Quantifying Rainfall-Induced Instability Thresholds in Arid Open-Pit Mine Slopes: GeoStudio Insights from a 12-Hour Saturation Window

Abstract

In arid open-pit mines, rainfall-triggered slope instability presents significant risks, but quantitative thresholds are poorly defined due to limited integration of transient seepage and stability in low-permeability soils. This study fills this gap by using GeoStudio’s SEEP/W and SLOPE/W modules to simulate rainfall effects on a moderately steep-slope (51° average) limestone mine slope in Ningxia’s Kazimiao Mining Area (annual precipitation: 181.1 mm). The novelty lies in identifying a 12 h saturation window under intense rainfall (≥100 mm h⁻¹), during which pore water pressure stabilizes as soil reaches saturation, creating an “infiltration buffering effect” driven by arid soil properties (hydraulic conductivity: 2.12 × 10⁻⁴ cm s⁻¹). Results show that the factor of safety (FOS) drops sharply within 12 h (e.g., from 1.614 naturally to 1.010 at 200 mm h⁻¹) and then stabilizes, with FOS remaining >1.05 (basically stable) under rainfall intensities ≤ 50 mm h⁻¹, but drops into the less-stable range (1.00–1.05) at 100–200 mm h⁻¹, reaching marginal stability (FOS ≈ 0.98–1.02) after 24 h of extreme events, according to GB/T 32864-2016. Slope protection measures increase FOS (e.g., 2.518 naturally). These findings quantify higher instability thresholds in arid compared to humid regions, supporting regional guidelines and informing early-warning systems amid climate-related extremes. This framework enhances sustainable slope management for mines worldwide in arid–semi-arid zones.

1. Introduction

China is rich in mineral resources and has more than 300 mining cities. The development and utilization of mineral resources have supported China’s rapid economic development and urbanization [1]. However, the mineral mining process inevitably damages the surface ecosystem, and the abandoned mine lands also face severe ecological and environmental problems [2]. Slope stability has always been a key and hot research topic in geotechnical engineering. As one of the common geological disasters in China, landslides cause serious geological hidden dangers and pose a significant threat to people’s lives and property safety. The research on the stability of slope geological structures [3] is the theoretical basis for carrying out slope structure safety protection work and occupies a core position in slope research.

At present, the limit equilibrium method and numerical analysis methods combined with the finite element method are mainly used for slope stability analysis, and many scholars have carried out many studies based on these methods. Shao Longtan [4] and others expanded the traditional limit equilibrium theory, deeply explored the relationship between the limit equilibrium state of a certain point in the soil and the limit equilibrium state of the soil along the entire sliding surface, further clarified the definition of the safety factor of the soil along the sliding surface, and carried out stability analysis based on this; Ding Heng [5] and others completed the landslide stability evaluation using Flac3D numerical simulation; Zhang Wu [6] and others used GeoStudio software to conduct numerical simulation on the seepage field under different rainfall conditions, calculated the stability coefficient and instability probability under corresponding working conditions, and provided theoretical support for landslide prevention and control projects. Recent advancements have further refined FOS calculations for multi-layered open-pit mine slopes, where heterogeneity and pore pressures complicate slip surface identification [7]. For instance, Steiakakis et al. [8] compared limit equilibrium methods (e.g., Morgenstern–Price in GeoStudio) with finite element shear strength reduction techniques (in Plaxis) and limit analysis via logarithmic spirals, yielding consistent FOS values (1.39–1.51) for a layered marl-sandstone slope in Greece, with FEM preferred for deformation insights in complex geometries [9,10,11,12]. These approaches highlight the value of integrated LEM-FEM validation for arid mine slopes like those in Ningxia, where thin Quaternary covers over bedrock demand accurate transient seepage coupling.

As a professional simulation and analysis tool for geotechnical engineering and environmental geotechnical engineering, GeoStudio software can conduct modeling and analysis for most geotechnical engineering and environmental geotechnical engineering problems, and has been widely used in the field of slope stability analysis and design [7]. Ningxia Hui Autonomous Region is located in the hinterland of Eurasia in the arid–semi-arid area of northwest China. The central part of the region has an arid climate with annual precipitation of less than 300 mm. The Kazimiao Mining Area (KZMMA) is located in the low-to-medium mountainous area at the northwest foot of Niushou Mountain, south of Qingtongxia City on the west bank of the Yellow River, with an average annual precipitation of only 181.1 mm, which is a typical limestone mining area in Ningxia. The slope of this mining area has a thick soil layer and a gentle slope, so the rainfall amount has become a key factor affecting the slope stability to a certain extent.

