Instability Mechanism of a Soil–Rock Binary-Structure Slope Under Rainfall Conditions

Abstract

Rainfall-induced instability of highway slopes with a soil–rock binary structure may be strongly influenced by the hydraulic barrier effect of low-permeability shale. This study investigated the right-side slope along the D-ramp section from DK0+230 to DK0+660 at Deze Interchange on the Zhanhui Expressway, China. A two-dimensional coupled seepage–stress model was developed based on the engineering geological conditions and rainfall records to simulate the slope response under a 72 h extreme rainfall scenario with an intensity of 175.6 mm/d. Field displacement monitoring data were used to validate the modeled deformation pattern under natural conditions. Under natural conditions, the reinforced toe zone remained stable, deformation was concentrated along the interface between the block-stone layer and strongly weathered limestone in the middle and rear portions of the slope, and the factor of safety was 1.1344, indicating a basically stable state. During prolonged rainfall, infiltrating water accumulated near the interface between the strongly weathered shale and the underlying shale owing to the hydraulic barrier effect of the low-permeability shale, forming a continuous transient saturated zone. The plastic zone progressively extended from the upper shallow weak interface to the lower deep interface and eventually became fully connected, while the factor of safety decreased to 0.9886, indicating overall instability. The results reveal a coupled mechanism involving interfacial water accumulation, increased pore-water pressure, the formation of a transient saturated zone, and a shift in the controlling zone of slope deformation and failure from shallow to deeper layers. These findings provide a reference for disaster prevention and mitigation of similar soil–rock binary-structure slopes.

1. Introduction

Rainfall is one of the principal external factors that induce slope deformation and instability [1,2]. Soil–rock binary-structure slopes generally consist of an overlying loose soil or block-stone layer and underlying bedrock, with marked differences among the materials in pore structure, permeability, and shear strength. During rainfall, water can rapidly infiltrate along surface cracks, pores in the coarse-grained layer, and bedrock fractures. When the infiltrating water reaches a low-permeability stratum or a weakly permeable interface, downward drainage is impeded, causing a local increase in water content, a reduction in matric suction, and a rise in pore-water pressure, which in turn reduce the effective stress and available shear resistance along the interface. Therefore, the stability of soil–rock binary-structure slopes under rainfall depends not only on rainfall intensity and duration, but also on the combined spatial configuration of the upper conductive medium, the deep hydraulic barrier, and the soil–rock interfaces.

Previous studies have mainly focused on rainfall infiltration and the hydraulic response of unsaturated slopes. Han et al. [3] derived an analytical solution for rainfall infiltration into homogeneous slopes based on unsaturated seepage theory and clarified the advancement of the wetting front and changes in water content. Wu et al. [4] and Jiang and Cui [5] used saturated–unsaturated coupling simulations and field monitoring, respectively, and showed that rainfall intensity, duration, and the initial hydraulic state jointly govern pore-pressure development and stability degradation. Chang et al. [6] demonstrated through model tests that preferential infiltration paths formed by cracks accelerate local saturation and progressive failure. Jayakody et al. [7] further showed that, even for the same cumulative rainfall, the temporal distribution of antecedent rainfall can markedly alter the time of slope initiation. Levinna and Yang [8] reported that hysteresis in the soil–water characteristic curve and the initial matric suction affect calculated pore-water pressures and factors of safety. Collectively, these studies indicate that water migration, loss of matric suction, and development of positive pore-water pressure are the fundamental hydraulic processes that reduce effective stress and available shear resistance.

With advances in monitoring and numerical methods, research on rainfall-affected slopes has gradually shifted from separate seepage or stability analyses to integrated evaluation of hydrological processes, deformation responses, and failure evolution. Liu et al. [9] combined field monitoring data, historical performance records, and numerical models to dynamically update slope stability during rainfall. Wang et al. [10] developed a hydro-mechanical coupling method incorporating surface runoff, rainfall infiltration, and deformation development to describe the entire process from water migration to slope failure. For binary-structure and layered slopes, Wu and Wang [11] and Wang et al. [12] showed through physical model tests that interlayer lithologic combinations, coarse-layer particle characteristics, and slope angle significantly affect the barrier and drainage performance against rainfall infiltration. Zhao et al. [13] and Liu et al. [14] revealed pore-pressure accumulation above aquitards and gently dipping weak interlayers, respectively. Jiang et al. [15] further demonstrated that contrasts in permeability among multilayer media, transition-layer thickness, and spatial variability jointly determine the distributions of the wetting front and water content. For shale-bearing slopes, Yu et al. [16] found that rainfall infiltration and shale hydration-induced weakening promote the extension and coalescence of plastic zones from local areas toward deeper layers. Zhang and Pei [17] and Xu et al. [18] improved slope stability assessment by considering tensile-strength cut-off and three-dimensional slopes subjected to variable rainfall, respectively. Related studies of fractured shale reservoirs have further shown that natural-fracture geometry, geological and fluid properties, and fluid–solid interactions can markedly affect fracture propagation, fluid filtration, and particle transport within fractured media [19,20,21]. Although these studies address reservoir stimulation rather than rainfall-induced slope failure, they highlight the importance of structural heterogeneity and transport processes in controlling fluid migration through fractured geological media.

