A Laboratory Simulation Experiment to Assess Permeability and Shear Strength of a Gravel Soil Colluvium

Abstract

Landslides are caused by rainfall as one of the main factors. In order to study the effect of rainfall on the physical and mechanical parameters of landslides, a physical model of the colluvium landslide is created in laboratory conditions with silty clay, river sand, and gravel, taking Shuping landslide in the Three Gorges Reservoir area as the prototype. The artificial rainfall is applied to the accumulation model, which is steady for 60 h, and then the gravel soil is taken out along the different elevations of the colluvium for the permeability test and direct shear test, and the evolution law of changes in porosity, the permeability coefficient, and the shear strength parameters along the elevation are studied. Combined with XRF and NMR tests, the spatial variation of the permeability coefficient and shear strength parameters is discussed from the perspective of chemical elements, minerals content, and porosity, and the stability analysis of a colluvium landslide is carried out considering the influence of parameters along the elevation. The results show that under the action of rainfall seepage, the fine particles of clay are transported from upslope to downslope, resulting in more and more fine particles of clay at the toe slope. The original pores are gradually filled, the cementation between particles is stronger, the corresponding cohesion is increased, and the permeability coefficient is reduced. Due to the loss of fine particles at the upslope, the relative content of coarse particles increases, leading to an increase in the internal friction angle. The variability of the slope’s physical and mechanical parameters is a result of the spatial transport of clay particles in the colluvium caused by the rainfall seepage above. Specifically, the permeability coefficient and internal friction angle from upslope to downslope decrease linearly under the action of rainfall, but the law of the cohesion increases linearly. The upslope’s permeability coefficient and internal friction angle decrease by 11% and 8% compared to those of the downslope, while the cohesion increases by 168%. The results of FLAC^3D numerical calculation of Shuping landslide show that the maximum deformation in the X direction of 145 m and 175 m water level increases by 12% and 42%, and the safety factor decreases by 0.63% and 5% under the combined action of rainfall and the reservoir water level, that is, when considering the variation of parameters along the elevation of the landslide. The research findings provide a better understanding of the spatial parameters in similar colluvium bodies under rainfall action.

1. Introduction

Slope instability is a prevalent natural hazard, albeit often not perceived as being as catastrophic as other types of hazards. Nevertheless, landslides are considered a significant geoenvironmental concern and a crucial geomorphological feature influenced by surface processes. The complexity of landslides encompasses a wide range of processes and factors, surpassing other natural hazards. Among these factors, precipitation plays a particularly vital role in triggering soil erosion within landslide contexts. Therefore, it is necessary to investigate the stability of the slopes in the reservoir area. Many causal factors are at the root of slope instability, but it is reported that most slope failures are caused by rain seepage into the Three Gorges Reservoir area [1]. At present, on-site monitoring and laboratory tests are some of the main methods used to collect data for the study of the stability of slopes [2,3,4]. A large number of model tests are used to study the stability, deformation characteristics, and failure mechanism of landslides in the Three Gorges Reservoir area under water level fluctuations and rainfall conditions [5,6,7]. To examine the effect of rainfall infiltration on slope stability, Xiong et al. [8] conducted model tests with three different combinations of rainfall and reservoir water levels. Lukić, T et al. [9] proposed a geomorphic model with which to describe the nature of the erosional processes on the loess cliffs of the Zemun loess plateau. Li et al. [10] used a physical simulation model to simulate rain-induced landslides under different rainfall intensities. Morar C. et al. [11] analyzed the relationship between selected meteorological parameters, their occurrence, and their temporal distribution in an environment susceptible to landslides due to the specific sedimentological and human land-use characteristics.

The variability of rock mass itself is one of the uncertainties in slope stability, along with rainfall and other external factors [12]. Schieber [13], Huang et al. [14], Xiao et al. [15], Hua et al. [16], and Yang et al. [17] used random field theory and geostatistical theory to study the spatial variability of rock and soil parameters of colluviums. A new probabilistic inverse analysis method was proposed by Rana H et al. [18] to evaluate the uncertainty of soil parameters in slope observation data. Jiang et al. [19] predicted the reliability of soil slopes by analyzing the spatial distribution of soil properties in field test data and monitoring data. Zhang et al. [20] established a rock slope model with weak layers and proposed a stability evaluation framework for rock slopes with weak layers considering the spatial variability of rock strength characteristics by using the random field method. Mori [21] studied the effect of soil shear strength parameter variability on sliding distance by stochastic field simulation and proposed a probabilistic framework by which to evaluate sudden landslide hazards caused by the failure of loose-fill slopes. Li et al. [22] successfully applied remeshing and interpolating with the LDFE small stump approach (RITSS) to simulate the landslide process with spatially variable soils using the force reduction method. Chen et al. [23] studied, in detail, the effects of slope length, soil spatial variability, and peak horizontal acceleration on landslide failure mode and runout distance through the 3D dynamic large-deformation finite element method. Ding et al. [24] characterized the soil with structural anisotropy as a random field, used the finite element method to calculate the safety factor of anisotropic soil slopes, and estimated the factor of safety (FS) statistical properties of undrained clay slopes. Xia et al. [25] analyzed a three-dimensional weak zone slope stability analysis method that takes into account spatial variability based on two-phase random media and the finite element method.

