# Comparative Study of Three Fine Grains Infiltration Techniques to Re-Fill Granular Materials Eroded by Suffusion

Abhijit Hegde, Nadia Benahmed, Antoine Wautier, Pierre Philippe

► To cite this version:

Abhijit Hegde, Nadia Benahmed, Antoine Wautier, Pierre Philippe. Comparative Study of Three Fine Grains Infiltration Techniques to Re-Fill Granular Materials Eroded by Suffusion. Transport in Porous Media, 2026, 153 (2), pp.28. 10.1007/s11242-025-02271-4. http://dx.doi.org/10.1007/s11242-025-02271-4

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Comparative study of three fine grains infiltration
techniques to re-fill eroded granular materials by
suffusion

Abhijit Hegde¹*, Nadia Benahmed¹, Anotine Wauiter¹,
Pierre Philippe¹

¹INRAe, Aix- Marseille Univ., RECOVER, 3275 Rte. Cezanne,
Aix-en-Provence, 13100, France.

*Corresponding author(s). E-mail(s): abhijit.hegde@inrae.fr;

Contributing authors: nadia.benahmed@inrae.fr;

antoine.wautier@inrae.fr; pierre.philippe@inrae.fr;

**Abstract**

With the aim of remediating soils eroded by suffusion, three different techniques were explored and compared at the laboratory scale in this study to effectively infiltrate fine grains into a porous granular filter. In the first technique, which serves as a reference owing to its simple implementation in the field conditions, a pure layer of fine grains is deposited on the upstream side of the filter. However, this technique is found inefficient due to a collective effects between the fine grains which induces formation of surface cake, preventing thus their penetration into the filter. A second technique is therefore proposed in which the fine grains are mixed homogeneously with coarse particles and deposited on the upstream of the filter. Besides, a third technique was designed, where the fine grains are put in suspension in the water seeping through the filter in order to limit their collective clogging. The influence of size ratio and fine grains shape for both the mixture and suspension techniques, and fine grains shape in the case of suspension technique were also explored. For the latter, the cumulative efficiency was further investigated through multiple rounds of infiltration. The results showed that, for a given size ratio between the coarse and fine grains, there is a significant increase in the amount of infiltrated fine grains for the mixture and suspension techniques, that is respectively twice and eight times larger than
the value obtained with the reference one, respectively. In the mixture technique, fine grains infiltration is found to increase with the size ratio up to a limiting value whereas, in the suspension method, it decreases as the size ratio increases. Moreover, rounded fine grains are found to infiltrate more easily than angular ones. This work should contribute to improve engineering protocols for achieving deep infiltration through the selection of an appropriate fine grains infiltration technique, with the objective of developing an effective remediation method.

**Keywords:** Fine-grains infiltration, Remediation of eroded embankments, Depth filtration, Preferential flowpaths

# 1 Introduction

Instances of migration and filtration of fine grains in porous granular media occur in both natural phenomena and engineering applications such as internal erosion by suffusion of soil [1-4], sediment transport across river beds [5-7], water filtration [8-10], microplastics intrusion [11-14], and during oil and petroleum extraction [15, 16]. This wide range of contexts has led to extensive experimental and numerical investigations across geotechnical, hydraulic, environmental, chemical, and petroleum engineering. In various contexts, such as petroleum extraction and sediment transport in rivers, filtration of fine particles can lead to adverse outcomes. In petroleum production, the clogging of extraction pathways can indeed significantly reduce yield and operational efficiency [16]. In natural systems like riverbeds, excessive deposition of sediment can harm local ecosystems by hindering fish spawning and contributing to biodiversity loss [7]. Conversely, controlled filtration can play a protective role in many engineered systems, such as in the stabilization of river embankments, earthen dams, and the treatment of wastewater. Despite the contrasting outcomes, these phenomena are governed by the same fundamental transport processes that control the migration and retention of fine particles in porous media.

In geotechnical engineering applications, particularly with regards to water-retaining structures such as embankments and earthen dams, fine grains transport
mechanisms are critically important as internal erosion processes are responsible for nearly half of the dams and dikes failures [17]. Erosion in earth dams is frequently associated with the development of concentrated leaks caused by the formation of cracks or suffusion as shown in Figure 1. For concentrated leaks, two types of core cracks can be identified, called as Type A core cracks which extend from the interior of the core to the downstream face and Type B cracks extending across the entire core of the dam [18, 19]. In order to prevent the continuation of internal erosion, granular filters composed of significantly coarser soils are commonly placed along the downstream end to intercept the migrating fine grains. Such filters have been hitherto designed keeping Type A cracks and suffusion in mind and several empirical criteria have been established through studies involving various combinations of fine and coarse grains [20–24]. Although erosion cannot be completely avoided, well-designed filters can promote self-healing, wherein certain combinations of the particle size between the core and filter materials, may encourage gradual closure of cracks and preferential flowpaths through the formation of a plug or filter cake at their interface and through depth filtration of fine grains [18, 25]. Nonetheless, as noted in previous studies [19], the self-healing process cannot be reliably predicted using current empirical approaches, and the recommended particle size ratios are often highly conservative[19]. Therefore, it is reasonable to consider alternative strategies to repair the damage caused by internal erosion, specifically suffusion. One such strategy would be to re-infiltrate the eroded fine grains back into the core to compensate for the previously eroded material, thereby reducing the progression of internal erosion while restoring the soil integrity. But it must be ensured that the infiltrated fine grains migrate deeper into the soil skeleton to reach the eroded zone and deposit within the internal pore network, rather than accumulating at the surface. In this context, a simple yet conceptually direct approach to achieve depth filtration involves placing a stock of pure fine grains on the upstream face of the hydraulic structure. These fine particles are then expected to be mobilized
and transported by the seepage flow, enabling their progressive infiltration into the fil-
ter zone [26], as depicted in Figure 1. However such a straightforward implementation
is likely to be inhibited by collective effects between the fine grains which can hinder
infiltration at the upstream face [2, 27, 28].

