Introduction

Seepage-induced internal instability refers to the detachment and transport of fine particles within porous materials under the action of pore water flow. For literature, two distinct phenomena associated with soil internal instability have been identified: suffusion and suffosion. Suffusion involves the removal of fine particles from the matrix without significantly disturbing the soil skeleton, whereas suffosion is characterized by the movement of fine particles accompanied by collapse or deformation1,2,3,4.

Suffosion poses a greater threat to dam safety than suffusion as it can induce deformation (cracks) and concentrated leaks and ultimately breakage. Notably, incidents such as the one at Tarbela Dam in Pakistan5 demonstrate the consequences of suffosion. In this case, upon filling the reservoir, suffosion-induced erosion of fines occurred, leading to severe leakage, 362 sinkholes, and 140 cracks on the blanket, ultimately requiring the emptying of the reservoir. Similar sinkhole accidents induced by suffosion have occurred at WAC Bennett Dam in 19966,7,8, Austin Dam9, and Balderhead Dam10, where the loss of fines resulted in higher void ratios and subsequent collapses. Suffosion, therefore, emerges as a critical factor contributing to failures of sand-gravel foundations and embankment dams. However, suffusion does not typically cause significant deformation or collapse. In Durlassboden Dam in Austria, although seepage and leakage caused by suffusion were observed downstream due to uneven geological conditions and deep alluvial deposits, no notable deformation was observed. The issue was successfully resolved by conducting a sealing injection, and the dam has since operated normally for over 50 years11.

For the investigation of suffosion, two crucial questions that require further investigation raised: (a) to what extent can the deformation resulting from fines loss during erosion be classified as suffosion? (b) Which factors determine the susceptibility of soil to suffosion?

For the first question, researchers have provided various descriptions of suffosion, but none have clearly defined the extent to which deformation can be classified as suffosion. Parker12 defined suffosion as the mechanical removal of loose particles. Garner and Sobkowicz13 described suffosion as the mass movement of the fine fraction within the skeleton of a dispersed, potentially unstable coarse fraction, resulting in increased permeability. Richards and Reddy14 and Moffat, et al.7 referred to suffosion as particle migration leading to a reduction in total volume and a potential collapse of the soil matrix. Fannin and Slangen1 reported suffosion as seepage-induced mass loss accompanied by volume reduction and changes in hydraulic conductivity. Consequently, it is imperative to conduct a quantitative evaluation of suffosion.

Regarding the second question, extensive research has been conducted to evaluate the likelihood of suffusion in soils. However, these existing criteria are only used to predict the occurrence of suffusion. Suffusion mainly occurs when the soil exhibits internal instability in its particle size distribution (PSD). Several assessment criteria based on PSD have been developed over the years, such as those proposed by Kenney and Lau15, Indraratna, et al.16, Wan and Fell17, Li and Fannin18, Chang and Zhang19, To, et al.20. Unfortunately, these criteria have failed to accurately predict suffosion. Experiments conducted by Ouyang and Takahashi21, Prasomsri and Takahashi22, Prasomsri, et al.23 have indicated that the fines content (Ff) in the soil significantly influences the volumetric change. The fine fraction plays different roles in the stress transfer in the underfilled, transitional, and overfilled microstructures, consequently impacting the progression of internal instability. Furthermore, DEM simulations conducted by Shire, et al.24, Hu, et al.25, Sufian, et al.26 have reported that the size ratio, which represents the relationship between coarse and fine fraction, can affect the stress distribution and transfer, further influencing soil deformation. Therefore, there is an urgent need for a dedicated criterion based on fines content and size ratio that can reliably forecast the occurrence of suffosion.

Fines content plays a significant role in determining soil permeability and a variety of other geotechnical properties. Fines migration can either enhance or obstruct fluid flow in reservoirs, thereby influencing overall permeability, especially under varying effective stress and brine salinity conditions27. In expansive soils, increasing the content of coarser particles like sand significantly reduces permeability and compressibility, which enhances soil performance by decreasing the swelling potential and water retention, emphasizing the balancing effect of fines and coarse material28,29. Laboratory studies show that adding sand to expansive clays improves permeability by modifying the physical structure and reducing the fines’ proportion, which helps in controlling the adverse effects of shrink-swell behavior30. Effective soil replacement techniques, such as introducing high-permeability materials, can significantly mitigate differential heave and water retention challenges in expansive soils, highlighting the critical influence of fines reduction31. Additionally, backfill material with reduced fines content (less than 5%) is preferred to eliminate hydrostatic pressures, though studies suggest that up to 10% nonplastic fines could still be acceptable without significantly compromising permeability32. Together, these studies demonstrate that the fines content in soil, and the relationship between fine and coarse particles, have an important influence on the stability of soil permeability.