At present, most of the research focuses on the deformation characteristics, failure mechanism, and probability or reliability index of landslides under rainfall, and it is equally important to analyze the stability of landslide via the spatial variability of the properties of the soils in the landslide and the shear strength parameters of soils in the landslide along the elevation of colluvium. When evaluating the stability of colluvium landslides, it is important to take into account the spatial variability of the parameters. In this study, the spatial variability of the physical and mechanical parameters of the colluvium under rainfall is considered, and an evolution equation between the permeability coefficient, shear strength parameter, and elevation is proposed. The stability calculation results validate the impact of geotechnical spatial variability on landslide stability. The paper is arranged as follows: After the Introduction, the general situation of the landslide of the Shuping colluvium in the Three Gorges Reservoir area is introduced in Section 2, and the test material and test plans are illustrated in Section 3. Section 4 presents the experimental results and analysis. Section 5 presents the mechanism for parameter evolution based on microscopic characteristics. The stability of the colluvium in Section 6 is calculated using numerical software. Finally, the conclusions is reached in Section 7.

2. Brief Introduction to Shuping Colluvium Landslide

Most of the landslides in the Three Gorges Reservoir area occur in the colluvium, which is a typical colluvium slip and is mainly affected by the strength of the colluvium and bedrock sliding zone, rainfall, and reservoir water level fluctuation [5]. The landslide colluvium of the rainfall physical test model constructed in this paper is used to characterize Shuping colluvium landslide, and it is also representative of other colluvium landslides in the Three Gorges Reservoir area. The plane view of the Shuping colluvium landslide is shown in Figure 1a, which is approximately 47 km away from the Three Gorges Dam. The plane view of the shape of the landslide is U-shaped, and the slope is roughly in the range of 19° to 30°. The elevation of the trailing edge of the landslide is between 380 m and 400 m, the front edge is straight to the Yangtze River, and the elevation of the cut outlet is about 60 m. The length of the slide body is about 800 m from north to south, the width from east to west is about 700 m, the area is about 5720 m², and the average thickness is about 50 m. The slope is mainly composed of colluvial soil and silty clay mixed with gravel, and one of these sections is shown in Figure 1b.

3. Test Plan

3.1. Model Test Apparatus

The structure of this test is similar to a frame model test and mainly consists of a model groove and a rainfall control system. The pattern of the colluvium body test is shown in Figure 2a. According to the prototype size of the Shuping landslide, a physical model was created using the principle of geometric similarity, and the similarity ratio was 1:320. The model’s design size is 2.2 m (length) × 1 m (width) × 1.3 m (height), the model is closed around the perimeter, and the top surface is open. The model’s photograph can be seen in Figure 2b.

To prevent the precipitation seepage, waterproof materials were applied to the bottom and side of the model tank. An automatic watering controller, flow meter, pressure gauge, rainfall sprinkler, and other equipment are the main components of the rainfall control system.

3.2. Model Test Material

In the model test, silty clay, river sand, and gravel were used to configure the colluvium, and gravel with a particle size larger than 3 cm were replaced via the equivalent substitution method. Through the direct shear test and the constant head penetration test, the basic physical and mechanical parameters of the colluvium body model and the Shuping landslide soil were obtained [26], as shown in

Table 1. Physical and mechanical parameters of test landslide colluvium and Shuping landslide rock mass.

Soil Sample Category	Density ρ/g·cm−3	Content of Stone/%	Water Ratio/%	c/kPa	$\mathit{\phi }/$°	k/cm·s−1	Coefficient of Nonuniformity	Coefficient of Curvature
Shuping landslide	2.01	68	23.4	20.7	23.5	1.02 × 10−2	30.36	1.21
Test landslide colluvium	2.0	68	8.0	33.66	36.78	1.60 × 10−3	28.0	1.90

. The colluvium material is used in this experiment with a homogeneous medium.

According to the comparison of physical and mechanical parameters in Table 1, combined with the actual situation of the test, three materials—clay, river sand with particle sizes of 1~2 mm and 2~5 mm, and gravel (with particle sizes of 5 mm~1 cm and 1~3 cm, respectively)—were finally selected as the raw materials for this model test to fill the piles. During the filling process, the layered compaction method is adopted, the thickness of each filling is about 11 cm, and each layer of filling is manually compacted. After the filling is completed, the slope surface of the colluvium is manually repaired to the shape designed by the experiment. After the model is made, a transparent rainproof film is hung on the left, right, and rear sides of the model groove to prevent rain splashing during the rainfall process and causing rainfall loss.

