A MaxEnt-TRIGRS hybrid model with dynamic safety factor mapping for enhanced debris flow susceptibility assessment in rainfall-triggered terrains

This study proposes a multi-stage modeling framework for systematic debris flow risk assessment. Initially, the Maximum Entropy (MaxEnt) model was employed to delineate regional debris flow susceptibility patterns, utilizing 36 historical debris flow events and 13 environmental predictors (including topographic, lithological, and rainfall factors). The model performance was rigorously validated through receiver operating characteristic (ROC) analysis, with high-susceptibility zones identified as priority areas for subsequent investigations. Subsequently, 20 representative debris flow sites within these high-risk zones were selected for parameter calibration of the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability (TRIGRS) model. Key hydro-mechanical parameters were determined through inverse analysis integrated with field surveys and laboratory geotechnical tests.

The process of the hybrid model for the new combination (Fig. 3) can be summarized as follows:

MaxEnt model calculation results

Debris flow susceptibility was assessed using MaxEnt³⁷ with disaster locations and environmental variables meeting model specifications. 13 factors (e.g., slope, rainfall, distance to roads) were selected based on material source, transport capacity, and triggering mechanisms (Fig. 4).

The dataset was partitioned into 80% training and 20% testing subsets, and the susceptibility zonation (Fig. 5) revealed high-risk areas concentrated along tectonic lineaments and Quaternary deposits.

During the susceptibility evaluation process, the influence of various factors on historical disaster points is calculated, represented as the contribution of each factor to the model. This contribution expresses the extent to which different factors impact debris flow. Using the Jackknife module of the MaxEnt model, the contribution rate of each factor to debris flow susceptibility can be analyzed. The dark blue bars represent the contribution rate of each factor to susceptibility distribution when no other environmental factors are considered, while the light blue bars represent the total contribution of all other variables when a particular factor is removed. The contribution results of the influencing factors are shown in Fig. 6.

In the debris flow susceptibility assessment, the Jackknife module of the MaxEnt model was utilized to quantify the independent contribution rates of environmental predictors to hazard spatial distribution (Fig. 6). Results identified elevation (32.7%), annual cumulative rainfall (28.1%), and distance to rivers (19.4%) as dominant controlling factors. Dark blue bars represent the independent contribution rate of individual factors (excluding interference from other variables), while light blue bars indicate the comprehensive contribution rate of remaining variables after removing the target factor.

TRIGRS model calculation results

Critical geotechnical parameters for TRIGRS simulations included soil thickness, cohesion (c), internal friction angle (φ), unit weight (γ), initial groundwater level, infiltration rate, and rainfall intensity³⁸. To improve model robustness and capture soil heterogeneity, we divided the study area into three zones according to soil characteristics. Within each zone, we selected representative sampling locations to collect soil specimens.

We quantified parameter uncertainty using laboratory data from Zone 1. We conducted a normal-distribution analysis (Fig. 7d) on Zone 1 parameters to guide conservative parameter selection. Based on field surveys and laboratory tests (Fig. 7a–c), we obtained the following parameter ranges for the study area:

• Cohesion (c): 13.15–22.90 kPa (mean 19.7 kPa, SD 1.8 kPa)

• Internal friction angle (φ): 10.29°–25.56° (mean 20.3°, SD 1.8°)

• Unit weight (γ): 13.27–28.51 kN/m³ (mean 23.5 kN/m³, SD 2.1 kN/m³).

For cohesion and friction angle, we used the mean minus one standard deviation (c = 19.7 kPa − 1.8 kPa = 17.9 kPa; φ = 20.3° − 1.8° = 18.5°). This corresponds to roughly the 16th percentile under a normal distribution, offering a conservative estimate of shear strength while avoiding overestimation of stability. To account for saturation effects, we chose the 75th percentile for unit weight (mean + 0.675 SD = 23.5 kN/m³ + 1.4 kN/m³ ≈ 24.9 kN/m³), reflecting higher bulk density under partial or full saturation.

The single-parameter Sensitivity Analysis in Zone 1 (Fig. 7e): Results show that the factor of safety (FS) is most sensitive to slope angle (θ), cohesion (c), and unit weight (γ). Specifically, Slope angle (θ): 35° ± 5.6° perturbation (reflecting DEM vertical accuracy of ± 2 m) in areas with slopes above 35° altered FS by up to ± 16.0%. Cohesion (c): 19.7 kpa ± 1 SD perturbation (± 4.8 kPa) around the mean (19.7 kPa) altered FS by ± 24.4%. Unit weight (γ): 23.5 kN/m³ ± . SD perturbation (± 1.8 kN/m³) around the mean (23.5 kN/m³) altered FS by ± 7.5%. Similarly, parameter selections for Zones 2 and 3 are presented in Table 3.

Additionally, we observed that stability classifications fluctuate between “marginally stable” and “marginally unstable. These observations support the use of ± 1 SD as the uncertainty bound for c and φ.

