Assessment of landslide hazard under specific rainfall scenarios based on a hybrid CNN-TRIGRS and matrix approach: a case study of Meishan Town, Zhejiang Province, China

Abstract

As a frequent and devastating global geological hazard, landslides pose significant threats to communities, infrastructure, and the environment. The study area in Meishan Town, China, is particularly susceptible to rainfall-induced landslides due to frequent typhoons and rainstorms. This study proposes a novel hybrid framework that integrates a Convolutional Neural Network (CNN) with the TRIGRS physical model for landslide hazard assessment under four rainfall scenarios. The core innovation is a transparent and interpretable matrix-based coupling method that combines a CNN-derived landslide susceptibility index with the Factor of Safety (Fs) computed by TRIGRS, enabling a more comprehensive hazard zonation. To address the prevalent issue of imbalanced data in landslide inventories, we optimized the CNN training by comparing SMOTE-TL and RUS sampling strategies, finding SMOTE-TL significantly superior (AUC: 0.87 vs. 0.83). Our approach, which does not require extensive pre-failure rainfall data, produces hazard maps that are strongly consistent with the historical landslide inventory. This study provides an efficient and practical solution for landslide hazard assessment, particularly in data-scarce regions.

Introduction

As one of the most frequent and serious geological disasters, landslides result in considerable casualties and economic losses globally, with mountains as the well-recognized places of their occurrence^1–3. Many external factors, such as earthquake, intense rainfall, storm waves, and/or human activities, may trigger the occurrence of landslides, among which the rainfall is the most important and common one^4–6. Owing to the rapid urbanization and global climate change, both the occurrence frequency and damage extent of landslides may increase gradually in future decades⁷. Therefore, effective hazard assessment and management should be further conducted to reduce the probability of landslide occurrence.

It is of great importance for landslide mitigation to map the landslide hazard⁸. Currently, the hazard is generally assessed by two approaches. The first one is on the base of the spatial and temporal probabilities of landslide occurrence^9,10. The landslide hazard is generally expressed by multiplying the spatial probability, which is frequently described by the rainfall threshold, by temporal probability, which is basically represented by the landslide susceptibility index^11,12. For example, Nguyen et al.¹³ predicted the temporal probability of landslide occurrence by combining the physics-based model and extreme value analysis, and then obtained the landslide hazard probability by separately multiplying the predicted temporal probability by those achieved by CNN model, logistic regression model, and naive Bayes model. Kim et al.¹⁴ developed a technique to predict the probability of rainfall-induced landslides on the base of nonstationary extreme value analysis (NS-EVA) and random forest approach. However, both the determination of rainfall threshold and selection of rainfall data may have great effect on the prediction accuracy, and the temporal probability models do not consider the effect of soil depth and geotechnical properties¹⁵. The second one is dependent on the factor of safety (Fs) of a slope and the probability of slope instability. The Fs is computed according to physical models¹⁶, such as the SHALSTAB model¹⁷, TRIGRS model¹⁸, and Scoops3D model¹⁹, and the Fs is converted into the probability of slope instability, namely the hazard index, by probabilistic analysis methods such as Monte Carlo approach²⁰, Poisson model²¹, and point estimation²². In this paper, we present a novel technique based on an assessment matrix for more effective hazard prediction of rainfall-induced shallow landslides. This technique integrates landslide susceptibility and slope stability while accounting for the spatial distribution of landslides and geotechnical properties.

The models for landslide susceptibility assessment (LSA) are generally categorized into three classes, namely, statistical models, machine learning (ML) models, and deep learning (DL) models. The statistical models mainly include the information volume (IV) model³, analytical hierarchy process (AHP)²³, and weight of evidence (WoE)²⁴. The ML models generally include the logistic regression (LR)²⁵, decision tree (DT), and support vector machine (SVM)²⁶. The DL models basically include the CNN model and deep neural network (DNN) model²⁷. While classical machine learning (ML) models such as Random Forest (RF) and Support Vector Machines (SVM) have been widely and successfully applied in landslide susceptibility assessment (LSA) for their robustness, they typically rely on manually selected and engineered features. This process can be subjective and may not fully capture the complex, non-linear relationships and spatial context among various conditioning factors. In contrast, Deep Learning (DL) models, particularly Convolutional Neural Networks (CNNs), offer a distinct advantage through their ability to perform automatic feature extraction. In this paper, LSA was conducted by the CNN model which outperforms the conventional ML models²⁸. Furthermore, 10 factors including elevation, slope, aspect, plane curvature, distance to rivers, distance to roads, lithology, SPI, TWI, NDVI were selected and then validated by means of Pearson correlation analysis and multicollinearity method. The original database were separately sampled by SMOTE-TL and RUS techniques to train the constructed CNN model, and finally analyzed the prediction precision under two sampling approaches. Subsequently, the Fs of rainfall-induced landslides was calculated based on the TRIGRS model which is on of the most widely used models for transient stability analysis of slopes²⁹ and has been successfully applied in landslide assessment at various basin levels³⁰. Recent advancements have further demonstrated its utility; for instance, it has been dynamically coupled with run-out models for detailed post-failure analysis and integrated with machine learning models to enhance debris flow susceptibility assessment under rainfall scenarios. Its application in hybrid modeling frameworks continues to be a vibrant area of research^31–33. Additionally, landslides may be triggered by either short-duration intense rainfall or long-duration rainfall. Therefore, four conditions, namely, long-duration moderate rain, heavy rain, torrential rain, and short-duration intense rain, were considered for the slope stability analysis. Finally, the landslide hazard was mapped by combining the slope stability results and LSA results. To achieve this integration, we propose a novel matrix-based coupling framework. Unlike conventional weighted overlay or black-box ensemble methods, our matrix approach provides a transparent and rule-based system for fusing the probabilistic output of the CNN (susceptibility) with the deterministic output of the TRIGRS model (Fs). This allows for an interpretable hazard classification where each category (e.g., ‘high hazard’) has a clear physical and statistical meaning derived from the intersection of a specific stability state and susceptibility level. This framework is designed to offer a more comprehensive and practical hazard assessment tool, particularly valuable for data-scarce regions.