3.3. Test Program

3.3.1. Rainfall Design

The maximum rainfall in the Hubei section of the Three Gorges Reservoir area within 1 h is in the range of 55~110 mm, and the average annual rainfall is in the range of 1100~1200 mm [27]. Considering the difference in the amount of water sprayed by different sprinklers in the test, the amount of water sprayed is greatly affected by the water pressure, the arrangement of sprinklers, and the size of the nozzle aperture. Before the model is filled, a rainfall rate test is carried out to determine the rainfall intensity and rainfall uniformity. The calculated rainfall intensity is about 45 mm/h, combined with the limitations of the test environment and water pressure. To increase the migration of soil particles to make the testing effect more obvious, the duration of rainfall is designed to be 60 h, and the duration of a single, continuous rainfall is 10 h, which is divided into 6 periods in total, and the accumulated rainfall is 2700 mm.

3.3.2. Sampling Point Layout

To explore the variation law of the chemical elements, mineral content, permeability, and shear strength parameters of the particles in the colluvium body model after rainfall, five points were arranged in a section along the long side of the colluvium body model to sample the colluvium particles. The first section numbers are DW1-1, DW2-1, DW3-1, DW4-1, and DW5-1, respectively. The No. 1 position of the second and third profiles are numbered DW1-2 and DW1-3, respectively, and the rest of the points are numbered by analogy for a total of 15 sampling points. Among them, the elevations of DW1 to DW5 are 16 cm, 55 cm, 94 cm, 16 cm, and 55 cm, respectively. The horizontal distances from DW1 to DW5 to the bottom of the slope are 40 cm, 94 cm, 148 cm, 40 cm, and 94 cm, respectively. The sampling point layout is shown in Figure 3.

3.3.3. Test Scheme

When the rainfall of the colluvium body model is over, the model is left standing for 24 h in order to allow the rainwater to flow fully. Then, the colluvium particles are sampled at each sampling point and the permeability, shear strength, element mineral content, and porosity are measured. We used 0.4 MPa, 0.3 MPa, and 0.2 MPa pressure water to conduct a 5 min constant head penetration test to measure the permeability coefficient, and the average value of the permeability coefficient under three-stage water pressure was taken as the permeability coefficient of each sampling point. After rainfall, the shear strength parameters of the colluvium particles were obtained by taking 3 groups of samples at each sampling point and performing the unconsolidated and undrained direct shear tests with normal stress values of 100 kPa, 200 kPa, and 300 kPa in the YZW1000 electric direct shearing instrument. At the same time, the EDX-7000 X-ray fluorescence spectrometer and the nuclear magnetic resonance (NMR) system were used to determine the content of elements and minerals and the porosity of colluvium particles after rainfall.

4. Analysis of Test Results

4.1. The Deformation and Failure Characteristics of the Landslide Colluvium Model

Figure 4 shows the process of colluvium destruction under rainfall. During the initial rainfall stages, water primarily infiltrated the colluvium slope’s interior. Minor surface runoff ensued, causing a lightening of the colluvium’s color. After 8 h of rainfall, the runoff phenomenon of the colluvium surface increased significantly, a gully was formed in the upper part of the colluvium surface, and there was a small amount of turbid water at the bottom of the colluvium. After 24 h of continuous rainfall, the colluvium exhibited a downward sliding motion, accompanied by the gradual emergence of coarse-grained gravel on the surface. Pronounced deformations and subsequent gradual collapse were evident at the colluvium’s base. After 60 h of rainfall, the coarse particles of gravel soil on the colluvium surface were exposed, the collapse of the colluvium’s bottom was obvious, the fine particles were concentrated, and the overall height of the colluvium body sank by 1 to 2 cm compared with the initial model.

4.2. The Variation Law of Permeability along the Elevation

To quantitatively describe the variation pattern of gravel soil parameters across various elevations within the colluvium, the rates of parameter change and phase change in the downslope direction were introduced. This analysis facilitates an examination of the colluvium’s permeability, as shown in Equations (1) and (2). The average value of the permeability coefficient and the rate of change of permeability coefficient parameters at the elevation sampling points are shown in

Table 2. The permeability coefficient of sampling points at different elevations.

Point Number		Elevation h/cm	k/cm·s−1	${\mathit{L}}_{\mathit{i}}$	$\mathbf{\Delta }{\mathit{L}}_{\mathit{i}}$/k·cm−1
Surface	DW1	16	1.56 × 10−3	−0.025	/
	DW2	55	1.62 × 10−3	0.0125	1.5 × 10−6
	DW3	94	1.76 × 10−3	0.10	3.6 × 10−6
Interior	DW4	16	1.59 × 10−3	−0.006	/
	DW5	55	1.71 × 10−3	0.069	3.1 × 10−6

. Additionally, Figure 5 depicts the correlation between the permeability coefficient of colluvium particles and elevation.

$$L_i=\frac{l_i-l_0}{l_0},i=n,\dots ,2,1$$

(1)

$$\mathrm{\Delta }{L}_i=\frac{l_i-l_{i-1}}{H_i-H_{i-1}},i=n,\dots ,2,1,$$

(2)

where $i$ is the sampling point number; $L_i$ is the parameter change rate; $\mathrm{\Delta }{L}_i$ is the parameter down-slope phase change rate; $l_0$ is the initial parameter value; $l_i$ and $l_{i-1}$ are the parameter values of two adjacent sampling points; and $H_i$ and $H_{i-1}$ denote the elevation of two adjacent sampling points.

