Prediction of Shallow Landslide Runout Distance Based on Genetic Algorithm and Dynamic Slicing Method

Abstract

Shallow landslides are often unpredictable and seriously threaten surrounding infrastructure and the ecological environment. Traditional landslide prediction methods are time-consuming, labor-intensive, and inaccurate. Thus, there is an urgent need to enhance predictive techniques. To accurately predict the runout distance of shallow landslides, this study focuses on a shallow soil landslide in Tongnan District, Chongqing Municipality. We employ a genetic algorithm (GA) to identify the most hazardous sliding surface through multi-iteration optimization. We discretize the landslide body into slice units using the dynamic slicing method (DSM) to estimate the runout distance. The model’s effectiveness is evaluated based on the relative errors between predicted and actual values, exploring the effects of soil moisture content and slice number on the kinematic model. The results show that under saturated soil conditions, the GA-identified hazardous sliding surface closely matches the actual surface, with a stability coefficient of 0.9888. As the number of slices increases, velocity fluctuations within the slices become more evident. With 100 slices, the predicted movement time of the Tongnan landslide is 12 s, and the runout distance is 5.91 m, with a relative error of about 7.45%, indicating the model’s reliability. The GA-DSM method proposed in this study improves the accuracy of landslide runout prediction. It supports the setting of appropriate safety distances and the implementation of preventive engineering measures, such as the construction of retaining walls or drainage systems, to minimize the damage caused by landslides. Moreover, the method provides a comprehensive technical framework for monitoring and early warning of similar geological hazards. It can be extended and optimized for all types of landslides under different terrain and geological conditions. It also promotes landslide prediction theory, which is of high application value and significance for practical use.

1. Introduction

Landslides are a common and highly destructive geological hazard worldwide [1]. Among these, shallow landslides form a major category, characterized by limited thickness and volume [2]. Shallow landslides are characterized by their suddenness and group occurrence, making it consistently challenging to accurately predict their runout distance in engineering contexts [3]. Gentle terrain can conceal most shallow landslides, complicating disaster prevention and mitigation efforts. For instance, numerous shallow landslides have occurred in regions like southwest China, southeast Brazil, and Portuguese interior regions [4]. These disasters have had a significant impact on human activities such as housing and transportation.

In recent years, extreme rainfall events induced by climate change have drawn increased attention to the triggering mechanisms and prediction research of shallow landslides [5,6,7]. Some scholars have employed data-driven approaches to analyze large-sample landslide datasets, including traditional statistical models and emerging machine learning techniques. Random forest [8] and deep learning [9] methods have significantly improved prediction accuracy by integrating multi-source data. However, they still heavily rely on historical data [10]. For individual landslides, scholars have employed numerical simulation software, such as PFC 2D (Version 5.0) [11], MATLAB (Version R2021b) [12], and UDEC, to accurately simulate landslide movement. These methods have achieved breakthroughs in accounting for fluid–solid coupling effects [13] and variations in matric suction [14]. However, significant challenges remain in obtaining various parameters. These include viscosity coefficients and creep parameters in viscoelastic models, dynamic variations in friction coefficients, and particle stiffness and bond strength in discrete element models [15,16]. This is due to difficulties in experimental measurement, scale dependency, and the need for inverse calibration. Consequently, computational models still struggle to accurately reproduce complex geological and engineering conditions, ultimately limiting the applicability and accuracy of simulation results. Therefore, further investigation into landslide movement mechanisms is still required.

