# Fine Grain Dispersion Behavior in 3D Spherical Packing-Numerical and Experimental Investigations

Fan Chen, Abhijit Hegde, Antoine Wautier, Nadia Benahmed, Pierre Philippe

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Fan Chen, Abhijit Hegde, Antoine Wautier, Nadia Benahmed, Pierre Philippe. Fine Grain Dispersion Behavior in 3D Spherical Packing-Numerical and Experimental Investigations. IS Grenoble 2024, Sep 2024, Grenoble, France. IOP Conference Series: Earth and Environmental Science, 1480 (1), pp.012086, 2025, 10.1088/1755-1315/1480/1/012086. [hal-05457901](https://hal.inrae.fr/hal-05457901v1)

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# Fine Grain Dispersion Behavior in 3D Spherical Packing-Numerical and Experimental Investigations

To cite this article: Fan Chen et al 2025 IOP Conf. Ser.: Earth Environ. Sci. 1480 012086

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# FINE GRAIN DISPERSION BEHAVIOR IN 3D SPHERICAL PACKING-NUMERICAL AND EXPERIMENTAL INVESTIGATIONS

Fan Chen¹✉, Abhijit Hegde¹, Antoine Wautier¹ Nadia Benahmed¹ Pierre Philippe¹

¹ INRAE, Aix-Marseille Université, RECOVER, Aix-en-Provence, France

✉ fan.chen@inrae.fr

## Abstract

Suffusion-induced loss of fine grains can induce mechanical instabilities in granular soils. A conceptual countermeasure could be the re-injection of fines from upstream to induce clogging in the soil matrix as a remediation method. This work attempts to study the dry and fluid-driven infiltration behaviors of fine sand in granular columns from numerical and experimental aspects. The base soil used in this work adopts the particle size distribution (PSD) of typical Hostun Sand HN1/2.5 mm. Different governing factors, such as size ratio *R*, base soil packing density, particle morphology (angular Hostun 1/2.5 and spherical glass beads) and flow conditions (operated by peristaltic and gear pumps), are analyzed. The results from numerical and experimental aspects on the fine retention distribution within coarse grain matrix are compared and a simple probabilistic model based on pore-constriction size statistics is put forward to interpret the clogging distributions.

## 1. Introduction

Suffusion, a prevalent issue in geotechnical engineering, refers to the internal erosion process where finer soil particles are washed away by fluid flow, resulting in the potential loss of the finer fraction of the soil. This process may significantly undermine the mechanical stability of the soil, posing a risk of structural damage or failure over time [1, 2, 3]. The phenomenon mainly involves the percolation of fines driven by internal flows [4, 5]. To counteract suffusion, one strategy involves using the hydraulic flow to reintroduce fine particles into the coarser soil matrix. Successful remediation of internal erosion via fine particle infiltration necessitates a comprehensive understanding of the factors influencing this behavior. Research on grain infiltration has considered variables such as the size ratio of coarse and fine particles *R*, the amount of injected fine particles (affecting collective arching), the coefficient of restitution between particles, and the friction coefficient [6]. Traditionally, studies simplified the infiltration process using mono-dispersed, gravity-driven infiltration where the particle size ratio is within a limited range, often overlooking the complexities of fluid-driven infiltration in poly-dispersed soils with varying packing density conditions that are typical in the remediation methods for internal erosion. Thus, this work attempts to study the dry and fluid-driven fine grain infiltration behaviors from numerical and experimental aspects. The results from numerical and experimental aspects on the fine retention distribution within coarse grain matrix are compared and a novel probabilistic model based on pore-constriction size statistics is used to interpret the characteristic infiltration depth.

## 2. Experimental and numerical model setups

Using a suffusion permeameter presented in Fig.1(a), experiments have been carried out investigating the infiltration behavior under the coarse columns of different relative densities, the shapes of the coarse grains, the different injection flow conditions, etc [7].

