Laboratory Model Tests and Numerical Investigation of Gravelly Silt Slope Instability Under Extreme Rainfall Conditions

Abstract

Rainfall-induced instability of gravelly silt slopes is strongly affected by infiltration, runoff erosion, pore water pressure evolution, and particle-scale degradation. In this study, laboratory rainfall model tests were conducted on gravelly silt slopes under three extreme rainfall intensities of 80, 120, and 160 mm/h, and an FVM-DEM coupled model was developed to investigate the associated hydromechanical response and failure mechanism. The tested soil was obtained from the Shanghai East Railway Station project, and the 30% gravel content was selected to represent the typical field condition. Pore water pressure gauges and laser displacement sensors were used to monitor the infiltration response and slope deformation. The results show that all three slopes developed shallow instability, but the deformation rate and failure mode changed with rainfall intensity. Under the tested infiltration-excess conditions, the additional rainfall mainly increased surface runoff, toe erosion, and failed mass mobility rather than proportionally increasing the infiltration depth. The numerical results further indicate that failure evolved through equivalent fine matrix mobilization, gravel destabilization, skeleton collapse, and matrix-entrained gravel movement. These findings clarify the progressive instability mechanism of gravelly silt model slopes under extreme rainfall and provide experimental evidence for slope protection under short-duration, high-intensity rainfall.

1. Introduction

Rainfall-induced slope instability is one of the most common and destructive geohazards in mountainous and urbanized regions, particularly where rapid land use change, steep terrain, and extreme rainfall events coexist. Lumb proposed that rainwater infiltration into surficial residual soils caused saturation and apparent cohesion loss in many Hong Kong slope failures [1]. Li et al. reported that cumulative rainfall exceeding 250 mm, with a peak hourly intensity of 61.2 mm/h, triggered 867 clustered shallow landslides in Wuping County, China [2]. Chen et al. found that rainfall was the primary trigger of the Zhoujia landslide deformation, with a lag of about one to two months [3]. Choy et al., Li and Duan, and Zhuang et al. showed that typhoon-related rainfall and extreme rainfall can trigger slope failures through damage accumulation, frequent cyclone strikes, preferential infiltration, strength reduction, and wind-related effects [4,5]. Bellprat et al. emphasized that extreme weather risk assessment should consider model reliability and probabilistic uncertainty [6].

From a hydromechanical perspective, rainfall-induced slope failure is governed by infiltration, wetting front migration, suction reduction, pore water pressure increase, and shear strength degradation. Iverson proposed a framework linking transient rainfall infiltration with landslide triggering time, depth, and acceleration [7]. Ling et al. used centrifuge tests and found that rainfall-induced instability can be interpreted as apparent cohesion loss caused by suction reduction [8]. Liu et al. conducted artificial rainfall tests and found that higher rainfall intensity caused earlier water content increase, suction decrease, pore pressure response, and shallow landslide initiation [9].

Rainfall intensity, duration, pattern, and antecedent conditions control failure timing and mode. Song and Tan investigated five rainfall patterns using physical model tests and CFD–DEM simulations, and identified thrust load failure, surface sliding failure, and retrogressive failure [10]. Qu et al. performed 23 model slope tests and found that failure mode transformed from retrogressive failure to surface slide and then to flow slide as rainfall intensity increased [11]. Prabowo et al. found that short-duration, high-intensity rainfall caused the greatest factor-of-safety reduction in unsaturated silty sand slopes by increasing pore water pressure and reducing matric suction [12]. Durukan proposed that antecedent rainfall can shorten the time required for failure under subsequent extreme rainfall, while Natalia and Yang found that antecedent rainfall combined with delayed or uniform main rainfall produced the most critical conditions [13,14].

Silty slopes require attention because silt-dominated soils are sensitive to water migration, suction variation, dry–wet cycling, erosion, and particle migration. Guo et al. proposed that rainfall infiltration and runoff can cause hydration, erosion, and imbricate layered sliding of silt subgrade slopes [15]. Li et al. found that silt strength and cohesion first increased and then decreased under dry–wet cycles, with obvious nonlinear strength behavior under low normal stress [16]. Xia et al. showed that fine-grained silt is sensitive to pore water migration and environmental boundary conditions [17]. Quan et al. found that slope gradient and soil type-controlled runoff, sediment concentration, erosion rate, and deposition in loess soils [18]. He et al. found that bulk density, gravel content, and silt content controlled severe erosion of spoil heaps [19]. Zhao et al. showed that sediment yield on gravel-containing sloping farmland was more sensitive to rainfall intensity than to gravel content or slope gradient [20]. Valencia-Gallego and Montoya found that soil loss on unpaved roads increased with rainfall intensity and slope, and that sandy silt had higher erosion rates than loam silt [21].

Physical model tests and field rainfall experiments provide evidence for progressive slope failure. Chen et al. found rapid pore water pressure and water content responses in a field artificial rainfall test on a loess slope, with fissures and macropores forming preferential paths [22]. Ganesh Kumar and Sarkar used a large-scale flume and showed that pore pressure, moisture content, strain increment, and displacement can reveal failure initiation and propagation [23]. Wang et al. analyzed the effects of rock content, fines migration, water content, soil pressure, and pore water pressure in accumulation landslide model tests [24]. Askarinejad and Springman developed deformation sensors and showed that high-frequency monitoring can identify shear band initiation and propagation [25]. Kang et al. found that long-term rainfall–soil interaction caused strength reduction, whereas typhoon rainfall mainly induced transient deformation [26]. Li et al. showed that continuous rainfall caused shallow saturation, plastic zone expansion, toe bulging, and crown tension cracking in a siltstone slope [27].

Numerical simulation helps explain internal mechanisms that are difficult to observe in physical tests. Wang et al. coupled rainfall hydrology and the material point method to simulate water migration, deformation, and failure [28]. Mburu et al. reviewed numerical approaches for unsaturated slopes and showed that seepage–stability coupling methods and slip surface search approaches affect safety factor and failure mode results [29]. Zeng et al. analyzed the effects of slope height, slope angle, cohesion, friction angle, and unit weight on safety factor by strength reduction and orthogonal design [30]. Compared with continuum methods, DEM and PFC better reveal particle displacement, contact force redistribution, and shear band development. Li et al. used face-to-face DEM to analyze jointed rock slope failure, while Chen and Liu incorporated interparticle adhesive force into DEM to account for suction effects [31,32]. Guo et al. used GeoStudio and PFC2D to simulate rainfall infiltration and erosion of silt subgrade slopes [15]. Cui et al. simulated rainfall-triggered shallow landslides by DEM and showed that rainfall intensity and duration affected particle displacement, velocity, and failure mass development [33]. Nie et al. combined field monitoring, model tests, three-dimensional reconstruction, and DEM simulation, and proposed displacement and soil pressure as warning variables [34].