Some scholars have combined physical modeling and kinematics to derive equations for landslide runout distances, such as the material point model (MPM) [17] and the dynamic slicing method (DSM) [18]. The MPM considers factors like physical properties, topography, geologic structure, and hydrologic conditions. In contrast, the DSM employs the equivalent fluid concept. It simplifies landslides with complex compositions into continua or non-Newtonian fluids [19,20] to establish governing equations of motion. This approach enables the back-analysis of landslide movement processes with different rheological properties and the prediction of potential landslide behavior. By assuming the shape and position of the sliding surface, this method can rapidly yield relatively reliable results, making it widely applicable in engineering practice [21]. Accurate sliding surface identification improves landslide runout distance calculations, but traditional methods relying on expert experience and qualitative analysis lack scientific rigor and accuracy [22,23], and geological surveys are resource-intensive. Advances in computing have enabled modern optimization algorithms, such as genetic algorithms, to be applied to landslide hazard characterization. For example, a GA was used to identify the sliding surface with the smallest stability coefficient in the Simian Mountain landslide [24]; ant colony algorithms optimized model parameters for the Bazhimen landslide [25]; and Monte Carlo methods evaluated key destructive surfaces in the Aso Bridge landslide [26]. Cutting-edge research has significantly enhanced search performance by integrating particle swarm optimization with neural networks [27]. GA simulate natural genetic mechanisms for adaptive global search, offering excellent global optimization, robustness, and wide applicability. However, practical applications face limitations like constraint handling and scalability, with performance heavily dependent on parameter choices and fitness functions. Poor parameter selection can degrade performance [28], and inadequate fitness functions may fail to guide the search process effectively. Improved genetic algorithms have achieved breakthroughs in convergence speed and accuracy through adaptive mutation and elitist strategies [29]. The multi-objective optimization framework [30] simultaneously considers safety factors and geometric characteristics. This allows it to effectively overcome the limitations of traditional ellipsoidal or wedge-shaped assumptions [31]. Meanwhile, non-regular slip surface discretization methods [32] demonstrate superior adaptability to complex geological conditions.

This study aims to enhance the prediction accuracy of shallow landslide runout distances. To achieve this, we innovatively integrate a GA with the DSM. The superiority of this technical framework is validated through comparisons between simulated results and actual case studies. The GA optimizes the slip surface search process, overcoming limitations of traditional morphological assumptions, while the DSM dynamically simulates movement processes based on an improved depth-averaged theory. The proposed approach incorporates an adaptive parameter adjustment strategy, enabling it to more realistically reflect the mechanical behavior of shallow landslides while maintaining practical applicability. It provides reliable theoretical support for disaster prevention and mitigation efforts.

2. Study Area

2.1. Introduction to Landslide in Tongnan District

The shallow soil landslide is located in Xindu Village, Tongnan District, Chongqing, at 105°47′15″ E and 29°56′21″ N (Figure 1). From 15–29 June 2019, there was continuous rainfall in Tongnan District, Chongqing, with the maximum daily rainfall exceeding 110 mm, causing tensile cracks on the landslide surface. These cracks were about 200 m long and 0.05–0.4 m wide at the trailing edge, with localized collapses at the leading edge. Over time, more tensile cracks appeared in the middle of the landslide, causing road bulging and eventual destabilization on June 28. The landslide slid about 5–6 m with a volume of about 100,000 m³, destroying a house at the front edge (Figure 1c).

The landslide’s rear edge was bounded by a steep sandstone wall with a maximum elevation of 438 m. The front edge was cut from the road wall at 398 m, with an elevation difference of 40 m. The landslide was 127 m long and about 8 m thick. The cross-section of the landslide body was delineated along the profile line shown in Figure 1b. Figure 2 clearly shows that the slope has an overall gradient of approximately 26°, with the primary sliding direction oriented at 67°. The bedrock attitude is measured at 248° dip direction with a 2° dip angle. The overlying stratum is Quaternary Holocene landslide accumulation ($Q_4^{del}$), primarily gray–brown powdery clay with crushed stones, offering good water permeability, allowing rainwater to seep downward and increase the landslide body’s weight. The underlying strata are sand and mudstone interbeds from the Upper Jurassic Suining Formation ($J_3^{SN}$), prone to micro-fractures.

Overall, the slope exhibits characteristic features of loose soil mass, a free face at the front edge, and good structural integrity. The slope body can be appropriately modeled as a continuous Bingham fluid [33], which facilitates segmentation using the slice method. This makes it particularly suitable for modeling and analysis using a GA and the DSM.

2.2. Landslide Soil Parameters

Before calculating the landslide runout distance, relevant physical parameters had to be determined. Continuous rainfall was the main cause of this landslide’s destabilization [34,35]. Considering rainfall effects, the simulation used the saturated density of the landslide soil, more closely representing the actual situation [36]. Therefore, in March 2025, we conducted on-site sampling at the landslide location in Tongnan District, Chongqing. After collecting samples, we performed saturation and direct shear tests in the laboratory to obtain soil parameters under saturated conditions. Considering that the landslide had been stabilized for many years and the soil properties might differ from those at the time of the incident, we reviewed the relevant literature to calibrate the parameters, ultimately deriving more reasonable soil parameters (

Table 1. Soil parameters of the Tongnan shallow landslide (data verified based on [4]).