The Z-model developed by Saulnier³⁹ is used to estimate the soil thickness Based on data, it is assumed that the maximum and minimum soil thicknesses are 5 m and 2.24 m, respectively. Thus, the soil thickness of the Z-model can be estimated by Eq. 11.

The K_S value is obtained from a 1 km-resolution global KS map⁴⁰. D0 and IZLT are computed via Eqs. (12) and (13). TRIGRS requires ASCII grid inputs, with significant pre-processing time. This study employs MAT.TRIGRS (V1.0)⁴¹ to calculate the factor of safety (FS). The MATLAB version directly processes GeoTIFF data, minimizing manual parameter adjustments and error risks compared to Fortran, while enhancing precision. All geotechnical parameters are listed in Table 3.

The study area experiences a subtropical humid monsoon climate with mean annual precipitation of 1230.5 mm (1980–2010 CMA data), where 85% rainfall concentrates in July–August monsoons. We derived storm intensity parameters by upscaling annual mean precipitation using intensification factors (1.15 × baseline). TRIGRS simulations implemented:

• Transient rainfall sequences 6 cycles (2-h stepwise increases from 12 h duration)

• Hydraulic conductivity 5.2 × 10⁻⁵ m/s

• Failure criterion Factor of Safety < 1.0 with 15% exceedance probability.

Based on the results (Fig. 8), it can be observed that in the high mountainous areas, the regions where slope instability due to debris flow occurs are relatively fewer. In the mid-mountainous areas, the unstable regions with low FS are concentrated near rivers. This is because rainfall causes debris flow materials to accumulate and travel along the rivers, with the erosion of soil along both riverbanks increasing the likelihood of debris flow disasters in lower areas. In the low mountainous and hilly regions, the significant elevation differences provide sufficient momentum for debris flow, making the Fs in these areas the most critical of the three regions. This aligns with actual debris flow cases observed in Beichuan County.

When applying the TRIGRS model to assess debris flow susceptibility, it is important to consider the simplifications inherent in the model, particularly the use of the infinite slope assumption. TRIGRS bases its slope stability analysis on infinite slope theory, which simplifies the complexity of actual terrain. However, in areas with non-parallel slip surfaces or heterogeneous soils, this assumption may be overly simplistic and fail to accurately capture the mechanisms of debris flow initiation. In such cases, the TRIGRS model may either overestimate or underestimate debris flow-prone areas, leading to misjudgments of actual terrain conditions.

Specifically, the infinite slope assumption fails to account for soil heterogeneity, which is common in complex terrains and can significantly influence debris flow initiation mechanisms. Research has shown that, under heterogeneous soil conditions, the physical properties of the soil (e.g., permeability and cohesion) and changes in topography play a crucial role in slope stability. The homogeneous soil conditions assumed by the TRIGRS model may not capture these variations.

Therefore, the accuracy of model evaluations may be affected, especially in areas with complex slip surface morphology, where the traditional infinite slope theory may not provide sufficiently accurate predictions.

Debris flow susceptibility assessment based on gis-integrated spatial coupling weights

This study integrated predictions from the MaXent model and the TRIGRS physical–mechanical model using a weighted overlay algorithm (weights: 0.55 for MaXent, 0.45 for TRIGRS) on a GIS platform, generating a debris flow susceptibility map (Fig. 9). The dynamic safety factor (FS) was classified into six levels via the Jenks Natural Breaks method (Table 4).

This study integrated the MaXent ecological niche model and the TRIGRS physical–mechanical model through a GIS-based weighted overlay algorithm (0.55:0.45) to generate a debris flow susceptibility map. The dynamic safety factor (FS) was classified into six levels using the Jenks Natural Breaks method (Table 4), achieving high predictive accuracy. Results reveal significant spatial heterogeneity: Stable zones (FS ≥ 1.0) dominate 92.62% (960.1 km²) of the 1036.4 km² study area, with extremely stable zones (FS > 2.0) accounting for 78.37% (812.3 km²). In contrast, unstable zones (FS < 1.0) cover 7.38% (76.3 km²), of which the extremely unstable zones (FS < 0.5, 30.4 km²) exhibit a 92.3% spatial match with historical debris flow points. Critical thresholds were identified: When FS declines to 0.5, the area of extremely unstable zones increases exponentially, driven by synergistic interactions between MaXent-derived dominant factors (annual rainfall > 1200 mm, slope > 35°, Dem > 800 m).

Regarding the weight ratio of MaxEnt (0.55) and TRIGRS (0.45), the rationale for choosing this ratio is as follows: The MaxEnt model primarily analyzes the nonlinear relationships between environmental factors and debris flow occurrence, placing greater emphasis on climatic, topographic, and other environmental variables. Therefore, it was assigned a higher weight (0.55) to reflect the importance of these factors. In contrast, the TRIGRS model simulates slope stability under physical conditions, but it has limitations in handling complex terrain and soil heterogeneity. As such, it was given a lower weight (0.45). By setting this weight ratio, we balance the advantages of both statistical analysis (MaxEnt) and physical modeling (TRIGRS) in debris flow susceptibility assessments.