From Table 2 and Figure 5, it can be seen that the permeability coefficient of the particles in the colluvium on the landslide surface increases, gradually, with the increase in the sampling point elevation from 1.56 × 10⁻³ cm/s at the bottom of the landslide (DW1) to 1.76 × 10⁻³ cm/s at the top of landslide (DW3). Compared with the initial permeability coefficient of the colluvium particles before the rainfall, the permeability coefficient of the sampling point DW1 decreased significantly by 2.5%, while the permeability coefficient of the sampling point DW3 increased by 10%. In the interior of the landslide, the permeability coefficient increased from 1.59 × 10⁻³ cm/s to 1.71 × 10⁻³ cm/s from sampling points DW4 to DW5. The permeability coefficient decreased by 0.6% and remained almost unchanged, while the permeability coefficient of sampling point DW5 increased by 6.9%. Based on the above analysis, rainfall has changed the permeability coefficient of the colluvium. After the rainfall, whether it is on the surface of the colluvium slope or the interior of the slope, with the increase in elevation, the permeability coefficient increases linearly.

In summary, throughout the rainfall process, the colluvium slope’s surface runoff, due to rainwater scouring, leads to the accumulation of fine particles at the slope’s base. Consequently, at the downslope, fine particle content increases, resulting in diminishing permeability. Conversely, the upslope exhibits increasing porosity, enhancing penetration capacity. Similarly, rainwater infiltration causes fine particles within the colluvium mass to migrate from upslope to downslope. However, this migration phenomenon is less pronounced than that observed on the colluvium surface. To quantitatively describe the relationship between the permeability of the colluvium particles and the elevation, the average value of the parameter change rate at the same elevation was taken as the change rate of the permeability coefficient at the corresponding elevation (as shown in

Table 3. Change rate of permeability coefficient.

Elevation	16 cm	55 cm	94 cm
Average value	0.0155	0.041	0.1

).

The relationship between the permeability coefficient change rate and the elevation is obtained by fitting the average value of the elevation and the parameter change rate, as shown in Equation (3):

$$L_{ki}=0.0147+1.2804h_i+1\times {10}^{-5}{h}_i^2,i=n,\dots ,2,1,$$

(3)

where $L_{ki}$ is the rate of change in the coefficient of permeability at h_i; and h_i is the elevation of the colluvium model.

According to the test results, the relationship between the change rate of the permeability coefficient parameter and the permeability coefficient is analyzed, and the relationship between the permeability coefficient and the elevation of the colluvium model can be obtained, as shown in Equation (4):

$$k_i=k_0(1+L_{k1})+2.73\times {10}^{-6}{h}_i,i=n,\dots ,2,1,$$

(4)

where $k_i$ is the permeability coefficient at h_i; and k₀ is the initial permeability coefficient of the colluvium model before the test. The average value of the phase change rate of the permeability coefficient is $2.73\times {10}^{-6}$. $L_{k1}=0.0147$ is the rate of change of the permeability coefficient of the colluvium at h_i = 0.

4.3. The Variation Law of Shear Strength Parameters along Elevation

Following the application of normal stresses of 100 kPa, 200 kPa, and 300 kPa in the direct shear test on colluvium particles at each elevation sampling point subsequent to rainfall, the shear strength parameter values for each sampling point were derived and are presented in

Table 4. The shear strength parameters of sampling points at different elevations.

Point Number	Points	c kPa/cm	${\mathit{L}}_{\mathit{i}}$ of c	$\mathbf{\Delta }{\mathit{L}}_{\mathit{i}}$ c kPa/cm	φ/°	${\mathit{L}}_{\mathit{i}}$ of φ	$\mathbf{\Delta }{\mathit{L}}_{\mathit{i}}$ φ °/cm
Surface	DW1	71.3	1.119	/	34.22	−0.0696	/
	DW2	48.08	0.428	−0.595	35.75	−0.028	0.039
	DW3	26.56	−0.211	−0.552	37.6	0.0223	0.047
Interior	DW4	65.03	0.932	/	34.99	−0.0487	/
	DW5	51.48	0.529	−0.347	36.13	−0.0177	0.021

.

Similarly, to better represent the change between the shear strength parameter and the elevation, the parameter change rate and the phase change rate of the parameter along the down-slope were introduced, respectively, to analyze the internal friction angle and cohesion. This calculation method mirrors the approach used for calculating the parameter change rate of the permeability coefficient as shown in Equations (1) and (2). The calculation results of the internal friction angle and cohesion of each elevation sampling point are shown in Table 4. Figure 6 illustrates the correlation between shear strength parameters and elevation.

It can be seen from Table 4 and Figure 6 that compared with the initial values before the rainfall, the cohesion and internal friction angle of the colluvium particles have changed, either increasing or decreasing. Concerning cohesion alterations, with the exception of DW3, which decreased by 21.1% from an initial value of 33.66 kPa to 26.56 kPa, the cohesion values of the remaining four sampling points exhibited increases relative to their pre-rainfall values. Notably, the most substantial cohesion increase occurred at sampling point DW1, rising from 33.66 kPa to 71.3 kPa, reflecting a remarkable 111.9% augmentation.