Although these studies have advanced rainfall-induced slope failure research, the instability process of silty slopes under different rainfall intensities remains insufficiently explained by combining internal hydromechanical responses with external deformation characteristics. Laboratory rainfall tests can monitor pore water pressure and surface displacement, revealing the relationship among infiltration, deformation accumulation, and failure. However, they cannot directly identify particle displacement, contact force redistribution, or internal shear zone development. PFC simulations can reveal these mesoscopic mechanisms, but their coupling with instrumented rainfall tests remains limited for silty slopes.

The present study is motivated by the engineering background of the Shanghai East Railway Station project. The exposed slope involves gray sandy silt overlying lower-permeability muddy silty clay. Under rainfall, this stratigraphic condition may promote perched water, lateral seepage, pore pressure accumulation, and shallow instability. Shanghai is also affected by seasonal rainfall concentration and typhoon-related short-duration heavy rainfall. Therefore, it is necessary to investigate the hydromechanical response and instability mechanism of gravelly silt slopes under short-duration extreme rainfall.

Compared with previous studies on homogeneous soil slopes or continuum seepage stability analysis, this study focuses on gravelly silt slopes and highlights the coupled effect of infiltration-excess runoff, toe erosion, and particle-scale failure evolution. The objectives are: (1) to observe the deformation and failure process of gravelly silt model slopes under different extreme rainfall intensities; (2) to measure the pore water pressure response and surface displacement during rainfall; and (3) to use an FVM-DEM coupled model to interpret the relative sequence of equivalent fine matrix mobilization, gravel destabilization, skeleton collapse, and matrix-entrained gravel movement.

2. Materials and Methods

2.1. Experimental Apparatus and Materials

The laboratory atomized rainfall test system mainly consisted of a model box, a rainfall simulation system, and a monitoring system, as shown in Figure 1. The internal dimensions of the model box were 1.0 m × 0.5 m × 0.5 m (length × width × height). The box was composed of transparent tempered glass and a steel frame, allowing direct observation of slope surface deformation, seepage outflow, and local failure during the test. Water storage tanks were arranged at both ends of the model box. A specially designed acrylic plate, with a thickness of 5 mm, was installed between the model box and the water storage tanks. The plate was uniformly perforated with a 10 × 10 array of holes in both the vertical and horizontal directions. Each hole had a diameter of 5 mm and a spacing of 50 mm. A geotextile was placed at the bottom to simulate the drainage boundary of the slope and prevent the loss of fine particles.

The artificial rainfall system used atomizing nozzles to simulate rainfall. A total of 18 nozzles were arranged above the model box in three rows and six columns. The rainfall intensity was adjusted using a flowmeter. The monitoring system consisted of pore water pressure gauges and laser displacement sensors, which were used to synchronously obtain the pore water pressure, and slope displacement responses during rainfall. Pore water pressure gauges were full bridge sensors with a measuring range of 200 kPa. The laser displacement sensor had a total measuring range of 70 mm, an accuracy of 0.07 mm, and a resolution of 0.01 mm. During the test, pore water pressure data were synchronously collected using a DH3819 wireless static strain acquisition system, while displacement data were recorded in real time by the corresponding data acquisition system. The layout of the monitoring system is shown in Figure 2.

As shown in Figure 2, the pore water pressure gauges were embedded at different elevations along the slope profile. Taking the lower-left corner of the model box as the coordinate origin, P1, P2, P3, and P4 were located at approximately (0.60 m, 0.10 m), (0.50 m, 0.20 m), (0.40 m, 0.30 m), and (0.30 m, 0.35 m), respectively. The vertical cover depths of P1–P3 were approximately 0.10 m, while P4 was located approximately 0.05 m below the crest platform. The specific location is shown in

Table 1. Coordinates and cover depths of pore water pressure gauges.

Gauge	x-Coordinate (m)	z-Coordinate (m)	Vertical Cover Depth (m)	Monitoring Zone
P1	0.60	0.10	0.10	Lower slope/toe-adjacent region
P2	0.50	0.20	0.10	Middle-lower slope
P3	0.40	0.30	0.10	Middle-upper slope
P4	0.30	0.35	0.05	Shallow crest region

. Therefore, the monitoring system was designed to capture the pore pressure response from the shallow crest region to the lower slope/toe-adjacent region.

The soil used in the tests was obtained from the excavation area of the Shanghai East Railway Station project. The target soil layer was gray sandy silt. The permeability coefficient was determined by a falling head permeability test, and the measured value was 6.0 × 10⁻⁶ m/s. To reflect the gravel-bearing characteristics of the field soil, gravel particles with a narrow size range of 6–9 mm were mixed with the sandy silt. A gravel content of 30% by dry mass was selected as the representative condition for the rainfall intensity comparison. According to the laboratory test results, the gradation curve of the sample with 30% gravel content is shown in Figure 3. The initial water content was uniformly controlled at approximately 30%. The basic physical and mechanical indices of the gravelly silt are listed in

Table 2. Basic physical and mechanical indices of the tested gravelly silt.

Specific Gravity, $\mathbf{G}\mathbf{s}$	Unit Weight,$\mathit{\gamma }$ $\left(\mathbf{k}\mathbf{N}/{\mathbf{m}}^3\right)$	Cohesion, $\mathit{c}$ $\left(\mathbf{k}\mathbf{P}\mathbf{a}\right)$	Internal Friction Angle, $\mathit{\phi }$ $\left(°\right)$	Permeability Coefficient, $\mathit{k}$ $\left(\mathbf{m}/\mathbf{s}\right)$	Uniformity Coefficient, Cu	Curvature Coefficient, Cc
2.70	19.2	3.8	31.4	6.0 × 10−6	13.3	0.58

.

2.2. Model Slope Preparation

The model slope was prepared by a layered filling and compaction method. Before filling, the gray sandy silt obtained from the Shanghai East Railway Station project was air-dried, crushed, sieved, and mixed with 6–9 mm gravel according to the designed gravel content. Water was then added to reach an initial water content of approximately 30%, and the mixture was sealed before placement to improve moisture uniformity. During model preparation, the soil mass required for each layer was calculated according to the target unit weight of 19.2 kN/m³ and the corresponding layer volume. Each layer was compacted to the designed thickness before the next layer was placed. The slope’s surface was finally trimmed using a 45° template.

During layered filling, the pore water pressure gauges were embedded at the designed positions. The pore water pressure gauges were saturated before installation to reduce the influence of trapped air. After the slope surface was trimmed, the laser displacement sensor was installed above the slope surface and protected using an acrylic cover to reduce water mist and reflection interference. The pore water pressure gauges and the laser displacement sensor are shown in Figure 4.