Study area

The study area of Meishan township, located in the northwest of Changxing county, Zhejiang Province, China is dominated by low mountains basically ranging from 160 to 250 m, with longitudes 119°36′51.54″E to 119°47′32.31″E and latitudes 31°1′14.95″N to 31°10′58.38″N, and covers 214.3km², as shown in Fig. 1. The lithology of the study area consists mainly of quartz sandstone, quartzite, sandstone, and shale, with the oldest strata of Devonian Wutongshan Formation and Silurian Tangjiawu Formation near the basin border (based on the 1:50,000 Regional Geological Map of Changxing County). The weathering characteristics of these lithologies vary significantly. Shale and argillaceous sandstone, for instance, are prone to deep weathering, typically forming thicker residual and colluvial soil covers. In contrast, quartzite and thick-bedded quartz sandstone are more resistant, often outcropping as bedrock or with only a thin veneer of weathered material. The Quaternary strata, mostly observed in the plain, are basically composed of Holocene alluvial and lacustrine deposits. The geological structures primarily include faults and folds, which may further influence local weathering and soil thickness.The observed failure mechanism is predominantly shallow translational, with slip surfaces often located at the contact zone between the weathered soil and the underlying less permeable bedrock. This characteristic makes the infinite slope assumption, a foundation of the TRIGRS model, a reasonable approximation for stability analysis in this setting.

Fig. 1.

Location and landslide inventory of study area. This map shows the specific geographical location, topographic elevation, and distribution of historical landslide points. The landslide inventory was compiled based on historical disaster records, interpretation of high-resolution remote sensing images (e.g., Google Earth), and field verification. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com).

The study area experiences a humid subtropical monsoon climate with great rainfall difference in various seasons, and is easily subjected to long-duration moderate rain during the period from March to May and to torrential rain during the period from June to July. The study area has the average annual rainfall of 1347.3 mm, with maximum annual rainfall of 2383.8 mm in 2016 and minimum annual rainfall of 1012.2 mm in 2013.

The combination of the aforementioned geological and climatic conditions fundamentally predisposes this area to landslides. The hilly topography and relatively steep slopes (Fig. 1) provide the necessary topographic potential for slope failures. Weak rock layers such as shale are prone to weathering, resulting in overlying colluvial and residual soil deposits of varying thickness on the slopes. These soils are generally loose-structured and relatively permeable, providing both the material and pathways for rapid rainfall infiltration and shallow sliding. The observed failure mechanism is predominantly shallow translational, with slip surfaces often located at the contact zone between the weathered soil and the underlying less permeable bedrock. The characteristic rainfall patterns of the study area—whether prolonged spring rain or short-duration intense typhoon rain—can lead to rapid infiltration of substantial water. This process saturates the soil near the contact zone, causing a sharp increase in pore-water pressure and a decrease in effective stress, thereby triggering shallow landslides. Consequently, Meishan Town serves as a typical case for studying rainfall-induced shallow landslides. Total 45 historical landslides were recorded, mostly belonging to the shallow retrogressive type and occurring in the hilly regions.

Methodology and data

Methods

Figure 2 presents a methodological flowchart that outlines the overall framework of this study, illustrating the data flow and integration between the CNN and TRIGRS models. The subsequent subsections (3.1.1 to 3.1.3) provide detailed descriptions of each component.

Fig. 2.

Flowchart of this study. Methodological flowchart of the proposed hybrid CNN-TRIGRS framework. The diagram illustrates the data flow and integration process: input data (left) are fed into two parallel branches—the CNN model for susceptibility assessment and the TRIGRS model for stability analysis under various rainfall scenarios. The outputs from both branches, a landslide susceptibility map and a factor of safety (Fs) map, are then combined through the matrix-based coupling framework (Table 1) to generate the final landslide hazard zonation maps. The results are validated against historical landslide inventory using metrics such as frequency ratio and AUC.

TRIGRS model and rainfall scenarios

The TRIGRS model, developed by the United States Geological Survey, is a grid-based technique for computing the transient slope instability induced by rainfall, consisting of an infinite slope stability module, a transient rainfall infiltration module, and a hydrology module³⁴. The transient rainfall infiltration module was used to estimate the change in pore water pressure, and the infinite slope stability analysis was conducted to roughly calculate the safety factor of each pixel³⁵. The assumed boundary conditions for TRIGRS model are illustrated in Fig. 3. TRIGRS may consider the initial conditions of unsaturated soil derived by³⁶ or saturated soil proposed by³⁷. Furthermore, the TRIGRS model linearized the Richard equation which simulates the rainfall infiltration by vertically homogeneous and isotropic material³⁸. The Richard equation is expressed as:

1

Fig. 3.

Assumed boundary conditions for TRIGRS model. (modified from Baum et al.³⁵). This schematic, modified from Baum et al., depicts the boundary conditions used to simulate one-dimensional vertical fluid flow in homogeneous materials under both saturated and unsaturated conditions. The model calculates variations in pressure head and subsequently computes the factor of safety for slopes using an infinite-slope stability model.

where denotes the water content of soil, t is time, Z represents the vertically downward coordinate, is the hydraulic conductivity, denotes the slope surface, and represents the pore water pressure.