<figure><img src="image_2.png" /><figcaption>**Fig. 1:** Example of remediation of an eroded embankment through fine grains infiltration; adapted from [29]</figcaption></figure>

Therefore, to mitigate such collective behavior, it is essential to explore alterna-
tive infiltration strategies that promote the spatial separation and dispersion of fine
grains during their migration. In this regard, two alternative infiltration methods are
investigated in this study at the laboratory scale; the first involves by using a layer of
fine-coarse grain mixtures, while the second suspends the fine grains within the fluid
flow. The performance of both methods is systematically assessed by varying the size
and shape of the fine grains. Furthermore, multiple rounds of infiltration were per-
formed to evaluate the number of effective treatment cycles granular filters can undergo
before clogging completely. A study of this nature also accounts for real-world condi-
tions where the remediation must be implemented in multiple stages due to practical
constraints. This experimental study, focusing on the influence of infiltration condi-
tions, represents a novel contribution with substantial applicability to the sustainable
remediation of internally eroded earth structures. Approaches for implementing the
above three methods under field conditions are discussed.
Infiltration experiments were performed using a modified Suffusion Erosion Permeamter Test device (SEPT) [4]. The typical infiltration mechanisms and processes (referred to as infiltration behavior in this paper for brevity) are characterized and classified by analyzing the hydraulic signatures, the distribution of clogged fine grains and their average migration depth within the coarse soil (referred to as filter).

# 2 Experimental infiltration techniques

## 2.1 Materials

With regards to the filter material, a narrowly graded Hostun HN 1/2.5 sand composed of coarse sub-angular to angular grains was selected (Figure 2(a)). This particular choice for the filter material was made in line with the previous work conducted by Nguyen et al. [4], which provides a relevant background for comparing infiltration behavior with suffusion phenomena. The characteristic particle sizes commonly considered to be relevant for filtration, $D_{50}$ and $D_{15}$ of the sand, are equal to 1.71 mm and 1.37 mm, respectively, with a uniformity coefficient $C_u = 1.4$. The maximum and minimum void ratios $e_{max}$ and $e_{min}$ are about 0.61 and 0.82 respectively.

Fontainebleau NE34 sand, characterized by sub-rounded grains shape was selected as the fine grain material. Its characteristic particle sizes, $d_{50}$ and $d_{85}$, are equal to 0.210 and 0.285 mm, respectively, and the uniformity co-efficient $C_u$ is equal to 1.52. The grain size distribution curves for both, Hostun and Fontainebleau sand, are presented in Figure 2. The size of the infiltrating fine grains is quantified using the size ratio $R = D_{15}/d_{85}$ [30]. In order to obtain fine grains with different size ratios, $R$, the parent Fontainebleau sand was sieved into different size ranges as shown in Figure 2(b).

To specifically explore the fine grains' shape effects, Hostun HN34 sand, with angular grains and having similar $d_{50}$ and $d_{85}$ as Fontainebleau sand was also used as a fine material (Figure 2(c)). Note that this material was previously used for suffusion studies by Nguyen et al. [4].
<figure><img src="image_3.png" /><figcaption>**Fig. 2:** (a) Particle size distribution of the filter - Hostun HN 1/2.5 (b) Particle size distribution of the fine sand, Fontainebleau NE34. Fontainebleau fine grains are further sieved into different fractions to obtain different size ratios (c) Particle size distribution for the angular Hostun sand HN34 and rounded Fontainebleau NE34 fine sand.</figcaption></figure>

## 2.2 Specimen preparation

Infiltration experiments were conducted on specimen reconstituted in the Suffusion Erosion Permeameter Test (SEPT) device shown in Figure 3(a). This device was used to study suffusion mechanism previously by Nguyen et al. [4]. The specimens were prepared by the moist tamping method [31] in seven layers of 2 cm each, with the final dimensions being 14 cm in height and 7 cm in diameter. Loose sand with a relative density of 20% is considered in this study because of its susceptibility to liquefaction.
The sand prepared in this manner, without fines, represents an idealized, completely eroded state, assuming that all fine grains have been lost during suffusion. However, it is important to note that, in reality, the fine grains initially mixed in the soil with the coarse ones would never be totally removed by seepage flow. For example, Nguyen et al. [4] reported that around 50% of the fines were eroded from the specimen as a result of the suffusion processes. Nonetheless, evidence of specimen settlement during suffusion suggests that even fine grains lodged between coarser ones are indeed removed supporting the assumption underlying this protocol. Once prepared, the specimens are saturated, first by flushing carbon dioxide, CO₂, and then water through the specimen from bottom to top, at a small rate of 50 ml / min to minimize the disturbance of the loose microstructure within the specimen. Three different methods were used to carry out the infiltration, as presented in detail below.

## 2.3 Fine grains layer deposit method (Reference)

In field conditions, the simplest method for infiltrating fine grains into river embankments or dams is to deposit a stock of fine materials at the upstream end, allowing seepage forces to carry them into the body of the hydraulic structure (Figure 1). This process was replicated by placing a layer of fine sand between the uppermost filter layer composed of coarse grains, as illustrated in Figure 3(c). A sandwich configuration was used to prevent fine grains from rafting and floating out of the permeameter during the saturation stage. After specimen preparation and saturation, fine grains infiltration was performed under controlled flow conditions using linearly increasing flow rate, starting at 32 ml/min and reaching a maximum of 2500 ml/min. This flow ramp was essential as constant flow rates were ineffective at dislodging the fine grains placed in the uppermost layer of the filter. While such flow conditions may not be representative of in-situ conditions, the results are expected to provide upper bounds
<figure><img src="image_4.png" /><figcaption>**Fig. 3:** (a) Experimental setup used to perform infiltration of fine grains. (b) Schematic of the experimental setup. (c) Fine grains layer deposit method. (d) Fines and coarse grains mixture method. (e) Fine grains suspension method.</figcaption></figure>

for the infiltration efficiency of the fine grains layer deposit method, which serve as a baseline in this study.