Similarly, in regard to the internal friction angle, aside from the 2.23% increase observed at sampling point DW3 (rising from the initial 36.78° to 37.6°), the internal friction angle diminished at the remaining four sampling points relative to their pre-rainfall values. The most pronounced alteration was observed at sampling point DW1, indicating a decrease of 6.96% from 36.78° to 34.22°. Examination of the colluvium’s parameter values at each sampling point reveals that rainwater action causes the fine colluvium particles to migrate from upslope to downslope. This migration, in turn, leads to notable variations in shear strength parameters along the elevation. Specifically, the internal friction angle displays a linear decrease with elevation, while cohesion exhibits a linear increase with elevation.

The analysis of shear strength parameters follows the same methodology as the colluvium permeability analysis. The change rate of the corresponding elevation is determined by utilizing the average value of the parameter change rate at the same elevation, as seen in

Table 5. The change rate of internal friction angle and cohesion.

Parameter	16 cm	55 cm	94 cm
Internal friction angle φ/°	1.026	0.479	−0.211
Cohesion c/kPa	−0.060	−0.023	0.022

. The evolving relationship between shear strength parameters and elevation is deduced through the relationship between shear strength parameter change rate and elevation.

The average of the change rate of c and φ with the elevation are, respectively, fitted by formulae, as shown in Equations (5) and (6):

$$L_{ci}=1.6353-0.0419h_i-2.3642\times {10}^{-4}{h}_i{}^2,i=n,\dots ,2,1$$

(5)

$$L_{\phi i}=-0.0729+7.62\times {10}^{-4}{h}_i+2.6298\times {10}^{-6}{h}_i{}^2,i=n,\dots ,2,1,$$

(6)

where $L_{ci}$ is the change rate of the cohesion of at h_i; $L_{ci}$ is the change rate of the internal friction angle at h_i; and h_i is the elevation of the colluvium model.

According to the above test results, the relationship between the parameter change rate of the cohesion and the internal friction angle and the parameter value is analyzed, and the relationship between the shear strength parameter and the elevation of the colluvium model can be deduced via Equations (7) and (8):

$$c_i=c_0\left(1+L_{c1}\right)-0.4980h_i,i=n,\dots ,2,1$$

(7)

$${\phi }_i={\phi }_0\left(1+L_{\phi 1}\right)+0.0357h_i,i=n,\dots ,2,1,$$

(8)

where $c_i$ is the cohesion at h_i of the colluvium model; ${\phi }_i$ is the internal friction angle at h_i of the colluvium model; $c_0$ and ${\phi }_0$ are the initial values of the cohesion and the internal friction angle of the colluvium model before the test, respectively; and 0.498 and 0.0357 are the average values of the phase change rate of the cohesion and the internal friction angle, respectively. The change rate of the cohesion and the internal friction angle at h₁ = 0 are $L_{c1}=1.6353,L_{\phi 1}=-0.0729$, respectively.

5. Microscopic Analysis of the Variation of Particles in Colluvium along the Elevation

5.1. Variation Characteristics of Element and Mineral Content

Following colluvium particle filling and testing, the chemical element and mineral contents of colluvium particles from distinct elevation samples were ascertained via X-ray fluorescence spectroscopy (XRF). The resultant trend in element and mineral content within the colluvium particles is presented in Figure 7. Figure 7 illustrates that while the alteration pattern in the element and mineral content of colluvium particles at varying elevation sampling points post-rainfall may not be overtly apparent, notable changes in the content of individual elements or minerals are evident. The contents of Si, Al, and Fe elements exhibited substantial alterations compared to their initial pre-rainfall levels, regardless of whether the sampling point was on the colluvium surface or within the colluvium itself.

At the DW1 sampling point, the content of Si and Al elements, as well as the minerals SiO₂ and Al₂O₃, displayed increases of 4.32%, 1.5%, 4.5%, and 10.34%, respectively, in contrast to their initial pre-rainfall levels. These increments exceeded those observed at other sampling points. Conversely, the content of the Fe element and iron minerals were lower at this point in comparison to the other sampling locations. After the rainfall, whether on the slope surface or inside the slope, the content of Si and Al elements and the content of minerals SiO₂ and Al₂O₃ are higher at the toe slope position, while the content of Fe and iron minerals is bigger at the top slope. Within the colluvium’s raw materials, clay and river sand predominantly comprise Si elements and silicon minerals, whereas gravel is characterized by higher Fe elements and iron minerals; this underscores that rainwater-driven erosion and infiltration lead to the migration of fine-grained clay minerals within the colluvium from the upslope to the lower regions, while the transport impact of coarse gravel minerals through rainwater is either indistinct or minimal.