Parameters	Saturation Density	Bed Friction Angle	Internal Friction Angle	Cohesion	Modulus of Elasticity	Poisson’s Ratio
	(kg/m3)	(°)	(°)	(kPa)	(MPa)	(-)
Values	1900	16.5	22	26	8.92	0.35

).

3. Methods

This study integrated the genetic algorithm (GA) and the dynamic slicing method (DSM). Initially, soil parameters were obtained through field sampling, physical experiments, and a literature review. Subsequently, the research was conducted by combining a GA and the DSM. The GA, through population initialization and genetic operations, searches for irregular potential slip surfaces based on termination conditions. It breaks traditional assumptions of circular or elliptical slip surfaces, and derives the slip surface expression via polynomial fitting. The DSM employs depth-averaged theory to analyze post-failure landslide accelerations, velocities, and displacements through model construction, slice processing, and iterative calculations, achieving dynamic prediction of sliding distances, with model evaluation performed using relative error. Finally, to achieve precise predictions, modeling codes for both methods were developed using the Python (Version 2024.1.4) platform and integrated to derive the research results. The detailed procedure is depicted in Figure 3.

3.1. Hazardous Sliding Surface Search

A genetic algorithm (GA) is an adaptive global search algorithm that finds optimal or near-optimal solutions in complex search spaces by modeling natural selection and genetic mechanisms [37]. Its core steps include selection, crossover, and mutation [38]. Selection picks superior individuals from the current population for the next generation. Crossover simulates biological reproduction by exchanging genes between two individuals to generate new offspring. Mutation introduces new genetic diversity by randomly changing offspring genes, preventing the algorithm from falling into local optima [39,40,41].

3.1.1. Fitness Function

In a genetic algorithm, individual fitness represents convergence to an optimal solution. A suitable fitness function improves algorithm speed and convergence [42].

In geotechnical engineering, the safety factor serves as a critical indicator for stability assessment, exhibiting a significantly nonlinear negative correlation with the probability of instability. A lower safety factor indicates a substantial reduction in the safety margin of the geotechnical body. When the safety factor falls below 1, it signifies that the internal shear stress exceeds the shear strength, reaching a limit equilibrium state that ultimately leads to geotechnical failure [43]. The genetic algorithm needs to search for elite individuals within the population during its operation, where higher fitness values correspond to superior performance. To enhance the algorithm’s efficiency and convergence, this study employed the reciprocal of the stability coefficient as the fitness function, thereby ensuring the search process concentrated on the most instability-prone regions [44]. The fitness function is defined as follows:

$$K={\displaystyle \frac{F_{as}}{F_s}}$$

(1)

$$Fitness={\displaystyle \frac{1}{K}}$$

(2)

where F_as denotes the slope resistance, F_s denotes the slope sliding force, K denotes the stability coefficient, and Fitness denotes the fitness function.

Current methods often assume landslide sliding surfaces as regular circular arcs or ellipsoids [45], but actual surfaces are irregular and difficult to represent with common functions. This study searched for hazardous sliding points in each block using the slicing method (Figure 4). After completing the identification process, we employed highly adaptable and operationally efficient cubic polynomial fitting to approximate the complete sliding surface [46], with the goodness of fit evaluated using the coefficient of determination R². This procedure provided a reliable data foundation for subsequent calculations using the DSM.

The stabilization coefficient of the geotechnical body at this point is expressed as follows:

$$K={\displaystyle \frac{{\displaystyle \sum \Delta G_i\cos {\theta }_i+{\displaystyle \sum c_i{l}_i}}}{{\displaystyle \sum \Delta G_i\sin {\theta }_i}}}$$

(3)

where ΔG_i is the standardized value of the self-weight of the ith soil slice; c_i is the cohesive force of the ith soil slice at the sliding surface; l_i is the length of the sliding surface at the lower end of the ith soil slice; and θ_i is the angle between the sliding surface at the lower end of the ith soil slice and the horizontal line.