In summary, previous studies have clarified the responses of rainfall-affected slopes from the perspectives of unsaturated infiltration, antecedent rainfall, preferential flow through cracks, interlayer permeability contrasts, and hydro-mechanical coupling, providing a foundation for investigating the instability mechanisms of soil–rock binary-structure slopes. However, most studies have focused on homogeneous soil slopes, artificial fine/coarse capillary barriers, or a single weak interlayer. The combined effect of water transmission through an upper highly permeable medium and water blockage by a lower low-permeability stratum in complex natural soil–rock slopes remains insufficiently understood. In particular, the relationships among nonuniform pore-pressure growth along different segments of the strongly weathered shale interface, the evolution of a transient saturated zone from local formation to continuous connection, and the shift in the controlling deformation and failure zone from a shallow interface to a deep interface have rarely been jointly investigated using field deformation data and process-based coupled simulation. Therefore, this study investigates the soil–rock binary-structure slope at Deze Interchange of the Zhanhui Expressway. Engineering geological investigation and field displacement monitoring are used to characterize slope deformation under natural conditions, while coupled seepage–stress numerical simulation is employed to analyze the evolution of pore-water pressure, displacement, plastic zones, and the factor of safety under natural conditions and an idealized 72 h prolonged-rainfall scenario, with emphasis on the progressive instability mechanism controlled by the hydraulic barrier effect of low-permeability shale.

2. Study Area

2.1. Geological Conditions

Deze Interchange of the Zhanhui Expressway is located in northeastern Yunnan Province, China, at 103°35′7″ E and 25°58′56″ N (Figure 1). Field investigation showed that the slope is well vegetated, and no surface runoff or groundwater discharge was observed during the survey. The overall slope aspect is approximately 330°, and the slope is gentle in the lower part and steep in the upper part. The slope toe is a cut slope formed by engineering excavation, with slope ratios of 1:1 to 1:0.75 and slope angles of 45–53°. An unstable slope is developed above the cut slope at the transition between steep and gentle terrain (Figure 2). The rear part is relatively steep, generally 35–50°, whereas the middle and front parts are gentler, generally 10–25°. The unstable slope is mantled by Quaternary colluvial and talus deposits (Q₄dl+c), composed mainly of block stones in a medium-dense, openwork structure. The deposit is thick, continuously distributed, and the blocks are uncemented. It is underlain by strongly weathered Lower Carboniferous limestone in thin- to medium-thick beds with well-developed dissolution features and fractures, followed downward by strongly weathered shale and shale. The strongly weathered shale is soft and fractured, whereas the underlying shale is relatively intact and markedly less permeable. Their contact forms a deep zone of abrupt hydraulic and mechanical contrasts.

2.2. Climatic Characteristics

The study area lies north of the Tropic of Cancer and has a humid subtropical monsoon climate. Owing to the relatively high elevation, vertical climatic zonation is pronounced; summers are mild, winters are cold and dry, and strong winds are common. Annual precipitation is 700–1400 mm. The rainy season generally extends from June to October and accounts for more than 80% of the annual precipitation. Monthly precipitation is typically 150–250 mm and can exceed 400 mm in some localities, making this period the principal season of groundwater recharge. The pronounced alternation between dry and wet seasons strongly affects groundwater circulation. In recent years, short-duration heavy rainfall events have been concentrated, with a maximum daily rainfall of 175.6 mm; such intense rainfall has a substantial effect on slope stability.

3. Deformation Characteristics of the Unstable Slope

3.1. Surface Deformation Features

The main deformation features of the unstable slope are tensile cracks developed along the rear margin and in the middle–rear portion, locally accompanied by scarps and step-like microtopography. Several cracks were identified during field investigation, of which Figure 2 shows the four principal cracks, L1–L4. Cracks L1 and L2 are located at the rear margin and constitute the controlling tensile cracks. L3 occurs in the lower part of the slope and exhibits local compressive bulging, whereas L4 is located at the transition between steep and gentle terrain in the middle–rear portion and shows tensile deformation. The cracks generally strike nearly perpendicular to the slope direction, with good continuity and consistent orientations, indicating pronounced tensile deformation at the rear margin. L2 is the largest crack, extending approximately 146 m. The outer slope block is displaced downward by 0.2–0.6 m; the crack dips toward the outside of the slope, is 0.2–0.80 m wide, and is visible to a depth of approximately 5 m. It is the most prominent deformation feature at the rear margin. Together, L1 and L2 form a rear tension-crack zone, indicating that the rear part of the slope has undergone a certain degree of traction-induced deformation.

Overall, the cracks are concentrated at the rear margin and in the middle–rear portion of the slope. Apart from local compressive deformation near L3, no continuous bulging zone, shear outlet, or radial cracks have formed at the toe, and no throughgoing shear cracks are visible along the lateral boundaries. These features indicate that a complete sliding boundary has not yet developed and that the slope remains in a progressive deformation stage dominated by rear-margin tension and middle-slope creep.

3.2. Deformation Mode Analysis

The development of cracks L1 and L2 indicates that tensile deformation first occurred in the rear part of the slope and progressively formed a continuous tension-crack zone. The occurrence of L3 and L4 indicates that deformation has extended toward the middle part of the slope. Under long-term gravity loading, the overlying loose block-stone layer in the middle–rear portion creeps slowly along the soil–rock interface and exerts a traction effect on the rear margin. The absence of a continuous shear outlet at the toe indicates that the sliding boundary is not fully connected under natural conditions.

Rainfall is an important external factor governing the evolution of slope deformation. During rainfall, water can infiltrate into the slope along cracks and soil–rock contacts, promoting the extension of rear-margin cracks and further slope deformation. Under prolonged heavy rainfall or other disturbances, the slope may evolve from its current progressive deformation stage to overall instability.

The combined evidence indicates that, under natural conditions, the slope undergoes progressive deformation dominated by traction-induced cracking at the rear margin and creep in the middle–rear portion, while the reinforced toe zone has not exhibited sustained accelerating deformation. Accordingly, the rear-margin cracks, the upper soil–rock interface, and the deep strongly weathered shale interface are the key locations for subsequent analysis of rainfall seepage and instability mechanisms.