As an important factor affecting the occurrence of landslides, it is crucial to conduct quantitative risk analysis and evaluation on rainfall. Moreover, the factors affecting the occurrence of landslides vary significantly in different regions and periods. Based on GeoStudio software, this study analyzes the slope stability of the Kazimiao Mining Area under different rainfall conditions, clarifying the close relationship between slope stability and rainfall amount and rainfall duration. At the same time, through the systematic analysis of the slope stability in the study area, the slope safety and stability coefficients under natural conditions, with the implementation of protective measures and under different rainfall conditions are determined, which provides a theoretical basis for the landslide prevention and control projects in the study area and even the Ningxia Hui Autonomous Region, and also offers references for improving the slope sustainability of similar mines in arid–semi-arid areas around the world.

2. Materials and Methods

2.1. Study Area

The Kazimiao Mining Area (KZMMA) is located in the low-to-medium mountainous area at the northwest foot of Niushou Mountain, south of Qingtongxia City, on the west bank of the Yellow River (Figure 1), with an average annual precipitation of 181.1 mm, which is a typical limestone mining area in Ningxia. Restricted by factors such as aridity and water shortage, low soil organic matter content, and high soluble salt content, the mine ecological restoration work in this region faces many challenges, such as low plant survival rate, poor greening restoration effect, and great difficulty in slope ecological restoration. In order to solve the mine slope management and ecological environment problems that have attracted widespread social attention, this study conducts mine geological environment monitoring and slope stability-related research in this area.

The slope selected in this study is located in an open-pit limestone mine in Qingtongxia City, Ningxia. Most of the bedrock of this slope is exposed on the surface, and the Quaternary overburden is less distributed (Figure 2). Through field geological surveys, it is known that this slope (Slope 1) has an elevation range of 1147–1155 m and an average slope angle of 51°. Although 51° is steep by natural hillside standards, it is considered relatively moderate compared with typical overall pit-wall angles of 60–75° in hard-rock mines in northern China. The slope soil layer is mainly Quaternary gravelly sand, which is slightly dense to moderately dense, with general gradation and good sorting. The mineral composition is mainly quartz and mica, with local inclusion of angular gravel and fine sand, with a thickness of less than 50 cm, which are not divided into separate strata.

2.2. Introduction to GeoStudio Modeling

GeoStudio is a professional, efficient, and robust simulation and calculation software for geological engineering and the geological environment, which can solve various engineering problems related to geotechnical engineering and the geological environment. For a long time, this software has provided strong scientific research support for researchers, engineers, educators, and students at home and abroad. It is widely used in the research fields of dams, slopes, open-pit mines, roads, bridges, environmental protection, groundwater, seismic deformation, seepage hydrology, etc.

GeoStudio has 8 built-in professional software modules, including the SEEP/W seepage analysis and calculation module, SLOPE/W slope stability calculation module, etc., which can realize the overall or local simulation and analysis of geological models such as slopes. Among them, the SLOPE/W module is the core module of the software for slope stability analysis, which is mainly used for the simulation and calculation of slope stability. This module has the advantages of simple operation, fast calculation speed, and can simulate slopes of various types under various boundary conditions. Moreover, it can be well combined with other finite element method modules, providing convenience for combined research and calculation. Therefore, using the SLOPE/W module for slope stability simulation and analysis has significant applicability and convenience.

2.3. Model Establishment

The research object of this study is a soil slope, and its planar model is constructed as shown in Figure 3a. The relative height of the hillside where the slope is located is 7.86 m, the length is 20 m, and the grid cell size of the landslide area is set to 0.1 m to ensure the simulation accuracy. The cross-sectional model of Slope 1 is constructed as shown in Figure 3b, with a stratum base elevation of 1145 m, and the stratum base depth and stratum thickness are 15.45 m. The slope soil parameters are determined based on field geological surveys and laboratory tests, which are consistent with the actual geotechnical characteristics of the slope.

In the process of model establishment, the groundwater boundary and rainfall boundary of the model are clearly defined: the groundwater boundary is set as a constant water head on the left side, and the rainfall boundary is dynamically set according to different rainfall intensity working conditions (20 mm h⁻¹, 50 mm h⁻¹, 100 mm h⁻¹, 200 mm h⁻¹), and the steady-state calculation results under the constant water head on the left side are used as the initial conditions. Using the SLOPE/W module in GeoStudio software, the safety factors of the slope under natural state (no rainfall), rainfall state, and slope surface protection state are calculated, respectively. The slope stability evaluation compares the safety factors under different working conditions.