The physical model slope height was 0.4 m. Relative to the 11 m prototype slope height in the engineering background; the geometric similarity ratio was 27.5. The slope angle for the rainfall intensity comparison was fixed at 45°. This angle was selected because preliminary stability analysis showed that the 45° slope was initially stable but close to the critical state, allowing the rainfall-triggered failure process to be observed within the laboratory test duration.

2.3. Calibration of Rainfall Intensity and Test Conditions

Before the formal tests, the artificial rainfall system was calibrated using an array of rain gauges to determine the rainfall intensity and uniformity. Twelve rain gauges were uniformly arranged within the effective rainfall area of the model box. Calibration tests were conducted for the designed rainfall intensities of 80, 120, and 160 mm/h. The results showed that the measured average rainfall intensities were 79.58, 119.50, and 159.42 mm/h, respectively. The corresponding Christiansen uniformity coefficients (CUC) were 85.08%, 85.15%, and 85.07%, respectively, which satisfied the requirements for laboratory rainfall model tests.

The selected rainfall intensities should not be interpreted as ordinary low-, medium-, and high-rainfall conditions. The saturated permeability coefficient of the tested sandy silt was 6.0 × 10⁻⁶ m/s, equivalent to approximately 21.6 mm/h. Therefore, all three imposed rainfall intensities exceeded the infiltration capacity of the soil. The purpose of selecting 80, 120, and 160 mm/h was to investigate the hydromechanical response of the model slope under extreme infiltration-excess rainfall. Under this condition, the infiltration rate is mainly limited by soil permeability, and the excess rainfall is converted into surface runoff. Therefore, the comparison among the three cases focuses on the effects of increasing rainfall excess runoff, toe erosion, and failed mass mobility, rather than on the full transition from infiltration-controlled to runoff-controlled rainfall. The test conditions are shown in

Table 3. Test conditions for the laboratory rainfall model tests.

Case	Gravel Content (%)	Rainfall Intensity (mm/h)	Slope Angle (°)	Initial Water Content (%)	Test Purpose
E1	30	80	45	~30	Extreme rainfall with relatively lower rainfall excess runoff
E2	30	120	45	~30	Reference infiltration-excess rainfall case
E3	30	160	45	~30	Extreme rainfall with stronger runoff and toe erosion

.

2.4. Experimental and Numerical Methods

The study was carried out using a combined laboratory test and numerical simulation method. In the laboratory tests, the prepared model slope was subjected to three calibrated rainfall intensities after the monitoring system had been installed. During rainfall, the deformation process was recorded by cameras, while the surface displacement and pore water pressure responses were continuously measured using the laser displacement sensor and embedded pore water pressure gauges. The pore water pressure increment was obtained by subtracting the initial reading from the real-time measurement. The image records, displacement curve, and pore water pressure increments were jointly used to identify the deformation stage, failure initiation, failure mode, and hydromechanical response of the slope.

In the numerical part, an FVM-DEM coupled method was used as a complementary interpretive method to analyze the internal failure mechanism that could not be directly observed in the laboratory tests. The finite volume seepage solver was used to calculate the pressure head and hydraulic gradient fields, while the DEM model in PFC was used to simulate particle rearrangement, contact force redistribution, and mass transport. The numerical model was evaluated by comparing the simulated pore water pressure increments with the experimental measurements. The detailed implementation and validation of the FVM-DEM model are described in Section 4.

3. Model Test Results and Instability Evolution Analysis

The results presented in this section were obtained from the laboratory rainfall model tests described in Section 2. The instability process was recorded using cameras, while the pore water pressure and surface displacement responses were measured using embedded pore water pressure gauges and a laser displacement sensor, respectively.

3.1. Slope Deformation and Failure Process

The deformation and failure processes of the slopes under different rainfall intensities are shown in Figure 5. Under the three rainfall conditions, all slopes exhibited shallow instability induced by rainfall infiltration. The failure process generally included surface wetting, local sliding, development of shallow sliding collapse, and formation of deposits at the slope toe. However, the initiation time, development rate, and mobility of the collapsed mass varied significantly under different rainfall intensities.

Figure 5 shows that under 80 mm/h rainfall, deformation developed slowly, and the failure process was dominated by progressive shallow sliding. Under 120 mm/h rainfall, local sliding expanded more rapidly into shallow progressive instability. Under 160 mm/h rainfall, toe erosion occurred earlier, and the failed mass showed stronger mobility and flow-like transport. Therefore, the key difference among the three tested cases is not only the deformation rate, but also the enhanced runoff-driven toe erosion and failed mass transport under stronger infiltration-excess rainfall.

3.2. Multi-Source Monitoring Response Characteristics

The variations in displacement measured by laser sensor and pore water pressure increment under different rainfall intensities are shown in Figure 6 and Figure 7, respectively.

For displacement measured by laser sensor, the slope remained basically stable in the early stage under the rainfall intensity of 80 mm/h, while two obvious stepwise increases occurred in the later stage. Under the rainfall intensity of 120 mm/h, the displacement showed a fluctuating pattern characterized by “increase–decrease–increase–stabilization”. Under the rainfall intensity of 160 mm/h, the displacement measured by laser sensor accelerated significantly in the middle and later stages, followed by another abrupt increase near the end of the test. This indicates that higher rainfall intensity led to earlier deformation initiation, faster deformation development, and more obvious acceleration in the later stage. Overall, greater rainfall intensity resulted in faster seepage response, stress adjustment, and displacement development inside the slope.

In this study, pore water response refers to the pore water pressure increment measured by the embedded pore water pressure gauges during rainfall infiltration. The model slope was initially prepared at a water content of approximately 30%. During rainfall, the recorded pore water pressure increment reflects wetting, local saturation, and water pressure accumulation in different parts of the slope.

The pore water pressure increments generally showed that P4 responded first, P1 exhibited the largest increase, and P2 and P3 gradually increased thereafter. This indicates that rainfall first affected the shallow layer near the slope crest, then infiltrated downward along the slope body and formed an obvious accumulation near the slope toe. As rainfall intensity increased, the initial response time of pore water pressure at each monitoring point was clearly advanced, while both the growth rate and the affected area increased. Under the tested infiltration-excess conditions, this should be interpreted together with surface runoff and toe erosion, because the excess rainfall did not all enter the slope body, but partly became slope surface runoff.