4. Rainfall Seepage Mechanism

4.1. Rainfall Seepage Mechanism and the Role of the Hydraulic Barrier

During rainfall, the seepage state within the slope exhibits a distinct transition from unsaturated to saturated conditions as the water content changes. Because the strata differ markedly in permeability, infiltrating water tends to form local perched-water zones above low-permeability layers, causing pore-water pressure to rise. To characterize the coupled response of the seepage and stress fields during rainfall infiltration, this study adopts saturated–unsaturated seepage theory based on Darcy’s law and mass conservation and uses the Van Genuchten model to describe the relationships of matric suction with volumetric water content and relative permeability.

In the study slope, the overlying block-stone layer is highly permeable, allowing rainfall to percolate rapidly through pores and fractures, whereas the underlying shale has low permeability and provides a pronounced hydraulic barrier. In this study, the contact between the strongly weathered shale and the underlying shale is termed the “strongly weathered shale interface.” Under prolonged rainfall, infiltrating water tends to be retained near this interface, reducing matric suction, increasing pore-water pressure, and forming a transient saturated zone, thereby providing the hydrological conditions for deep deformation and coalescence of the plastic zone.

4.2. Governing Differential Equation for Saturated–Unsaturated Seepage

Rainfall seepage in the slope can be described by the saturated–unsaturated seepage differential equation derived from Darcy’s law and mass conservation [22]:

$${\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left({\mathrm{k}}_{\mathrm{x}}{\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{x}}}\right)+{\displaystyle \frac{\partial }{\partial \mathrm{y}}}\left({\mathrm{k}}_{\mathrm{y}}{\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{y}}}\right)+\mathrm{Q}={\mathrm{m}}_{\mathrm{w}}{\mathrm{\gamma }}_{\mathrm{w}}{\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{t}}}$$

(1)

where ${\mathrm{k}}_{\mathrm{x}}$ and ${\mathrm{k}}_{\mathrm{y}}$ are the permeability coefficients in the $\mathrm{x}$ and $\mathrm{y}$ directions, respectively (and are functions of matric suction in the unsaturated zone); H is the total head (elevation head + pressure head); Q is the internal source/sink term; rainfall in the present model is prescribed through the surface-flux boundary condition described below; ${\mathsf{\gamma }}_{\mathrm{w}}$ is the unit weight of water; and ${\mathrm{m}}_{\mathrm{w}}$ is the slope of the soil–water characteristic curve, defined as

$${\mathrm{m}}_{\mathrm{w}}=-{\displaystyle \frac{\partial \mathrm{\theta }}{\partial ({\mathrm{u}}_{\mathrm{a}}-{\mathrm{u}}_{\mathrm{w}})}}$$

(2)

where θ is the volumetric water content, ${\mathrm{u}}_{\mathrm{a}}$ is the pore-air pressure, ${\mathrm{u}}_{\mathrm{w}}$ is the pore-water pressure, and (${\mathrm{u}}_{\mathrm{a}}$ − ${\mathrm{u}}_{\mathrm{w}}$) is the matric suction. ${\mathrm{m}}_{\mathrm{w}}$ represents the change in water content per unit change in matric suction; ${\mathrm{m}}_{\mathrm{w}}$ = 0 in the saturated zone, whereas ${\mathrm{m}}_{\mathrm{w}}$ > 0 in the unsaturated zone.

To solve the equation for a specific slope, initial and boundary conditions must be prescribed. The initial condition is the hydraulic-head distribution throughout the domain at t = 0:

$$\mathrm{H}(\mathrm{x},\mathrm{y},\mathrm{t}){|}_{\mathrm{t}=0}={\mathrm{H}}_0(\mathrm{x},\mathrm{y})\cdots (\mathrm{x},\mathrm{y})\in \mathrm{\Omega }$$

(3)

The boundary conditions are divided into two types:

(1)

First-type boundary condition (prescribed-head boundary): the head on the boundary ${\mathrm{\Gamma }}_1$ is a known function.

$$\mathrm{H}(\mathrm{x},\mathrm{y},\mathrm{t}){|}_{{\mathrm{\Gamma }}_1}=\mathrm{f}(\mathrm{x},\mathrm{y},\mathrm{t})\cdots (\mathrm{x},\mathrm{y}\in {\mathrm{\Gamma }}_1)$$

(4)

where f(x, y, t) is the prescribed head function on the boundary.

(2)

Second-type boundary condition (prescribed-flux boundary): the inflow per unit area q on the boundary ${\mathrm{\Gamma }}_2$ is known.

$$\mathrm{K}{\displaystyle \frac{\partial \mathrm{h}}{\partial \mathrm{n}}}{|}_{{\mathrm{\Gamma }}_2}=\mathrm{q}(\mathrm{x},\mathrm{y},\mathrm{t})\cdots (\mathrm{x},\mathrm{y}\in {\mathrm{\Gamma }}_2)$$

(5)

where K is the permeability coefficient, h is the pressure head, n denotes the outward normal direction of the boundary, and q (x, y, t) is the prescribed infiltration flux (for the slope surface, q equals the component of rainfall intensity normal to the boundary). In the numerical model, rainfall was applied using the Surface Flux boundary in MIDAS GTS NX, with the flux-to-head conversion option activated. When the prescribed rainfall flux exceeded the infiltration capacity represented by the hydraulic conductivity of the surface material, the flux boundary was converted to a total-head boundary with the total head equal to the elevation head. This condition corresponds to a zero pressure head at the ground surface and prevents rainfall exceeding the admissible infiltration rate from being forcibly introduced into the slope. Surface runoff was not modeled as a separate overland-flow domain, and no additional positive ponding head was imposed on the slope surface. Therefore, only the portion of rainfall that could be accommodated by the seepage boundary condition contributed to subsurface infiltration.