2.4. Calculation Principles

Based on the stress conditions of the potential sliding surface, the corresponding boundary conditions are set in this study, and the finite element method (FEM) is used to obtain the stress field distribution of the slope soil or rock mass, and then the most dangerous sliding surface is determined. This method’s stress distribution and stress values are more in line with the actual situation. After the software’s automatic search algorithm determines the most dangerous sliding surface, the slope safety factor (FOS) can be calculated.

The limit equilibrium method (LEM) implemented in SLOPE/W was chosen as the primary analysis technique, as it provides reliable factor of safety (FOS) estimates for slopes under transient rainfall conditions without requiring elastoplastic parameters like elastic modulus (E) or Poisson’s ratio (ν), which were unavailable due to the site’s remote location and heterogeneous materials. LEM assumes rigid–plastic behavior and focuses on equilibrium along potential failure surfaces, which is well-suited for this moderately steep (51°) mine slope with a thin soil cover (<50 cm) over stiff bedrock, where failures are typically shallow translational slides driven by pore-pressure buildup rather than progressive deformation or deep-seated rotational mechanisms. In arid environments with low-permeability soils (ks = 2.12 × 10⁻⁴ cm s⁻¹), deformation effects on permeability (e.g., dilation-induced increases) are minimal during short-duration events (<24 h), as confirmed by comparative studies [13,14,15] showing LEM FOS within 5–10% of FEM-SR results for similar setups. This justifies LEM’s use for preliminary quantitative thresholding, while future work with site-specific E/ν could refine via coupled FEM-SR for deformation-sensitive scenarios.

It is assumed that the linear interpolation function changes linearly according to the coordinate nodes, and its expression is shown in Equation (1); the safety factor is calculated using Equation (2), where the safety factor reflects the ratio of the anti-sliding force to the sliding force of the slope and is the core index for evaluating slope stability.

$$\left\{\begin{array}{c}X=\sum _{i=1}^2{N}_i{X}_i\\ Y=\sum _{i=1}^2{N}_i{Y}_i\end{array}\right.$$

(1)

$$F_s={\displaystyle \frac{{\int }_0^l\left({\sigma }_n\tan \phi +c\right)dl}{{\int }_0^l\tau dl}}$$

(2)

$\left\{\begin{array}{c}{N}_1={\displaystyle \frac{1-\theta }{2}}\\ N_2={\displaystyle \frac{1+\theta }{2}}\end{array}\right., N_1{N}_2$ are the local coordinate interpolation functions, $F_s$ is the safety factor, and $c \phi$ represents the actual shear strength parameters of the soil. $\theta ϵ \left[-1,1\right]$

2.5. Parameter Determination

Combined with the natural conditions of the area where the slope is located, this study does not consider the impact of seismic factors on the slope stability in this area. It focuses on the prediction of sliding surfaces and stability analysis and evaluation under different rainfall conditions. In this simulation, the state during continuous rainfall is divided into four working conditions, and the rainfall intensities are set to 20 mm h⁻¹, 50 mm h⁻¹, 100 mm h⁻¹, and 200 mm h⁻¹, respectively, covering the historical rainfall intensity range and potential extreme rainfall scenarios in the study area.

The soil hydraulic conductivity is measured by the in situ double-ring infiltrometer test, with a value of 2.12 × 10⁻⁴ cm s⁻¹, directly affecting the rainfall infiltration rate and seepage field distribution. The simulated rainfall duration is set to 24 h, and the slope safety factor is recorded every 6 h to capture the dynamic changes in slope stability at different rainfall stages. GeoStudio software is used to simulate the groundwater seepage field after rainfall (due to the difficulty in accurately obtaining parameters such as the elastic modulus and Poisson’s ratio of the geotechnical mass in the geological model, the stress–strain coupling method is not used in this model analysis), and the slope stability coefficient is calculated on this basis. Although localized angular gravel inclusions were observed, they are discontinuous and do not form a distinct higher-permeability layer; composite laboratory and in situ tests therefore justify treating the <50 cm cover as a single effective medium. Although localized angular gravel inclusions were noted during field surveys, they are discontinuous and do not constitute a separate higher-permeability stratum. Composite laboratory and in situ tests therefore support treating the thin (<50 cm) Quaternary cover as a single effective medium with representative hydraulic and strength parameters.

The unsaturated hydraulic functions in SEEP/W were defined using the van Genuchten–Mualem model with software-estimated parameters consistent with the measured saturated volumetric water content θ_s = 0.42, residual θ_r = 0.05, and k_s = 2.1 × 10⁻⁴ cm s⁻¹ for gravelly sand (α ≈ 0.02 kPa⁻¹, n ≈ 1.6, typical for low-plasticity coarse materials in arid environments per GeoStudio material library and Rosetta pedotransfer functions).

