Numerical Simulation of Fine Particle Migration in Loose Soil Under Groundwater Seepage Based on Computational Fluid Dynamics–Discrete Element Method

Abstract

The seepage of groundwater in loose soil causes the migration of fine particles within the soil, which can significantly contribute to slope instability and trigger a series of geological issues, such as soil erosion, landslides, and debris flow. This study employed a coupled computational fluid dynamics and discrete element method (CFD-DEM) to investigate the migration process of soil particles under groundwater seepage. It elucidated the effects of key factors, including particle size ratio, particle quantity, and weight, on the migration behavior of fine particles within porous media. The results indicated that when the particle size ratio was less than or equal to 5, over 90% of fine particles accumulated on the surface of the medium. Additionally, an increase in the weight or quantity of fine particles intensified their accumulation. However, when the particle size ratio exceeded five, it became the dominant factor affecting displacement. Under the same weight conditions, the larger the particle size ratio, the longer the particle migration distance. Compared to a particle size ratio of 3, the accumulation percentages of fine particles with a particle size ratio of 20 increased by 26.88% and 31.46% in the middle and tail sections, respectively.

1. Introduction

Loose soil, characterized by significant porosity, is commonly found in natural alluvial deposits, collapse deposits, as well as artificially generated waste soil and waste residue. It contains interconnected pores that, when saturated with groundwater, facilitate the migration of fine particles along connected pore channels. This movement, driven by groundwater seepage, not only results in soil erosion and clogging but also alters the water pressure and internal pore structure of the soil, ultimately compromising its stability over time [1]. In environments such as eroded slopes, tailings reservoir, landslides and debris flow, the collapse or failure of loose soil may trigger natural disasters that negatively impact local economy and sustainable development [2,3,4,5,6]. These natural disasters are often associated with changes in groundwater dynamics. To mitigate the risks posed by such events, researchers have conducted extensive studies involving experiments and risk assessments to develop strategies for disaster prevention [7,8,9]. Additionally, to better understand the mechanism of disaster formation, researchers have also studied the stability characteristics of rock and soil from the perspective of internal structural interactions. For instance, Wang et al. [10] conducted laboratory experiments to study the internal structural damage of soil and found that fine particles infiltrating the soil pores reduced the internal porosity, thereby affecting the soil structure. While considerable research has focused on the fine particle migration within porous media under groundwater seepage conditions, the microscopic mechanism underlying this process remains unclear. Addressing this knowledge gap is crucial for advancing our understanding of natural disasters such as soil erosion, landslides, and ground subsidence caused by groundwater and soil particle erosion.

The migration of fine particles within pore channels can lead to sedimentation, clogging, or retention. These behaviors are influenced by various factors, including flow rate, size, concentration, surface roughness, and electrical properties of the particles [11,12,13,14,15]. Cui et al. [16] demonstrated through saturated sand box experiments that particle size and flow velocity significantly affected sedimentation processes. Bai et al. [17] conducted a series of particle migration experiments under varying particle sizes and flow rates, and they believed that particle size and concentration are important factors which affect the migration of fine particles in porous media. Wiacek et al. [11] numerically investigated the effect of particle size heterogeneity on the critical particle size fractions for packing materials with varying diameter ratios of the largest to smallest grains. In summary, particle size ratio and concentration critically affect the migration and clogging of fine particles within porous media under groundwater seepage conditions, while many microscopic mechanisms remain to be explored.

While understanding and reproducing the migration and clogging behavior of fine particles at the microscale is challenging due to the inherent complexity of porous media, numerous researchers have proposed innovative methods for studying these phenomena. Particle movement in porous media is governed by a combination of hydrodynamic and physicochemical mechanisms. While advanced laboratory techniques such as X-ray imaging and electron microscopy enable effective observation of migration and clogging processes of fine particles [18,19], these methods often require the suspension of water flow, which cannot fully elucidate the mechanism of particle motion under seepage conditions. To overcome this limitation, numerical simulations have emerged as a powerful alternative. Additionally, advances in computer technology allow researchers to model the particle migration processes with high accuracy. The numerical simulation method can offer powerful three-dimensional visualization capabilities, which enables the visualization of migration and clogging processes at the microscale during the experiment [20]. Therefore, these advantages make numerical simulation an indispensable tool for addressing scientific problems.