At the strongly weathered shale interface, the abrupt permeability contrast across the interface restricts further downward migration of infiltrating water during continuous rainfall infiltration, thereby increasing the pressure head along the interface.

4.3. Determination of Unsaturated Hydraulic Parameters

Unsaturated seepage analysis requires relationships between matric suction, volumetric water content, and relative permeability. The Van Genuchten model is adopted in this study:

$${\mathrm{\theta }}_{\mathrm{w}}={\mathrm{\theta }}_{\mathrm{r}}+{\displaystyle \frac{{\mathrm{\theta }}_{\mathrm{s}}-{\mathrm{\theta }}_{\mathrm{r}}}{{\left[1+{\left(\mathrm{a}\mathrm{\psi }\right)}^{\mathrm{n}}\right]}^{\mathrm{m}}}}$$

(6)

$${\mathrm{k}}_{\mathrm{w}}={\mathrm{k}}_{\mathrm{s}}{\displaystyle \frac{{\left[1-{\left(\mathrm{a}\mathrm{\psi }\right)}^{\mathrm{n}-1}{\left(1+{\left(\mathrm{a}\mathrm{\psi }\right)}^{\mathrm{n}}\right)}^{-\mathrm{m}}\right]}^2}{{\left[1+{\left(\mathrm{a}\mathrm{\psi }\right)}^{\mathrm{n}}\right]}^{\mathrm{m}/2}}}$$

(7)

where ${\mathrm{\theta }}_{\mathrm{\omega }}$ is the volumetric water content; ${\mathrm{\theta }}_{\mathrm{s}}$ and ${\mathrm{\theta }}_{\mathrm{r}}$ are the saturated and residual volumetric water contents, respectively; ψ is the matric suction; ${\mathrm{k}}_{\mathrm{w}}$ and ${\mathrm{k}}_{\mathrm{s}}$ are the unsaturated and saturated permeability coefficients, respectively; and a, n, and m are fitting parameters (usually m = 1 − 1/n). To characterize the unsaturated hydraulic responses of the different strata, the Van Genuchten model was used to define the matric suction–volumetric water content and volumetric water content–relative permeability relationships for silty clay, block stone, limestone, strongly weathered limestone, strongly weathered shale, and shale. The parameters listed in

Table 1. Unsaturated hydraulic parameters of the slope materials.

Lithology	Saturated Permeability Coefficient/(m·h−1)	VG Model Parameters
		a	n	m	θs	θr
Silty clay	3.6 × 10−4	0.01	1.35	0.26	0.42	0.10
Block stone	0.331	0.05	2.30	0.57	0.25	0.06
Strongly weathered shale	7 × 10−3	0.01	2.00	0.50	0.24	0.12
Shale	4.17 × 10−6	0.01	1.25	0.20	0.12	0.04
Strongly weathered limestone	0.01	0.10	2.00	0.50	0.22	0.10
Limestone	4.2 × 10−4	0.02	1.80	0.44	0.04	0.01

Note: The hydraulic parameters listed in Table 1 are adopted numerical parameters determined based on site-investigation constraints and typical parameter ranges for comparable geomaterials and engineering conditions.

are adopted numerical inputs rather than direct laboratory measurements in the present study. Their values were determined based on the lithological and permeability characteristics documented in the site investigation and typical parameter ranges for comparable geomaterials and engineering conditions (Table 1 and Figure 3). As shown in Figure 3a, volumetric water content generally decreases with increasing matric suction. Silty clay, strongly weathered shale, and strongly weathered limestone exhibit relatively broad ranges of water-content variation and therefore comparatively strong water-retention capacities. The block-stone layer has a high saturated permeability, allowing infiltrated water to migrate readily downward, whereas limestone has a generally low volumetric water content and limited pore-water storage capacity. Figure 3b shows that the relative permeability of all strata increases markedly with volumetric water content, indicating progressive enhancement of hydraulic conductivity during the transition from unsaturated to saturated conditions. Compared with block stone and strongly weathered limestone, strongly weathered shale and shale have lower saturated permeabilities and weaker deep drainage capacity, making water more likely to be retained near their interface.

5. Analysis of Potential Failure Mechanisms of the Soil–Rock Binary-Structure Slope

5.1. Engineering Geological Analysis

The study slope consists of an overlying Quaternary colluvial–talus block-stone layer and underlying limestone and shale, exhibiting a typical soil–rock binary structure. The slope is generally steep in the upper part and gentle in the lower part, with a large elevation difference and therefore high gravitational potential energy.

Field investigation and stereographic projection indicate that two dominant discontinuity sets are developed in the slope (Figure 4). The bedding orientation is 153°∠35° and dips into the slope; the orientations of discontinuities J1 and J2 are 335°∠80° and 262°∠85°, respectively. The stereographic projection shows that J1 dips approximately in the slope direction and has a steep dip angle, creating favorable conditions for downslope deformation and making toppling–bending deformation likely under gravity and rainfall. J2 intersects the slope at a high angle and is comparatively favorable to overall stability. In addition, the intersection line of J1 and J2 trends approximately in the slope direction, indicating that local block sliding may occur. The discontinuity combination not only controls the subdivision of the rock mass into blocks but also provides preferential pathways for rainfall infiltration.