## 2.4 Fines and coarse grains mixture method

To limit the collective effects among the fine grains, an alternative method, in which the average spacing between the fine grains is increased by thoroughly mixing them with the coarse grains of the filter, was implemented. This mixture is then placed at the upstream end of the filter, as shown in Figure 3(d). To maximize the infiltration
potential of fine grains while maintaining an under-filled condition that promotes migration, a fine grains content $F_c$ of 25% was chosen consistently with the numerical results obtained by Adesina et al. [32], which distinguish between under-filled and overfilled conditions. The fine grains content is defined as: $F_c = m_f/(m_c+m_f)$, where $m_f$ and $m_c$ represent the masses of fine and coarse grains, respectively. Infiltration was then carried out under controlled flow conditions, similar to those employed in the reference method. To implement this method in the field, the fine grains would need to be thoroughly mixed with coarse grains, gravel, and boulders, and then placed above the eroded zone at the upstream end of the embankment.

## 2.5 Fine grains suspension method

The third technique to increase further the average spacing between fine grains was to put them in suspension. To this end, the fine grains were placed separately in an air-tight reservoir and kept in suspension using a magnetic agitator placed inside the reservoir. The outlet of this reservoir is connected to the suffusion permeameter as shown in Figure 3(b). Infiltration process is then carried out by subjecting the specimen to a downward water flow transporting the suspension of fine grains at a constant flow rate of approximately 2500 ml/min. For each test, fine grains were added into the reservoir with the aim of reaching $F_c$ = 5% within the filter. The concentration of fine grains in the effluent discharged from the reservoir was measured to be about 0.25 g/L. Implementation of this method in the field would require a system to disperse the fines at the upstream end of the embankment to continuously agitate the fine grains prior to infiltration.

It is important to emphasize once again that the flow conditions used in this study, whether linearly increasing or constant flow rates, do not precisely replicate the in-situ scenarios experienced by infiltrating fines, which are more likely to encounter constant pressure conditions. This choice to perform infiltration under controlled flow
<table><caption>**Table 1:** List of experiments</caption><thead><tr><th>Infiltration Method</th><th>Filter</th><th>fine grains</th><th>Size range (mm)</th><th>Size ratio (R)</th></tr></thead><tbody><tr><td>Deposit</td><td>Hostun HN 1/2.5</td><td>Fontainebleau-NE34</td><td>0.063-0.6</td><td>4.9</td></tr><tr><td>Mixing</td><td>HN 1/2.5</td><td>NE34</td><td>0.063-0.6</td><td>4.9</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>NE34</td><td>0.063-0.6</td><td>4.9</td></tr><tr><td>Mixing</td><td>HN 1/2.5</td><td>NE34</td><td>0.2-0.315</td><td>4.6</td></tr><tr><td>Mixing</td><td>HN 1/2.5</td><td>NE34</td><td>0.16-0.2</td><td>7</td></tr><tr><td>Mixing</td><td>HN 1/2.5</td><td>NE34</td><td>0.125-0.16</td><td>8.8</td></tr><tr><td>Mixing</td><td>HN 1/2.5</td><td>NE34</td><td>0.1-0.125</td><td>11.3</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>NE34</td><td>0.2-0.315</td><td>4.6</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>NE34</td><td>0.16-0.2</td><td>7</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>NE34</td><td>0.125-0.16</td><td>8.8</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>NE34</td><td>0.1-0.125</td><td>11.3</td></tr><tr><td>Suspension</td><td>HN 1/2.5</td><td>Hostun-HN34</td><td>0.1-0.5</td><td>4.9</td></tr></tbody></table>

conditions was made to maximize the amount of infiltrating fines and thus, the results of this study can be considered as upper-bound estimates. Additionally, these flow conditions have been used in previous studies of suffusion [4], allowing meaningful comparisons of infiltration phenomena across similar materials.

The list of experiments with details on the different combinations of coarse filter and fine grains used are summarized in Table 1

## 3 Infiltration efficiency for different infiltration methods

The choice of grain size ratio relies primarily on Terzaghi's filter criterion, which states that for $R < 4$, fine grains are retained at the surface, effectively preventing depth filtration [30]. Accordingly, an initial size ratio of $R = 4.9$ was selected and the three infiltration techniques were evaluated by measuring the overall fine grains content and the profiles of fine grains content in the infiltrated specimen. The determination of fine grains content is performed in a destructive manner by carefully slicing the
specimen after the infiltration test into seven 2 cm thick slices. Each section was oven dried, and sieved to separate the coarse and fine fractions. The fine grains profiles, which corresponds to the distribution of fine grains along the height of the specimen, are presented in Figures 4(a), 4(b) and 4(c) for the three infiltration techniques. It is observed that the amount of fine grains that infiltrate the filter is strongly dependent on the infiltration method while the shape of distribution appears to be qualitatively similar. The global fine grains content retained in the specimen is about 0.6% for the fine grains layer deposit method (Reference), 1.1% for the mixture method, and 4% for the suspension method, corresponding respectively to 15%, 26% and 87% of the total mass of fines added upstream. The effectiveness of infiltration in the reference method relies heavily on dislodging the fine grains from the source layer. Given that the fine grains are packed tightly, the applied water flow appears insufficient to force fine grains migration on a large scale, with only ~ 15% of the total added fine grains migrating from the source layer for the fine grains layer deposit method. One would require a higher flow rate to dislodge the fine grains from this initial condition but at the risk of changing the microstructure of the coarse filter through densification. In the mixture method, the collective effects still persist but they are partially alleviated due to the presence of coarse grains separating the fine grains in the mixture layer. As a result, an increase in the amount of fine grains migration from the source layer is observed, reaching ~ 26%, and consequently the fine grains content.