3.1.2. Genetic Algorithm Model

To ensure smooth operation, the GA model introduces several parameters, including the population size N_p, the crossover probability P_c, the mutation probability P_m, and the number of termination generations N_t [47]. Suitable parameter settings improve efficiency and convergence. In this paper, the population size N_p and the number of termination generations N_t were selected empirically [48]. The crossover probability P_c and the mutation probability P_m were selected using the adaptive selection method proposed by Srinivas [49]. The proposed method dynamically generates differentiated mutation and crossover rates for each individual based on its fitness during every iteration, thereby significantly enhancing the algorithm’s exploration capability throughout the evolutionary process [50]. The adaptive selection method proposed by Srinivas is implemented as follows:

$$P_c=\left\{\begin{array}{cc}{\displaystyle \frac{k_1\left(f_{\max }-f\prime \right)}{f_{\max }-f_{avg}}}& f\ge f_{avg}\\ k_2& f<f_{avg}\end{array}\right.$$

(4)

$$P_m=\left\{\begin{array}{cc}{\displaystyle \frac{k_3\left(f_{\max }-f\right)}{f_{\max }-f_{avg}}}& f\ge f_{avg}\\ k_4& f<f_{avg}\end{array}\right.$$

(5)

where k₁, k₂, k₃, k₄ denote probability coefficients with values between 0 and 1; f_max denotes the maximum fitness of an individual in the population; f_avg is the average fitness of the population; fʹ denotes the larger fitness value of the two individuals to be crossed; and f is the fitness value of the individual to be mutated.

The steps of the genetic algorithm for searching potential sliding surfaces are as follows (Figure 5):

(a) Initialize the population. Divide the slope body into N_p blocks, generate hazard points randomly in each block, and connect all hazard points to form the initial sliding surface individual and hazard point populations.

(b) Assess adaptation. Calculate the overall hazard for each block hazard point and sliding surface according to a set fitness function.

(c) Construct new populations. Use roulette selection [51] to regenerate populations of the same size from highly adapted hazards, and form new populations by randomly performing crossover and mutation operations on individuals according to P_c and P_m.

(d) Judge the termination condition. Stop the algorithm when the number of iterations reaches N_t or the fitness of the optimal individual does not change significantly over several generations. If the termination condition is not met, continue the next round of evolution until it is satisfied.

3.2. Calculation of Landslide Runout Distance

The dynamic slicing method analyzes soil body stability with a strong theoretical foundation, accurately simulating internal stress distribution changes and potential damage mode evolution in dynamic environments, and offering good flexibility and applicability, providing a reliable theoretical basis for landslide risk assessment.

3.2.1. Dynamic Slicing Method Model

The movement mechanism of shallow landslides is primarily governed by the initial sliding surface morphology and soil saturation strength, with typically minimal erosion effects. Based on continuity and momentum equations in two-dimensional continuous fluid differential form [52], this study integrates along the landslide body’s depth direction. It considers dynamic boundary conditions that the free surface and bottom have no mass exchange with the outside, ignoring bottom erosion. It also assumes free boundary conditions of stress on the landslide surface, and applies depth-averaged theory to cumulative quantities of velocities and stress. These quantities are obtained by depth integration and then replaced by their depth means, simplifying the continuity and momentum equations [53]. The simplified equations effectively balance computational efficiency with engineering practicality, as specified below:

$${\displaystyle \frac{\partial h}{\partial t}}+{\displaystyle \frac{\partial (hu)}{\partial x}}=0$$

(6)

$${\displaystyle \frac{\partial (hu)}{\partial t}}+{\displaystyle \frac{\partial (h{u}^2+\frac{1}{2}{k}_{a/p}{g}_{\mathrm{y}}{h}^2)}{\partial x}}=g_{x}h-\mathrm{sgn}(u)R$$

(7)

where h is the depth of the landslide along the vertical slope direction; u is the depth-averaged velocity of the landslide along the slope direction; g_x and g_y are the components of gravitational acceleration along the slope direction and the vertical slope direction, respectively; k_a/p is the main/passive lateral pressure coefficient; R denotes the general friction term on the sliding surface; and sgn(u) denotes the labeling function of the direction of the velocity for judging the direction of R.

$$\mathrm{sgn}(u)=\left\{\begin{array}{ll}1& (u>0)\\ 0& (u=0)\\ -1& (u<0)\end{array}\right.$$

(8)

$$\left\{\begin{array}{l}{k}_a=2\left(1-\sqrt{1-{\cos }^2{\phi }_{\mathrm{int}}/{\cos }^2{\phi }_{\mathrm{bed}}}\right) \cdot {\sec }^2{\phi }_{\mathrm{int}}-1 ({\displaystyle \frac{\partial u}{\partial x}}\ge 0)\\ k_p=2\left(1+\sqrt{1-{\cos }^2{\phi }_{\mathrm{int}}/{\cos }^2{\phi }_{\mathrm{bed}}}\right) \cdot {\sec }^2{\phi }_{\mathrm{int}}-1 ( {\displaystyle \frac{\partial u}{\partial x}}<0)\end{array}\right.$$

(9)

where ${\phi }_{\mathrm{i}\mathrm{n}\mathrm{t}}$ is the angle of internal friction, and ${\phi }_{\mathrm{b}\mathrm{e}\mathrm{d}}$ is the bed friction angle.