The soil-water characteristic curve for unsaturated soil is approximated by the Gardner model³⁹, and the input parameters include the saturated water content , residual water content , Gardner’s fitting parameter (assumed to be proportional to capillary fringe height), and saturated hydraulic conductivity. The related parameters for hydraulic conductivity are determined by the Eqs. (2) and (3).

2

3

Another important role of TRIGRS is the infinite slope stability analysis on the assumption that the slope is horizontally homogeneous with potential rupture parallel to the surface. The slope stability is generally represented by the factor of safety (Fs), with Fs < 0.75 for very unstable, 0.75 ≤ Fs < 1 for unstable, 1 ≤ Fs < 1.25 for potential unstable, 1.25 ≤ Fs < 1.5 for moderately stable, and Fs ≥ 1.5 for stable. The Fs of each grid cell with respect to depth and time is computed by¹⁹:

4

where Z is the soil depth, is the effective soil cohesion, is the soil cohesion, is the internal friction angle, is the pressure head with respect to time and depth, is the slope angle, is the unit weight of water, and is the unit weight of soil.

According to the data about the rainfall of the study area collected in recent ten years, the average annual rainfall is 1524.2 mm, the maximum annual rainfall is 2383.8 mm in 2016, the minimum annual rainfall is 1012.2 mm in 2013, the maximum monthly rainfall is 252.4 mm in June, the minimum monthly rainfall is 58.7 mm in December, the maximum 24 h rainfall is 182.6 mm in 2019, the maximum 12 h rainfall is 137.5 mm in 2012, the maximum 6 h rainfall is 104.8 mm in 2016, the maximum 3 h rainfall is 91.3 mm in 2016, the maximum 1 h rainfall is 87.7 mm in 2016, and the maximum continuous rainfall duration is 8 days. The landslide may be triggered by either short-duration rainfall or long-duration rainfall⁴⁰. Therefore, four rainfall conditions were set in this paper, as listed in Table 2. In the simulations, a constant rainfall intensity was assumed throughout the specified duration for each scenario.

Table 2.

Parameters for various rainfall conditions.

No.	Condition	Duration	Intensity
1	Long-duration moderate rain	2d	15 mm/d
		4d
		6d
		8d
2	Long-duration intense rain	3 h	Heavy rain of 10 mm/h
		6 h
3		12 h	Torrential rain of 20 mm/h
		24 h
4	Short-duration intense rain	0.5 h	50 mm/h
		1 h
		2 h
		4 h

CNN model

The CNN model is a deep learning algorithm on the base of neural network, and a CNN structure commonly consists of an input layer, a convolutional layer, a pooling layer, a fully connected layer and an output layer⁴¹. Building upon prior comparative research which demonstrated its superior performance over conventional machine learning methods for this region⁴², the CNN models outperform the conventional ML models in may aspects such as feature extraction and considerable data processing. For example, the activation function of Rectified Linear Unit (ReLU) greatly accelerates the CNN training⁴³.

For LSA in this study, a one-dimensional Convolutional Neural Network (CNN-1D) architecture was specifically designed and implemented. The model was chosen for its efficiency in processing the vectorized format of our geospatial data, where each grid cell is represented by a 1D feature vector comprising the ten selected conditioning factors (elevation, slope, aspect, etc.)⁴⁴. The network architecture, as illustrated in Fig. 4, was constructed using the PyTorch framework. It begins with an input layer that receives the 1D feature vectors. These inputs are then processed through two consecutive blocks, each containing a one-dimensional convolutional layer followed by a max-pooling layer. The first convolutional layer employs 32 filters with a kernel size of 3, while the second uses 64 filters with a kernel size of 2. Both convolutional layers use the Rectified Linear Unit (ReLU) activation function to introduce non-linearity. A max-pooling operation with a pool size of 2 is applied after each convolution to reduce dimensionality and enhance feature invariance.

Fig. 4.

CNN model structure. Architecture of the 1D Convolutional Neural Network (1D-CNN) used in this study. The schematic illustrates the network structure comprising an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. A dropout layer is incorporated to mitigate overfitting.

To mitigate overfitting—a critical concern given the complex nature of the model and the limited landslide samples—a dropout layer with a rate of 0.5 is incorporated after the final pooling layer. The extracted features are then flattened and passed through a fully connected layer, which maps them to the output layer. The output layer utilizes the Softmax activation function to generate the final probabilistic prediction for the two classes: landslide and non-landslide.

The model was trained using the Adam optimizer with an initial learning rate of 0.001. The loss function was categorical cross-entropy. Training was conducted for a maximum of 100 epochs with a batch size of 64. To prevent overfitting, early stopping was implemented, monitoring the validation loss with a patience of 10 epochs, restoring the best model weights. Key hyperparameters (number of filters, kernel sizes, dropout rate, learning rate) were optimized through a manual grid search process, where different combinations were evaluated based on model performance (accuracy and loss) on the validation set. The final selected parameters are summarized in Table 3.

Table 3.

Parameters related to CNN.