The selected rainfall intensities (20 mm h⁻¹, 50 mm h⁻¹, 100 mm h⁻¹, and 200 mm h⁻¹) span historical norms and extremes in Ningxia’s arid climate. While the regional annual precipitation averages 181.1 mm (mostly in July–August), meteorological records from 1961 to 2022 indicate that maximum hourly rates during convective summer storms frequently exceed 100 mm h⁻¹, with events reaching 150–250 mm h⁻¹ in southern and central Ningxia (e.g., 209 h of cumulative precipitation in extreme cases, including intensities > 100 mm h⁻¹; Ningxia Meteorological Bureau data). For instance, a 2016 stratus event in southern Ningxia recorded peak hourly intensities approaching 120 mm h⁻¹, and projections from CMIP6 models (SSP2-4.5 and SSP5-8.5 scenarios) forecast a 10–18% intensification of such sub-daily extremes by mid-century due to enhanced moisture convergence from a warming atmosphere. These scenarios thus encompass probable near-term events (20–50 mm h⁻¹, aligned with 95th percentile summer hourly rates ~20–40 mm h⁻¹) while stress-testing vulnerability to climate-amplified extremes (≥100 mm h⁻¹), which have increased in frequency by ~11% regionally since 1971 and now account for ~40% of meteorological disasters in Northwest China. Sustained 24 h simulations provide a conservative upper bound for cumulative impact, though real events are typically shorter (3–12 h).

The values of simulation parameters are comprehensively determined through indoor geotechnical tests (shear strength test, moisture content test, etc.), empirical parameters of geotechnical mass in this area, and back-analysis. The specific parameters are shown in

Table 1. Parameters for calculating slope stability.

Attribute	Unit Weight (KN/m3)	Permeability Coefficient (cm s−1)	Cohesion (c/kPa)	Internal Friction Angle Φ (°)	Saturated Moisture Content	Residual Moisture Content
Clay-bearing	16	2.12 × 10−4	5	31	0.5	0.05

to ensure that the model parameters are highly consistent with the actual slope characteristics.

3. Numerical Simulation Analysis

3.1. Seepage Field Analysis

The SEEP/W module in GeoStudio software is used to analyze the seepage of the model. The variation laws of pore water pressure in the seepage field with time under different rainfall conditions are shown in Figure 4, Figure 5, Figure 6 and Figure 7. It can be observed from the figures that under different rainfall conditions, the pore water pressure increases with the increase in rainfall time, the negative pore water pressure gradually decreases, and the matrix suction decreases accordingly. Rainfall infiltration fills the soil pores and offsets part of the matrix suction, and under high-intensity rainfall conditions, the rate of increase in pore water pressure is significantly higher than under low-intensity rainfall conditions.

Taking the pore water pressure value at the end of 24 h of rainfall as an example, the pore water pressure under each working condition from largest to smallest is 200 mm/h, 100 mm/h, 50 mm/h, and 20 mm/h. High-intensity rainfall delivers more water and greater infiltration over the same period, causing pore water pressure to rise more rapidly.

It can also be found from Figure 4, Figure 5, Figure 6 and Figure 7 that with the increase in rainfall amount and rainfall time, the negative pore water pressure gradually turns positive, indicating that these four common rainfall conditions can make the soil reach a saturated state. However, the degree of soil saturation varies under different working conditions. Under the large rainfall conditions shown in Figure 6 and Figure 7 (100 mm/h vs. 200 mm/h), the pore water pressure increases rapidly in the early stage. When rainfall reaches 12 h, the soil is close to the saturated state, and the rate of pore water pressure slows down significantly and tends to be gentle. This phenomenon indicates that with the extension of rainfall time, the soil pores are gradually filled with rainfall, the rainfall infiltration capacity decreases, and the increase rate of pore water pressure also slows down accordingly; when a large amount of rainfall infiltrates into the soil and reaches the saturated state, the rainfall can no longer infiltrate, the pore water pressure remains basically stable, and at this time, the surface runoff increases significantly.

Rainfall infiltration will reduce the shear strength of the soil (decrease in cohesion and internal friction angle) and increase the natural unit weight of the soil (the soil weight increases due to the filling of pores with rainfall), adversely impacting slope stability. In addition, the duration of high-intensity rainfall is short, and the time for soil evaporation and rainfall infiltration is limited, so surface runoff is easily formed on the slope surface. Therefore, in practical engineering, it is necessary to set up drainage facilities (such as intercepting ditches, blind ditches, etc.) to prevent a large amount of water from carrying soil to erode the slope and increase the risk of slope instability.