Numerical simulation methods, equipped with versatile functions and modules, have been widely used in geotechnical applications, water conservancy, energy production, and other fields [21,22,23]. They are particularly effective in capturing microscale morphological changes in materials [24,25,26]. Soil and sand, often modeled as aggregates of discrete particles, are well-suited for analysis using the discrete element methods (DEMs). In such models, the motion law between particles is calculated using Newton’s second law, while groundwater seepage is solved by a computational fluid dynamics (CFD) solver based on the Navier-Stokes equation to obtain the force from the liquid on particles. Coupled CFD-DEM simulations provide a robust framework for modeling the interaction between sandy media and fluids. Many scholars have used this method to study the motion of particles and fluids [27,28]. However, there are relatively few simulation studies on the influence of parameters such as particle size ratio, particle quantity, and weight on the migration process of fine particles in loose soil under groundwater seepage.

Studying the migration and clogging processes of fine particles under groundwater seepage conditions is beneficial for revealing the mechanism of internal erosion in loose soil and for preventing related natural disasters. This study considered loose soil as a porous medium and established a CFD-DEM coupling model to investigate the effects of particle concentration and particle size ratio on the migration and clogging processes of fine particles in loose soil under groundwater seepage conditions. The model was developed with reference to the standards of the United States Department of Agriculture (USDA) and defined a particle size of 1 mm as the threshold for distinguishing between coarse and fine particles. It assumes that coarse particles form the skeleton of porous medium, while fine particles are movable. Additionally, the model considers the porous medium to be saturated with groundwater, which serve as the primary driving force for particle migration. The innovative contributions of this study are as follows. Firstly, the migration rate and distance of fine particles with varying particle size ratios within porous media in loose soil was investigated. Subsequently, the influence of particle concentration on particle migration rate and distance was analyzed. Finally, a comprehensive analysis was conducted on the migration and clogging processes of different particle components in porous media, along with an evaluation of the feasibility of the CFD-DEM model for studying particle migration in loose soil. The findings of this study are expected to provide a scientific reference for understanding the migration characteristics of fine particles at the microscale.

2. Basic Modeling Principles

To simulate the infiltration effect of groundwater seepage on soil particles, the CFD-DEM coupling calculation method was adopted. PFC 5.0 (Particle Flow Code 5.0) is a simulation software designed to study discrete elements, such as soil particles, and it incorporates the CFD-DEM coupling method as part of its functionality. Within this software, the particle motion is modeled using the DEM module, which is governed by Newton’s second law and the force-displacement law for control and calculation [29,30]. The groundwater flow component in the model is represented through CFD grids, where flow dynamics are primarily calculated using the Navier-Stokes equations. This effectively simulates the fluid’s dynamic behavior during particle migration [29,30]. A key aspect of this approach is that as particles migrate within the CFD grid, the porosity of the grid changes, thereby influencing fluid flow [29]. In this study, the linear contact model was used to simulate the interaction between particles. A brief overview of the primary modeling principles is provided below.

(1)

Equations for the motion of groundwater

The study of groundwater movement in saturated porous medium is conducted using CFD methods, which are also employed by PFC software for fluid flow simulations. The primary focus is on groundwater flow within porous medium, where the fluid is assumed to be incompressible and of constant density. Fluid calculations are derived from the Navier-Stokes equations and momentum equations. Porosity and drag force terms are introduced to the basic Navier-Stokes equation to ensure effective coupling between the fluid and solid particles [29,30].

$${\rho }_f{\displaystyle \frac{\mathsf{\partial }ϵ\overrightarrow{v}}{\mathsf{\partial }t}}+{\rho }_f\left(\overrightarrow{v}·\nabla \right)\left(ϵ\overrightarrow{v}\right)=-ϵ\nabla p+\mu {\nabla }^2\left(ϵ\overrightarrow{v}\right)+{\overrightarrow{f}}_b$$

(1)

$${\displaystyle \frac{\mathsf{\partial }ϵ}{\mathsf{\partial }t}}+\nabla ·\left(ϵ\overrightarrow{v}\right)=0$$

(2)

where $ϵ$ is the porosity of the porous medium, $\overrightarrow{v}$ is the fluid velocity in porous flow, ${\rho }_f$ is the density of the fluid, ∇ is a gradient operator, $p$ is the fluid pressure, $\mu$ is the dynamic viscosity of the fluid, and ${\overrightarrow{f}}_b$ is the body force per unit volume.