In this study, a comprehensive analysis was conducted by collecting a large amount of experimental data from literature. After thorough data analysis, a threshold in volume strain after erosion was recommended as the criterion to distinguish suffosion from suffusion. Two characteristic parameters were identified for assessing the susceptibility of soils to suffosion. Subsequently, a series of erosion tests were conducted, culminating in the development of a criterion for predicting the occurrence of suffosion.

Definition of significant skeleton deformation

In this study, a comprehensive collection of 129 erosion tests from various literature sources was compiled. The detailed information is provided in the supplemental materials as the table itself is too long to be included in the main text. The database includes 49 different soils, some of which underwent multiple tests under varying conditions such as different stress states, relative densities, or particle styles. In certain cases, repeatability tests were also conducted to ensure the specimen reconstitution method and the responses to seepage flow are both repeatable and reliable, such as tests FR8-25-D0, FR8-25- D1, and FR8-25-D2 by Li33, tests 35E-50, 35E-50-R, 35E-100, 35E-100-R, 35E-200 and 35E-200-R by Ke and Takahashi34. For repeatability tests results, maximum value in the results was selected as indicators to assess soil susceptibility to suffusion or suffosion. This metric was chosen because it reflects the soil’s maximum deformation capacity under consistent experimental conditions. These tests7,21,22,25,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51 can be categorized into two groups: triaxial erosion tests and rigid-wall erosion tests. The triaxial erosion tests encompass both axial deformation and volume strain as test results. The rigid-wall erosion tests provide only axial deformation, with the volume strain being equivalent to the axial deformation. Slangen and Fannin3 suggested that volume strain can better reflect the skeleton deformation compared to axial deformation. For instance, in the case of 6.5GB35-100 test, the axial deformation and volume strain were recorded as 0.04% and 1.68%, respectively, after the loss of fines. Similar observations were made in the tests of 6.0GB35-100, 6.0GB35-100(R), and 6.5GB35-50. Similar findings were also reported in the tests conducted by Prasomsri and Takahashi22. Hence, volume strain was selected as the primary characteristic parameter to describe the skeleton deformation.

In most researches, volume strain exceeding 1% is commonly considered indicative of significant skeleton deformation. For example, Ke and Takahashi34 identified a range of 1.8–2.4% volume strain as an indicator of significant skeleton deformation. Chang, et al.52 identified volume strain exceeding 6.5% as significant skeleton deformation. Sibille, et al.37 classified the volume strain ranging from 1.7 to 7.7% as significant skeleton deformation. Similarly, Slangen and Fannin3 defined the volume strain ranging from 1.54 to 2.19% as indicative of significant skeleton deformation. In this study, a threshold of 1% in volume strain after erosion was recommended as the criterion of evident and unacceptable deformation. This recommendation was based on a conservative interpretation of the lower limits of the ranges reported in the literature. The choice of the 1% threshold aims to ensure the identification of any significant deformation indicative of suffusion or suffosion while acknowledging that no universal consensus exists regarding a precise value. The absence of statistical evidence or granulometric support for this threshold is recognized as a limitation of this study. Future investigations will aim to provide further validation through sensitivity analysis and granulometric data.