In the case of the suspension method, the fine grains are completely dispersed in water under the intense agitation provided by the magnetic stirrer and hence, makes it easier for them to migrate through the specimen and to be trapped as isolated grains. This results in a substantial eightfold increase in the fine grains content compared to the reference method. However, surface spanning cake of fine grains, also called filter cake or blanket depositional layers [10, 33], are observed at the top surface of the filter during the final stages of infiltration. The formation of a filter cake signals the end
<figure><img src="image_5.png" /><figcaption>**Fig. 4:** Fine grains distribution in the filter. Zero depth corresponds to the top of the coarse material to be infiltrated. (a) Fine grains layer deposit method. (b) Fine and coarse grains mixture method. (c) Fine grains suspension method - P1 and P2 indicate the positions of the pressure sensors used to measure the hydraulic conductivity. The size ratio used is 4.9</figcaption></figure>
point of the infiltration/clogging process as demonstrated by Tang et al. [10] using tomography imaging. Though the quantity of fine grains that infiltrate the granular filter is strongly influenced by the infiltration technique, the shape of the fine grains content profiles shown in Figures 4(a), 4(b) and 4(c) is found to be qualitatively similar to each other. These fine grains concentration profiles are highly non-homogeneous with the majority of the fine grains being clogged in the uppermost layers of the specimen with the corresponding fine grains content in the first layer being ~ 3%, 5% and 12% for the reference, mixture and suspension methods respectively. This finding aligns closely with previous observations on clogging dynamics reported by several authors across different experimental conditions [10, 33–36]. Further, to quantify the infiltration depth, the passing fraction of fine grains in the filter can be satisfactorily adjusted by an exponential function: $P(z) = e^{-z/L_0}$. This provides a characteristic infiltration length scale $L_0$, which coincides with the average infiltration depth of the infiltrating fine grains [29]. It is found here that this mean penetration depth $L_0$ corresponds to 3 times, 5 times and 14 times the characteristic particle size of the filter ($D_{50}$), for the reference, mixture and suspension methods, respectively. When trying to reach the core of an eroded embankment, knowing this length scale $L_0$ presents practical implications as it allows to estimate the average depth over which the fine grains would effectively clog the filter, to reduce permeability and possibly improve the mechanical strength.

A meaningful comparison can be drawn with the work of Nguyen et al. [4], in which the suffusion of fine grains has been studied using the same filter media. Interestingly, the maximum amount of infiltrated fine grains in the uppermost layer (around 12–13%) is of the same order of magnitude as the amount of fine grains removed during the suffusion process. This observation, that no more than approximately 10% of fine grains (by mass) could be eroded or infiltrate could be attributed to the fact that certain regions of the pore network within the soil matrix remain inaccessible
for the transport of fine grains. Their results also revealed that the erosion of fine
particles predominantly occurs along preferential flow paths, with fines near the spec-
imen boundaries being more susceptible to removal than those located in the middle.
Therefore, in order to investigate whether similar preferential patterns exist during
the infiltration process, a complementary set of experiments was conducted using glass
beads. The grain size distributions of the two types of glass beads were selected to
match those of HN 1/2.5 and NE34 sands, respectively. Fine particles of glass beads
were dyed with methylene blue to ease visualization. Infiltration was performed using
the mixture method, with an initial fine grains content F~c~ of 25%. Upon completion of
the experiment, the specimen was sliced and one of the representative cross-sections
is presented in Figure 5. The results demonstrate that the majority of the clogged fine
particles were concentrated in the core region of the specimen, with minimal clogging
observed near the boundaries. The resulting spatial distribution of the clogged fine
grains also reflects the preferential pathways characteristic of suffusion processes at the
lab scale where larger pores and constrictions exist close to the specimen boundaries.

<figure><img src="image_6.png" /><figcaption>**Fig. 5:** Horizontal section of the infiltrated glass beads filter reveals distinct preferential flow paths concentrated near the boundaries.</figcaption></figure>
Even if the size ratio of 4.9 exceeds the threshold established by Terzaghi's filter rule, the infiltration depth still remains limited regardless of the infiltration method. Therefore, in addition to the infiltration method, the influence of the size ratio *R* must be considered to ensure that the infiltrated fine grains can reach the internal area of the structure to be specifically treated, which is one of the main objectives of this study.

## 3.1 Effect of size ratio on the infiltration behavior

To further characterize the fine grains infiltration mechanism, infiltration experiments have been performed with fine grains having different size ratios using both the mixture and suspension methods. The size of the fine grains is parameterized using the size ratio $R = D_{15}/d_{85}$.