Item	Value	Item	Value
Kernel size	3 (first layer) 2 (second layer)	Error function	Cross-entropy
Max pooling	2 × 2	Optimizer	Adam
Activation function	ReLU	Learning rate	0.001
Dropout rate	0.5	Epoch	100

Matrix-based analysis

Traditional landslide hazard assessment requires consideration of both spatial and temporal probabilities of occurrence. The core logic of the matrix-based fusion method proposed in this study is as follows: the landslide susceptibility index predicted by the CNN model is treated as a proxy for spatial probability, while the real-time factor of safety (Fs) calculated by the TRIGRS model under specific rainfall conditions serves as an indicator of the slope’s physical state (i.e., instability propensity). By constructing the decision matrix shown in Table 1, we couple these two dimensions of information. This framework is not merely another ensemble method, such as weighted linear combination or Bayesian averaging, which often operate as ‘black boxes’. Instead, it provides a rule-based decision system where the final hazard level is determined by the intersection of discretized classes from two interpretable dimensions: the inherent spatial propensity for landslides (susceptibility) and the transient physical state of the slope (stability). The matrix explicitly maps combinations of ‘Susceptibility (Very Low to Very High)’ and ‘Stability (Stable to Very Unstable)’ to a final ‘Hazard (Very Low to Very High)’ level. For example, a grid cell classified as having ‘High Susceptibility’ and being ‘Unstable’ is logically assigned a ‘High Hazard’. This enables the spatial identification of ‘hotspot’ grids that are not only located in high susceptibility zones but also tend to be unstable under current hydrological conditions⁴⁵. This approach essentially integrates ‘where landslides are likely to occur’ with ‘when/under what conditions failure is likely,’ achieving a quasi-dynamic hazard assessment for rainfall-induced shallow landslides⁴⁶. Compared to other assessment models, the matrix-based model is straightforward and intuitive, easy to create and use, with low cost and time efficiency. It does not require complex datasets and is particularly suitable for landslide hazard assessment in most regions.

Table 1.

Matrix for landslide hazard assessment.

Data sources

As mentioned, this study integrates a CNN model and the TRIGRS model to assess landslide susceptibility and slope stability, respectively. The execution of both models relies on a suite of high-quality spatial and attribute data. Therefore, this section systematically details the sources, processing procedures, and justification for all input data and parameters.

The landslide occurrence is generally influenced by various external and internal factors⁴⁷. For LSA, only geological environment conditions such as terrain and lithology are considered and the selection of appropriate factors is very essential. The remote sensing approaches such as high resolution satellite images and aerial photographs can achieve crucial information about landslides in a cost-effective manner⁴⁸. Therefore, total 10 factors, namely, elevation, lithology, slope aspect, slope, plane curvature, distance to rivers, distance to roads, topographic wetness index (TWI), stream power index (SPI), and normalized difference vegetation index (NDVI), were selected for LSE according to previous research, remote sensing interpretation, field survey, and geological environment, as shown in Fig. 5. The topographic factors such as slope and profile curvature were extracted from DEM data with spatial resolution of 30 m × 30 m. The distance to roads, distance to rivers, and NDVI were obtained from Landsat-8 remote sensing images with a spatial resolution of 30 m.

Fig. 5.

Landslide factor maps. (a) Elevation/m, (b) aspect, (c) slope /°, (d) plane curvature, (e) distance to rivers /m, (f) distance to roads/m, (g) lithology, (h) SPI, (i) TWI, (j) NDVI. Classification maps of ten landslide conditioning factors. These maps were generated through ArcGIS analysis, where color gradients represent distinct classification zones. The classified data will be used to construct the dataset for subsequent Convolutional Neural Network (CNN) modeling. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com)

For the TRIGRS model, given the complexity of its parameter configuration and data preparation, we employed a simplified MATLAB-based algorithm (MAT.TRIGRS) developed by Ma Siyuan⁴⁹ to efficiently handle the model inputs and perform the computations. The TRIGRS model needs a great number of parameters involving terrain, soil hydrology, soil strength, and rainfall. The elevation, slope, and flow direction were extracted from DEM by ArcGIS. Soil hydrology data include the soil depth, saturated hydraulic conductivity (Ks), initial surface flux (I_ZLT), and saturated diffusion coefficient (D0). Moreover, the soil depth is vital for TRIGRS model in the calculation of slope stability. The slope is assumed to be inversely proportional to soil thickness depth ranging from 0.1 m to 5 m, and the soil depth approaches 0 m when the slope is greater than 45°⁴⁷. Thus, the function of soil depth y with respect to slope x, according to the field survey data, can be approximated by a linear function (Eq. 5), an empirical relationship supported by field survey data and consistent with common practices in regional-scale modeling⁴⁹. While acknowledging its simplification of complex natural processes, this linear function provides a first-order approximation suitable for regional-scale analysis where high-resolution soil thickness data are unavailable (Fig. 6). The equation is as follows:

5

Fig. 6.

Soil depth map. This map, generated using an established empirical formula, represents the soil depth across the study area and serves as a critical input parameter for the TRIGRS (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability) model. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com)

The saturated hydraulic conductivity (Ks) was determined primarily based on field infiltration tests and laboratory permeability measurements, with regional empirical values referenced where necessary. The initial infiltration flux (I_ZLT) and saturated diffusivity (D0) were set conventionally as 1% and 200 times Ks, respectively¹⁸. The geotechnical parameters (cohesion, friction angle, and unit weight) were obtained by measuring the soil samples collected in the field. To address the inherent uncertainty of input parameters and identify the most influential factors controlling slope stability, we conducted a preliminary sensitivity analysis using the Morris method to evaluate the sensitivity of the Factor of Safety to variations in key parameters. Preliminary results indicate that Fs is most sensitive to changes in friction angle and soil depth, followed by cohesion, while exhibiting relatively low sensitivity to Ks within the tested range. This underscores the importance of accurately constraining shear strength parameters and soil thickness in future applications. The study area was divided into five different weathering soil regions, zone A to zone E (Fig. 5g). Table 4 lists the related soil parameters for TRIGRS model.

Table 4.

Parameters for TRIGRS model.