In terms of the soil–rock assemblage, the overlying block-stone layer is thick, uncemented, highly porous, and highly permeable. The underlying limestone contains well-developed joints and fractures that provide pathways for further downward infiltration, whereas the shale layer has markedly lower permeability and acts as a relative aquitard. Controlled by these permeability contrasts, rainfall can migrate rapidly downward through pores in the block-stone layer and the fracture network and then form a local perched-water zone near the top of the underlying low-permeability shale.

As rainfall continues, water infiltrates progressively deeper into the slope and accumulates near the strongly weathered shale interface. Owing to the hydraulic barrier effect of the underlying low-permeability shale, matric suction at the interface continuously decreases, pore-water pressure gradually rises, and a transient saturated zone forms. From an engineering-geological perspective, the strongly weathered shale is susceptible to softening and slaking upon wetting. In the present numerical model, however, the rainfall-induced response is primarily represented through changes in matric suction, pore-water pressure, and effective stress rather than through explicit moisture-dependent degradation of the shear-strength parameters. This simplification may underestimate the additional mechanical weakening associated with wetting-induced softening of the strongly weathered shale. Under prolonged heavy rainfall, pore-pressure accumulation and the associated reduction in effective stress further enhance the tendency for sliding along the weak interface.

The combined analysis shows that deformation and instability of the study slope are jointly controlled by topography, discontinuity combinations, and permeability contrasts among the strata. The topography provides the gravitational driving potential; rear-margin cracks and discontinuities form preferential infiltration pathways; the upper block-stone layer–strongly weathered limestone interface controls the principal deformation zone under natural conditions; and the deep strongly weathered shale interface controls the location of pore-pressure accumulation and the development of a potential sliding surface after rainfall.

5.2. Numerical Simulation Analysis

To investigate the deformation zoning and progressive instability of the soil–rock binary-structure slope under natural conditions and prolonged heavy rainfall, a representative geological section passing through the principal deformation zone and approximately aligned with the main slope direction was selected based on geological mapping, geophysical exploration, field investigation, and available geological data (Figure 5). A geometrically simplified two-dimensional model was subsequently established in MIDAS GTS NX 2024. A plane-strain assumption and the Mohr–Coulomb constitutive model were adopted. At the engineering scale considered in this study, the weathered and fractured rock masses were treated as equivalent continua. The mapped J1 and J2 discontinuity sets were therefore not introduced as discrete joint elements; instead, their mechanical influence on rock-mass integrity was represented indirectly through reduced equivalent rock-mass parameters, while lithological contacts were represented by contrasts in material properties between adjacent strata. Accordingly, the model was intended to characterize the overall shear-yielding response and evolution of the potential failure zone rather than the opening or sliding of individual discontinuities. The two-dimensional model represents the dominant in-plane seepage and deformation response of the selected section, whereas out-of-plane deformation, lateral seepage, and the three-dimensional connectivity of individual discontinuities are not explicitly reproduced.

The baseline model contained 12,746 elements and 12,857 nodes. An element size of 1.0 m was adopted for the strongly weathered shale, strongly weathered limestone, block-stone layer, and silty clay, whereas the element size in the remaining strata gradually increased from 1.0 to 4.0 m. To assess mesh sensitivity, the four key strata were locally refined to 0.5 m while the mesh configuration of the remaining strata was kept unchanged, resulting in 28,821 elements and 28,946 nodes. The factors of safety obtained with the baseline and refined meshes were 1.1344 and 1.1407 under natural conditions and 0.9886 and 0.9989 after 72 h of rainfall, respectively, corresponding to relative differences of approximately 0.6% and 1.0%. The refined mesh also reproduced a similar spatial distribution and coalescence of the plastic zone along the strongly weathered shale interface after 72 h of rainfall. The small differences in the factor of safety, the unchanged stability classification, and the consistent plastic-zone pattern indicate that the main numerical results and the identified failure mechanism are not significantly affected by local mesh refinement.

The physical and mechanical parameters used in the numerical model were determined based on the lithological characteristics, weathering degree, rock-mass structure, and engineering geological conditions identified from the site investigation, together with the relative mechanical contrasts among the strata and engineering experience for comparable geological conditions. The displacement monitoring data were not used for parameter adjustment and were retained as an independent field dataset for subsequent evaluation of the modeled deformation pattern under natural conditions. The adopted material parameters are listed in

Table 2. Physical and mechanical parameters of the slope materials.

Material Type	Natural Unit Weight/(kN·m−3)	Saturated Unit Weight/(kN·m−3)	Natural Shear Strength		Elastic Modulus/MPa	Poisson’s Ratio
			c/kPa	φ/(°)
Silty clay	19	19.5	24	17	40	0.35
Block stone	19	21	35	22	800	0.3
Limestone	25	26	200	30	30,000	0.25
Strongly weathered limestone	22	22.8	150	28	3000	0.28
Shale	22	23	150	30	10,000	0.3
Strongly weathered shale	21	22	35	21	800	0.3
Marl	22	23	260	30	15,000	0.25
Quartz sandstone	21	21.5	330	30	30,000	0.25
Dolomite	22	22.5	280	30	25,000	0.25

. The anchor cables in the reinforced cut slope were modeled using embedded truss elements with an elastic modulus of 195 GPa. According to the project design report, each anchor cable consists of four 15.2 mm low-relaxation steel strands with a tensile strength of 1860 MPa, and the design anchoring force of a single cable is 500 kN. For the mechanical boundary conditions, horizontal displacement was constrained along the left and right boundaries, whereas both horizontal and vertical displacements were constrained along the base.