Figure 1 illustrates the step-by-step procedure proposed for distinguishing suffosion from suffusion. The first step involves separating the fine fraction and coarse fraction based on H/F curves plotted against F, suggested by Wan and Fell53, where F (< 40%) represents the weight fraction (Weight Fraction = Mass of Component / Total Mass of Mixture, expressed as a percentage) passing at particle size d, and H represents the weight fraction of particles ranging from d to 4d. For example, in the PSD curve of soil T-0 by Moffat, et al.7, when d = 0.10 mm, Fd=0.10 = 4.76%, 4d = 0.40 mm, F4d = 0.40 = 30.85%. Here H = F4d = 0.40 - Fd=0.10 = 26.09%. Follow this method to calculate the value of H for d = 0.07 ~ 1.93 (corresponding F = 0 ~ 40%) and F-H/F curve of soil T-0 was shown in Figure  2. The critical particle size of the fine fraction from the coarse fraction is determined by d(H/F)min, which corresponds to the grain diameter providing the minimum value of (H/F). For soil T-0, (H/F)min = 3.12, correspondingly, F(H/F)min = 37.94 (Fig. 2), d(H/F)min = 1.05 (Fig. 3). The second step is the estimation of internal stability of the soil according to the retention ratio, D’15/d’85, where D’15 and d’85 are the particle size corresponding to 15 and 85% passing of the coarse and fine fractions, respectively. The PSD curves of coarse and fine fractions for soil T-0 were shown in (Fig. 4). According to Kezdi54, a soil is considered internally stable if the value of D’15/d’85 is less than 4. For soil T-0, D’15 = 5.89 and d’85 = 0.45 (Fig. 4). So, D’15/ d’85 = 13.09, which is greater than 4, means soil T-0 is internally unstable. The last step is to determine whether the soil is prone to suffusion or suffosion by checking the maximum deformation after erosion (Defmax), which is considered suffosion if it is equal to or greater than 1%. According to Moffat, et al.7, the maximum volume strain (equal to axial deformation in rigid-wall erosion test) was 7%. Therefore, soil T-0 is susceptible to suffosion.

Fig. 1
figure 1

Chart describing the procedure to distinguish suffosion from suffusion. d is arbitrary grain diameter in the soil PSD curve, while d(H/F)min is the grain diameter providing the minimum value of (H/F).

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Fig. 2
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F-H/F curve of soil T-0 by Moffat, et al.7. H is defined as the weight fraction of particles ranging between d to 4d.

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Fig. 3
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Particle size distribution of soil T-0 by Moffat, et al.7.

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Fig. 4
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PSD curves of coarse and fine fractions for soil T-0 by Moffat, et al.7.

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Initially, a preliminary evaluation (suffusion or suffosion) was conducted by analyzing each individual test result (a total of approximately 129 tests) following the methodology depicted in (Fig. 1). Subsequently, a comprehensive evaluation was performed on each soil (49 different soils, as previously described, some soils were subjected to multiple tests under varying conditions and even repeated tests). A summary of the evaluation for each soil is shown in (Table 1). Due to the space limitation, the detailed data of 129 tests cannot be shown here, which can be found in the supplemental materials.

Figure 5 depicts the correlation between suffusion or suffosion, D’15/d’85 and Ff. The results show that out of 49 soils in the dataset, 18 soils with Ff ≥ 35% suffer suffosion, while 15 soils with Ff ≤ 20% exhibit suffusion. However, in soils with 20% < Ff < 35%, there is no apparent distinction between suffusion and suffosion. Furthermore, some blank zone is observed for the soils with 10 < D’15/d’85 < 30.

Table 1 Primary parameters and the experimental results from literature on suffusion.
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Fig. 5
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Relationship between suffusion or suffosion, D’15/d’85, and Ff (data from literature).

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Laboratory experiments

Materials

To provide a more comprehensive understanding of the correlation between suffusion or suffosion, D’15/d’85 and Ff, a series of laboratory tests were conducted on 12 gap-graded soils (referred to as G1 ~ G12) and 14 broadly graded soils (referred to as B1 ~ B14) to supplement the blank zone in (Fig. 5). The PSD curves of the tested soils were presented in Fig. 6 (for gap-graded soils) and Fig. 7 (for broadly graded soils), while the main granular parameters were summarized in (Table 2). The 26 tested soils exhibit a fines content in the range of 5 ~ 35 and a retention ratio D’15/d’85 in the range of 5.10 ~ 21.50. Additionally, the uniformity and curvature coefficients of the tested soils are in the range of 1.88 ~ 303.0 and 0.17 ~ 24.52, respectively.

Fig. 6
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Particle size distribution of 12 tested gap-graded soils.

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Fig. 7
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Particle size distribution of 15 tested broadly graded soils.