5.2. Particle Gradation and Porosity Variation Characteristics

As the rainfall duration gradually increased, clay particles on the slope surface were transported downslope. A substantial accumulation of fine clay particles took place at the slope toe due to surface runoff, while gravel became exposed at the slope’s summit. Figure 8 illustrates the particle sieving distribution curve for the accumulated particles at each individual sampling point. It can be seen from Figure 8 that the content of fine particles in the clay at the toe of the slope DW1 (h = 16 cm) increases significantly. The fine particles in the colluvium at DW2 (h = 55 cm) in the middle of the slope surface are smaller than the initial content before rainfall, but the particle size is not much different from the original gradation. The gravel content in the soil at DW3 (h = 94 cm) at the top of the slope surface increased, the fine-grained clay was seriously lost, and the effective particle size, continuous particle size, and limiting particle size were all larger than the initial particle gradation. The content of fine particles at DW4 (h = 16 cm) and DW5 (h = 55 cm) in the slope increased, and the effective particle size decreased significantly. Consequently, precipitation prompts water flow to propel colluvium particles from elevated regions towards the slope’s base, engendering the depletion of both coarse and fine particles from the surface of the colluvium body. Notably, fine particles exhibit significant migration. Concurrently, as rainfall duration extends, the infiltration of rainwater into the slope becomes more pronounced. This intensifies the seepage effect, thereby facilitating the continued downslope transportation of fine colluvium particles during the infiltration process.

Figure 9 and Figure 10 are, respectively, the porosity T₂ spectral distribution curve and the pore radius and pore size distribution of the colluvium particles at different elevation sampling points. It can be seen from Figure 9 that there are mainly two relatively obvious peaks in the nuclear magnetic resonance (NMR) of the colluvium particles, and the peaks are around the relaxation times of 1.5 ms and 1000 ms, respectively. The signal amplitude of the DW1 point near the 1 ms relaxation time is larger than that of other points, and the signal peak is reached the fastest, indicating that the number of micro-pores at the toe of the slope is large [28], and the pores are densely distributed. As the elevation of the sampling point increases, the area of the T₂ spectral curve increases, indicating that the greater the elevation at the higher points after rainfall, the greater the number of pores inside the colluvium particles. Compared with the sampling point DW1 at the toe of the slope, the T₂ spectral curve of the DW2~DW5 sampling point is panned to the right as a whole, and the NMR signal appears again within the relaxation time of 500~1000 ms, indicating that the colluvium particles at each elevation contain larger pore sizes after rainfall, and with the increase in elevation, the longer the relaxation time, the stronger the NMR signal that appears again, and the larger the pores. With an elevated colluvium elevation, the relaxation time proportionally extends, leading to a more robust re-emergence of the NMR signal, indicative of augmented pore size.

Figure 10 shows that after the rainfall, the porosity of DW1 to DW5 at different colluvium heights was 28.37%, 29.17%, 32.72%, 28.72%, and 30.80%, respectively, mainly between 25.0% and 35.0%. Among them, the porosity of micropores with pore radii of 0–0.1 μm was 22.14%, 18.38%, 17.70%, 20.72%, and 17.68%, respectively. Comparing the particle porosity of the sampling points at each elevation, it can be seen that with the increase in elevation, the porosity of the colluvium gradually increases. Compared with the DW1 sampling point, the particle porosity of the DW3 sampling point at the top of the slope surface increased the most (i.e., by about 4%). The pore radius distribution curve of the DW1, DW2, and DW3 sample points is offset to the right and flattened, indicating that with the increase in elevation, the porosity increases, but the microporous distribution rate decreases and the pore radius increases. This aligns with the findings of the T2 spectral distribution analysis. The analysis of the T2 spectral distribution, pore radius, and pore size distribution reveals that as the elevation of the colluvium model decreases during rainfall, the porosity diminishes, while the count of micropores expands. Additionally, rainwater scouring transports fine particles within the colluvium particles to lower positions, thereby altering the pore distribution within the landslide colluvium.

5.3. Mechanism Analysis of Variation of Parameters along Elevation

From the Coulomb formula and the Terzaghi effective stress principle [29], it can be discovered that the shear strength of soil particles is composed of the frictional resistance caused by the inter-particle occlusion and the inter-particle cementation and electrostatic attraction. The frictional resistance is generally represented by the friction angle (φ). In addition, the more stone content of the colluvium particles, the greater the value. Cohesion (c) is related to the cementation and electrostatic attraction between the particles. The stronger the electrostatic attraction, the greater the cohesion (c) value. At the same time, the porosity reflects the compactness of the soil.

The greater the porosity, the lower the compactness, and the stronger the permeability [30]. Figure 11 and Figure 12 show the relationship between the minerals content, porosity, permeability coefficient, and shear strength parameters of the colluvium. It can be seen from Figure 11 and Figure 12 that the content of SiO₂ and Al₂O₃ minerals and the porosity of the colluvium body have different effects on the permeability coefficient and shear strength parameters. From DW3 to DW1 at the sampling point, from the top to the bottom of the slope, with the increase in mineral content, the permeability coefficient and internal friction angle decrease, while cohesion increases. On the contrary, with the decrease in porosity, the permeability coefficient and internal friction angle decrease, and the cohesion increases.