Parameter	Zone A	Zone B	Zone C	Zone D	Zone E
Cohesion (kN/m2)	22	15	24	30	18
Friction angle (°)	19	24	18	35	20
Weight (kN/m3)	20	17	21.5	23.5	22
Ks (m/s)	2.7 × 10− 6	3.8 × 10− 6	2.5 × 10− 6	2.3 × 10− 6	3.1 × 10− 6
D0 (m2/s)	5.4 × 10− 4	7.6 × 10− 4	5.0 × 10− 4	4.6 × 10− 4	6.2 × 10− 4
IZLT (m/s)	2.7 × 10− 8	3.8 × 10− 8	2.5 × 10− 8	2.3 × 10− 8	3.1 × 10− 8

LSA

Selection of factors

Pearson correlation analysis

The selected factors for LSA should be independent of each other to eliminate the influence of correlation between these factors. The Pearson analysis is one of the most widely used techniques to find the correlation between variables⁵⁰. The heat map for correlation matrix about various variables is demonstrated in Fig. 7, and each cell has a correlation coefficient ranging from − 1 to 1. The color reflects the correlation degree, with lighter shade denoting higher positive correlation and darker shade denoting greater negative correlation⁵¹. It is generally considered that two factors has very high correlation if the coefficient is over 0.8. All the factors selected in this paper match the correlation requirements.

Fig. 7.

Results about correlation matrix for study area. Pearson correlation analysis heatmap of ten evaluation factors. The heatmap depicts correlation coefficients between factor pairs, where increasing intensity of red hues denotes stronger positive correlations, while deeper blue hues indicate stronger negative correlations.

Multicollinearity analysis

The multicollinearity analysis should be performed before LSA to verify the linear independence of factors in terms of tolerance (TOL) and variance inflation factor (VIF). A factor is generally considered to be independent when TOL>0.2 and VIF<5⁵². Table 5 lists the TOL and VIF values of ten factors, indicating that all the factors are mutually independent.

Table 5.

TOL and VIF for various factors.

Factor	TOL	VIF
Elevation	0.246	1.897
Slope	0.392	2.548
Aspect	0.993	1.007
Plane curvature	0.795	1.258
Lithology	0.987	1.013
Distance to rivers	0.243	3.227
Distance to roads	0.267	3.749
SPI	0.943	1.061
TWI	0.729	1.371
NDVI	0.631	1.584

Training samples

Imbalance datasets are frequently encountered in machine learning classification, which may bias the minority class and then deteriorate the model performance⁵³. Moreover, the number of landslides is commonly far less than that of non-landslides when LSA is taken as a task of binary classification. Therefore, this study employs a hybrid sampling technique combining RUS (Random Under-Sampling) and SMOTE-TL to balance the dataset, selecting a more appropriate sampling strategy for subsequent analysis. RUS is a simple yet effective method widely applied in data processing for LSA. It addresses class imbalance by reducing the number of samples in the majority class. The synthetic minority over-sampling technique (SMOTE), one of most extensively used over-sampling methods, was proposed by Chawla et al.⁵⁴. This technique creates new minority samples by interpolating, but is subjected to data overlapping which may be mitigated by the Tomek Links (TL) approach. The SMOTE-TL technique may minimize potential overlapping and enhance class separation⁵⁵ by the following steps:

(1) Randomly select a sample from k nearest neighbors for any minority instance , and then create a new minority instance in terms of , where is a random number between 0 and 1, and .

(2) Randomly select samples from majority class, and the Tomek links will be removed if the nearest neighbors comes from the minority class.

The study area was divided into 252,550 grids, including 40,876 landslide grids and 211,674 non-landslide grids, and all the grids are 30 m 30 m in dimension. Before model training, 70% of landslide samples (28,613 grids) and 70% of non-landslide samples (148,172 grids) were randomly selected and then over-sampled by SMOTE to make the landslide number equal to non-landslide number, leading to the training data of 296,344 grid in total. Subsequently, the Tomek technique was applied to verify the training data, and 84 Tomek links (168 grids) were removed, finally obtaining 296,176 grids. Similarly, the original grids were sampled by RUS technique, finally obtaining 81,752 grids after some non-landslide grids were eliminated. Two types of datasets were input into CNN for training separately. The SMOTE-TL and RUS techniques were implemented by Imblearn of Python, and the CNN model was constructed with PyTorch.

LSA results

The landslide susceptibility indices were calculated after inputting all the data into the trained CNN model. These indices were then introduced to ArcGIS and the landslide susceptibility map was achieved by reassigning each grid with a corresponding value. The susceptibility was conveniently grouped by natural breaks method into five categories: very high, high, medium, low, and very low. Figure 8 illustrates the LSA results by SMOTE-TL and RUS techniques, respectively.

Fig. 8.

(a) SOMTE-TL-CNN, (b) RUS-CNN. Landslide susceptibility maps produced by SMOTE-TL-CNN and RUS-CNN models. The susceptibility is classified into five levels: very low (dark green), low (light green), moderate (yellow), high (orange), and very high (red). Black circles represent recorded landslide locations. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com)

The spatial susceptibility distribution pattern (Fig. 8) shows that high and very high susceptibility zones are predominantly concentrated in two geomorphic units: the steep mountainous areas near the basin margins and the high hills within the basin interior. This spatial pattern is primarily governed by the synergistic effects of the following predisposing factors: firstly, the outcrop of weak rock layers such as shale in these areas, which are prone to weathering and have formed relatively thick weathered soil covers, providing material sources for landslides. Secondly, the terrain in these zones generally features steeper slopes, supplying potential energy for movement. Finally, from a hydrological perspective, these areas typically exhibit higher TWI and greater water convergence capacity, which facilitate rainfall concentration and infiltration, making it easier to reach the critical moisture content that triggers landslides.

Evaluation of model accuracy

Frequency ratio (FR) analysis

The FR approach can be adopted to estimate the prediction accuracy of CNN model. The larger the FR, the higher the probability of landslide occurrence⁵⁶. The FR is generally expressed as:

6

where A is the landslide number in a given susceptibility zone, is the landslide number in the study area, B is the grid number in a given susceptibility zone, and is the grid number in the study area.