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Apparatus

The testing apparatus, illustrated in Fig. 8, consisted of three components: an axial loading system, a vertical settlement transducer, and a modified seepage control system. The axial loading system replicated the overburden load acting on the foundation, such as that from an embankment dam, and provided a maximum load of 0.50 MPa (with a accuracy of ± 0.01 MPa) concerning the dam of interest. The vertical settlement transducer had a measurement range of 0–25.40 mm with an accuracy of ± 0.02 mm. The seepage control system featured a constant head water tank that delivered a water head of less than 3 m and a constant pressure pump that provided a load equivalent to a water head ranging from 3.0 ~ 50.0 m with an accuracy of 0.2 m. One of the noteworthy features of the uniaxial erosion apparatus was its capacity to accurately and promptly measure the vertical settlement while controlling the axial load precisely. Each specimen had a height of 35 cm and a diameter of 25 cm.

Fig. 8
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Schematic draw of the testing apparatus.

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Table 2 Main parameters of the tested soils.
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Experimental procedure

To ensure experimental accuracy, a rigorous experimental protocol was assessed consisting of four distinct stages: specimen preparation, saturation, consolidation, and seepage pressure application.

Firstly, specimens were prepared using moist tamping as described by Ladd56, to prevent the segregation of the two different particle sizes. The preparation procedure consisted of several steps: (a) The tested soil was oven-dried at 105 ℃ for 24 h and then was cooled inside a desiccator; (b) The dried soil was sieved into different groups (according to selected granular fractions) based on the particle size, as shown in (Fig. 9a, c). The tested soil was mixed following the targeted PSD in Figs. 6 and 7, as shown in (Fig. 9b), and the de-aired water was added to reach the optimum content of 10%, as shown in (Fig. 9c, d) moist, well-mixed soil was then stored in a humidity and temperature-controlled container for approximately 24 h to allow equalization of moisture levels; (e) the wet mixture was equally separated into seven equal pieces and compacted (static compaction) as layers of 5 cm thick each, according to the recommendation of maximum layer thickness < 6.25 cm (1/4 of the specimen diameter, as reported by Ladd56); (f) a layer of glass beads was put on the top of the specimen to buffer the inlet flow. The prepared specimen was shown in (Fig. 9d).

Fig. 9
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The procedure of specimen preparation: (a) different groups (after sieving) of the tested soil; (b) tested soil after mixture based on the targeted PSD; (c) tested soil with 10% water content; (d) the prepared specimen.

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After the preparation of the specimen, the next step in the testing process was to apply an axial load of 0.3 MPa. (Based on findings from previous internal erosion research22,26,42,46,57, axial strain is observed to increase with axial load. In this study, the choice of an axial load of 0.3 MPa was dictated by the experimental apparatus’s limitations, as 0.3 MPa represents its maximum capacity. To maximize axial strain within these constraints, this load level was selected.) This load was applied stepwise, with a rate of 0.05 MPa per 30 min, in order to homogenize the specimen consolidation. After reached the target axial load, it was maintained at a constant level for the duration of the test.

Then, complete saturation of the specimen was achieved by subjecting it to an upward flow using a constant-head water tank. To avoid any potential erosion of the specimen, a low hydraulic gradient (nearly zero) was maintained throughout the process. The elevation of the constant-head water tank was then incrementally increased at a rate of 5 cm every 20 min to achieve a high level of specimen saturation. The saturation process was continued until water started to emerge from the valve on the specimen top cover, which took approximately 2.5 h to be completed.

Finally, the seepage pressure was applied step by step into the specimen among tests in order to simulate reservoir filling. Throughout the entire test procedure, the settlement of the specimen, the data in piezometric tubes, and the flow rate at the outlet were continuously recorded. Each test proceeded to the next step of water head when the flow rate reached a stable value, data in piezometric tubes became stable, and settlement did not increase. The test was terminated upon suffusion failure, which is characterized by strong erosion occurring over a short time, and a rapid and significant change in local hydraulic gradient or settlement37,58. All tests were conducted under fully saturated conditions to ensure accuracy and consistency of the results.

Results and discussion

Typical test results

In total, all 26 tests were conducted under consistent conditions, including stress states, relative density and particle type. The summarized test results can be found in (Table 3). The performance of G1 is presented in the following as an example. The evolutions of the local hydraulic gradients, flow rate and deformation are illustrated in (Figs. 10 and 11).