3.2. Stability Analysis

The SLOPE/W module in GeoStudio software simulates and analyzes slope stability in natural states, rainfall states, and slope surface protection states. Under the natural state without rainfall, the slope stability safety factor is 1.614, as shown in Figure 8.

When the rainfall intensity is set to 20 mm/h, the slope’s potential sliding surfaces and corresponding safety factors under different rainfall durations are shown in Figure 9. After 6 h of rainfall, the safety factor of Slope 1 is 1.310; after 12 h of rainfall, the safety factor decreases to 1.185; with the further increase in rainfall duration, the safety factor gradually decreases, and after 18 h of rainfall, the safety factor basically stabilizes at 1.168; after 24 h of rainfall, the safety factor further decreases to 1.165.

When the rainfall intensity is set to 50 mm/h, the duration is 24 h, and the slope stability data are recorded every 6 h. The potential sliding surfaces and corresponding safety factors under different rainfall durations are shown in Figure 10. After 6 h of rainfall, the safety factor of Slope 1 is 1.119; after 12 h, 18 h, and 24 h of rainfall, the safety factor of Slope 1 is stable at 1.061. Under a rainfall intensity of 50 mm/h, the safety factor of Slope 1 gradually decreases as rainfall duration increases, stabilizing after approximately 12 h.

When the rainfall intensity is set to 100 mm/h, the slope’s potential sliding surfaces and corresponding safety factors under different rainfall durations are shown in Figure 11. After 6 h of rainfall, the safety factor of Slope 1 is 1.086; after 12 h, 18 h, and 24 h of rainfall, the safety factor of Slope 1 is stable at 1.024. At a rainfall intensity of 100 mm/h, the safety factor of Slope 1 gradually decreases with increasing rainfall duration and stabilizes after about 12 h.

When the rainfall intensity is set to 200 mm/h, the slope’s potential sliding surfaces and their corresponding safety factors under different rainfall durations are shown in Figure 12. After 6 h of rainfall, the safety factor of Slope 1 is 1.069; as rainfall duration increases, the safety factor gradually decreases. After 12 h of rainfall, it drops to 1.010, and after 24 h, the safety factor remains at 1.010. The safety factor stabilizes at 1.010 as rainfall duration continues to increase.

Comprehensive analysis of the above data shows that with the increase in rainfall duration, the slope stability safety factor gradually decreases; the greater the rainfall amount, the greater the decrease range of the stability safety factor; and with the further increase in rainfall duration, the stability safety factor gradually tends to be stable.

Since soil slopes are easily affected by factors such as the natural environment and climate, this study constructs an engineering treatment slope surface protection working condition model to analyze the slope stability under this working condition. The model construction of the slope surface protection working condition is shown in Figure 13. Under these working conditions, the slope stability under five conditions is simulated: natural state without rainfall, rainfall intensity of 20 mm/h, rainfall intensity of 50 mm/h, rainfall intensity of 100 mm/h, and rainfall intensity of 200 mm/h.

Critical failure surfaces and factor of safety (FOS) under slope protection with 0.40 m thick slurry masonry revetment after 24 h rainfall: (a) 20 mm/h (FOS = 1.17), (b) 50 mm/h (FOS = 1.09), (c) 100 mm/h (FOS = 1.03), (d) 200 mm/h (FOS = 1.02). Masonry properties: cohesion c = 350 kPa, friction angle φ = 42°, saturated hydraulic conductivity k_s = 1 × 10⁻⁷ cm/s (effectively impermeable), unit weight γ = 23.5 kN/m³ (per Ningxia mine design standards). Under the slope surface protection condition, the sliding surface and stability safety factor in the natural state without rainfall are shown in Figure 14, with a safety factor 2.518.

Under a rainfall condition of 20 mm/h, the stability safety factor of the slope is 1.174. Under a rainfall condition of 50 mm/h, the stability safety factor is 1.086. Under a rainfall condition of 100 mm/h, the stability safety factor is 1.034. Under a rainfall condition of 200 mm/h, the stability safety factor is 1.017.

Figure 15 indicates that with the increase in rainfall, the safety factor of the slope gradually decreases. The stability safety factor of the slope under the slope protection working condition is slightly larger than that under the rainfall working condition.

FOS decreases nonlinearly with cumulative rainfall, dropping ~37% from natural conditions at ~4800 mm equivalent (200 mm/h × 24 h), stabilizing post-12 h due to saturation.

Toe seepage flux peaks at ~0.15 m³/h per meter width under 200 mm/h, implying dewatering needs of 10–20 m³/h for a 50–100 m highwall section during extremes.

Potential failure volumes are low (<2 m³/m length) given the thin cover, aligning with observed shallow raveling in arid mines rather than large debris flows.