4. Numerical Modeling of Rainfall-Induced Failure Mechanisms in Gravelly Silt Slopes

4.1. Development and Validation of the Numerical Model

This section investigates the rainfall-induced failure mechanism of gravelly silt slopes from a micromechanical perspective. A finite-volume-method and discrete-element-method (FVM-DEM) coupled model was developed by integrating a Python-based seepage solver with PFC2D 9.00.179 (Itasca Consulting Group, Minneapolis, MN, USA). The finite-volume seepage solver and data exchange procedure were implemented in a Python 3.10 environment. This numerical modeling is conducted in parallel with physical model tests. Finally, the model is evaluated using the pore water pressure data measured during these experiments.

4.1.1. Development of the Coupled Macro–Micro Fluid–Solid Model

The numerical geometry was constructed according to the model box profile, as shown in Figure 8. The computational domain was bounded by the bottom horizontal boundary, right drainage boundary, lower horizontal step, 45° slope surface, upper horizontal platform, and left boundary. In the Gmsh mesh, the main geometric points were set as (0, 0), (1.0, 0), (1.0, 0.1), (0.625, 0.1), (0.325, 0.4), and (0, 0.4) m. A finer mesh size of 0.02 m was used near the slope surface and shallow region, while a coarser size of 0.05 m was used in the deeper and less variable regions. As shown in Figure 8, the mesh was locally refined near the slope surface to resolve the rapid hydraulic gradient variation during rainfall infiltration and surface runoff while maintaining acceptable computational efficiency.

For the DEM model, equivalent coarse-grained particles were adopted to reduce computational cost. Therefore, the numerical particles should not be interpreted as real silt and gravel grains with identical sizes to those in the physical test. Instead, they represent equivalent particle groups used to reproduce the overall deformation pattern, the relative mobility of the fine matrix and gravel fractions, and the progressive failure process. The layout of the numerical data extraction points is shown in Figure 9. These points were arranged to evaluate the pore water pressure response at representative monitoring zones with burial depth equivalent to the physical sensors. The equivalent soil particles had radii of 0.78–1.38 mm, and the equivalent gravel blocks had characteristic radii of 7–13 mm. The gravel content was controlled 30% by dry mass, consistent with the representative physical test condition. Because of this coarse-graining treatment, the particle migration results are interpreted qualitatively and comparatively rather than as exact pore throat scale migration of real silt particles. The detailed parameters are listed in

Table 4. Parameters in numerical simulation.

	Soil Parameters	Gravel Parameters
Density, $\rho \left(\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3}\right)$	2.7 $\times$ 103	2.8 $\times$ 103
Radius, $R\left(\mathrm{m}\mathrm{m}\right)$	0.78~1.38	7~13
Friction coefficient, $\mu$	0.64	0.8
Normal stiffness, $k_n \left(\mathrm{N}\cdot {\mathrm{m}}^{-1}\right)$	1.0 $\times$ 108	2.8 $\times$ 108
Shear stiffness, $k_n \left(\mathrm{N}\cdot {\mathrm{m}}^{-1}\right)$	1.214 $\times$ 108	3.0 $\times$ 108
Normal damping ratio, ${\beta }_n$	0.7	0.7
Shear damping ratio, ${\beta }_S$	0.7	0.7
Rolling resistance coefficient, ${\mu }_{\Gamma }$	0.1	0.4
Rolling resistance moment $M^{\Gamma } \left(\mathrm{N}\cdot {\mathrm{m}}^{-1}\right)$	0.1	0.4

.

The coupled calculation was performed using a staggered FVM–DEM scheme rather than solving the seepage field at every DEM critical time step. At each hydraulic update interval, the current particle positions and block positions in PFC were assigned to the finite volume cells through a geometry-based cell grouping scheme. The solid area in each cell was then calculated from the ball areas and rigid block areas, and the local porosity was updated as the ratio of void area to cell area. The updated porosity was limited to a physically reasonable range of 0.1–0.7 to avoid numerical instability. The cell-scale saturated hydraulic conductivity was then updated using a Kozeny–Carman-type relationship with a permeability reduction factor to represent the low permeability of sandy silt. The upper slope boundary was reconstructed by dividing the horizontal domain into 100 vertical bins and searching for the uppermost contacted particles or rigid blocks in each bin. This reconstructed surface envelope was used to determine the rainfall boundary and the surface particles subjected to runoff and raindrop impact forces. The seepage field was solved using the mixed-form Richards equation for variably saturated flow. The pressure head ψ was defined as the primary unknown. The initial pressure head was set to −0.3 m. The hydraulic parameters used in the van Genuchten water retention relationship were ${\theta }_s=0.40$, ${\theta }_r=0.05$, $\alpha =5.0{\mathrm{m}}^{-1}$, $n=1.7$, $m=1-1/n$, and $S_s=1.0\times {10}^{-5}$. Within each coupling interval, the hydraulic time step was divided into 20 substeps. At each substep, up to 10 Picard iterations were performed, and the iteration was terminated when the residual was less than $1.0\times {10}^{-5}$. The face hydraulic conductivity was obtained from the harmonic average of cell conductivity to improve numerical stability. The seepage field was not updated at every DEM critical time step. In the simulation, the DEM calculation was advanced with its own explicit time step, while the hydraulic field was updated every 50,000 DEM steps. The coupling interval was calculated as:

$$\Delta t_c=N_c\Delta t_{DEM}{\lambda }_t$$

(1)

where $N_c=\mathrm{50,000}$ is the number of DEM cycles per hydraulic update, $\Delta t_{DEM}$ is the PFC critical time step, and ${\lambda }_t=90$ is the time-scale factor used in the model. Within each coupling interval, the fluid forces were kept constant and then updated after the new porosity, pressure head, hydraulic gradient, and surface morphology were recalculated [35]. The hydraulic boundary conditions were defined according to the rainfall and drainage conditions of the model slope. A prescribed pressure head of 0.006 m was applied to the top platform, slope surface, and lower step to represent rainfall supply and shallow surface water. The left boundary was treated as a no-flow boundary. The bottom and right boundaries were treated as drainage boundaries with zero-gradient conditions, corresponding to the free drainage treatment in the physical model.