The FR accuracy may be referred to as the ratio of the FR summation of very high and very low zones to the FR summation of all zones⁵⁷.

The FR values of various zones and accuracy are listed in Table 6. Both RUS-CNN and SMOTE-TL-CNN have the greatest FR value in the very high zone, indicating this zone may promote the landslide occurrence, and have the smallest FR value in the very low zone. Moreover, the historical landslide are almost in the high and very high zones, which indicates that the prediction results reflect better the spatial distribution of landslides. The SMOTE-TL-CNN model outperforms the RUS remarkably in the prediction accuracy, indicating that the SMOTE-TL-CNN can considerably improve the recognition capacity and prediction performance of CNN model.

Table 6.

FR values for each susceptibility zone.

	Zone	Landslide number		Grid number		FR	Accuracy
RUS-CNN	Very low zone	4	0.089	137,756	0.545	0.163	0.755
	Low zone	6	0.133	54,912	0.217	0.613
	Moderate zone	9	0.200	25,008	0.099	2.020
	High zone	12	0.267	19,845	0.079	3.394
	Very high zone	14	0.311	15,029	0.060	5.228
SMOTE-TL-CNN	Very low zone	0	0	111,096	0.440	0.000	0.920
	Low zone	1	0.022	55,940	0.222	0.100
	Moderate zone	8	0.178	50,081	0.198	0.898
	High zone	15	0.333	18,487	0.073	4.566
	Very high zone	21	0.467	16,946	0.067	6.965

ROC analysis

The ROC curve is frequently adopted to visualize the accuracy of a binary classification model by.

Plotting the false positive rate (FPR) against the true positive rate (TPR) for classification threshold values, with area under the curve (AUC) denoting the model performance. The AUC ranges from 0 to 1, and the greater the AUC, the better the model performance⁵⁸. The AUC values by SMOTE-TL-CNN and RUS-CNN are 0.87 and 0.83, respectively, as illustrated in Fig. 9, indicating that the SMOTE-TL outperforms RUS in LSA.

Fig. 9.

ROC curves (a) SOMTE-TL-CNN, (b) RUS-CNN. Receiver operating characteristic (ROC) curves of SMOTE-TL-CNN and RUS-CNN models. The curves were generated using the testing dataset, with higher area under the curve (AUC) values indicating better predictive performance of the models.

Comprehensive classification performance metrics

To more comprehensively evaluate the classification performance of the CNN models under different sampling strategies, additional metrics including Accuracy, Precision, Recall, and F1-Score were calculated based on the predictions of the testing set. Their definitions and implications in the context of LSA are as follows: Accuracy measures the overall proportion of correct classifications; Precision (for the landslide class) indicates the proportion of true landslides among grids predicted as landslides, relating to the reliability of warnings; Recall (for the landslide class) represents the proportion of actual landslides correctly identified by the model, concerning the completeness of hazard identification; The F1-Score is the harmonic mean of Precision and Recall, providing a single metric to evaluate the model’s performance on imbalanced data. A detailed performance comparison between the SMOTE-TL-CNN and RUS-CNN models is presented in Table 7.

Table 7.

Comparison of classification performance between SMOTE-TL-CNN and RUS-CNN models.

Model	Accuracy	Precision	Recall	F1-Score
SMOTE-TL-CNN	0.916	0.882	0.894	0.888
RUS-CNN	0.873	0.821	0.847	0.834

The analysis reveals that the SMOTE-TL-CNN model consistently outperforms the RUS-CNN across all evaluation metrics. Specifically, SMOTE-TL-CNN achieved a higher overall Accuracy (0.916 vs. 0.873), indicating fewer overall classification errors. More importantly, its balanced and superior performance in both Precision (0.882) and Recall (0.894) is reflected in the highest F1-Score (0.888). This confirms that the SMOTE-TL sampling strategy, by synthesizing minority samples and cleaning the decision boundary, effectively improves the data distribution. It enables the CNN model to achieve both high-reliability landslide localization (high Precision) and high-completeness landslide identification (high Recall). In contrast, the RUS-CNN, by simply discarding a large number of majority class samples, loses significant contextual information, resulting in relatively weaker generalizability and overall performance (F1-Score of 0.834). This comparative result is consistent with the conclusions drawn from the FR and ROC analyses, collectively validating the superiority of the SMOTE-TL-CNN for the LSA task in this study.

Results

Stability results

The Fs values of landslide without rainfall were computed after putting the parameters concerning the terrain, soil, hydrology, and soil strength into the TRIGRS model, as shown in Fig. 10. Then, The Fs values of landslide under four different rainfall conditions were obtained after putting the rainfall intensity into the TRIGRS model, as shown in Fig. 11.

Fig. 10.

Stability results without rainfall (a) Fs contour, (b) grid number of various zones. Stability index map of the study area under non-rainfall conditions. The stability index is classified into five levels: very low (dark green), low (light green), moderate (yellow), high (orange), and very high (red). The corresponding number of grid numbers for each stability class is also indicated. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com)

Fig. 11.

Stability results under four various rainfall conditions (a) Fs values, (b) zone%. Comparative analysis of stability index maps under four rainfall conditions. The maps display the classified stability levels and the percentage distribution of grid numbers for each class, with comparative reference to non-rainfall conditions. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com).