(2)

Equations for the motion of solid particles

The motion of solid particles in this study was simulated using the DEM method, which is highly effective in modeling the behavior and failures of discrete materials. During the calculation of the deformation process, the motion of each particle is governed by Newton’s equations of motion. By determining the force acting on the particle, its subsequent motion can be calculated [31].

$$m_p{v}_p=m_{p}g+F_d+\sum _{c=1}^n{F}_c$$

(3)

$$I_p{\omega }_p=\sum _{c=1}^n{(R}_c\times F_c)$$

(4)

where m_p is the mass of the particles, $F_d$ is the drag force exerted by the fluid on the particles, $v_p$ is the translational velocity vector of the particle, ${\omega }_p$ is the rotational velocity vector of the particle, $I_p$ is the rotational inertia of the particle, $F_c$ is the contact force at each contact point of the particle, and $R_c$ is the vector from the center of the particle to the contact point.

The dragging force $F_d$ is derived from the buoyancy and fluid particle interaction:

$$F_d=\left({\displaystyle \frac{F_i}{1-ϵ}}-\nabla p\right)V$$

(5)

where $F_i$ is the vector of fluid–particle interaction, $ϵ$ is the porosity, $\nabla$ is a gradient operator, $V$ is average particle volume, and $P_f$ is the fluid pressure.

The contact force $F_c$ between two particles consists of both normal $F_n$ and tangential $F_s$ components. The contact model between particles is represented by a system of springs, dampers and sliders. The normal component of the contact force is expressed as follows:

$$F_n=K_n{d}_n^r+C_n{v}_n^r$$

(6)

where $K_n$ is the normal stiffness in the contact direction, $C_n$ is the normal damping coefficient in the contact direction, $d_n^r$ is the normal relative displacement between the contacting particle, and $v_n^r$ is the normal relative velocity between contacting particles.

The tangential component of the contact force is given by

$$F_s=K_s{d}_s^r+C_s{v}_s^r$$

(7)

where $K_s$ is the tangential stiffness in the contact direction, $C_s$ is the tangential damping coefficient in the contact direction, $d_s^r$ is the tangential relative displacement between contacting particle, and $v_s^r$ is the tangential relative velocity between contacting particle [29,32].

(3)

Coupling process of the fluid-solid interaction force

To achieve the coupling calculation between particles and fluids, the effect of fluid on a single particle is influenced by the distribution of particles within the fluid element. To enhance the accuracy of the calculation, it is essential to account for cases in which a single particle penetrates two or more fluid elements when determining porosity. The total force exerted by the fluid on a particle comprises both the drag force $F_d$ and buoyancy [32].

$$F_d={\displaystyle \frac{4}{3}}\pi r^3{\displaystyle \frac{F_b}{(1-ϵ)}}$$

(8)

$$F_f=F_d+{\displaystyle \frac{4}{3}}\pi r^3{\rho }_{f}g$$

(9)

where $r$ is the particle radius and $F_f$ is the total force exerted by the fluid acting on the particles.

By solving the above formulas, key fluid-related metrics such as pressure and flow rate can be determined for each fluid element. The interaction between the fluid and the particles drives the migration of fine particles within the medium’s skeleton, resulting in changes in the porosity of the fluid element. These changes in porosity, in turn, affect the fluid behavior. This iterative interaction ultimately establishes a bidirectional coupling computing effect between the particles and the fluid.

3. Model and Numerical Simulation Procedure

3.1. Model Setting

In this study, particles were classified into coarse particles and fine particles, with 1 mm serving as the threshold for this distinction. The particle size ratio of each experimental model was set to be greater than five or equal to five. According to the design criteria proposed by Terzaghi, the empirical value D15/d85 is a critical parameter for evaluating whether fine particles can migrate through the pores in the skeleton formed by coarse particles [33]. Parameters D15 and d85 require the designation of a specific particle size as the boundary between coarse and fine particles. D15 represents the particle size corresponding to a 15% cumulative percentage content of coarse particles, while d85 represents the particle size corresponding to an 85% cumulative percentage content of fine particles [33]. Many researchers regard D15/d85 as a reliable criterion for assessing particle migration in porous media [34]. To observe the migration of fine particles in this study, different particle size ratios between coarse and fine particles were defined for the experimental group. This distinction between coarse and fine particles is beneficial for studying the effects of particle size ratios on porous media. Fine particles were generally defined as those with sizes smaller than 1 mm and greater than 1 micrometer; thus, the influence of other subtle forces was ignored during the movement of fine particles.