Concurrently, the Hortonian infiltration-excess mechanism [36] and the kinematic wave equation are applied at the surface boundary [37]. The net rainfall intensity is determined by the difference between the specified rainfall rate and the local infiltration capacity. By spatially integrating the net rainfall intensity along the slope, the unit width discharge is obtained. Subsequently, the Manning equation is inversely solved to compute the actual water film thickness and the runoff velocity. In this study, the Manning roughness coefficient was set to n = 0.03 according to the surface condition of the laboratory model slope. The core governing equation for calculating the water film thickness is expressed as follows:

$$h={\left({\displaystyle \frac{q\cdot n}{\sqrt{S_0}}}\right)}^{0.6}$$

(2)

$$v={\displaystyle \frac{q}{h}}$$

(3)

where $h$ is the water film thickness, $q$ is the unit width discharge, $n$ is the Manning roughness coefficient of the slope, $S_0$ represents the local hydraulic gradient, and $v$ is the runoff velocity. Finally, the suction effect was introduced into the DEM model through a continuum-to-discrete equivalent strength mapping. In the revised model, matric suction was not directly converted into a capillary force acting at individual particle contacts. Instead, the suction contribution was first evaluated at the continuum grid cell scale using the Bishop-type effective stress concept for unsaturated soils. The shear strength of unsaturated soil can be expressed as:

$${\tau }_f=c^{\prime }+\left({\sigma }_n-u_a\right)\tan {\phi }^{\prime }+\chi \left(u_a-u_w\right)\tan {\phi }^{\prime }$$

(4)

where ${\tau }_f$ is the shear strength, $c^{\prime }$ is the effective cohesion, ${\sigma }_n$ is the total normal stress, $u_a$ is the pore air pressure, $u_w$ is the pore water pressure, ${\phi }^{\prime }$ is the effective internal friction angle, and $\chi$ is the effective stress parameter. In this study, the effective stress parameter was approximated by the effective saturation, namely $\chi =S_e$. Therefore, the suction-induced shear strength increment in each finite volume cell was calculated as:

$$\Delta c_i={\chi }_i{\psi }_i\tan {\phi }^{\prime }$$

(5)

where $\Delta c_i$ is the suction-induced equivalent cohesion increment in cell $i$, ${\chi }_i$ is the effective stress parameter, ${\psi }_i=u_a-u_w$ is the matric suction, and ${\phi }^{\prime }$ is the effective internal friction angle. The calculated $\Delta c_i$ is a continuum-scale strength increment rather than a contact-scale capillary force. To introduce this strength contribution into the DEM model, $\Delta c_i$ was distributed to the contacts located within the corresponding finite volume cell as an equivalent bonding parameter:

$$F_{b,k}^{eq}={\eta }_b{\displaystyle \frac{\Delta c_i{A}_i}{N_{c,i}}}$$

(6)

where $F_{b,k}^{eq}$ is the equivalent bonding force assigned to contact k, ${\eta }_b$ is the calibration coefficient, $A_i$ is the area of the finite volume cell i in the two-dimensional model, and $N_{c,i}$ is the number of active contacts in cell i. In this study, ${\eta }_b$ was used only as a numerical calibration coefficient to transfer the continuum-scale suction-induced strength contribution to the DEM contact model.

This formulation differs from the previous direct expression of apparent cohesive force at a single contact. The term $F_{b,k}^{eq}$ should not be interpreted as a physically resolved liquid bridge capillary force. It does not explicitly describe meniscus curvature, liquid bridge geometry, pore size distribution, or contact-scale water retention. Instead, it provides a homogenized equivalent bonding parameter that allows the DEM model to reflect the reduction of suction-induced shear strength during wetting. Therefore, the micromechanical results are interpreted in terms of relative contact degradation, force chain redistribution, and progressive failure evolution rather than exact capillary forces between real soil particles. Concurrently, seepage forces are applied to the particles based on the local hydraulic gradient. Furthermore, the surface scouring force derived from the macroscopic flow field is directly exerted on the active particles at the slope surface. Specifically, the runoff drag force, $F_d$, is dynamically calculated using classical fluid dynamics principles:

$$F_d={\displaystyle \frac{1}{2}}{C}_d{\rho }_{w\mathrm{A}}{v}^2$$

(7)

where $C_d$ is the drag coefficient, ${\rho }_w$ is the density of water, $A$ represents the projected cross-sectional area of the particle, and $v$ is the runoff velocity. At this stage, the model establishes a complete closed-loop coupling cycle. Specifically, particle displacements dynamically update the local pore spaces and geometric boundaries. These physical changes subsequently trigger the iterative resolution of the flow field. Finally, the updated fluid forces are fed back into the micromechanical response of the particles. During this dynamic process, the main equivalent hydromechanical actions considered in the coupled model include seepage force, buoyancy force, suction-dependent equivalent bonding, raindrop impact force, and runoff drag force, as illustrated in Figure 10.

4.1.2. Cross Validation Between Physical Experiments and the Numerical Model

To evaluate the capability of the proposed FVM-DEM coupled model in reproducing the rainfall-induced pore water pressure response, four virtual monitoring points were arranged in the numerical model. The virtual points were not placed along a prescribed potential slip surface. Instead, they were arranged according to the burial depth relationship of the pore water pressure gauges in the physical model test. In the laboratory test, P1–P3 were embedded below the inclined slope surface with an approximately identical vertical cover depth, while P4 was embedded beneath the horizontal crest platform with a smaller cover depth. Following the same principle, the numerical monitoring points were placed at corresponding relative depths below the local ground surface, so that they could represent the lower slope, middle-lower slope, middle-upper slope, and shallow crest region, respectively.

Specifically, the coordinates of the virtual monitoring points were P1 (0.525 m, 0.100 m), P2 (0.450 m, 0.175 m), P3 (0.375 m, 0.250 m), and P4 (0.225 m, 0.350 m). For P1–P3, the vertical distance from the local inclined slope surface was approximately 0.10 m, which is consistent with the cover depth arrangement of the corresponding pore water pressure gauges in the physical model. For P4, the vertical distance from the crest platform was approximately 0.05 m, also consistent with the shallow crest monitoring point in the physical test. Therefore, the numerical probes were designed to maintain cover depth equivalence and relative monitoring zone consistency with the experimental sensors, rather than to imply an exact point-to-point geometric coincidence. The layout of the virtual monitoring points is shown in Figure 9.

Figure 11 compares the pore water pressure increment curves obtained from the physical experiments and the numerical simulations across three rainfall scenarios. The simulated and measured pore water pressure increments show similar response sequences and comparable peak ranges. This comparison indicates that the model can reproduce the main pore pressure evolution trend under the tested rainfall conditions. However, the validation should be interpreted as model evaluation rather than complete verification of all micromechanical processes, because the DEM model uses equivalent coarse-grained particles and simplified suction-dependent bonding. Quantitative error indices, including RMSE, MAE, relative peak error $Ep$, and $R^2$, were introduced to evaluate the agreement between simulated and measured pore water pressure increments. Furthermore, the hydraulic response at each monitoring point demonstrates highly pronounced spatiotemporal variations. These dynamic variations are primarily driven by the combined effects of boundary conditions and sensor burial depths.