According to the above test results, under the action of rainfall, the internal friction angle and permeability coefficient of the colluvium gradually decreases from the top to the toe of the slope, and the cohesion gradually increases. Since the colluvium is mainly composed of minerals SiO₂ and Al₂O₃, under the action of rainfall, the fine particles of the colluvium are transported to the toe of the slope, while the coarse particles are unchanged. Therefore, there are more and more fine particles of clay at the toe of the slope, the original pores are gradually compacted, and the cementation between particles is stronger, increasing cohesion. On the contrary, due to the migration of fine particles, the content of coarse particles in the colluvium at the top of the slope increases relatively, and the friction resistance and porosity increase, so the internal friction angle and permeability coefficient increase. In summary, under the action of rainfall, the changes in shear strength parameters and the permeability coefficient of colluvium particles along the elevation are mainly due to the effect of water flow, which leads to the spatial migration of fine particles such as clay inside the landslide along the seepage direction and changes the internal particle distribution of the slope.

6. Analysis of Landslide Stability of Shuping Colluvium

The Shuping landslide is still in continuous deformation due to rainfall, and it is likely to be unstable in the future. In order to explain the relationship between reservoir water level variation, rainfall effect, and landslide deformation, a numerical model of Shuping colluvium was established by using FLAC^3D based on relevant geological data. The length, width, and height of the numerical calculation model are 760 m × 50 m × 330 m, respectively. The model grid is divided into 11,776 units and 11,036 nodes. The bottom surface and the vertical surface of the model are set as fixed boundaries, and the slope surface is free boundaries at x and z. The numerical calculation model is shown in Figure 13.

This paper conducts a simplified calculation of the colluvium to examine the impact of parameters across elevation changes on the rainfall-induced landslide stability. The colluvium landslide is segmented into three sections: bedrock, sliding zone, and landslide. Homogeneous particles constitute the landslide mass, while the bedrock is formed from limestone; seepage within the bedrock is excluded, designating it as impermeable. The physical and mechanical parameters of the landslide are shown in

Table 6. Physical and mechanical parameters of the Shuping landslide.

Category	${\mathit{\rho }}_0$/g·cm−3	$\mathbf{k}$/cm·s−1	$\mathit{E}$/MPa	v	$\mathit{K}$/Pa	$\mathit{G}$/Pa	$\mathit{c}$/kPa	$\mathit{\phi }$
Landslide	2.01	1.02 × 10−2	300	0.255	2.04 × 108	1.19 × 108	20.7	23.5
Sliding zone	-	/	300	0.45	1 × 109	1.03 × 108	19.2	20.4
Bedrock	2.61	/	5000	0.22	2.98 × 109	2.05 × 109	3.38 × 103	46

.

The calculation process used, the fluid–structure coupling calculation function of FLAC^3D, is mainly divided into two stages: (1) seepage calculation—in this stage, the model is cycled to equilibrium to obtain a steady-state seepage field; (2) based on the strength reduction method, the mechanical calculation of the safety factor of the colluvium is automatically performed. The Mohr–Coulomb criterion of the linear elastic–plastic constitutive model is used to characterize the colluvium, and the rainfall effect is simulated by the variation formula of the permeability coefficient and shear strength parameters along the elevation mentioned in Section 4. Since the completion of the Three Gorges Dam, the reservoir water level has changed between 145 m and 175 m. According to the actual situation, this paper set up four (①~④) working conditions for simulation analysis: ① 145 m reservoir water level; ② 175 m reservoir water level; ③ 145 m reservoir water level combined with rainfall; ④ 175 m reservoir water level combined with rainfall.

Figure 14 depicts the plastic deformation zones of the landslide across distinct operational scenarios. In Condition 1, with the reservoir water level set at 145 m, the plastic zone of the landslide aggregates in the lower central region of the slope, particularly proximate to the 145 m water level. Under Condition 2, where the reservoir water level elevates to 175 m, the plastic zone of the landslide primarily clusters on the slope surface near the 175 m water level, with a minor extension onto the landslide’s trailing edge. Condition 3 incorporates the dual influence of a 145 m reservoir water level and rainfall. Here, the plastic zone gathers in the mid-slope surface and the middle of the slide zone, both situated below the water surface. These central plastic zones interconnect, accompanied by a limited extension onto the landslide’s trailing edge. Transitioning to Condition 4, which combines a 175 m reservoir water level with rainfall, the plastic zone emerges in the upper-mid slope surface and within the sliding belt beneath the 175 m water level, with a more substantial extent of complete penetration compared to Condition 3.

Figure 15 illustrates the safety factors of landslides across different operational scenarios. In Condition 1, with a reservoir water level of 145 m, the landslide exhibits a safety factor of 1.270, indicating a stable condition. Under Condition 2, characterized by a reservoir water level of 175 m, the landslide’s safety factor is 1.170, signifying stability. However, when both the 145 m reservoir water level and rainfall synergize in working Condition 3, the landslide’s safety factor reduces to 1.262, placing it in a state of under-stability attributed to parameter variations induced by rainfall. Analogously, the combination of a 175 m reservoir water level and rainfall in working Condition 4 yields a landslide safety factor of 1.11, underscoring under-stability.