As shown in Figure 1a, the dimensions of the simulation model established in this study are 40 mm × 40 mm × 210 mm. The model consists of two sections: the upper part, which is 50 mm high and contains transferable fine particles, and the lower part, which is 160 mm high and filled with skeleton particles. During the simulation, the fine particles from the upper part were allowed to migrate into the porous medium. The lower part was designed to simulate the migration of soil particles and their physical clogging during groundwater seepage.

The model is governed by the following principles. The model contains 2428 skeleton particles (Figure 1a), which are assumed to be stationary and do not migrate or move during the simulation. The porosity of skeleton particle medium is 0.379. Different particle sizes were color-coded to facilitate the observation of migration or clogging locations of fine particles during the simulation. Monitoring particles were also preset to track displacement and motion characteristics, enabling an analysis of the depth of particle migration and infiltration within porous media. Ultimately, the migration and clogging behavior of fine particles under groundwater seepage was determined

The sand particles comprising the porous medium are abundant and dense. To better capture the influence of particle size ratio and particle weight on the migration process, all particles in the model were treated as perfectly spherical. This simplification ignored the influence of particle shape. However, the model accounted for the effects of particle friction, which plays a crucial role in simulating the interactions between migrating particles. The actual friction coefficient of natural sand particles typically ranges from 0.5 to 0.7. In this study, considering the slight variations caused by fluid infiltration, the friction coefficient of particles was set to 0.5. Additionally, since the migration of fine particles is primarily influenced by water flow, the effect of gravity was neglected in the model calculations. The density of fine particles is mainly based on the density of natural sand particles. Parameters for the model were established with reference to prior modeling studies and experimental data [35,36,37]. The key parameters used in this study are summarized in

Table 1. Parameters used in the numerical simulation.

Parameters	Material Type
	Porous Medium Particle	Migrating Fine Particle	Wall	Fluid
Density (kg/m3)	2450	2160	-	1000
Normal stiffness, kn (N/m)	6.0 × 103	4.0 × 103	1.0 × 104	-
Shear stiffness, ks (N/m)	3.0 × 103	2.0 × 103	1.0 × 104	-
Friction coefficient	0.5	0.5	0.5	-
Viscous coefficient	-	-	-	1.0 × 10−3
Radius (m)	2.5 × 10−3	-	-	-

.

3.2. Fluid and Simulation Settings

As shown in Figure 1b, the simulated flow domain was discretized into 8 × 8 × 25 = 1600 grids along the x, y and z directions, respectively. The model assumed that the sidewalls (the surfaces along the XZ and YZ planes) are impermeable boundaries. This study primarily considered fluid flow along the Z direction. The plane at Z = 0.21 m served as the fluid inlet, while the plane at Z = 0 was used as the fluid outlet. The seepage pressure at the outlet was set to 0. The parameter settings were based on Zhang’s findings [37] from fluid–structure coupling simulation experiments. They set the step size for particle computation to 1 × 10⁻⁶ and the step size for fluid computation to a similar size. The step sizes for particle and fluid calculations were set to 1 × 10⁻⁶ and 1 × 10⁻⁴, respectively.

The migration of fine particles in porous media is influenced by several factors, including particle size ratios, particle concentration, and particle composition. In this study, 1 mm was adopted as the boundary between coarse and fine particles. Coarse particles constitute the skeleton of the porous media, while fine particles are migratory. The particle size ratio (D/d) is defined as the ratio of coarse particle size D to fine particle size d. Particle concentration refers to the number of particles generated within a fixed volume. Different particle compositions refer to fine particles having different particle size ratios and concentrations. To study the migration behavior of fine particles in porous media under different particle size ratios and particle concentrations, three experimental series were designed for analysis and comparison, as summarized in

Table 2. Analysis cases for the numerical simulation study.

Analysis Case	Group	Radius (m)	Particle Size Ratio (D/d)	Number	Density (kg/m3)
Series A	AG-1	8.30 × 10−4	3	200	2160
	AG-2	5.00 × 10−4	5	200	2160
	AG-3	2.50 × 10−4	10	200	2160
	AG-4	1.78 × 10−4	14	200	2160
	AG-5	1.25 × 10−4	20	200	2160
Series B	BG-1	8.30 × 10−4	3	43	2160
	BG-2	5.00 × 10−4	5	200	2160
	BG-3	2.50 × 10−4	10	1600	2160
	BG-4	1.78 × 10−4	14	4432	2160
	BG-5	1.25 × 10−4	20	12,800	2160
Series C	CG-1	5.00 × 10−4	5	100	2160
	CG-2	5.00 × 10−4	5	200	2160
	CG-3	5.00 × 10−4	5	400	2160
	CG-4	5.00 × 10−4	5	800	2160
	CG-5	5.00 × 10−4	5	1600	2160

. For consistency, all experimental groups were initialized with the same flow rate. During the simulation, the seepage characteristics of each group—considering different particle size ratios, particle concentrations, and particle compositions—were observed over the same seepage calculation period. The model was saved every 0.2 s, with the total simulation time for seepage set to 2 s.