Measurement point P4 is located in the shallow surface layer near the slope crest. It demonstrates the fastest initial response but the lowest subsequent growth rate, accompanied by a distinct hydro-mechanical oscillation. Because of its minimal overburden, P4 is highly sensitive to early rainfall infiltration. Consequently, it is the first to exhibit a step-like response in both the experiment and the simulation. Notably, the downward progression of the wetting front through this shallow, low confinement zone reduced the effective stress, triggering local shear yielding and volumetric dilation. Because the external rainfall recharge lagged behind this transient pore expansion, the local effective saturation dropped sharply. This induced an instantaneous rebound in matric suction and a corresponding negative drop in pore pressure. This specific mechanism is accurately captured around 650 s in both datasets. In the later stages of rainfall, gravity rapidly drains water downwards through this region. Thus, P4 records the slowest late-stage pore pressure growth and the lowest steady state increment across the entire field.

Points P2 and P3, located in the upper-middle and middle-lower parts of the slope, represent transitional monitoring zones for water migration. Their response times and final pore water pressure increments generally fall between those of P4 and P1, with P3 responding slightly earlier than P2. This sequence indicates that the simulated seepage field captures the main downward propagation trend of rainfall infiltration from the shallow crest region toward the lower slope. However, the comparison is interpreted as an evaluation of the dominant pore pressure response rather than a complete verification of the detailed internal seepage path.

P1, located in the lower slope/toe-adjacent region, shows a delayed initial response but a relatively large later-stage increase in pore water pressure. This behavior is consistent with the accumulation of infiltrated water and lateral seepage toward the lower part of the slope. During the middle-to-late stages of the simulation, the pore water pressure increment at P1 reaches approximately 1.55 kPa, which is close to the 1.5–1.6 kPa peak range observed in the physical tests. This comparison suggests that the model can reasonably reproduce the main pore pressure accumulation trend near the slope toe, although local deviations may still exist because of the equivalent coarse-grained DEM representation and simplified hydromechanical coupling.

In summary, the proposed FVM-DEM model reproduces the main temporal sequence and magnitude range of pore water pressure response observed in the laboratory tests. At the macroscopic scale, it captures the later-stage pore pressure accumulation near the lower slope. At the particle scale, it provides a qualitative interpretation of local skeleton adjustment and contact force redistribution during wetting. Therefore, the model is used here as an evaluation tool for the dominant hydromechanical response and progressive failure process, rather than as a complete reproduction of all pore-scale seepage and contact-scale capillary mechanisms.

4.1.3. Quantitative Evaluation of Pore Water Pressure Simulation

To quantify the agreement between the numerical and experimental pore water pressure increments, four indices were used: root mean square error (RMSE), mean absolute error (MAE), relative peak error ($E_p$), and coefficient of determination ($R^2$). These indices were calculated as follows:

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left(p_i^{sim}-p_i^{exp}\right)}^2}$$

(8)

$$MAE={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|p_i^{sim}-p_i^{exp}\right|$$

(9)

$$E_p={\displaystyle \frac{\left|p_{max}^{sim}-p_{max}^{exp}\right|}{p_{max}^{exp}}}\times 100\%$$

(10)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^N{\left(p_i^{exp}-p_i^{sim}\right)}^2}{{\sum }_{i=1}^N{\left(p_i^{exp}-\overline{p^{exp}}\right)}^2}}$$

(11)

where $N$ is the number of sampling points, $p_i^{sim}$ is the simulated pore water pressure increment at the sampling point $i$, $p_i^{exp}$ is the experimental pore water pressure increment at the sampling point $i$, $p_{max}^{sim}$ is the simulated peak pore water pressure increment, $p_{max}^{exp}$ is the experimental peak pore water pressure increment, and $p_{mean}^{exp}$ is the mean value of the experimental pore water pressure increment. The quantitative comparison results are summarized in

Table 5. Quantitative comparison between experimental and simulated pore water pressure increments.

Rainfall Intensity	Monitoring Point	RMSE (kPa)	MAE (kPa)	Relative Peak Error $\mathit{E}\mathit{p}$ (%)	${\mathit{R}}^2$	Evaluation
80 mm/h	P1	0.34	0.28	10.8	0.70	Acceptable
80 mm/h	P2	0.27	0.22	23.5	0.64	Acceptable
80 mm/h	P3	0.23	0.18	31.4	0.61	Acceptable
80 mm/h	P4	0.24	0.19	38.6	0.58	Acceptable
120 mm/h	P1	0.39	0.31	5.2	0.72	Good
120 mm/h	P2	0.29	0.23	13.8	0.68	Acceptable
120 mm/h	P3	0.31	0.24	35.7	0.57	Acceptable
120 mm/h	P4	0.26	0.20	28.9	0.60	Acceptable
160 mm/h	P1	0.42	0.34	15.6	0.69	Acceptable
160 mm/h	P2	0.37	0.30	11.2	0.66	Acceptable
160 mm/h	P3	0.40	0.32	9.8	0.63	Acceptable
160 mm/h	P4	0.28	0.22	25.4	0.62	Acceptable
Average	All points	0.32	0.25	20.8	0.64	Acceptable

.

As shown in Table 5, the average RMSE and MAE between the experimental and simulated pore water pressure increments are 0.32 kPa and 0.25 kPa, respectively. The average coefficient of determination is 0.64, indicating that the numerical model can capture the main increasing trend and relative response sequence of pore water pressure under different rainfall intensities. The relative peak error $Ep$ is relatively small at P1 and P2, while larger deviations occur at P3 and P4. This is mainly because the upper and middle monitoring points are more sensitive to local infiltration paths, particle rearrangement, and the equivalent coarse-grained representation in the DEM model. Overall, the comparison indicates that the model is capable of reproducing the dominant pore pressure response, although local deviations remain due to the simplified hydromechanical coupling and particle upscaling.

The rainfall input, effective infiltration, and rainfall-excess runoff were recorded at each hydraulic update step. Because the DEM model uses equivalent particles and a reconstructed free surface, strict pore-scale water-volume conservation was not imposed. Instead, the runoff calculation was used to estimate the relative increase in surface flow intensity among rainfall cases. Therefore, the runoff-related results are interpreted as model-scale indicators of hydraulic erosion intensity.

4.2. Spatiotemporal Evolution of the Rainfall-Driven Multiphase Flow Field

Rainfall infiltration and surface runoff are the primary hydrological triggers that disrupt the initial mechanical equilibrium of a slope. Under free-draining boundary conditions, the infiltration process is primarily characterized by the downward propagation of a wetting front. In this section, the evolution of the y-directional hydraulic gradient is employed to characterize the propagation of the wetting front. As illustrated in Figure 12, different colors represent the magnitude of the hydraulic gradient. The simulated hydraulic gradient and saturation fields show that, under the tested extreme rainfall conditions and the same rainfall duration, the wetting front depths were close among the three rainfall cases. This does not mean that rainfall intensity has no general influence on wetting front propagation. Rather, within the present test range, all imposed rainfall intensities exceeded the saturated permeability of the gravelly silt, so the infiltration flux was mainly limited by the soil hydraulic capacity. The additional rainfall was mainly converted into surface runoff and therefore enhanced toe erosion and failed mass mobility.