The average velocity u of the landslide in the direction of the slope is a function u = u (x, t) of the displacement x of the landslide along the slope and the time t. The acceleration of the landslide in the direction of the slope is as follows:

$$a_x={\displaystyle \frac{\mathrm{d}u}{\mathrm{d}t}}={\displaystyle \frac{\partial u}{\partial t}}+u{\displaystyle \frac{\partial u}{\partial x}}$$

(10)

where a_x represents the acceleration in the direction of the slope.

To calculate the change in displacement in the horizontal direction, the coordinate system needs to be converted. The horizontal direction is the x-axis and the vertical direction is the y-axis. Assuming that the acceleration of the slice is approximately constant during the tiny time period Δt, the motion of the nth slice in time Δt can be approximated as a uniformly accelerated motion, and the velocity of the right edge of the slice at the time t + Δt can be approximated as the average of the center velocities of the two adjacent slices:

$$u_{n,t+\Delta t}={\displaystyle \frac{1}{2}}\left(u_{x,t+\Delta t}+u_{x+1,t+\Delta t}\right)$$

(11)

where u_n denotes the velocity at the right edge of the nth slice, and u_x and u_x+1 denote the center velocities of the nth and n + 1th slices.

The horizontal position, width, and height of the right edge of the nth slice at moment t + Δt can be approximated as follows:

$$\left\{\begin{array}{l}{x}_{n,t+\Delta t}=x_{n,t}+{\displaystyle \frac{1}{2}}\left(u_{n,t}+u_{n,t+\Delta t}\right)\Delta t\cos {\theta }_n\\ d_{n,t+\Delta t}=x_{n,t+\Delta t}-x_{n-1,t+\Delta t}\end{array}\right.$$

(12)

$$\left\{\begin{array}{l}{H}_{c,n,t+\Delta t}={\displaystyle \frac{m_n}{\rho d_{n,t+\Delta t}}}\\ H_{n,t+\Delta t}={\displaystyle \frac{1}{2}}\left(H_{c,n,t+\Delta t}+H_{c,n+1,t+\Delta t}\right)\end{array}\right.$$

(13)

where x_n is the horizontal position of the right edge of the nth block, θ_n is the angle between the bottom surface of the nth block and the horizontal plane, d_n is the width of the nth block, H_c is the height at the center of the nth block, m_n is the mass of the nth block, ρ represents the density of the soil, and H_n is the height of the right edge of the nth block.

The entire landslide motion process is simulated by iterative computation, recording the slice acceleration, velocity, position, width, and height over time, and finally calculating the landslide runout distance.

3.2.2. Model Assessment

Calculating the error between simulated and actual values quantifies the model’s performance and accuracy [54]. To assess the optimized DSM model’s accuracy for simulating shallow soil landslide runout distances, the relative error was used to quantify the difference between predicted and actual values, calculated as follows:

$$E={\displaystyle \frac{P-A}{A}}\times 100\%$$

(14)

where E is the relative error, P is the simulated value, and A is the actual value.

4. Results

4.1. Hazardous Sliding Surface Search Result

To ensure algorithm reliability and reduce complexity, the GA model’s population size N_p and termination generation N_t were set to 100, with Tongnan landslide soil parameters inserted into the model.

During the model operation, we recorded the overall fitness value obtained from each iteration and the R² between the fitted sliding surface and the actual sliding surface. The resulting fitness and R² variation curves are shown in Figure 6. At the beginning of the iteration, the initial population’s fitness was 2.5063. When the iteration reached the 87th generation, the fitness function stabilized around 1.0113, with each block’s fitness near 1, indicating that they were at the landslide stabilization critical point. Excellent individuals selected in the next iteration were similar to the previous generation, with similar crossover and mutation probabilities, resulting in stable fitness.