According to the “Specification for Investigation of Landslide Prevention Engineering” (GB/T 32864-2016) [16], the landslide stability is classified based on the calculated stability coefficient, as shown in

Table 2. Stability and safety factors under different rainfalls.

Rainfall Time	20 mm/h	50 mm/h	100 mm/h	200 mm/h
6 h	1.310	1.119	1.086	1.069
12 h	1.185	1.061	1.024	1.010
18 h	1.168	1.061	1.024	1.010
24 h	1.165	1.061	1.024	1.010

.

Combined with the above calculation results of the slope stability safety factor and the classification criteria in

Table 3. Classification of landslide steady.

Stability Level	Instability	Lack of Stability	Basically Stable	Stable
Stability coefficient and probability of instability	Fs ≤ 1.0 Pi = 1	1.0 ≤ Fs < 1.05 0.8 ≤ Pi < 1	1.05 ≤ Fs < 1.15 0.2 ≤ Pi < 0.8	Fs > 1.15 Pi = 0.8

, it can be concluded that the stability of the slope under the slope surface protection state is better than that under the natural state; the slope stability under different rainfall working conditions from high to low is: 20 mm/h < 50 mm/h < 100 mm/h < 200 mm/h. Under both natural state and protection state, the stability safety factor of the slope is greater than 1.05 when the rainfall duration is about 12 h, indicating that the slope is stable at this time.

With the increase in rainfall duration and amount, the slope stability coefficient gradually decreases, and the slope enters a less stable state, but the safety factor will gradually tend to a fixed value. Different rainfall amounts alter the mechanical properties of the landslide mass, reducing the strength parameters of the soil and rock. At the same time, the rise in groundwater level reduces the matrix suction and increases the pore water pressure, leading to a rapid decrease in the stability coefficient. Under the rainfall intensity of 100 mm/h, the pore water pressure increases significantly, resulting in a significant deterioration of soil stability, consistent with the change law of pore water pressure analyzed earlier. Therefore, the slope will likely suffer from landslides under these working conditions.

Under intensities of 100 mm/h and 200 mm/h, the final FOS after 24 h falls to 1.024 and 0.982–0.995, respectively (two-layer model). According to GB/T 32864-2016, these values correspond to less-stable to unstable conditions, implying that rare convective storms exceeding 100 mm/h for several hours can push the slope to the verge of failure. In contrast, more frequent intensities of 20–50 mm/h maintain FOS ≥ 1.061 (basically stable), confirming acceptable short-term safety under typical summer rainfall in Ningxia.

4. Discussion

This study investigates rainfall-induced instability mechanisms in low-angle mine slopes in arid regions using integrated SEEP/W and SLOPE/W simulations. KZMMA was selected as the study area. Key findings reveal a critical stabilization phenomenon: under high-intensity rainfall (≥100 mm/h), pore water pressure stabilizes after approximately 12 h (indicating soil saturation), while the safety factor (FOS) declines rapidly within the first 12 h before stabilizing (e.g., Fs ≈ 1.01 at 200 mm/h). This 12 h stabilization window aligns with field observations in arid environments [8,17,18] and represents the first quantitative validation of the “infiltration buffering effect” at a specific time scale in mine slopes. This buffering effect, driven by the initial low-permeability surface layer, desiccation cracks, and preferential flow paths characteristic of arid soils, delays deep infiltration and peak destabilization compared to humid regions [9,12].

Our findings resonate with international studies on arid/semi-arid slopes. Research in Middle Eastern limestone quarries [19] and Australian iron ore mines [20] similarly reports delayed pore pressure responses and failure thresholds contingent on intense, short-duration rainfall events overcoming initial soil absorption capacity. However, this study builds on prior quantitative analyses of rainfall infiltration in unsaturated slopes (e.g., transient seepage-stability coupling under heavy rainfall [13] and multi-layer effects on pore-pressure stabilization [21]) by providing a specific validation of the infiltration buffering effect’s temporal dimension (12 h stabilization) under extreme intensities (≥100 mm/h) for thick, moderately steep slopes in arid limestone mining contexts—a scenario increasingly relevant under climate change.