This response can be interpreted within the framework of the Hortonian infiltration-excess mechanism. Because all three imposed rainfall intensities exceeded the saturated permeability of the gravelly silt, the actual infiltration rate was constrained by the soil hydraulic capacity, and the rainfall exceeding the infiltration capacity was converted into surface runoff. Therefore, under the tested extreme rainfall conditions and the same rainfall duration, the additional rainfall mainly increased the intensity of surface runoff rather than proportionally increasing the simulated wetting front depth. This interpretation is limited to the present model scale, boundary conditions, and rainfall duration. The wetting front pattern shown in Figure 12 should therefore be regarded as a numerical indicator of the relative seepage field evolution, while the runoff-related results are used to explain the enhanced toe erosion under higher rainfall intensity.

4.3. Macroscopic Instability and Morphological Evolution Driven by Fluid–Solid Coupling

Driven by the spatiotemporal evolution of the multiphase flow field, the internal stress field of the slope undergoes significant redistribution. This dynamic process, in turn, triggers the progressive evolution of the slope’s macroscopic morphology. According to the multi-physics monitoring data, the processes of runoff erosion and subsequent instability failure exhibit highly non-linear and stage-dependent characteristics.

4.3.1. Degradation Mechanisms of Matric Suction and Shear Strength

As rainfall infiltration progresses, the wetting front advances into the deeper soil layers, leading to an increase in effective saturation and a reduction in matric suction. In the present DEM model, this process is represented by the degradation of the suction-dependent equivalent bonding term introduced in Section 4.1.1, rather than by explicitly resolving real liquid bridge capillary forces at particle contacts. Therefore, the quantity shown in Figure 13 should be interpreted as an equivalent bonding force controlled by pressure head and effective saturation. As wetting continues, the reduction in this equivalent bonding weakens the contact resistance and load-bearing capacity of the shallow soil skeleton, thereby creating favorable internal mechanical conditions for local yielding and progressive failure.

4.3.2. Dynamic Redistribution of the Micromechanical Stress Field and Progressive Failure

Under the combined effects of rainfall infiltration, surface runoff, seepage force, and suction-dependent strength degradation, the internal stress field of the gravelly silt slope did not evolve through a uniform relaxation process. Instead, it showed a distinct spatial redistribution pattern among the lower slope, middle slope, and upper slope regions. Figure 14 presents the vertical earth pressure responses at three representative monitoring points under rainfall intensities of 80, 120, and 160 mm/h. In the figure, S1 represents the lower slope, S2 represents the middle slope region, and S3 represents the upper slope. It should be noted that the positive and negative values in Figure 14 are interpreted as the signed variation of the local vertical earth pressure response under the adopted numerical sign convention. They should not be directly regarded as continuum tensile and compressive stresses in the conventional geotechnical sense. In particular, the crossing of the zero line does not indicate that the gravelly silt sustained vertical tensile stress. Instead, it reflects local unloading, contact loss, or a change in the resultant vertical component of the contact force network during particle rearrangement. Therefore, the following analysis focuses on the relative changes in vertical earth pressure, unloading response, and force chain redistribution rather than on the development of tensile stress within the soil mass.

As shown in Figure 14a–c, the vertical earth pressure responses under different rainfall intensities exhibit distinct stage-dependent characteristics. Under 80 mm/h rainfall (Figure 14a), the curves of S1 and S2 fluctuate within a relatively small range, while S3 increases gradually during the early and middle stages. This indicates that the lower and middle slope mainly experienced slow unloading and internal adjustment, and the contact force network remained partly connected. Therefore, the slope deformation under 80 mm/h developed in a gradual and progressive manner. Under 120 mm/h rainfall (Figure 14b), the fluctuations of S1 and S2 become more pronounced, especially in the middle stage. The repeated decrease and recovery of S1 indicate alternating toe unloading and temporary resistance recovery, while the stronger fluctuation of S2 suggests that the middle slope became the main transition zone for stress redistribution. Meanwhile, the rapid rise and subsequent fluctuation of S3 indicate that the upper slope responded intermittently to the deformation of the lower sliding mass. Under 160 mm/h rainfall (Figure 14c), S1 and S2 decrease rapidly at the early stage, showing that intense runoff erosion and seepage softening caused rapid unloading in the lower and middle slope regions. Afterward, S2 remains at a relatively low level, while S3 continues to fluctuate at a higher level, indicating sustained weakening of the middle slope and continued adjustment of the upper slope. The gradual recovery of S1 in the later stage can be attributed to the accumulation of transported particles near the slope toe, which temporarily increases the local resistance.

Overall, the comparison among Figure 14a–c shows that increasing rainfall intensity changes the stress redistribution mode from slow and continuous adjustment to stronger fluctuation and progressive cascading failure. Under lower rainfall intensity, the internal force chain network is weakened gradually, and the slope maintains a certain degree of structural continuity. With increasing rainfall intensity, runoff erosion and seepage softening intensify at the lower slope, causing local unloading and contact force degradation. The middle slope then becomes the key zone of stress redistribution, and the deformation gradually propagates upward to the crest region. Therefore, the failure of the gravelly silt slope is not a simultaneous collapse of the whole slope, but a progressive process involving toe weakening, middle slope stress adjustment, temporary toe accumulation, and upward propagation of deformation.

4.3.3. Macroscopic Particle Displacement and Morphological Evolution

Analysis of the cumulative particle displacement field (Figure 15) reveals that the slope failure transitioned from localized spalling to a global sliding event. During the initial rainfall phase, a slow erosion process dominated. The equivalent surface particles in the DEM model were subjected to raindrop impact and runoff drag forces. Under this model-scale hydraulic action, the shallow surface layer was progressively mobilized and transported downslope. Because DEM particles are equivalent coarse-grained particles, this result should be interpreted as a relative particle mobility pattern rather than a direct simulation of real silt particle erosion at the pore scale. As rainfall persisted, intense hydraulic scouring rapidly eroded the leading edge of the slope toe. This critical loss of toe support swiftly disrupted the overall mechanical equilibrium. Subsequently, shear strain localized and propagated upslope through the shallow softened zone, eventually forming an irregular, continuous macroscopic sliding surface. Finally, during the post-collapse residual stability period, the displaced soil mass accumulated at the slope toe, gradually reshaping the surface into a depositional fan morphology.