The most hazardous sliding surface, obtained by fitting each block’s hazard points, is shown in Figure 7, with a stability coefficient of 0.9888. The sliding surface’s mathematical expression is as follows:

$$y=-0.0039x^3+0.2335x^2-7.5055x+518.45 (R^2=0.98)$$

Among the hazardous sliding surfaces obtained, the 14th–17th slices had the largest fitness value, with an average fitness of 1.3632 and a stability coefficient of 0.7336, making this area most likely to destabilize and slide. Comparing hazardous and actual slides, they were very close in the landslide shear exit and middle section, but differed more at the trailing edge, likely due to the actual slope’s significant steep drop section at the trailing edge, causing stress concentration under rainfall and higher instability probability, which the GA model does not consider.

4.2. Prediction of Landslide Runout Distance

After obtaining the hazardous sliding surface, the next step was to predict the landslide runout distance. This section uses the fitted functions of the original landslide surface and the hazardous sliding surface as upper and lower bound functions for subsequent power slice-splitting calculations.

4.2.1. Landslide Runout Distance

Shallow landslides move faster under rainfall excitation. Considering velocity magnitude, stability, and computational cost, 100 slices were selected as the best model parameter. The maximum velocity of the Tongnan landslide was approximately 3 m/s, with a movement time of around 12 s, consistent with shallow soil landslide characteristics.

Changes in the horizontal position of each slice over time were recorded (Figure 8), and the profile buildup during landslide movement was plotted (Figure 9). The map of slice block position changes reflects the entire landslide movement process. The landslide slid downward as a whole, but different slice blocks moved differently. The 1st slice block had almost no displacement in the first 4 s, while the 100th slice block gradually generated displacement after movement began. Due to the large influence of active and passive pressures on the motion process, the 1st slice, located at the back edge, remained stable initially, as its sliding resistance was larger than the downward force, while the 100th slice, at the front edge with a free surface, was subjected to active soil pressure from neighboring slices, causing instability and accelerated motion. The slice block width gradually increased over time, and without considering mass changes, the slice height gradually decreased, reducing active and passive lateral pressures between soil bodies, leading to decreased acceleration between slices and eventual deceleration.

Comparing the simulation accumulation profile with the UAV orthophoto (Figure 1c), at the start of the Tongnan landslide movement, the leading edge began to slide downward, and the trailing edge detached from the back wall, with a slight downward shift. Over time, the movement distance and range expanded, and accumulation-related morphological changes became more obvious. By 12 s, the landslide accumulation had nearly reached the slope bottom, with the overall slope slowing, and most of the accumulation staying on the sliding surface, burying the road; only a small part rushed out of the sliding surface, consistent with shallow soil landslide movement, showing good simulation results. Calculating the horizontal displacement difference before and after the 100th block’s movement, the final landslide runout distance was 5.91 m.

4.2.2. Results of Model Assessment

The actual landslide movement distance was between 5 and 6 m, so 5.5 m was used as the reference value. The estimated runout distance from the DSM model was 5.91 m, with a relative error of 7.45% (Figure 10), indicating good model performance.

To address the limitation of single-case validation, we further examined a high-mobility landslide that occurred in Saint-Jude, Quebec, Canada, in 2010, with a recorded runout distance of approximately 550 m. The high-fluidity characteristics of this landslide [55] make it particularly suitable for evaluation using our proposed GA-DSM model. When the landslide parameters were input into our model, the predicted runout distance was 507 m, yielding a relative error of 7.8% (Figure 10), demonstrating the model’s robust performance.

Despite the small relative error, differences between simulation results and actual runout distance existed. Possible reasons for this include deviations between the landslide surface contours derived from the GA and real topographies during slice discretization, and increased sliding resistance at the leading edge due to artificial structures like buildings, which the simulation did not consider, potentially leading to larger runout distances.

Overall, the GA-DSM technical framework proposed in this study provides an effective and comprehensive approach for predicting the runout distance of shallow landslides. In the case of the Tongnan landslide, both the sliding surface identified through the search algorithm and the dynamic characteristics calculated from the simulation demonstrate good agreement with field observations. The model also demonstrates equally good performance for other landslides. This technology significantly improves the accuracy of landslide hazard zone prediction, offering a scientific basis for establishing safety buffers and implementing protective engineering measures, while advancing the theoretical development of landslide forecasting.

5. Discussion

5.1. Impact of Soil Moisture Content

The main triggering factor for Tongnan landslides is prolonged continuous rainfall. Under such conditions, the soil moisture content changes significantly over time, affecting overall soil stability. Increased soil moisture content increases soil density, but decreases cohesion, increasing downward sliding force and decreasing sliding resistance, thus increasing landslide instability risk [56]. The previous model only considered the saturated state of the landslide soil body. To better explore the effect of soil water content on shallow landslide runout distance, multiple soil states must be considered.