Samples are prepared following moist tamping procedure with 7 layers of 2 cm thick, after mixing it thoroughly with 2-3% of water by mass. The final dimensions of the sample are 14 cm×7 cm. Once prepared, the samples are then flushed with CO₂ gas for about 20 minutes, and at a pressure of

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20kPa, due to its affinity to readily dissolve in water, thereby making saturation easier. Then the samples are saturated with water by applying a flow rate of 50 ml/min, from the bottom of the suffusion permeameter to the top. Once the saturation is completed, the injection experiments are performed by applying a downward uniform suspension fine flow on the samples. Differential pressure sensors are mounted on the permeameter in order to track the changes in hydraulic conductivity due to the migration of fines inside the coarse granular column.

<figure><img src="image_4.png" /><figcaption>Figure 1. (a) Suffusion permeameter for fine injection; (b) Numerical model for fine injection gravity- and fluid-driven by coupled DEM-PFV.</figcaption></figure>

Primary experiments were carried out on Hostun sand 1/2.5 as the coarse matrix, with a $D_{50}$ of 1.7mm and $C_u$ of 1.4. Rounded Fontainebleau sand is adopted as injecting fine grains with $d_{50}$ of 0.21mm, giving a size ratio of 8. Coarse columns were prepared at a relative density of 20% and 40%. Two different techniques were explored to inject the fines into the coarse layer, either using the sandwich method by placing a layer of fines inside the top-most layer of the coarse column or by introducing the same amount of fines in the form of a suspension at a fines concentration of 0.25g/L (as formation of filter cakes is rapidly observed at concentration larger than this). To explore further the shape effects, Hostun sand and Fontainebleau were replaced by spherical glass beads with the same PSD. Experimental results show that there is a difference in the amount of fines that one can inject with the sandwich method as opposed to when the fines are introduced as a suspension, but the essential characteristics of the infiltration behavior remain unchanged, with the concentration of injected fines decreasing exponentially with depth.

To obtain a micro-mechanical perspective, Discrete Element simulations (DEM) were conducted in parallel with the experiments. Numerical columns, with the same PSD used in our experiments, are generated using the gravity deposition method by tuning the inter-granular friction angle to reproduce the densest ($e = e_{min} = 0.61$) and the loosest ($e = e_{max} = 0.85$) sand columns. The same amount of fine particles of varying size $d$ (leading to $R = D_{50}/d$ from 5 to 12), were randomly positioned in the central area above the column (to avoid being influenced by boundary effects) and then were released under either gravity or hydraulic force resulting from an internal fluid flow (Fig.1(b)) for the two extreme densities. The inter-particle friction coefficient is set to 0 during the infiltration process. The gravity in dry infiltration cases is enlarged by 1000 times to reduce computational cost. In the fluid-driven infiltration case, the granular filters were exposed to a hydraulic gradient of 5.0 imposed in the same direction as gravity as shown in Fig.1(b). All the simulations are stopped either when all fine particles have either been trapped or reached the bottom of the column.
### 3. Fine retention distribution

From the numerical modeling, Fig.2 displays the gradual sieving process of fines using the passing fraction of fine grains, that is, the percentage of fines able to pass through a given depth along the column. As expected, the fines are filtered within a short distance with a smaller $R$. The comparison between Fig.2 (a) and (b) highlights the impact of the packing density. The curves in loose cases move to the upper right compared to the dense one, showing an enhanced penetration depth. Experimentally, the essential nature of the infiltration behavior remains the same, with a strong exponentially decaying profile in both cases as shown in Fig.2(c). We observe that the amount of fines retained per layer is higher in the case of angular Hostun sand, as more fines are allowed to pass through the filter when it is made of spherical glass beads.