4.3.4. Temporal Evolution of the Mass Transport Ratio (MTR)

The Mass Transport Ratio (MTR) is used to quantify the relative mass transported to the slope toe during rainfall-induced failure. In the present numerical model, the toe deposition region was defined as the lower horizontal area reached by the transported particles after they moved downslope to the slope toe. The MTR was calculated as

$$MTR\left(t\right)={\displaystyle \frac{M_{toe}\left(t\right)-M_{toe}\left(0\right)}{M_0}}\times 100\%$$

(12)

where MTR(t) is the toe deposition mass transport ratio, $M_0$ is the initial total mass of the model slope, $M_{toe}\left(0\right)$ is the initial mass in the toe deposition region, and $M_{toe}\left(t\right)$ is the mass accumulated in the toe deposition region at time t. Negative values were set to zero. Therefore, MTR represents the relative mass transported to the slope toe rather than the total mass physically lost from the model box.

The time series curve of MTR captures the multi-stage nature of slope failure. During the initial rainfall phase, shallow surface scouring dominates, resulting in a gradual increase in MTR. Once the slope toe is progressively weakened by runoff erosion and seepage softening, the mass transport process enters an accelerated transition stage, leading to a rapid increase in MTR. This acceleration is particularly evident under the 160 mm/h rainfall condition, where stronger rainfall excess runoff advances the onset of toe degradation and increases the mobility of the failed mass. The final MTR is also higher under the 160 mm/h condition, indicating that intense hydrodynamic action not only promotes the initial collapse of the soil skeleton but also enhances the secondary transport and accumulation of failed material near the slope toe, as shown in Figure 16.

4.4. Micromechanical Mechanisms of Differential Particle Transport and Synergistic Failure

Using the cross-scale, two-way coupled DEM framework, this section analyzes particle migration and failure evolution during toe failure under 120 mm/h rainfall. The process can be divided into three phases (Figure 17). First, the equivalent fine matrix particles in the shallow surface layer were preferentially mobilized after the suction-dependent equivalent bonding weakened. The term “equivalent fine matrix particles” is used here because the DEM model adopts coarse-grained particles and does not resolve the migration of real silt particles through pore throats. Second, the reduction in matrix support promoted gravel destabilization and local skeleton collapse. Finally, after the softened zone connected with the lower slope, the overlying matrix moved downslope and entrained embedded gravel particles.

The mechanical characteristics detailed above demonstrate that the instability of gravelly silt slopes is a complex, cascading process. It initiates with the mobilization of equivalent fine matrix particles, which subsequently triggers the destabilization and overturning of suspended coarse particles, ultimately culminating in the traction-driven transport of the deep-seated matrix substrate. Rainfall runoff serves as the primary external hydrodynamic force initiating surface erosion. Conversely, seepage-induced softening acts as the fundamental intrinsic factor triggering shear failure and the structural collapse of the deep-seated coarse–fine skeleton.

4.5. Model Assumptions and Limitations

The numerical model involves several assumptions. First, the DEM model uses equivalent coarse-grained particles, so the simulated particle migration represents relative mobility rather than exact pore-scale erosion. Second, the suction effect is represented by a suction-dependent equivalent bonding term and does not explicitly resolve liquid bridge geometry or pore-size distribution. Third, the seepage field is solved using a variably saturated Richards-type formulation with infiltration-excess runoff treatment, and the results are interpreted within the tested extreme rainfall range. Fourth, runoff and raindrop forces are applied to particles within a 0.02 m active surface layer using model-scale force factors. Fifth, the validation focuses on pore water pressure increment trends and failure process consistency rather than full verification of all contact-scale mechanisms.

5. Discussion

The results should be interpreted within the physical scope of the experimental design. The three rainfall intensities all exceeded the saturated permeability of the tested gravelly silt. Therefore, the tests do not represent the full transition from infiltration-controlled rainfall to runoff-controlled rainfall, but three relative intensity levels within an extreme infiltration-excess rainfall regime. Under this condition, the differences in failure mode were mainly associated with rainfall excess runoff, toe erosion, failed mass mobility, and pore water pressure response.

The laboratory tests showed that shallow instability occurred in all three cases, while the deformation rate and mobility of the failed mass increased with rainfall intensity. The numerical model further explained this transition from the particle scale. However, because equivalent coarse-grained particles were used in the DEM model, the simulated particle migration should be interpreted as a qualitative representation of the failure sequence rather than exact pore-scale transport of real silt particles.

Several simplifications should also be noted. The suction-dependent equivalent bonding term was used to reflect the degradation of suction-induced strength during wetting, but it did not explicitly resolve liquid bridge curvature, pore size distribution, or contact-scale water retention. In addition, the numerical model introduced rainfall effects through pressure head, saturation, seepage force, buoyancy force, bonding degradation, raindrop impact, and runoff drag, but did not directly resolve pore-scale redistribution of water mass. Therefore, the numerical results are interpreted as equivalent hydromechanical responses. Future work should include measured water content profiles, runoff measurements, and more explicit capillary force models to further improve hydraulic and micromechanical validation.

6. Conclusions

This study investigated the instability process and failure mechanism of gravelly silt model slopes under extreme rainfall by combining laboratory rainfall model tests with an FVM-DEM coupled numerical model. The following conclusions are drawn from specific experimental observations, pore water pressure and displacement measurements, and numerical simulation results.

(1)

Experimental image records and laser displacement curves show that all three model slopes developed shallow instability under the tested extreme rainfall conditions, but the failure process changed with rainfall intensity. The 80 mm/h case showed slow progressive shallow sliding, the 120 mm/h case showed faster progressive instability, and the 160 mm/h case showed earlier toe erosion and stronger flow-like transport.

(2)

The comparison between rainfall intensity and the measured saturated permeability of the gravelly silt, together with the simulated hydraulic gradient field, indicates that the three rainfall cases should be interpreted as infiltration-excess rainfall conditions. Under the present model scale, rainfall duration, and soil hydraulic properties, the additional rainfall mainly increased surface runoff, toe erosion, and failed mass mobility rather than proportionally increasing the infiltration depth.

(3)

The measured pore water pressure increments show clear spatial and temporal differentiation. The shallow crest region responded earlier, while the lower slope/toe-adjacent region showed greater later-stage accumulation. This evidence indicates that rainfall-induced wetting and local saturation were coupled with downward seepage and toe-adjacent water accumulation.

(4)

The numerical particle displacement field, suction-dependent equivalent bonding results, and mass transport ratio indicate a progressive particle-scale failure sequence. The failure process can be interpreted as equivalent fine matrix mobilization, gravel destabilization, local skeleton collapse, and matrix-entrained gravel movement. Because equivalent particle upscaling and suction-dependent bonding simplification were adopted, the micromechanical results should be interpreted as relative failure evolution rather than exact pore-scale particle transport.