Through field sampling employing the cutting-ring method and conventional direct shear tests, key geotechnical parameters were obtained [57]. These parameters covered the completely dry initial state, semi-saturated state at field capacity, and fully saturated state with maximum water content. These characteristic parameters were input into the GA-DSM model to estimate hazardous sliding surfaces (Figure 11) and runout distances (

Table 2. Model results under different soil moisture contents.

Moisture Content	Density (g/cm3)	Cohesion (kPa)	Internal Friction Angle (°)	R2 (Sliding Surface)	Runout Distance (m)	RE (%)
Initial state	1.60	52	28	0.93	8.12	47.64
Semi-saturation	1.75	37	25	0.96	6.39	16.18
Saturation	1.90	26	22	0.98	5.91	7.45

).

In the initial state, due to internal friction and cohesion, the shear strength is relatively high, and the structure is relatively stable [58]. Only when the downward sliding force reaches a certain degree will a landslide be triggered, with a relatively large range of soil involved in sliding, a deeper sliding surface, and the longest runout distance. In the saturated state, a large amount of water enters the soil pore space, reducing effective stress between soil particles and greatly reducing shear strength. The saturated soil weight increases significantly [59], making it easier to slide under gravity, with a smaller portion of soil more prone to unstable sliding, resulting in a shallower sliding surface and smaller runout distance than the original state. The sliding surface and runout distance in the semi-saturated state are intermediate.

In the process of model construction, the uncertainty of soil parameters is an inherent characteristic, which may introduce significant deviations in model outputs [60]. To quantify the impact of parameter uncertainty (under saturated water content conditions) on the prediction of landslide runout distance, we adopted a Monte Carlo simulation framework [61]. Soil parameters were assumed to follow a uniform distribution within a ±5% variation range [62], and 1000 random parameter sets were generated through sampling. These sets were then used to compute the runout distance. Finally, the quantile method [63] was applied to determine the 95% confidence interval (CI) of the runout distance (Figure 12), thereby validating the reliability of the results.

Figure 12 displays the 95% CIs obtained through Monte Carlo simulations. Under saturated conditions, while variations in soil parameters within a limited range lead to some dispersion in landslide runout distance predictions, all results consistently fall within the 95% CI. This demonstrates that parameter uncertainty has minimal impact on model outputs, confirming the GA-DSM model’s strong robustness to parameter variations and its high reliability in predictive performance.

Overall, for shallow landslide runout distance prediction, saturated soil characteristic parameters more accurately simulate real-world situations, offering effective data support for engineering practice.

5.2. Impact of Number of Slices

Using saturated soil parameters, the landslide was evenly divided into 50, 100, 200, and 300 parts, with all strips numbered sequentially from left to right. The time step was Δt = 0.01 s, and the velocity of strips at the same location was recorded (Figure 13) and analyzed for variations.

With the same number of slices, velocity changes differ at different locations. Landslide block velocities rise and then fall, but middle block velocities fluctuate more, with fluctuations more pronounced closer to the leading edge. This is because during sliding, back edge blocks receive different active and passive earth pressure constraints, allowing more stable sliding, while front edge blocks, with a free surface, experience smaller active earth pressure than passive earth pressure, causing accelerated sliding [64]. Deceleration occurs again when meeting the previous strip, causing velocity fluctuations.

As the number of slices increases, the maximum velocity of the foremost edge slice increases from 1.77 m/s to 4.99 m/s (

Table 3. Velocity changes and grid sensitivity analysis with varying numbers of slices.

Number of Slices	50	100		200		300
Velocitymax (m/s)	1.77	2.92		3.96		4.99
MCV (-)	0.69	1.11		1.15		1.29
GCI (%)	1.52		0.09		0.45

), and velocity fluctuations at the same position become more drastic. With a fixed total landslide length, increasing the number of slices reduces each strip’s mass and width, decreasing sliding surface friction [65,66]. Constant slice height leads to no obvious change in the active and passive lateral pressure on slices, gradually increasing the combined external force on slices and making slice acceleration changes more obvious, and resulting in more drastic velocity fluctuations at the same position, affecting calculation accuracy and leading to relatively large final result errors.

To quantitatively assess velocity variations under different discretization levels, the mean coefficient of variation (MCV) [67] was adopted to characterize velocity fluctuations. The Grid Convergence Index (GCI) methodology [68] was systematically implemented to evaluate the trade-offs between computational accuracy and velocity oscillation characteristics. This framework established a quantitative relationship between slice resolution and result reliability, with detailed comparative data presented in Table 3.