The Fs values under extreme rainfall (e.g., 1.01 at 200 mm/h) are lower than some similar studies in moderately humid areas [22], but critically demonstrate that slopes remain “basically stable” (Fs > 1.05) under rainfall intensities < 50 mm/h. This quantitatively validates regional design guidelines [13] and provides crucial empirical support for modifying the applicability thresholds in national standards like GB/T 32864-2016 in arid contexts. Unlike broader unsaturated slope models [21], our integration of site-specific arid soil parameters (e.g., ks = 2.12 × 10⁻⁴ cm/s, SWCC via van Genuchten) with GeoStudio reveals a distinct 12 h window where saturation buffers further destabilization, offering a refined framework for mine management in water-scarce regions like Ningxia. While GB/T 32864-2016 defines Fs ≤ 1.0 as the instability threshold (approached here at 200 mm/h), our results indicate that the critical rainfall intensity threshold triggering near-failure (Fs < 1.05) in arid mine slopes may be significantly higher (approaching 200 mm/h) than in humid regions, necessitating regionally tailored early-warning criteria [23]. Although an average angle of 51° is steep by natural hillside standards, in the context of limestone open-pit mines in northern China it represents a relatively moderate final bench/face angle compared with typical overall pit wall angles exceeding 60°. The inclusion of ≥100 mm/h scenarios, justified by observed increases in extreme convective events (e.g., 11.2% regional rise in maximum hourly rates since 1971), underscores the need for resilient designs beyond current guidelines like GB/T 32864-2016.

However, several limitations merit consideration. The homogeneous material assumption overlooks localized heterogeneity, particularly the thin gravel/sand interlayers observed in Section 2.2, potentially underestimating preferential flow paths that could accelerate instability; however, the cover is modeled as a single homogeneous layer since localized gravel lenses, although present, are not sufficiently continuous or thick to warrant a discrete higher-permeability layer given the available data. Stress–strain coupling was omitted due to unavailable elastoplastic parameters (E, ν), neglecting deformation-induced permeability changes (e.g., via microcracking under shear); however, this is justified given the study’s emphasis on rapid seepage response in low-permeability arid soils, where matrix suction loss dominates short-term instability, and the thin cover limits significant strain accumulation. LEM suffices for such cases, as it conservatively captures FOS thresholds without overpredicting stability from uncalibrated deformation models—aligning with GB/T 32864-2016 applications in Chinese mine engineering [11,13]. For validation, a scoping check with literature-typical values (E = 100–500 MPa, ν = 0.3 for gravelly sand) in a simplified FEM-SR analog yielded FOS differences of <7% from our LEM results under 200 mm/h rainfall, supporting LEM’s adequacy here without necessitating a full sensitivity analysis that could introduce parameter bias. While model consistency was verified through theoretical checks (continuity of seepage flux, force equilibrium) and parametric sensitivity analysis, field validation of pore pressure predictions was infeasible without instrumented slopes. The soil cover is modelled as homogeneous; while localized gravel lenses exist, available data do not support delineation of discrete layers with significantly different properties. This simplification is conservative for seepage (potentially underestimating preferential flow) but acceptable given the thin cover and focus on overall stability thresholds.

Critically, this study lacks direct comparison with real-world data, such as piezometer readings for transient pore-water pressure or inclinometer measurements for deformation, which are essential for calibrating seepage-stability models in practice. Historical failure records are also absent for the Kazimiao site, reflecting the rarity of intense rainfall events in Ningxia’s arid climate (annual extremes typically <50 mm/h); however, this omission heightens uncertainty, as simulations may over- or under-predict thresholds without empirical benchmarks. For context, regional analogs in northwestern China, such as rainfall-triggered slope instabilities in loess-covered open-pit coal mines (e.g., Fushun West) or mining-induced failures in iron pits (e.g., Yanqianshan), demonstrate similar mechanisms of rapid saturation and shallow sliding under rare storms, aligning qualitatively with our 12 h buffering effect but revealing a broader data scarcity in arid zones that limits quantitative validation [2,4,7,24,25]. This underscores that while our FOS thresholds (e.g., ~1.01 at 200 mm/h) provide a useful preliminary framework, they should be treated as conservative estimates until corroborated by monitoring programs, potentially overestimating stability in heterogeneous conditions or underestimating risks from unmodeled factors like desiccation cracks. Furthermore, the model introduces biases by neglecting vegetation effects, which in arid mine slopes, though sparse, could enhance stability via root cohesion (increasing FOS by ~0.1–0.3) and reduced infiltration through canopy interception and evapotranspiration, as seen in regional restoration studies [26]. Seismic influences were also omitted, despite Ningxia’s moderate risk (intensity VII–VIII zones per GB 18306-2015), where dynamic loading could synergize with rainfall to lower FOS by 20–40% in saturated conditions, exacerbating shallow failures in fractured bedrock [27].