The numerical analysis comprised two stages. First, the initial geostress and seepage fields were established under natural conditions, and the corresponding deformation and stability state were evaluated. Second, the recorded maximum daily rainfall of 175.6 mm/d for the study area was continuously applied to the slope surface for 72 h to construct an idealized extreme prolonged-rainfall scenario and investigate the progressive response of the slope. The 72 h duration was adopted to examine the evolution from shallow rainfall infiltration to deep instability rather than to reproduce a specific historical three-day rainfall event. Transient coupled seepage–stress analysis was performed using the unsaturated hydraulic parameters in Table 1 and the physical and mechanical parameters in Table 2. Rainfall infiltration modifies the hydraulic state through changes in matric suction, permeability, and pore-water pressure, with the resulting variation in effective stress governing the mechanical response. Cohesion and friction angle were not varied with moisture conditions during the transient rainfall analysis. Pore-water pressure, displacement, plastic-zone development, and the factor of safety at different rainfall durations were subsequently used to characterize the progressive evolution from infiltration to overall instability.

For stability evaluation, the factor of safety was calculated using the strength reduction method (SRM) in MIDAS GTS NX. For a trial reduction factor F, the shear-strength parameters were reduced according to ${\mathrm{c}}_{\mathrm{r}}$ = c/F and tan${\mathrm{\phi }}_{\mathrm{r}}$ = tan$\mathrm{\phi }$/F. The nonlinear iterations adopted a displacement-norm convergence criterion with a tolerance of 0.001. Numerical nonconvergence, together with the development of a continuous plastic zone, was used to identify the critical instability state. The corresponding critical reduction factor was taken as the factor of safety, while the displacement field was used as supplementary evidence for identifying the failure mode.

5.2.1. Stability Analysis Under Natural Conditions

To reproduce the initial stress state of the slope, stress–seepage equilibrium was first established under gravity loading, displacement boundary conditions, and the initial groundwater condition. The strength reduction method then yielded a factor of safety of 1.1344. According to the Specification for Investigation of Landslide Prevention and Control Engineering (GB/T 32864–2016) [23], the stability state under natural conditions was classified using

Table 3. Classification of landslide stability states.

Landslide Stability State	Unstable	Less Stable	Basically Stable	Stable
Factor of safety, Fs	Fs < 1.00	1.00 ≤ Fs < 1.05	1.05 ≤ Fs < 1.15	Fs ≥ 1.15

, and the slope was found to be basically stable. Figure 6 and Figure 7 show the numerical displacement and plastic-zone distributions at the critical strength-reduction state under the natural hydraulic condition. These results are used to identify the potential deformation and failure pattern rather than to represent the actual field displacement under natural conditions. At this critical state, deformation and yielding are mainly concentrated near the upper block-stone layer–strongly weathered limestone interface. The maximum numerical displacement reaches 42.14 cm; this value corresponds to the critical state generated by the strength reduction analysis and should not be interpreted as the actual displacement of the slope under natural conditions. The plastic-zone map shows a continuous plastic zone along the interface, with the maximum plastic strain occurring in the middle segment of the interface and near the slope crest. These results indicate that the upper block-stone layer–strongly weathered limestone interface is the principal potential sliding surface under natural conditions, whereas displacement and plastic deformation in the lower slope are relatively limited.

To evaluate the actual deformation of the reinforced cut slope at the toe, displacement monitoring data from Sections I, II, and III between 1 February and 12 March 2024 were analyzed (Figure 8); the monitoring locations are shown in Figure 2. Displacements at all monitoring points changed gradually during the monitoring period, with only small variations between successive measurements and no sustained acceleration. The maximum cumulative displacement at Section I was 73.5 mm at point 1-WP3; that at Section II was 54.5 mm at point 2-WP5; and that at Section III was 57.0 mm at point 3-WP4. Overall, displacements at the three monitoring sections fluctuated slightly or gradually stabilized, indicating that the reinforced cut slope at the toe remained stable.

Field investigation indicates that the principal deformation zone lies in the middle–rear portion of the slope, whereas displacement in the reinforced toe zone remained generally gradual during the 2024 monitoring period. The numerical model under the natural hydraulic condition reproduces the same overall spatial deformation pattern, with more pronounced deformation in the middle–rear slope and relatively limited response in the reinforced toe zone. Because the monitoring data in Figure 8 were not used for parameter adjustment, the observed agreement provides an independent qualitative evaluation of the modeled deformation zoning. This comparison is limited to the spatial deformation characteristics and the absence of sustained accelerating deformation at the reinforced toe, rather than the absolute displacement magnitude. The monitored period did not correspond to the idealized 72 h extreme prolonged-rainfall scenario adopted in the numerical analysis; therefore, the field data are not used as direct validation of the predicted deep instability under that scenario.

In summary, under natural conditions the reinforced cut slope at the toe is stable, while the principal potential deformation zone lies along the block-stone layer–strongly weathered limestone interface in the middle–rear portion. The overall slope is basically stable, and the deep strongly weathered shale interface has not yet developed into the controlling sliding boundary.

5.2.2. Effect of Rainfall Infiltration on Pore-Water Pressure

Under the 72 h prolonged-rainfall scenario defined in Section 5.2, transient coupled seepage–stress analysis was performed to investigate the evolution of pore-water pressure at different rainfall durations (Figure 9). To characterize the pore-pressure time-history response of the two key interfaces, monitoring points 1–3 were arranged along the upper block-stone layer–strongly weathered limestone interface, and points 4–6 were arranged along the deep strongly weathered shale interface. Their locations are shown in Figure 5, and the pore-pressure time histories are presented in Figure 10. Negative pore pressures above the groundwater table in the plots are equivalent negative pore pressures calculated by the model, and their absolute magnitudes are influenced by the initial groundwater level and hydraulic-head field. Accordingly, the influence of rainfall infiltration on the seepage field is evaluated mainly from the temporal trends at the monitoring points, the transition from negative to positive pore pressure, and the spatial expansion of the positive pore-pressure zone.