The fine grains profiles, taken at the mid-point of each layer, are presented in Figure 6(a) for the mixture method and in Figure 6(b) for the suspension method. It is observed that regardless of the method of infiltration, these profiles show two distinct behaviors as the size ratio of the fine grains is changed. For the size ratio 4.6, the non-uniform and exponentially decaying distribution observed for $R = 4.9$ is recovered, whereas for the size ratios $R \ge 7$ the profiles tend to become more homogeneous, with the infiltrated fine grains distributed nearly uniformly throughout the entire height of the specimen. Particularly for the suspension method, surface filter cake is observed at $R=4.6$, similar to $R=4.9$. Its thickness was observed to vary between 0.5 cm to 1 cm when measured from the surface of the filter, and may represent up to 10-20% of the added fine grains mass in agreement with the observations of Hua et al. [33]. In contrast, no filter cakes form for $R \ge 7$ where the profiles are relatively more uniform. Consequently, fine grains begin to percolate through the filter, with the proportion of percolating fine grains increasing with the size ratio *R*. The infiltrated fine grains at these size ratios are transported and deposited along the entire height of the specimen,
implying the occurrence of in-depth filtration within the filter [29, 35]. This finding is
encouraging, as it suggests the possibility of repairing not only the superficial layers
but also deeper zones within a hydraulic structure. The total amount of infiltrated
fine grains for different size ratios is presented in Figure 6(c). The main observation
is that at lower size ratios, the retention fraction of fine grains F_c resulting from the
suspension method is significantly higher than that of the mixture method. However,
this difference reduces at higher size ratios. Also, the evolution of F_c as a function
of R is different for the two methods of infiltration. For the mixture method, F_c
increases initially with the size ratio but then saturates to a plateau for larger size
ratios. On the contrary for the suspension method, the amount of retained fine grains
is much larger at small size ratios and progressively decreases with R. Both behaviors
converge to the conclusion that it is much easier for the smaller fine grains to get
dislodged and migrate through the pore network of the filter. Therefore, in the mixture
method, F_c values increase as the amount of fine grains migrating from the source layer
increases. Instead for the suspension method, the same results in increased percolation,
resulting in lower global F_c values. The characteristic infiltration depth L_0 is obtained
by fitting an exponential decay function on the passing fraction of fine grains and
is compared for the two infiltration methods in Figure 6(d). For both methods, the
infiltration depth L_0 is found to scale linearly with the size ratio R, though, at different
rates. This finding is consistent with the previously reported observations [10, 34].
The fine grains migrate the furthest inside the filter when infiltration is performed
in the form of a suspension instead as a mixture. The difference in L_0 values for the
two methods becomes more significant as R increases. It is also interesting to note
that the size ratio for which the characteristic infiltration depth is zero is around ~
4 for both infiltration methods, which is fairly consistent with the Terzaghi's filter
criterion. It would be tempting to extrapolate these trends for larger R values than
those studied here, while bearing in mind that (i) particles much smaller may be
subjected to electro-chemical forces that strongly modify infiltration mechanisms [26, 37] and (ii) the evolution of the global retention fraction is unknown and hard to infer in this range (Figure 6(d)). Furthermore, if the position and extent of the eroded zone relative to the upstream end of the embankment can be determined for instance through water temperature and piezometric measurements, a better informed selection on the fine grains size suitable for infiltration can be made. This can be achieved by leveraging the established linear relationship between $L_0$ and $R$. Numerous models have been put-forth to predict the distance traveled by the fines typically based on particle or constriction size distribution of the filter and size of the fine grains [29, 38–40]. But since these models are typically based on the assumption that fines-grains get clogged individually at the pore throats, and given that only collective clogging was observed in this study, theoretical modeling of the experimental results was not pursued. It may be necessary to describe an apparent size for the fine grain aggregates which can be then be used to determine the infiltration distance for the fine grains in the aforementioned models.

For the suspension technique, the infiltration process can be further investigated through the evolution of hydraulic conductivity of the whole filter column which is presented in Figure 7. Preliminary tests were performed to determine the initial hydraulic conductivity $k_0$ of the filter which stands at around 0.012 m/s. The hydraulic conductivity of the filter begins to drop as soon as infiltration starts. The magnitude of this drop, and the evolution path, are dependent on the size ratio of the infiltrating fine grains which aligns with previous findings of Tang et al. [10] and Banihashem and Karrabi [41] but differs from those of Reddi et al. [2]. For size ratios of 4.6 and 4.9, the hydraulic conductivity $k$ decreases to approximately 30% of its initial value. In contrast, for $R = 11.3$, the reduction in conductivity is minimal with $k$ retaining about 94% of $k_0$. This behavior is consistent with the observation that the fine grains content within the specimen is higher for smaller $R$ values, albeit not uniformly
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6:** (a) Fine grains profile resulting from infiltration using the fine and coarse grains mixture method. (b) Fine grains profile resulting from infiltration using the fine grains suspension method. (c) Comparison of specimen scale fine grains content $F_c$ for mixture and suspension methods, for different size ratios. (d) Characteristic infiltration depth as a function of size ratio $R$, for mixture and suspension methods.</figcaption></figure>
distributed. Consequently, a more pronounced decline in *k* is expected at lower size
ratios. Further, during the evolution of *k* for R = 4.6 and 4.9, two distinct phases are
observed. During the first phase, *k* decreases linearly with time before tending sharply
to a near-constant value, and remains constant despite further infiltration. The end
of infiltration, where *k* reaches a constant value, coincides with the formation of a fil-
ter cake. For larger size ratios, R ≥ 7, the drop in conductivity *k* is much smaller,
reaching 70% and 78% of k₀ for R=7 and R=8.8 respectively. It is found that after
a significant drop during the initial stages of infiltration, *k* gradually decreases to an
asymptotic value. Similar observations regarding the transition between conditions
that lead to the formation of filter cake and those that do not, and its subsequent
influence on the evolution of hydraulic conductivity, have been reported in previous
studies [35, 42, 43]. Some authors [42, 43], attribute this shift in trend between low
and high R values to a change in the dominant mechanism of clogging, which was
also observed previously in the present study as a change in the shape of the clogging
profiles. At low R values, the nearly linear reduction in hydraulic conductivity arises
as a consequence of single-pore blocking mechanism. In contrast, at higher R values,
the pores get clogged gradually due to accumulation of smaller fine grains at the pore
throats leading to a hyperbolic reduction in *k*. Furthermore, the post-infiltration val-
ues of hydraulic conductivity indicates that the change (or variation) is within an
order of magnitude, corroborating previous findings [2, 10, 41]. This suggests that
the behavior under controlled flow conditions are likely to align with the ones under
constant head conditions. This is further supported by the conclusions of Alem et al.
[26], where a slightly higher clogging rate under constant head conditions was iden-
tified as being the main difference between infiltrating the fine grains under constant
flow and constant pressure conditions. Thus, it can be stated that the current find-
ings are relevant to the on-site implementation of the proposed methodology of fine
grains infiltration. Nonetheless, future investigations under constant head conditions
are recommended to further validate and complement the current results.