Other biases include ignoring freeze–thaw cycles, common in Ningxia’s continental climate, which could weaken soil structure and reduce shear strength by 10–15% annually. Quantitatively, these arid-specific thresholds contrast sharply with humid regions: for instance, in subtropical India (MAP > 2000 mm), FOS drops to ~1.0 at 50–65 mm/h over 24 h in clayey/sandy slopes [28], while in humid-tropical Puerto Rico, landslide thresholds are I = 91.46 D^−0.82 (mm/h, h), requiring only 20–30 mm/h for 10 h durations, 2–3 times lower than our arid buffering allows before saturation [29]. In Mediterranean mine slopes (semi-humid, MAP ~600 mm), FOS falls below 1 at just 18 mm/h over 7 days [30]. This highlights higher arid instability thresholds (~100–200 mm/h for FOS < 1.05) due to initial low moisture and slow infiltration, versus rapid suction loss in pre-wetted humid soils, emphasizing the need for climate-specific guidelines amid global wetting trends. Additionally, idealized constant-intensity rainfall scenarios may not capture short-duration convective bursts common in semi-arid climates.

Despite these limitations, the Fs outputs (1.01–2.52) align with Chinese slope stability standards (GB/T 32864-2016) and regional case studies [11], supporting the model’s utility for preliminary hazard assessment and mitigation planning (e.g., drainage design). Most significantly, by quantifying the infiltration buffering effect’s time scale and establishing intensity thresholds relevant to arid zones, this work provides a framework adaptable to mining slopes in similar global arid/semi-arid regions (e.g., central Asia, the Middle East, western North America, Australia) facing intensifying rainfall extremes. Future work should incorporate spatial heterogeneity, vegetation effects, and stochastic rainfall patterns to refine predictions, prioritizing field instrumentation (e.g., piezometers, rain gauges) and post-event forensic analysis of any failures to bridge the simulation-reality gap and enhance early-warning systems amid climate change.

Practical implications for Kazimiao and similar arid-zone limestone mines in Northwest China include:

• Routine monitoring is sufficient under normal summer rainfall (≤50 mm/h).
• When short-term forecasts predict intensities ≥ 80 mm/h or cumulative rainfall > 150 mm in ≤12 h, operators should activate Level-II or Level-I early-warning protocols (restricted access, intensified drainage, and temporary suspension of blasting/loading near the highwall).
• Permanent mitigation should prioritize surface drainage systems capable of handling 150–200 mm/h runoff (e.g., crest intercepting ditches, armored downhill channels) and rapid-response dewatering pumps, rather than costly full-slope reinforcement, given the rarity of triggering events.

5. Conclusions

This study quantifies rainfall-induced instability thresholds for a moderately steep (51°) limestone open-pit mine slope in arid Ningxia using GeoStudio’s coupled SEEP/W and SLOPE/W modules, revealing distinct arid-zone behaviors compared to humid regions.

i.

In the natural state, increasing rainfall duration and amount cause gradual infiltration into the soil cover, elevating pore-water pressure. Under intensities ≥ 100 mm/h, pressures peak and stabilize after ~12 h as the low-permeability gravelly sand (k_s ≈ 2.1 × 10⁻⁴ cm/s) reaches saturation, demonstrating an “infiltration buffering effect” unique to arid soils with high initial suction. This leads to sharp shear-strength reduction along potential failure surfaces, triggering shallow translational sliding.

ii.

The slope maintains acceptable stability (FOS > 1.05, basically stable per GB/T 32864-2016) under intensities ≤ 50 mm/h over 24 h. At ≥100 mm/h, FOS declines rapidly within the first 12 h, stabilizing in the less-stable range (1.00–1.05) or becoming unstable (FOS ≈0.98 at 200 mm/h without protection). These thresholds are 2–3 times higher than in humid regions (e.g., FOS < 1 at 20–50 mm/h), highlighting arid resilience to short convective bursts but vulnerability to climate-intensified extremes.

iii.

Slope protection with 0.40 m thick mortared rubble masonry (c = 350 kPa, φ = 42°, effectively impermeable) elevates natural FOS to 2.52 and maintains FOS > 1.01 even under 200 mm/h rainfall, primarily by blocking infiltration and adding resisting forces. This simple measure substantially enhances safety, with failure surfaces shifting deeper or becoming non-critical.

iv.

Practical implications include operational thresholds: routine monitoring for ≤50 mm/h forecasts; and Level-II/I early-warning (restricted access, drainage activation) for >80–100 mm in 6–12 h. Mitigation should prioritize low-cost drainage (e.g., crest ditches for 200 mm/h runoff) over full reinforcement, given event rarity in Ningxia (annual precipitation 181 mm).

Despite limitations like omitted vegetation/seismic effects and lack of field validation, these findings provide a transferable framework for arid/semiarid mine slope management globally, informing early-warning systems amid rising extremes. Future work should incorporate heterogeneity, stochastic rainfall, and monitoring data for refinement.