Previous research has demonstrated that a stable skeleton structure in soil requires a sufficient quantity of coarse particles. When the particle size of fine particles is smaller than the pore size of the skeleton, fine particle migration may occur [1]. Based on this principle, the radii of the skeleton particles in the porous medium for all experimental groups were set to 2.5 mm. Throughout the numerical simulation process, the coarse skeleton particles were assumed to remain stationary, unaffected by flow rate or displacement. This approach ensured that the migration process of fine particles could be better observed. Meanwhile, to minimize errors arising from the arrangement of coarse particles, the same skeleton structure was used across all simulations.

As shown in Table 2, numerical simulations were conducted on 15 samples to examine the effects of particle size ratios, particle quantities, and weights on fine particle migration. These samples were further classified into three series for systematic analysis. The green particles in Figure 1a represent movable fine particles. Table 2 provides detailed parameter information for each sample, including the sample ID, particle radius, particle size ratio, particle count, and fine particle density. Series A (AG): This series consists of samples AG-1, AG-2, AG-3, AG-4, and AG-5, each containing 200 fine particles. The particle size ratios are 3, 5, 10, 14, and 20, respectively. Series B (BG): Samples BG-1, BG-2, BG-3, BG-4, and BG-5 belong to Series B, with particle size ratios of 3, 5, 10, 14, and 20, respectively. The numbers of fine particles in this series are 43, 200, 1600, 4332, and 12,800, respectively. Series C (CG): This series consists of samples CG-1, CG-2, CG-3, CG-4, and CG-5, all with a fixed particle size ratio of 5. The numbers of fine particles in this series are 100, 200, 400, 800, and 1600, respectively. In all experiments, fine particles were generated at the entrance of the porous media. The simulation process for each experimental group followed a similar procedure.

4. Results

4.1. Validation of the Model Between Fluid and Particles

In this study, the fluid flow in porous media was modeled as the movement of fluid around a large number of fixed spherical particles. To validate the accuracy of the simulated interaction between the fluid and particles, the force acting on a single particle in a uniform flow field was analyzed. Specifically, the relationship between the drag coefficient and the Reynolds number (Re) was compared and, subsequently, compared with findings from previous numerical studies. The relationship is illustrated in Figure 2, which depicts a clear non-linear relationship between the drag coefficient and the Reynolds number. As observed in Figure 2, the variation in the drag coefficient was relatively insignificant in the range of Reynolds numbers between 1 and 10, with a gradual change trend. However, the drag coefficient exhibited a more pronounced change when the Reynolds number lay between 0.1 and 1. This result aligns well with the research findings of Rimon, who investigated the changes in resistance and Re of water flowing around a sphere within a low Reynolds number range (0.4–1000). Rimon’s results also demonstrated a non-linear relationship between the drag coefficient and the Reynolds number [38]. Therefore, current simulation methods can effectively simulate the dynamic characteristics of groundwater in porous media.

4.2. Particle Migration Process

Figure 3 shows the migration behavior of fine particles within the sample at different times. In the simulation model, the inlet flow velocity was set to 0.1 m/s. At the initial moment (t = 0 s), fine particles were randomly generated and relatively uniformly distributed in the upper region of the model. As the simulation began, the red fine particles started to migrate downward under the influence of the water flow. As revealed in Figure 3a, at t = 0.1 s, the red fine particles migrated from the generation zone toward the porous media due to the water flow. By t = 0.7 s, a small portion of fine particles migrated into the porous medium in each experimental group. However, the majority of fine particles—particularly those with lower mobility—either migrated slowly or deposited near the inlet of the porous medium. By t = 2.0 s (Figure 3c), a significant number of fine particles remain clogged at the surface of the porous medium, and only a small fraction of fine particles had successfully entered the porous medium. From Figure 3b,c, it can be observed that the migration state of the particles did not change significantly over time. Similarly, the fluid flow state, as shown in Figure 3e,f, also exhibited minimal variation. These observations indicated that more fine particles had been deposited or clogged, which further affected the fluid dynamics. In addition, a small number of fine particles were capable of rapidly migrating to deeper locations within the porous medium. This behavior was likely influenced by the particle size ratio. In light of this observation, multiple particle size ratios were investigated in this study to evaluate their impact on the migration process of fine particles.