<figure><img src="image_5.png" /><figcaption>Figure 2. Passing fraction curves of fines in numerical fluid-driven infiltration along penetration depth in dense (a) and loose (b) columns and experimental inside the coarse filter layer made up of angular Hostun sand and spherical glass beads.</figcaption></figure>

A global exponential fitting curve can be adopted for the passing fraction of fines retention $P(z) = e^{(-z/L_0)}$, where $z$ is the penetration depth. A rather exponential growing pattern of $L_0$ with $R$ is found in both loose and dense columns, and the mean traveling distance of fines in the loose column is two or three times greater than in the dense one. The magnitudes of $L_0$ obtained from experiments are also comparable between the two cases (14.0 for angular Hostun sand and 17.0 for spherical glass beads), and are close to the characteristic infiltration depth obtained from numerical simulations. These results support the use of spherical-shaped particles for simulations. Finally, with fines suspensions, injection experiments were also performed at different flow rates. It is found that the final profile of the fines inside the coarse granular column is unaffected by the flow velocity. Fluctuations were further introduced into the flow but was found not to affect the final fines profile.

### 4. Probabilistic model for interpretation of $L_0$

A probabilistic model is proposed here to predict fine retention in soil, based on the diameter of fine particles $d$ and pore-constriction size statistics. Knowing the probability density functions for constriction sizes, we can define the probability $P_d$ that a fine particle of diameter $d$ can pass through a constriction in the coarse matrix. Under assumptions of a homogeneous pore network and equal spacing of constrictions, the model the model relies on two parameters: the probability $P_d$ for a grain of diameter $d$ to go through a constriction and the distance $\Delta z$ between two successive constrictions. Knowing the probability density functions for constriction sizes, $P_d$ determined as the fraction of constrictions larger than $d$ ($d_{cons} > d$). Assuming a fixed pore size $D_{p50}$ as the median value of pore size distribution, the local penetration depth increments by $\Delta z$ can be estimated by the specific granular configuration in Fig.3(a):
$$ \Delta z = \lambda D_{p50} = \frac{\sqrt{6}}{3(\sqrt{6} - 2)} D_{p50} \quad (1) $$

Under these hypotheses, the fine retention probability decays exponentially with depth, allowing the computation of characteristic decay length $L_0$ from:

$$ L_0 = \frac{-1}{(3 - \sqrt{6})} \frac{D_{p50}}{\ln(P_d)} \quad (2) $$

Simulations validate the model by showing a linear trend between the log of $L_0$ and R across different soil densities, confirming that the average probability $P_d$ of fines passing through constrictions effectively captures the essential physics of infiltration. The proposed probabilistic model, governed by passing probability $P_d$ and the mean pore size $D_{p50}$, is proved to effectively predict $L_0$ of fine retention distribution, highlighting the model's potential utility in predicting soil infiltration phenomenon. For real materials, we may thus be able to predict the mean infiltration depth by estimating the mean pore size and the constriction size distribution.

<figure><img src="image_6.png" /><figcaption>Figure 3. Build-up of a probabilistic model predicting $L_0$: schematic of the ideal granular configuration and derivation of $\Delta z$ from $D_{pore}$ and $L_0$ obtained from simulations and probabilistic approach.</figcaption></figure>

## References

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[2] Bonelli, S. (2013). *Erosion in geomechanics applied to dams and levees*. John Wiley & Sons.

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[4] Sibille, L., Marot, D., and Sail, Y. (2015). A description of internal erosion by suffusion and induced settlements on cohesionless granular matter. *Acta Geotechnica*, **10**, 735–748.

[5] Luo, Y., Luo, B., and Xiao, M. (2020). Effect of deviator stress on the initiation of suffusion. *Acta Geotechnica*, **15**, 1607–1617.

[6] Cooke, M., Bridgwater, J., and Scott, A. (1978). Interparticle percolation: lateral and axial diffusion coefficients. *Powder Technology*, **21**, 183–193.

[7] Nguyen, C. D., Benahmed, N., Andò, E., Sibille, L., and Philippe, P. (2019). Experimental investigation of microstructural changes in soils eroded by suffusion using x-ray tomography. *Acta Geotechnica*, **14**, 749–765.