As shown in Figure 9, before rainfall, the pore-water pressure above the groundwater table is generally negative, and both the block-stone layer–strongly weathered limestone interface and the strongly weathered shale interface are unsaturated. During the initial stage of rainfall, water first wets the shallow surface layer, and pore-water pressure gradually increases from the slope surface inward; however, no distinct positive pore-pressure zone has yet formed within the slope. As rainfall continues, water migrates deeper along pores in the block-stone layer, fractures in the limestone, and soil–rock contacts, progressively enlarging the affected pore-pressure zone.

As shown in Figure 10a, pore-water pressure along the upper block-stone layer–strongly weathered limestone interface generally increases with rainfall duration. Points 1 and 2 remain under negative pore pressure throughout the 72 h rainfall period, indicating that the corresponding portions of the upper interface remain predominantly unsaturated. In contrast, point 3, located near the downslope end of the interface, changes from negative to positive pore pressure during the late stage of rainfall, indicating localized water accumulation in this region. Overall, the upper interface primarily acts as a preferential pathway for downward water transmission, although local positive pore pressure can develop near its downslope end as rainfall persists.

In contrast, the lower strongly weathered shale interface responds much more strongly to rainfall. At approximately 34 h, monitoring point 6 near the slope toe is the first to change from negative to positive pore pressure, indicating that downward migration becomes impeded after the infiltrating water reaches the top of the shale and water begins to accumulate near the toe. At 48 h, positive pore pressure remains concentrated mainly in the lower toe segment. By 58–60 h, positive pore pressure has developed in the upper segment of the interface and at the toe, while the steep middle segment remains under negative pressure, producing a discontinuous pattern of “positive at both ends and negative in the middle.” Figure 10b shows that point 4 becomes positive at approximately 56 h. Point 5, located in the steep middle segment where drainage is relatively favorable, responds later and becomes positive at approximately 64 h. By 72 h, points 4–6 all show positive pore pressure, and the positive-pressure zones expand from the toe and upper interface segment toward the middle, forming a continuous transient saturated zone along the strongly weathered shale interface.

Overall, the upper block-stone layer–strongly weathered limestone interface primarily serves as a preferential pathway for downward water transmission, with only localized positive pore pressure developing near its downslope end during the late stage of rainfall. In contrast, the strongly weathered shale interface is the principal zone of water retention, positive pore-pressure accumulation, and transient saturation owing to the hydraulic barrier effect of the underlying low-permeability shale. Interface geometry further controls the timing of positive-pressure development, with an earlier response in the gentle segments and a delayed response in the steep middle segment.

5.2.3. Displacement Response of the Slope After Rainfall

To further evaluate slope deformation under prolonged rainfall, the total-displacement contour after 72 h of rainfall was extracted, as shown in Figure 11. The displacement field exhibits distinct zoning, with high-displacement areas near the upper block-stone layer–strongly weathered limestone interface and in the slope mass overlying the deep strongly weathered shale interface.

After 72 h of rainfall, the maximum total displacement is approximately 48.9 cm and occurs in the slope mass overlying the deep strongly weathered shale interface. Displacement contours extend from the middle slope toward the toe, indicating that continued infiltration shifts the controlling deformation zone from the upper shallow soil–rock interface toward the deep strongly weathered shale interface. Displacement in the deep bedrock beneath the affected sliding zone remains small, indicating that deformation is controlled primarily by the two interfaces with pronounced lithologic and permeability contrasts rather than developing uniformly throughout the bedrock.

Unlike the natural condition, in which displacement is mainly concentrated along the upper block-stone layer–strongly weathered limestone interface, after 72 h of rainfall a more pronounced displacement concentration develops in the slope mass overlying the strongly weathered shale interface. This change corresponds to the transition of pore-water pressure at the interface from negative to positive and to the formation of a continuous transient saturated zone. The underlying low-permeability shale impedes further downward drainage, causing water to accumulate near the interface, reducing matric suction, increasing pore-water pressure, and consequently decreasing effective stress. These hydraulic changes promote deformation concentration along the deep interface. Consequently, the deep strongly weathered shale interface gradually becomes the principal zone controlling slope deformation and sliding.

It should be noted that the displacement contour identifies the spatial concentration of slope deformation but cannot alone be used as the criterion for overall instability. The instability state must therefore be evaluated together with plastic-zone coalescence and the factor of safety obtained by the strength reduction method.

5.2.4. Evolution of the Plastic Zone Under Rainfall

The distribution and expansion of plastic zones reflect the formation of potential sliding surfaces. As shown in Figure 12, during the initial stage of rainfall, the plastic zone is distributed mainly as a band along the upper block-stone layer–strongly weathered limestone interface and is more extensive than under natural conditions. At this stage, no continuous plastic band has formed along the deep strongly weathered shale interface, and deformation remains dominated by shallow local failure. By 60 h, isolated plastic zones begin to appear near the strongly weathered shale interface as pore-water pressure rises. The upper shallow plastic zone continues to develop while deep plastic deformation increases simultaneously, indicating a transition from single shallow deformation to combined shallow and deep deformation. The plastic zone in the steep middle segment is not yet connected, so the slope has entered a critical deformation stage but a complete deep sliding boundary has not yet formed.

By 72 h, the plastic zone is fully connected along the strongly weathered shale interface, forming a continuous potential sliding surface. Its position corresponds to the high-displacement zone in Figure 11 and the continuous positive pore-pressure zone in Figure 9, demonstrating that pore-pressure accumulation, displacement concentration, and plastic yielding are successive manifestations of the coupled evolution of the seepage and stress fields under the hydraulic barrier effect of low-permeability shale.