The TRIGRS results reveal distinct instability patterns under different rainfall scenarios. In the absence of rainfall, the area is predominantly stable (74.08% in stable/very stable zones), confirming rainfall as the primary trigger. The expansion of very unstable zones is most pronounced under short-duration, high-intensity rainfall (peaking at 22.15% after 4 h of intense rain), underscoring the critical role of rainfall intensity over duration in rapidly reducing slope stability. Spatially, unstable areas consistently correlate with steeper terrain near basin margins and central hills—regions where all historical landslides are located. Notably, rainfall primarily amplifies hazard in already susceptible zones, while areas initially modeled as stable remain largely unaffected. These patterns collectively demonstrate TRIGRS’s effectiveness in simulating the hydromechanical processes leading to shallow, rainfall-induced landslides in the study area.

Landslide hazard map

The landslide hazard level of each grid was determined with the matrix approach by combining the susceptibility results by SMOTE-TL-CNN and stability results by TRIGRS, and then landslide hazard maps under dry and four rainfall conditions were plotted, as shown in Figs. 12 and 13.

Fig. 12.

Landslide hazard level under dry condition (a) hazard zone, (b) grid number. Hazard index map of the study area under non-rainfall conditions. The hazard index is classified into five levels: very low (dark green), low (light green), moderate (yellow), high (orange), and very high (red). The corresponding number of grid numbers for each hazard class is also indicated. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com)

Fig. 13.

Landslide hazard level under four rainfall conditions. Comparative analysis of hazard index maps under four rainfall conditions. The maps display the classified hazard levels and the percentage distribution of grid numbers for each class, with comparative reference to non-rainfall conditions. (Generated using ArcGIS 10.7, Esri. Available at: https://www.esri.com).

In Fig. 12, there is no very high hazard zone under dry condition. Due to the addition of susceptibility results, the percentage of low and very low zones are 45.366%, slightly smaller than that of stable and relatively stable zones.

Under dry conditions (Fig. 12), there is no very high hazard zone in the study area. The combined percentage of low and very low hazard zones is 45.366%, slightly lower than that of the stable and relatively stable zones, confirming that physical stability defined by the TRIGRS model is the dominant factor in the absence of rainfall. As shown in Fig. 13b, the percentages of very high and high hazard zones increase gradually with rainfall duration, while those of very low and low hazard zones decrease correspondingly, implying an expansion of potentially unstable areas. For the same duration, the overall hazard level increases with rainfall intensity. This trend aligns with the physical mechanism of shallow landslides: higher intensity and longer duration rainfall promotes greater infiltration, leading to a more rapid rise in pore-water pressure and a consequent more pronounced reduction in soil shear strength.

Table 8 lists the Frequency Ratio (FR) values under various rainfall conditions. The FR values for high and very high hazard zones are all greater than 1 across the four conditions, with the very high zone possessing the maximum FR values, indicating it most favors landslide occurrence. Quantitatively, over 90% of historical landslide points fall within the high and very high hazard zones, with none observed in the very low hazard zone. This strong spatial correspondence demonstrates that the proposed matrix-based coupling framework not only effectively integrates static susceptibility and dynamic stability information but also yields predictions that accurately capture the spatial distribution of landslides governed by both geological conditions and rainfall infiltration processes. Therefore, by identifying zones with high and extremely high hazard levels, targeted monitoring and early warning measures can be implemented in these regions, significantly enhancing the efficacy and efficiency of landslide disaster management.

Table 8.

FR values under four different rainfall conditions.

Short-duration intense rain	2d	4d	6d	8d
Very low zone	0	0	0	0
Low zone	0.405	0.398	0.390	0.381
Moderate zone	0.836	0.831	0.825	0.818
High zone	1.712	1.886	1.956	2.176
Very high zone	5.912	5.663	6.280	6.260
Heavy rain	3 h	6 h	12 h	24 h
Very low zone	0	0	0	0
Low zone	0.407	0.384	0.369	0.358
Moderate zone	0.843	0.826	0.866	0.860
High zone	1.686	2.005	2.316	2.459
Very high zone	5.623	6.496	6.254	7.618
Torrential rain	3 h	6 h	12 h	24 h
Very low zone	0	0	0	0
Low zone	0.455	0.413	0.385	0.367
Moderate zone	0.533	0.796	0.831	0.869
High zone	1.956	1.756	1.981	2.321
Very high zone	4.811	5.230	6.186	6.149
Long-duration moderate rain	0.5 h	1 h	2 h	4 h
Very low zone	0	0	0	0
Low zone	0.486	0.442	0.402	0.377
Moderate zone	0.367	0.535	0.846	0.878
High zone	2.126	2.012	1.712	2.068
Very high zone	4.654	4.947	5.663	5.992

Discussion

Advantages

Selecting appropriate techniques for landslide hazard mapping is crucial for the planning, management, and mitigation of mountain landslides. In this paper, a matrix-based approach was adopted to classify landslide hazard into five levels by integrating landslide susceptibility and slope stability analysis, assigning each grid in the study area a calculated hazard (or warning) level. The results indicate that the proposed approach can effectively identify hazard zones and their levels, showing general agreement with the spatial distribution of historical landslides. The core innovation of this study lies in proposing a matrix-based assessment framework that couples CNN and TRIGRS.

As a deep learning algorithm, CNN can automatically recognize features vital for classification through complex layer-by-layer analysis, outperforming conventional machine learning algorithms in many aspects^59,60. The SMOTE-TL technique can effectively augment landslide sample data to some extent and significantly improve prediction accuracy, particularly in cases of inadequate data^61,62. For Landslide Susceptibility Assessment (LSA), the SMOTE-TL-CNN hybrid technique achieves better accuracy than conventional under-sampling. In most literature, rainfall-induced shallow landslides are associated with several hours of intense rainfall or several days of continuous rainfall, which the TRIGRS model can effectively address³⁰. Despite issues of data deficiency and parameter uncertainty, the TRIGRS model remains a valuable tool. The methodology employed in this study is applicable for predicting rainfall-induced shallow landslides in regions with geological conditions comparable to the study area. It offers simplicity and efficiency, eliminating the need for complex computational procedures and thereby significantly reducing operational costs. Furthermore, compared to areas equipped with mature monitoring systems, township regions often suffer from data scarcity. This method does not require detailed pre-failure rainfall data, making it particularly suitable for data-deficient regions. Consequently, it enables decision-makers to intuitively identify zones of high landslide hazard and formulate appropriate management strategies accordingly.