<figure><img src="image_9.png" /><figcaption>**Fig. 7:** Evolution of specimen scale hydraulic conductivity between pressure sensors P1 and P2 (Figure 4) for fine grains of different size ratio, using the suspension infiltration method.</figcaption></figure>

**3.2 Effect of fine grains shapes**

The shape effects on the infiltration mechanism have been investigated by changing
the fine grains type. Angular Hostun fine sand HN34 and rounded Fontainebleau fine
sand NE34, having the same size ratio and grain size distribution were chosen (Figure
2(c)). NE34 fine grains will be referred to as rounded fine grains and HN34 will be
referred to as angular grains. For the same amount of added fine grains, the retention
profiles for angular and rounded fine grains are compared in Figure 8(a). For angular
fine grains, the distribution profile is qualitatively similar to the rounded ones but a
significant difference in terms of the retention capacity is observed. The amount of
fine grains retained inside the filter is much lower for the angular fine grains, with the
overall F<sub>c</sub> being as low as 1% in comparison to 4% obtained with the rounded fine
grains for the same size ratio. This indicates that only about 20% of the added fine
grains were able to infiltrate into the filter, and the rest were trapped in the filter cake.
In contrast, nearly 87% of the infiltrated rounded fine grains were trapped within the
filter. The characteristic infiltration length, L₀/D₅₀, for angular fine grains is found to
be ~ 3.5, which corresponds to a significant 75% reduction in the average migration
depth in comparison to the rounded fine grains which is around 14. The corresponding
drop in the hydraulic conductivity for both set of fine grains is presented in Figure
8(b). For angular fine grains, the reduction in conductivity exhibits a steeper trend
compared to that of rounded fine grains, followed by a stabilization. This implies that
angular fine grains are filling up the pores of the filter at a much faster rate than the
rounded fine grains. However, no significant difference in the final conductivity ratio
k/k₀ was observed between the two type of fine sands, which is around 39% of k₀ for
angular fine grains and 33% of k₀ for the rounded fine grains.

<figure><img src="image_10.png" /><figcaption>**Fig. 8:** (a) Effect of fine grains shape on the infiltration mechanism: Infiltration profile comparison for Rounded (Fontainebleau) and Angular (Hostun) fine grains having the same characteristic particle size *d*₅₀. (b) Effect of fine grains shape on the evolution of hydraulic conductivity.</figcaption></figure>
In conclusion, similar to the observations from previous works [10, 44], it is found that the shape of infiltrated fine grains influence the trapping efficiency of a filter, with angular fine grains showing significantly reduced penetration due to their shape and this finding needs to be strictly taken into account for modeling the migration behavior of fine grains in a porous media on one hand, and for the choice of materials to infiltrate in the case of remediation of hydraulic works.

### 3.3 Multiple rounds of fine grains infiltration

In order to optimize the infiltration process and increase the retention capacity of fine grains, the response of the filter to multiple rounds of infiltration was investigated using the suspension method. Recent studies [36] have shown that performing infiltration in multiple stages can allow the fine grains to be carried deeper into the filter. A set of infiltration experiments was performed using NE34 fine grains with $R = 11.3$ in which the same amount of fine grains are added during each infiltration round. The evolution of fine grains content profiles and global content in the filter after each round of infiltration is presented in Figure 9(a) and Figure 9(b) respectively. During the first two round of infiltration, it is observed that the fine grains continue to get clogged almost uniformly along the height of the specimen, however slight inhomogeneities gradually appear in the boundary layers during the subsequent infiltration rounds, along with the formation of a thin filter cake layer at the top of the specimen. Unlike the behavior observed for size ratios $R = 4.6$ and $R = 4.9$, this caking does not span across the entire surface of the filter and therefore did not prevent further infiltration of fine grains. But due to the formation of the cake, after each round of infiltration, the retention capacity of the filter decreases and the fine grains content of the filter seems to tend towards a limiting value, which corroborates well with observations of Gerber et al. [35]. Figure 9(b) shows the evolution of the global fine grains content $F_c$ within the filter over multiple rounds of infiltration. Quantitatively, a 53% increase of $F_c$ is
measured during the second round of infiltration, which then reduces to 11% during
the third round, and to 7% during the fourth round of infiltration. Next, the evolu-
tion of the hydraulic conductivity with the progression of infiltration is presented in
Figure 9(c). Four distinct regions can be identified that correspond to each infiltration
round. At the start of each round, a temporary increase in permeability is observed,
attributed to the initial washout of fine grains prior to the resumption of clogging, a
trend consistent with previous studies [10, 36]. After the first round of infiltration, the
hydraulic conductivity value drops to 87% of k₀, 76% of k₀ after the second, 69% of
k₀ after the third, and finally to 61% of k₀ after the fourth round of infiltration. The
evolution of *k* during a round shows a rapid drop at the very start of the infiltration,
visible only for the two first rounds, followed by a much slower decrease, and almost
reaches a steady value by the end of the final stage of infiltration.

4 Conclusions and Perspectives

With the aim of optimizing the process of fine grains infiltration and retention in granular filters, a set of experiments were performed on a coarse Hostun sand filter under controlled flow conditions in a modified Suffusion Erosion Permeameter Test (SEPT) device. To effectively infiltrate the coarse filter medium with fine grains, three infiltration methods were developed and proposed for the supply of fine grains (i) Fine grains layer deposit method, (ii) Fines and coarse grains mixture method and (iii) Fine grains suspension method. In the first method, infiltration was performed though fine grains migration from fine grains layer which was sandwiched between two topmost layers of the coarse filter. The distribution of fine grains inside the filter was found to decay exponentially along the depth of the specimen. Although the technique is easy to implement on site, results from the laboratory experiments indicate that the efficiency is poor. To improve the infiltration efficiency while keeping the infiltration protocol as simple as possible to be transferred to field conditions, the fine grains were dispersed
<figure><img src="image_11.png" /><figcaption>**Fig. 9:** (a) Evolution of the fine grains profile with number of rounds for multiple infiltration performed using the suspension method with $R = 11.3$. (b) Fine grains content of the filter measured after each round of infiltration. (c) Hydraulic conductivity evolution for multiple rounds of infiltration.</figcaption></figure>