Overall, the plastic zone first develops locally along the upper block-stone layer–strongly weathered limestone interface and then progressively extends to and becomes continuous along the deep strongly weathered shale interface. Coalescence of the deep plastic band provides direct mechanical evidence for the formation of a potential sliding surface and indicates that the controlling failure zone has shifted from the shallow soil–rock interface to the deep strongly weathered shale interface.

The maximum axial force of the anchor cables was further examined to characterize the response of the reinforcement system (Figure 13). Before rainfall, the maximum axial force was approximately 150 kN and was mainly concentrated in the lower part of the reinforced cut slope. After 72 h of rainfall, the maximum axial force increased to approximately 489 kN, remaining below the design anchoring force of 500 kN, and its location shifted upward to the intersection between the anchor cables and the strongly weathered shale interface. This spatial shift corresponds to the coalescence of the plastic zone along the strongly weathered shale interface, suggesting that the development of the deep potential sliding zone enhanced deformation and load transfer to the anchor cables intersecting this interface.

5.2.5. Evolution of the Factor of Safety During Rainfall

To further examine the evolution of overall slope stability during rainfall, the factor of safety was extracted at different rainfall durations (Figure 14). The factor of safety generally decreases with increasing rainfall duration, but the rate of decrease varies markedly among stages.

During the initial 0–48 h, rainfall mainly affects the shallow surface layer and the upper soil–rock interface. No extensive positive pore-pressure zone has formed within the slope, and no continuous plastic band has developed along the strongly weathered shale interface; consequently, the factor of safety decreases only slightly. As water migrates deeper through pores in the block-stone layer, fractures in the limestone, and soil–rock interfaces, it progressively accumulates above the underlying low-permeability shale. The resulting increase in pore-water pressure and reduction in matric suction decrease the effective stress near the strongly weathered shale interface, thereby reducing the available shear resistance and promoting the development of deep deformation. During the late stage of rainfall (60–72 h), a continuous transient saturated zone forms along the strongly weathered shale interface, the high-displacement zone rapidly expands, and the plastic zone progressively extends and ultimately becomes continuous along the deep strongly weathered shale interface. The factor of safety therefore decreases more rapidly. At 72 h, it reaches 0.9886, indicating overall slope instability.

The combined evolution of pore-water pressure, displacement, plastic zones, and the factor of safety shows that rainfall-induced instability of the slope is distinctly staged. During the initial stage, water infiltrates through rear-margin cracks, pores in the block-stone layer, and limestone fractures, and deformation along the upper block-stone layer–strongly weathered limestone interface gradually develops. During the middle stage, infiltrating water reaches the deep strongly weathered shale interface and first accumulates in gentle segments with poor drainage. During the late stage, the positive pore-pressure zone expands along the interface and forms a continuous transient saturated zone, continuously reducing effective stress and shear resistance. The high-displacement zone shifts deeper, the plastic zone becomes continuous, and overall instability is triggered.

6. Conclusions

Based on field investigation and displacement monitoring, together with coupled seepage–stress analysis of a 72 h prolonged-rainfall scenario, this study reveals the instability mechanism of the soil–rock binary-structure slope from three perspectives: deformation zoning under natural conditions, the rainfall seepage response, and coalescence of the plastic zone. The main conclusions are as follows:

(1)

Under natural conditions, monitored displacements of the reinforced cut slope at the toe change gradually, indicating that the reinforced toe zone remained stable during the monitoring period. The middle–rear portion is the principal deformation zone, and potential deformation is concentrated mainly along the upper block-stone layer–strongly weathered limestone interface. The strength reduction analysis gives a factor of safety of 1.1344, indicating that the overall slope is basically stable and that the deep strongly weathered shale interface has not yet developed into the controlling sliding boundary.

(2)

Under rainfall, water progressively accumulates near the strongly weathered shale interface owing to the hydraulic barrier effect of the underlying low-permeability shale, and pore pressure along the interface gradually changes from negative to positive. Owing to the interface geometry, the positive pore-pressure zone expands from the upper interface segment and the gentle toe segment toward the middle and eventually forms a continuous transient saturated zone. As pore pressure rises and effective stress decreases, the high-displacement zone shifts from shallow to deep layers, the plastic zone expands from local areas to full connection, and the factor of safety decreases to 0.9886, marking the transition from progressive deformation to overall instability.

(3)

Engineering geological investigation and numerical simulation show generally consistent spatial deformation characteristics, while displacement monitoring confirms the relatively stable response of the reinforced toe during the monitoring period. The rainfall-induced instability mechanism can be summarized as “water conveyance through rear-margin cracks–transmission along the upper interface–hydraulic barrier at the strongly weathered shale interface–pore-pressure accumulation–coalescence of the deep plastic zone–overall instability.” This mechanism indicates that the hydraulic barrier effect of low-permeability shale, pore-pressure accumulation along the deep interface, and coalescence of the plastic zone are the key factors controlling rainfall-induced instability of this type of soil–rock binary-structure slope. For slopes controlled by low-permeability shale or weakly permeable bedrock, engineering mitigation should therefore focus on drainage along the deep interface, sealing of rear-margin cracks, and pore-pressure monitoring during rainfall.

The present results are site-specific and are based on a representative two-dimensional section, an equivalent-continuum representation of fractured rock masses, and an idealized 72 h extreme prolonged-rainfall scenario. Accordingly, out-of-plane deformation, lateral seepage, and the three-dimensional connectivity of individual discontinuities are not explicitly represented. Future studies may incorporate three-dimensional geological structures and more diverse rainfall scenarios to further evaluate the applicability of the proposed instability mechanism.