To further justify this ratio, we conducted sensitivity analysis using different weight combinations. The results showed that when MaxEnt’s weight exceeded 0.55, the model overly emphasized environmental factors, leading to an overly concentrated susceptibility zone that did not account for the complexity of topography and rainfall. Conversely, when the TRIGRS weight was too high, the model’s physical component became too limited, failing to capture the nonlinear relationships. Therefore, the 0.55:0.45 ratio was found to be the optimal choice, effectively combining the strengths of both models while maintaining high accuracy in debris flow susceptibility mapping.

We evaluated the impact of model weighting on debris-flow susceptibility by testing three ratios: (1) 70% MaxEnt/30% TRIGRS, (2) 55% MaxEnt/45% TRIGRS, and (3) 30% MaxEnt/70% TRIGRS.

Figure 10 shows that scenario 1 markedly expanded high-susceptibility areas. While it successfully identified most historical debris-flow locations, it also overestimated the high-risk extent, potentially complicating targeted risk management. By contrast, scenario 3 produced a generally low-risk map and failed to identify known debris-flow locations. This outcome reflects the limitations of TRIGRS’s infinite-slope assumption, which simplifies terrain complexity and overlooks soil heterogeneity. Therefore, this weighting is inappropriate for regional susceptibility mapping. Scenario 2 (55% MaxEnt/45% TRIGRS) achieved the optimal balance by reducing false-positive areas and maintaining accurate detection of historical debris flows. Notably, Li et al⁴² used a similar 55:45 ratio in mapping debris-flow susceptibility in Yunyang County, further validating this weighting for regional-scale applications.

Our study introduces a novel hybrid model by integrating the MaxEnt and TRIGRS models for debris flow susceptibility assessment. The primary innovation lies in the unique coupling of machine learning (MaxEnt) with a physical-based model (TRIGRS), addressing the limitations of previous approaches that either relied solely on statistical methods or physics-based models. Unlike purely data-driven models, which often neglect physical mechanisms, our approach incorporates environmental factors while reflecting the underlying geomechanical processes of rainfall-triggered debris flow events. Additionally, this study goes beyond conventional susceptibility mapping by generating a dynamic safety factor distribution, which more accurately predicts the spatial variability of debris flow risk.

Despite the novel integration of MaxEnt and TRIGRS, our study acknowledges several limitations that align with common challenges identified in similar research. First, the quality and resolution of input data, such as Digital Elevation Models (DEM) and meteorological records, play a crucial role in the accuracy of the susceptibility assessment. As Ajin et al.⁴³ emphasized in their study, data quality significantly influences the prediction outcomes of landslide susceptibility models. Similarly, Janizadeh et al.⁴⁴ highlighted that optimizing hyperparameters and improving the quality of input data can substantially enhance model performance, especially in hazard susceptibility assessments. Our work also shares the limitation of being sensitive to the spatial and temporal variability of meteorological data, which can lead to inconsistent predictions in certain regions.

And, while our model improves predictive accuracy by incorporating both statistical and physical models, the hybrid ensemble methods still face challenges related to the integration of diverse data sources and model uncertainty. The model’s performance could be further improved by expanding the dataset, integrating more refined environmental factors, and enhancing uncertainty quantification techniques. For instance, applying Bayesian optimization methods (as seen in Sala et al.⁴⁵) or exploring multi-model ensembles could better address the uncertainties inherent in physical models and machine learning algorithms.

Potential consequences of anthropogenic impacts on ecosystem services and livelihoods

Human activities, such as deforestation, urbanization, and agricultural expansion, significantly influence ecosystem services and local livelihoods, particularly in geohazard-prone regions like Beichuan⁴⁶. These anthropogenic impacts exacerbate the frequency and intensity of natural disasters, such as debris flows and landslides, leading to serious consequences.

Firstly, Natural landscapes, including forests and wetlands, provide vital services such as flood regulation, soil stabilization, and carbon sequestration⁴⁷. However, land-use changes, particularly deforestation, compromise these functions, increasing the vulnerability of slopes to erosion and debris flow. Studies indicate that deforestation contributes to increased surface runoff and soil instability, which directly elevates the risk of landslides.

Secondly, Communities that rely on agriculture and natural resources are particularly vulnerable to the effects of geohazards. The damage to infrastructure, agricultural land, and homes disrupts local livelihoods. Additionally, the loss of ecosystem services, such as fertile soil and clean water, exacerbates these impacts. Displacement due to high-risk areas further contributes to social and economic instability⁴⁸.

Last, This study contributes to this body of knowledge by assessing debris flow susceptibility in Beichuan, offering insights that can inform sustainable land-use planning and disaster risk management, ultimately helping to mitigate human impacts on both the environment and local communities.