Figure 16 illustrates the evolving trends in the maximum displacement and stability coefficient of the landslide across distinct operational contexts. It is evident from Figure 16 that at reservoir water levels of 145 m and 175 m, the maximum displacements in the X direction are 4.7535 cm and 3.7626 cm, respectively. Factoring in the combined impact of reservoir water level and rainfall, the maximum displacements in the X direction are amplified to 5.3625 cm for the 145 m reservoir water level (Condition 3) and 6.0874 cm for the 175 m reservoir water level (Condition 4). In cases where the safety factor of the landslide diminishes, the maximum displacement in the X direction proportionally increases across most operational scenarios. Consequently, under the joint influence of rainfall and reservoir water level (namely, accounting for parameter alterations along the landslide’s elevation), the maximum deformation of the landslide in the X direction for the 145 m and 175 m water levels escalates by 12.81% and 42.52%, respectively. Concurrently, the coefficients experience reductions of 0.63% and 5.13%.

Based on numerical calculations of plastic deformation, safety factors, and maximum displacement in the X direction across various landslide scenarios, it becomes evident that the combined influence of reservoir water level and rainfall triggers the greatest displacement in the X direction at the trailing edge of the landslide. In contrast, solely acting reservoir water levels lead to a stable state with localized plastic deformation. Combining reservoir water level with rainfall introduces variability in the physical and mechanical parameters of the landslide due to the migration of fine particles toward the slope’s toe. Consequently, this variation produces an expanded plastic zone, gradual penetration of the slip zone, and a reduction in the safety factor, ultimately rendering the landslide less stable.

7. Conclusions

This study investigates the evolution and mechanism of permeability and the shear strength parameters of colluvium along the elevation through a rainfall model test. The assignment of mechanical parameter changes along the elevation is accomplished using the Fish language in FLAC^3D numerical analysis software. The analysis explores landslide stability utilizing the Shuping landslide as a prototype, considering the impact of reservoir water level and rainfall. Analysis of the results yields the following key research findings:

(1)

Amidst intermittent rainwater seepage and runoff, notable alterations in the permeability and shear strength parameters of the colluvium transpire along the elevation gradient. With descent from the slope’s summit to its base, the permeability coefficient (k) and internal friction angle (φ) both manifest a linear decline. In contrast, cohesion (c) undergoes a linear increase. The most pronounced impact is attributable to rainfall on cohesion, succeeded by the permeability coefficient, while the internal friction angle experiences the least influence.

(2)

When compared to the initial model parameters, characterized by the absence of rainfall, noteworthy variations emerge. Specifically, the permeability coefficient (k) at the downslope surface decreased by 2.5%, while the cohesion (c) increased by a substantial 111.9%, and the internal friction angle (φ) experienced a reduction of 6.96%. In contrast, the upslope surface exhibited a distinct behavior, with a 10% increase in k, a decrease of 21.1% in c, and a 2.23% rise in φ. In terms of the colluvium body’s overall structure, subsequent to rainfall, the permeability coefficient, cohesion, and internal friction angle at the upper slope demonstrated values 1.13, 0.37, and 1.09 times, respectively, in comparison to those at the lower portion. While the internal modifications within the colluvium body followed a pattern akin to that near the surface, the magnitude of these alterations was comparatively less pronounced.

(3)

In contrast to the initial state of the colluvium prior to rainfall, a rise in clay mineral content along elevation is observed, followed by a reduction post-rainfall. Notably, the key constituents Si, Al, and the minerals SiO₂ and Al₂O₃ in the clay located at the base of the colluvium model register increments of 4.32%, 1.5%, 4.5%, and 10.34%, respectively. Concurrently, a decline in elevation corresponds to a reduction in both the number and dimensions of pores within the colluvium. This phenomenon underscores that under the influence of rainfall-driven seepage, fine clay particles migrate towards the slope toe, aligning with the seepage direction. Accumulation of fine clay particles at the slope toe leads to the gradual filling of original pores, intensifying particle cementation, resulting in elevated cohesion and diminished permeability coefficient. Simultaneously, the transportation of fine particles triggers a relative surge in coarse particle content upslope, amplifying friction resistance and augmenting the internal friction angle.

(4)

Considering the combined impact of rainfall and reservoir water level, including the variation of parameters along the landslide elevation, in contrast to scenarios solely involving the effect of reservoir water level at the same elevation, the maximum deformation of the Shuping landslide increased by 12.81% and 42.52% in the X direction at the water levels of 145 m and 175 m, respectively. Nonetheless, the safety factor experienced reductions of 0.63% and 5.13%, respectively. This highlights the significance of accounting for the variability in the physical and mechanical parameters of the landslide along the elevation during numerical calculations. Ignoring this variability can result in an overestimation of the calculated safety factor, subsequently leading to an inflated estimation of colluvium stability. Consequently, incorporating the variability of physical and mechanical parameters induced by rainfall in slope engineering design enhances the reliability of the design outcomes.