by mixing them with coarse grains of the filter referred to as the mixture method. A significant improvement is observed in terms of both the overall fine grains content as well as the characteristic infiltration depth achieved by the fine grains, which is
nearly twice that of layer deposition method (reference method). In the third method proposed in this work, the fine grains infiltrated the filter as a suspension in the water, which improves the infiltration efficiency in terms of the amount of infiltrated fine grains as well as the infiltration depth although the technique appears quite difficult to implement on site. Therefore, the best way to optimize fine grains infiltration in practice would be to combine the above prescribed methods as deemed necessary. Along with the infiltration method, the other parameter that may help optimizing the infiltration process is the size ratio between the fine and the coarse grains. Fine grains having different size ratios, ranging from 4.6 to 11.3, were infiltrated into the coarse filter using mixture and suspension method. The results show two distinct infiltration regimes for both methods and the infiltration depth increases with $R$ (up to a full percolation threshold that was not reached in the experiments). At the lab scale, size ratios $R \ge 7$ enable to obtain rather uniform fine grains distribution within the specimen as the characteristic length $L_0$ becomes comparable with the specimen height. The effect of fine grains shape on the infiltration/clogging mechanism was also investigated. The results show that it is harder for the more angular particles to infiltrate the filter as a four fold reduction in the amount of fine grains retained and a 75% reduction in the infiltration depth was observed.

In conclusion, the key findings from this study provide a practical framework for optimizing the fine grains infiltration process in granular materials, paving the way for remediation of eroded embankments and anti-seepage restoration of earth dams in an environmentally sustainable manner. A proposal to extrapolate the present three infiltration techniques from the lab to the field is illustrated, as a guidance, using the flowchart presented in Figure 10. Despite good results in the controlled lab conditions, the application on the field remains challenging and the impact of heterogeneity still need to be assessed. In particular, in real eroded dams, preferential flow paths may
<figure><img src="image_12.png" /><figcaption>**Fig. 10:** Plan to implement fine grains infiltration on site to provide remediation to an eroded embankment.</figcaption></figure>

exist. Therefore, intermediate scale experiments will be needed to scale up the infiltration technique toward real applications. On another aspect, only non-cohesive fine grains were considered in this study. In some cases, the use of slurry with silt or clay in suspension could be necessary. For such cases, clogging by aggregation of particles will need to be considered as well.

**Acknowledgements.** This study was financially supported by Institut Carnot Eau & Environment under the CLAPMECA project. For Open Access, a CC-BY public copyright license has been applied by the authors to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission. Data generated or analyzed during this study are provided in full within the published article. In addition, special thanks to the lab technicians of G2DR-INRAe, Alexis Doghmane, Faustine Byron and Yves Gremeaux for their assistance in performing and designing the experiments.
# 5 Authorship contributions

**Abhijit Hegde**: Conceptualization; Investigation; Formal analysis; Writing - Original draft; Visualization. **Nadia Benahmed**: Conceptualization; Formal analysis; Writing - Review & Editing; Supervision; Visualization; Funding acquisition. **Antoine Wautier**: Conceptualization, Methodology; Writing - Review & Editing; Supervision; Visualization; Funding acquisition. **Pierre Philippe**: Conceptualization, Writing - Review & Editing.

# 6 Conflict of interest

The authors whose names are listed above certify that they have NO affiliations with or involvement in any organization or entity with any financial interest.

# References

[1] Chapuis, R.P.: Similarity of internal stability criteria for granular soils. Canadian Geotechnical Journal **29**(4), 711–713 (1992)

[2] Reddi, L.N., Ming, X., Hajra, M.G., Lee, I.M.: Permeability reduction of soil filters due to physical clogging. Journal of geotechnical and geoenvironmental engineering **126**(3), 236–246 (2000)

[3] Benamar, A., Ahfir, N.-D., Alem, A., Wang, H.: Contribution of the transport of suspended particles to the internal erosion in soils: particle migration in porous media. Revue européenne de génie civil **11**(4), 493–506 (2007)

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

[5] Carling, P.A.: Deposition of fine and coarse sand in an open-work gravel bed. Canadian journal of fisheries and Aquatic Sciences **41**(2), 263–270 (1984)

[6] Gibson, S., Abraham, D., Heath, R., Schoellhamer, D.: Vertical gradational variability of fines deposited in a gravel framework. Sedimentology **56**(3), 661–676 (2009)

[7] Huston, D.L., Fox, J.F.: Clogging of fine sediment within gravel substrates: Dimensional analysis and macroanalysis of experiments in hydraulic flumes. Journal of Hydraulic Engineering **141**(8), 04015015 (2015)
[8] Kandra, H.S., McCarthy, D., Fletcher, T.D., Deletic, A.: Assessment of clogging phenomena in granular filter media used for stormwater treatment. Journal of Hydrology **512**, 518–527 (2014)

[9] Yang, M., Lu, M., Bian, H., Sheng, L., He, C.: Effects of clogging on hydraulic behavior in a vertical-flow constructed wetland system: A modelling approach. *Ecological Engineering* **109**, 41–47 (2017)

[10] Tang, Y., Yao, X., Chen, Y., Zhou, Y., Zhu, D.Z., Zhang, Y., Zhang, T., Peng, Y.: Experiment research on physical clogging mechanism in the porous media and its impact on permeability. *Granular Matter* **22**, 1–14 (2020)

[11] Herzig, J., Leclerc, D., Goff, P.L.: Flow of suspensions through porous media—application to deep filtration. *Industrial & Engineering Chemistry* **62**(5), 8–35 (1970)

[12] McDowell-Boyer, L.M., Hunt, J.R., Sitar, N.: Particle transport through porous media. *Water resources research* **22**(13), 1901–1921 (1986)

[13] Waldschlager, K., Schuttrumpf, H.: Infiltration behavior of microplastic particles with different densities, sizes, and shapes—from glass spheres to natural sediments. *Environmental science & technology* **54**(15), 9366–9373 (2020)

[14] Song, S., Le-Clech, P., Shen, Y.: Microscale fluid and particle dynamics in filtration processes in water treatment: A review. *Water Research* **233**, 119746 (2023)

[15] Pang, S., Sharma, M.M.: A model for predicting injectivity decline in water-injection wells. *SPE Formation Evaluation* **12**(03), 194–201 (1997)