Limitations

Currently, there is no universally accepted technique for effectively conducting landslide hazard assessment, and the approach proposed in this paper also has some limitations. Firstly, the quality of sample data directly affects the prediction accuracy of the model used for LSA⁶³. SMOTE-TL can only reduce but not completely eliminate noise, and the sampling techniques themselves influence LSA accuracy. Secondly, the determination of hyperparameters and factor weights may affect model accuracy. Thirdly, while the CNN model performed well in this study area, its prediction accuracy may vary across different regions⁶⁴. There are numerous models for LSA, and their accuracy remains debated, underscoring the necessity for developing new techniques.

Furthermore, the proposed methodology has several inherent limitations at the data and model levels. First, the 30-m resolution DEM data, upon which the TRIGRS model relies, while appropriate for regional-scale assessment, may not adequately capture micro-topographic features (e.g., local depressions, scarps) that control the initiation of shallow landslides, potentially leading to over- or under-estimation of local instability. Second, the critical soil depth in the model is estimated using a simplified linear slope-depth relationship (Eq. 1). Although this empirical assumption is based on field surveys, it does not fully account for the nonlinear controls on soil spatial distribution exerted by lithological differences, weathering degree, and long-term geomorphic processes, introducing additional uncertainty. Third, the TRIGRS model incorporates a linearized form of the Richards’ equation and employs an infinite-slope assumption. These simplifications, while enhancing computational efficiency, may not accurately simulate the nonlinear characteristics of unsaturated infiltration processes or the failure mechanisms of complex three-dimensional slopes. Finally, the model’s predictive capability is highly dependent on the input geotechnical and hydrological parameters (see Table 2). These parameters are often derived from limited point tests or regional empirical values. Their spatial variability and dynamic changes under intense rainfall conditions are not fully considered, constituting one of the primary sources of uncertainty in the model predictions. It is also important to clarify that the CNN-extracted features do not directly alter the unsaturated seepage calculations within the TRIGRS framework; rather, they serve as a spatial weighting factor in the subsequent matrix coupling stage, where the static susceptibility background adjusts the dynamic stability output to produce the final hazard zonation. Future research should focus on quantifying uncertainty propagation within the coupled framework, for instance by employing Monte Carlo simulations to account for parameter spatial variability, and could further enhance reliability by integrating higher-resolution topographic data, developing process-based soil depth models, and exploring more sophisticated landslide mechanics models; furthermore, while the framework is generic, its transferability to other geomorphological and climatic settings warrants further investigation, as model retraining and parameter recalibration would be necessary when applying it to new regions with different geological and environmental conditions³⁴.

Conclusions

Landslide hazard assessment is crucial for hazard analysis and geological disaster control. In this paper, the landslide hazard levels of Meishan Town, Zhejiang Province, China, under various rainfall conditions were assessed by integrating landslide susceptibility and slope stability. The main conclusions and implications are as follows:

(1) Ten factors, including elevation, lithology, and slope aspect, were selected for landslide susceptibility evaluation (LSE), and their independence was verified using correlation and multicollinearity analyses. Samples were balanced using SMOTE-TL and RUS techniques separately, and susceptibility indices were calculated using a CNN model. Results show that SMOTE-TL-CNN (AUC = 0.87, FR = 0.920) outperformed RUS-CNN (AUC = 0.83, FR = 0.755). This approach effectively mitigated sample imbalance and enhanced model generalizability in data-scarce regions, and provides a reliable technical pathway for high-precision susceptibility mapping at the township scale.

(2) The TRIGRS model was applied to analyze the impact of four rainfall scenarios (long-duration moderate rain, heavy rain, torrential rain, and short-duration intense rain) on the stability of shallow rainfall-induced landslides. Results indicate that the extent of very unstable zones (Fs < 0.75) gradually expands with increased rainfall duration, and regional stability decreases significantly with increased rainfall intensity. This reveals that short-duration, high-intensity rainfall constitutes the most hazardous triggering scenario in the study area, clarifies the critical role of rainfall thresholds in early warning, and confirms the practical utility of the TRIGRS model for scenario-based stability analysis of regional rainfall-induced landslides.

(3) A matrix-based approach was employed to integrate susceptibility and stability results, categorizing hazards into five levels. Hazard zonation maps under various conditions were generated by assigning calculated values to each grid. Frequency Ratio verification demonstrates that the hazard zonation derived from this method aligns well with the spatial distribution of historical landslides and achieves good prediction accuracy for landslide occurrence under different rainfall conditions. The coupled assessment framework developed in this study enables effective integration of static susceptibility and dynamic stability. The resulting hazard zonation maps can directly inform township-level territorial spatial planning, hazard risk zoning management, and graded early warning, providing an intuitive and efficient decision-support tool for landslide prevention and mitigation in relatively data-deficient regions.

Author contributions

ZFW, FGS and XSZ: conceptualization, designed the methodology; ZXW implemented methods, curated the data, analyzed the data, visualized the data, and wrote the original draft; DB and LYQ: writing–review and editing.

Funding

This work was supported by the foundation of Hunan Provincial Key Laboratory of Hydropower Development Key Technology (Grant No.PKLHD202203).

Data availability

The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.