According to the data analysis in Table 3, it can be observed that as the number of slices increases, the MCV value shows a gradual upward trend, while the GCI exhibits a pattern of first decreasing, and then increasing. Specifically, when the number of slices for the geotechnical body increases from 50 to 100, the velocity fluctuation amplitude increases, and the GCI remains relatively high, indicating that the mesh division with 50 slices is too coarse, leading to insufficient convergence of the calculation results.

As the number of slices further increases from 100 to 200, although the MCV continues to rise, the decrease in GCI suggests that the calculation results are gradually converging. However, when the number of slices reaches 300, both the MCV and GCI increase simultaneously, implying that certain objective instability factors may be causing deviations in the calculation results. Additionally, it should be noted that an increase in the number of slices typically leads to a significant rise in computational load and longer processing times.

Considering the balance between computational accuracy and efficiency, the 100-slice configuration offers a relative advantage—it maintains smaller velocity fluctuations while ensuring convergence, achieving an optimal trade-off between calculation precision and computational cost.

5.3. Limitations and Prospects

Despite the model’s good results, practical applications do not consider the consolidation effect of buildings above the landslide and continuous rainfall, so these complex environmental factors need further integration in specific engineering applications. Additionally, actual landslide motion mechanisms are very complex, and this study simplifies the landslide motion and shear outlet impact processes, ignoring some secondary influencing factors. Although this simplification improves computational efficiency, it limits the model’s applicability in more complex scenarios. For other landslide types, accurate on-site soil parameters are needed, and whether the landslide motion process aligns with debris fluid motion characteristics must be considered in order to further improve prediction accuracy and model applicability.

Future work could explore combining other optimization algorithms (e.g., particle swarm optimization, simulated annealing) to improve algorithm efficiency and robustness, incorporate the layered structure of the soil body into the model for finer landslide discretization, and more accurately simulate landslide movement processes and runout distances. Additionally, the model could be applied to more shallow landslide cases in different regions to verify its generalization ability and applicability.

6. Conclusions

This study has developed an innovative analytical framework for predicting shallow landslide runout distances by synergistically integrating the global search capability of a GA with the dynamic simulation features of the DSM. This approach effectively overcomes the constraints of traditional methods relying on simplified geometric assumptions of sliding surfaces. Using the Tongnan landslide in Chongqing as a representative case, the method’s effectiveness in landslide hazard prediction was successfully validated. The results demonstrate that the GA-optimized sliding surface exhibited high consistency with the actual landslide morphology, achieving a R² of 0.98 and a stability coefficient of 0.9888. The predicted runout distance of 5.91 m showed only a 7.45% relative error compared to field measurements. Additionally, validation with the Saint-Jude landslide case in Canada yielded a relative error of less than 10%, further confirming the model’s reliability and generalizability. Notably, the soil moisture content significantly influenced landslide dynamics. Predictions under saturated conditions showed the closest alignment with reality, while parameter uncertainty had a minimal impact on model performance. Furthermore, increasing the number of slices enhanced computational accuracy, but also increased velocity fluctuations. Systematic analysis identified 100 slices as the optimal balance between precision and computational efficiency.

The study also identifies several limitations of the current model, including oversimplification of landslide movement mechanisms, static treatment of rainfall conditions, and insufficient consideration of external factors, such as the effects of structural reinforcement. These findings highlight critical directions for future improvements. These include incorporating stratified soil structure models or hybrid algorithms like Particle Swarm Optimization to enhance model robustness. They also involve thoroughly accounting for pore pressure variations in soils under dynamic rainfall conditions and fully integrating complex anthropogenic resistance factors during model construction.

The developed GA-DSM methodology provides crucial technical support for landslide prevention. At the practical level, the model’s output of shallow landslide runout distances enables early prediction of hazard zones. This provides reliable data for establishing safety buffers and designing protective structures (e.g., retaining walls). Theoretically, its adaptive framework can be extended to landslide monitoring and early-warning systems across diverse geological settings. During periods of continuous rainfall, by inputting real-time soil moisture content, the model can predict both the potential sliding surface location and runout distance, enabling proactive evacuation of residents. This research not only advances landslide prediction methodology, but also demonstrates the tremendous potential of computational optimization in geohazard studies, building a critical bridge between theoretical innovation and engineering applications.