4.3. Velocity and Displacement of Fine Particles

Figure 4 presents the migration rate of monitored particles along the migration direction (Z direction) for each experimental group. An analysis of the velocity data of particles during migration revealed that, in the initial stage, the velocity of fine particles in the Z direction exhibited an upward trend. However, as particles entered the porous medium over time, their velocity began to fluctuate frequently, with large amplitude in the fluctuations. This suggested that the particles encountered resistance during migration within the porous medium. The collisions between fine particles during movement further contributed to changes in their migration directions, thereby altering their migration behavior. Meanwhile, the observed rapid increase in particle velocity during migration indicated that the pore channels facilitated the simultaneous flow of both fine particles and liquid.

In this study, all fine particles commenced migration simultaneously. The length of the porous medium was set to 0.16 m. Figure 5 illustrates the displacement variations in monitored particles over time for each experimental series. It was found that the migration distance of monitored particles increased rapidly over time and stabilized after 1.5 s. In Series A, the final displacements of monitored particles in AG-1 and AG-2 were 0.0215 m and 0.0923 m, respectively; while the displacement of the monitored particles in AG-3, AG-4, and AG-5 was approximately 0.16 m. Similar observations were made for Series B. With the exception of BG-1 and BG-2, the maximum displacement of monitored particles in BG-3, BG-4, and BG-5 was also approximately 0.16 m. In contrast, the displacement of monitored particles in Series C along the Z direction was less pronounced. The final displacements of monitored particles in CG-1, CG-2, CG-3, CG-4, and CG-5 were 0.0524 m, 0.0923 m, 0.0933 m, 0.0923 m, and 0.0509 m, respectively. This indicated that when the particle size ratio exceeded five, the particle size ratio became the dominant factor affecting displacement. Conversely, when the particle size ratio was less than or equal to five, the weight and quantity of fine particles were the primary factors influencing displacement. In addition, a comparison of Figure 5a,b revealed that while the final displacements of fine particles in Series A and B were 0.16 m, there was a noticeable time difference. Specifically, in Series B, the increase in the number of fine particles did not significantly affect the migration distance. However, it did result in a longer migration time compared to Series A.

4.4. Fine Particle Clogging Area

Figure 6 illustrates the migration and clogging positions of fine particles under different influencing factors. The porous media skeleton in the model was divided into three sections along the Z direction: the entrance section, Q; the middle section, Z; and the exit section, W. The lengths of sections Q, Z, and W are 0.05 m, 0.06 m, and 0.05 m, respectively. Section Q represents the surface area of the porous medium. Section Z represents the middle region of the porous medium. Section W represents both the end and the deeper locations of the porous medium. When fine particles are only located within section Q and fail to progress further, it indicates that particle migration is hindered, making further migration difficult. Conversely, if the fine particles are located within section W, it suggests their migration process is less affected. As shown in Figure 6a, at t = 0.1 s, fine particles from different series were distributed within section Q. By t = 0.7 s (Figure 6b), some fine particles gradually migrated into sections Z and W. At t = 2.0 s (Figure 6c), there was a slight increase in the number of fine particles in section W. Overall, during the migration of fine particles, section Q contained significantly more fine particles than sections Z and W. This behavior could be attributed to the screening effect of fine particles during their infiltration and migration, which led to clogging near the surface of the porous medium. Similar phenomena were also observed in previous studies [39,40,41]. It is worth noting that, in the early stages, a decrease in particle size ratio or an increase in quantity intensifies the fine particle clogging. Therefore, more attention needs to be paid to the migration characteristics of fine particles in section Q over time.

To further investigate the effects of weight, quantity, and particle size ratio on the migration ability of fine particles under groundwater seepage conditions, the fine particle data from the numerical model were reorganized to calculate the percentage of fine particles clogging the surface of porous medium; the results are illustrated in Figure 7. The results revealed that when the particle size ratios were three and five, the number of fine particles trapped in section Q initially increased before stabilizing. Notably, a smaller particle size ratio prolonged the time required to reach a stable state and reduced the migration rate. In Series A and B, when the particle size ratios were 10, 14, and 20, the number of fine particles retained in section Q showed a trend of first increasing, then decreasing, and finally stabilizing. When the particle size ratio exceeded five, it became the dominant factor contributing to clogging. In contrast, when the particle size ratio was less than or equal to five, an increase in the weight and number of fine particles caused them to aggregate on the medium’s surface. This aggregation reduced the migration speed of fine particles, thereby negatively affecting their movement efficiency.

