced by various factors, potentially leading to biased inferences. The study area contains 99 landslide sites, represented by 4498 landslide grid cells. Among these, 3149 cells were used for training and 1349 for validation. While this sample size can generally meet the basic requirements for model training, increasing the number of landslide samples would likely improve predictive performance. When landslide grid cells are limited, pre-training the model with landslide samples from other regions, followed by transfer learning using samples from the study area, can also help achieve optimal modeling results. Furthermore, employing cross-validation for model parameter tuning and constructing hybrid algorithms through ensemble learning can effectively mitigate the inherent randomness and bias of a single model. Future research should continue to address these issues in greater depth.