[16] Mousavi, S.M.R., Jafari, S., Schaffie, M., Norouzi-Apourvari, S.: Experimental study and modeling permeability damage in porous media due to asphaltene deposition. *Journal of Petroleum Science and Engineering* **193**, 107396 (2020)

[17] Foster, M., Fell, R., Spannagle, M.: The statistics of embankment dam failures and accidents. *Canadian Geotechnical Journal* **37**(5), 1000–1024 (2000)

[18] Kakuturu, S., Reddi, L.N.: Mechanistic model for self-healing of core cracks in earth dams. *Journal of Geotechnical and Geoenvironmental Engineering* **132**(7), 890–901 (2006)

[19] Kakuturu, S., Reddi, L.N.: Evaluation of the parameters influencing self-healing in earth dams. *Journal of Geotechnical and Geoenvironmental Engineering* **132**(7), 879–889 (2006)

[20] Kenney, T., Lau, D.: Internal stability of granular filters. *Canadian geotechnical journal* **22**(2), 215–225 (1985)
[21] Sherard, J.L., Dunnigan, L.P.: Critical filters for impervious soils. Journal of Geotechnical Engineering 115(7), 927-947 (1989)

[22] Li, M., Fannin, R.J.: Comparison of two criteria for internal stability of granular soil. Canadian Geotechnical Journal 45(9), 1303-1309 (2008)

[23] Witt, K., et al.: Reliability study of granular filters. Filters in geotechnical and hydraulic engineering, 35-42 (1993)

[24] Vincens, E., Witt, K.J., Homberg, U.: Approaches to determine the constriction size distribution for understanding filtration phenomena in granular materials. Acta Geotechnica 10(3), 291-303 (2015)

[25] Foster, M., Ronnqvist, H., Fell, R.: The performance of embankment dams with filters coarser than no-erosion design criteria. International Journal of Hydropower and Dams 20(4), 64-71 (2018)

[26] Alem, A., Ahfir, N.-D., Elkawafi, A., Wang, H.: Hydraulic operating conditions and particle concentration effects on physical clogging of a porous medium. Transport in Porous Media 106, 303-321 (2015)

[27] Agbangla, G.C., Climent, É., Bacchin, P.: Experimental investigation of pore clogging by microparticles: Evidence for a critical flux density of particle yielding arches and deposits. Separation and purification technology 101, 42-48 (2012)

[28] Marin, A., Souzy, M.: Clogging of noncohesive suspension flows. Annual Review of Fluid Mechanics 57 (2024)

[29] Chen, F., Wautier, A., Philippe, P., Benahmed, N., Nicot, F.: Micromechanics of fine-grain infiltration in coarse grain sands. Acta Geotechnica, 1-16 (2024)

[30] Seblany, F., Vincens, E., Picault, C.: Determination of the opening size of granular filters. International Journal for Numerical and Analytical Methods in Geomechanics 45(9), 1195-1211 (2021)

[31] Benahmed, N., Canou, J., Dupla, J.-C.: Structure initiale et propriétés de liquéfaction statique d'un sable. Comptes rendus mécanique 332(11), 887-894 (2004)

[32] Adesina, P., Wautier, A., Benahmed, N.: A micromechanics-based classification of the regimes delineating the behaviour of gap-graded soils. Computers and Geotechnics 168, 1061-1075 (2024)

[33] Hua, G., Zhu, W., Zhao, L., Huang, J.: Clogging pattern in vertical-flow constructed wetlands: Insight from a laboratory study. Journal of Hazardous Materials 180(1-3), 668-674 (2010)

[34] Kandra, H., McCarthy, D., Deletic, A.: Assessment of the impact of stormwater
characteristics on clogging in stormwater filters. Water resources management **29**,
1031–1048 (2015)

[35] Gerber, G., Rodts, S., Aimedieu, P., Faure, P., Coussot, P.: Particle-size-exclusion clogging regimes in porous media. Physical Review Letters **120**(14), 148001 (2018)

[36] Zaidi, M., Ahfir, N.-D., Alem, A., Taibi, S., El Mansouri, B., Pantet, A., Zhang, Y., Wang, H.: Effects of alternating injection-interruption periods on the fine particle transport and retention in granular media. European Journal of Environmental and Civil Engineering **27**(1), 578–592 (2023)

[37] Molnar, I.L., Pensini, E., Asad, M.A., Mitchell, C.A., Nitsche, L.C., Pyrak-Nolte, L.J., Miño, G.L., Krol, M.M.: Colloid transport in porous media: a review of classical mechanisms and emerging topics. Transport in Porous Media **130**, 129–156 (2019)

[38] Indraratna, B., Vafai, F.: Analytical model for particle migration within base soil-filter system. Journal of Geotechnical and Geoenvironmental Engineering **123**(2), 100–109 (1997)

[39] Locke, M., Indraratna, B., Adikari, G.: Time-dependent particle transport through granular filters. Journal of geotechnical and geoenvironmental engineering **127**(6), 521–529 (2001)

[40] Sjah, J., Vincens, E.: Determination of the constriction size distribution of granular filters by filtration tests. International Journal for Numerical and Analytical Methods in Geomechanics **37**(10), 1231–1246 (2013)

[41] Banihashem, S., Karrabi, M.: Investigation of suspended particle size effects on clogging of soil filters under laminar flow. European Journal of Environmental and Civil Engineering **26**(6), 2294–2303 (2022)

[42] Bigna, Y., Oyeneyin, M., Peden, J.: Investigation of pore-blocking mechanism in gravel packs in the management and control of fines migration. In: SPE International Conference and Exhibition on Formation Damage Control, p. 27342 (1994). SPE

[43] Liu, S., Shikhov, I., Arns, C.: Mechanisms of pore-clogging using a high-resolution cfd-dem colloid transport model. Transport in Porous Media **151**(4), 831–851 (2024)

[44] Xiong, H., Zhang, Z., Yin, Z.-Y., Chen, X., Zhou, W.: Microscopic origins of shape effects on migration and clogging of fines in porous media using coupled cfd-idem. Acta Geotechnica, 1–29 (2024)