To analyze the migration and clogging characteristics of fine particles, the distribution data at t = 2 s were collected and organized. Figure 8 displays the cumulative distribution of fine particles at different depths at this time point. In Series A, over 90% of fine particles in AG-1 and AG-2 remained within section Q. However, in sections Z and W, the proportion of fine particles in AG-3, AG-4, and AG-5 significantly increased, with average increases of 16.50% and 13.83%, respectively, compared to AG-1 and AG-2. In Series B, the larger the particle size ratio, the greater the accumulation of fine particles in sections Z and W. Compared with BG-1, the accumulation percentage of fine particles in sections Q, Z, and W of BG-5 changed by −58.34%, 26.88%, and 31.46%, respectively. These findings suggest that in loose soil, soil particles with small particle size ratios were more prone to clogging the surface of porous media, while soil particles with large particle size ratios tended to migrate farther and were more likely to cause soil erosion. In Series C, over 90% of fine particle migration and deposition occurred within section Q. Across all experiments, when the particle size ratio was larger than 5, more than 20.00% of fine particles successfully passed through the porous medium. Furthermore, at the same particle size ratio, increasing the number of fine particles had a relatively smaller impact on their migration and clogging behavior.

5. Discussion

5.1. Effect of Particle Size Ratio

The simulation results from this study demonstrated that the particle size ratio could serve as an important indicator for assessing the risk of fine particle clogging. Numerous studies have identified particle size as a critical parameter in understanding particle migration behavior. Researchers have extensively evaluated the influence of particle size on particle migration behavior from various perspectives. By incorporating different indicators such as particle content and the nonuniformity coefficient, existing studies have empirically analyzed the migration characteristics of soil particles to investigate the particle infiltration and migration processes in soil samples [16,42]. Previous experimental results have consistently shown that the particle size ratio and concentration have significant effects on migration behavior. The model used in this study yielded similar results. Nonetheless, a key distinction of the numerical simulation methods is their ability to provide a microscopic perspective of fine particle migration under groundwater seepage, allowing for the observation of dynamic migration characteristics and the capture of particle distribution at different times. The model results also revealed that when the particle size ratio was less than or equal to five, more than 90% of fine particles aggregated on the surface of the medium. When the particle size ratio was greater than five, fine particles achieved a longer migration distance.

Analyzing parameters such as the particle size ratio can improve our understanding of the migration characteristics of fine particles within pore channels. The simulation results from Series A and B confirmed that the particle size ratio was related to the migration ability of fine particles in the medium. A comparison of displacement and distribution patterns of fine particles in Series A and B indicated that small particle size ratios were more likely to cause surface clogging of the medium, while large particle size ratios were associated with faster migration rates and greater migration distances. Increasing the mobility of larger particle size ratios can facilitate internal soil erosion, potentially triggering geohazards. The underlying mechanism is that when the particle size ratio is very large, small particles can migrate smoothly through the porous medium, and a greater number fine particles can migrate to the deeper locations of the medium. However, when fine particles with diameters comparable to certain pore channel sizes are involved, these particles may encounter pore channels that are difficult to traverse. These slightly larger fine particles may either be trapped within the pore channels or bounce off the walls of the pore channels and migrate to deeper locations through other pore channels. Therefore, reducing the proportion of large particle size is an effective measure for preventing geological hazards or controlling the migration of particulate pollutants.

Soil samples commonly found in nature typically have mixed particle sizes, which means that migrating soil particles also vary in size, thickness, and fineness. In the samples used in this study, the focus was primarily on coarse particles and fine particles with uniform particle size. However, for mixed particle sizes, it is important to choose representative particle sizes to calculate the particle size ratio of fine particles. This is why many scholars adopt parameters such as average particle size or continuous particle size in their studies. Further studies are needed to explore fine particle migration using the particle size ratio, as well as the influence of particle size on migration behavior, which holds significant practical value.

5.2. Analysis and Prospect of Particle Clogging

The concentration of fine particles plays a critical role in their migration behavior and has been extensively studied in both laboratory settings and practical applications. As demonstrated by the samples in Series B and C, increasing the number of particles per unit volume directly leads to a higher fine particle concentration, thereby intensifying the inter-particle collisions. This reduces the migration capability of certain fine particles and hinders their smooth movement into porous media. Consequently, the migration process slows down, potentially causing the deposition of some fine particles within porous media.

For smaller fine particles, however, an increase in particle concentration does not necessarily exert a significant effect on the channel. Similarly to an hourglass, fine particles continue to move freely, regardless of their quantity or concentration. However, when the particle size closely matches the pore channel size, an increase in particle concentration can impact the connectivity of the pore channels. This can alter pore channels and cause changes in porosity. Therefore, in flow-driven models, the particle size ratio has certain limitations, and a specific range of particle size ratios is more conducive to fine particle migration. Therefore, further exploration of this phenomenon is essential for improving our understanding of fine particle behavior in porous media.

In fact, the migration of fine particles driven by groundwater flow in porous media is inherently a complex process. This study investigated the migration and clogging characteristics of fine particles in various components of loose soil under groundwater seepage. In this research, soil particle sizes were primarily defined within the range of 0.1 to 10 mm, with 1 mm designated as the threshold distinguishing coarse particles from fine particles. Future research could explore larger particle sizes to achieve a more comprehensive understanding of fine particle migration behavior. In addition, incorporating additional mechanical properties of particles is essential to deepen insights into their interactions within porous media.

Numerical simulation methods such as the CFD-DEM method can accurately describe the migration and clogging of fine particles in porous media under groundwater seepage conditions. Through simulation experiments, it is possible to clearly observe changes in the position and movement of individual particles at any time. These methods not only allow for the adjustment of particle and groundwater flow parameters but also enable the customization of the porous medium skeleton. By modifying the migration environment for the migrating particles, numerical models can closely replicate real-world scenarios observed in laboratory or field experiments. This makes the CFD-DEM modeling approach a highly efficient and reliable tool for studying the migration behavior of fine particles under groundwater seepage.

Notably, it is meaningful to study the migration law of fine particles in the medium, whether they migrate freely or become clogged. In terms of engineering construction, the large-scale migration of fine particulate can affect the structural stability of soil and lead to macroscopic instability, such as slope failure or soil erosion. Similarly, in environmental pollution research, contamination in loose soil often manifests as fine particles. Understanding the migration pathways and behavior of these particles can effectively aid in controlling the diffusion of pollutants. Meanwhile, detergents may also be in the form of fine particles. The findings of this research indicate that reducing the particle size ratio of particulate pollutants helps to intercept them on the surface of the medium, thereby preventing pollutants from diffusing deeper and achieving better cleaning effects.

6. Conclusions

In this study, a CFD-DEM model with different components was employed to investigate the microscale characteristics of fine particle migration and clogging in loose soil under groundwater seepage. The analysis focused on the effects of particle size ratio, particle quantity, and weight on the migration of fine particles within the medium under groundwater seepage. The main conclusions are as follows:

In the early stages, the migration and clogging of fine particles were jointly influenced by the particle size ratio, particle mass, and weight. A decrease in particle size ratio and an increase in the number and weight of fine particles prolonged their residence time on the medium’s surface, though this hindrance diminished over time.

The particle size ratio is the principal factor affecting both migration and clogging of fine particles. When the particle size ratio of fine particles with the same weight was less than or equal to five, a smaller particle size ratio led to a higher likelihood of clogging on the surface of porous medium. Conversely, when the particle size ratio exceeded five, an increase in this ratio resulted in faster migration speeds, longer migration distances, and even lateral movements within the medium. These findings indicated that in loose soil, particles with larger particle size ratios were more likely to cause erosion.

The clogging of fine particles mainly occurred on the surface of porous medium. Experimental results demonstrated that the fine particles causing clogging in section Q accounted for approximately 40% to 90% of the total. Furthermore, when the particle size ratio was greater than five, over 20.00% of fine particles could migrate smoothly through the porous medium. This indicated that reducing the proportion of soil particles with large particle size ratios was beneficial for preventing and controlling internal erosion.

Although numerical simulation still has certain limitations, it can address issues that cannot be described or observed in laboratory experiments. The CFD-DEM model established in this study facilitates the investigation of the migration and clogging mechanisms of fine particles under groundwater seepage. The findings provide new insights for the prevention and treatment of natural disasters such as soil erosion and particle pollutant migration in loose soil.