In Fig. 10, an increase in the global hydraulic gradient (iG) from 1.66 to 2.18 resulted in a sharp decrease in the local hydraulic gradient i1 − 2, indicating the opening of a seepage channel due to fines loss. Simultaneously, the local hydraulic gradient i2 − 3 experienced a sudden increase, suggesting the accumulation of fine particles in that location. Additionally, in Fig. 11, the flow rate continued to increase linearly when iG ≤ 1.66. However, when iG > 1.66, the rate of increase decreased until iG = 3.29, primarily due to the movement of fine particles. Moreover, in Fig. 11, negligible deformation occurred when iG ≤ 1.23, but when iG increased from 1.23 to 1.66, the deformation abruptly increased to 0.013%. These observations collectively indicate that suffusion initiated in layer 1–3 at iG = 1.66.

When iG increased from 2.18 to 2.84, i1 − 2 increased abruptly, while i2 − 3 decreased sharply (Fig. 10), indicating clogging in layer 1–2 and fines loss in layer 2–3. The flow rate increased linearly between iG = 1.66 and 3.29 (Fig. 11). However, when iG increased from 3.29 to 3.91, the flow rate increased abruptly. Additionally, for iG > 3.29, there were no significant changes in deformation (Fig. 11) or the local hydraulic gradients i1 − 2, i2 − 3, i3 − 4, and i4 − 5 (Fig. 10). This suggests that blowout occurred at iG = 3.29. Throughout the erosion test, the maximum deformation of the specimen was 0.02% (Fig. 11). Considering the criteria previously described for distinguishing suffusion and suffusion, it can be concluded that soil G1 is prone to suffusion. Similar evaluations were conducted for other tested soils.

Fig. 10
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Local hydraulic gradient variation against global hydraulic gradient in soil specimen G1.

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Fig. 11
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Flow rate and deformation variation against global hydraulic gradient in soil specimen G1.

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Table 3 Summary of the test results and suffusion or suffosion assessment.
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Combination of the data from literature and the data from this study

A total of forty-six erosion test data points from the literature and twenty-six test results from this study were plotted together in Fig. 12, creating a two-dimensional representation of soils characterized by D’15/d’85 and Ff. This representation divides the data into four zones (A, B, C, and D), each with distinct erosion behaviors and soil microstructures.

Fig. 12
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Relationship among suffusion or suffosion, D’15/d’85, and Ff (data included the test results from this study).

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In Zone A, soils exhibited maximum deformation caused by erosion of less than 1%, indicating suffusion as the primary erosion mechanism. These soils were under-filled, with coarse particles forming a continuous matrix and constrictions (Fig. 13a). Fine particles floated within these constrictions23, allowing coarse particles to bear most of the effective stress. Consequently, fine particles migrated or became trapped without compromising the matrix integrity at relatively low hydraulic gradients22. However, when the hydraulic gradient exceeded a critical threshold, the suspended fines were eroded. Liu, et al.59 found that in samples with Ff = 20%, the original load-bearing skeleton remained stable, as shown by the constant axial force of the strong force chain and unchanged force chain angle during suffusion. Salgado, et al.60 noted that coarse particles in soils with Ff = 15% could displace sideways, increasing direct contacts between coarse particles and enabling efficient load transfer. Alnmr61 reported that compressibility in sandy soils decreases when the fine material content is below a critical threshold, a behavior consistent with the Hardening Soil model. Thus, in Zone A, the erosion of fine particles caused negligible deformation, as the coarse particle framework remained intact.

In Zones B and C, Soils displayed both suffusion and suffosion. A boundary between Zone B and Zone C is proposed using the equation Ff = 2.73 D’15/d’85 + 0.89, with suffusion dominant in Zone C and suffosion in Zone B. The microstructure in these zones was filled, with both coarse and fine particles contributing to effective stress (Fig. 13b)22,23. In zone B, the value of D’15/d’85 (which shows the soil’s internal stability) is relatively lower than the value in soils with the same Ff in zone C, which indicates that the fine particles participated in self-filtration and stress transfer to some extent before erosion. After erosion, the self-filtration was destroyed and more fine particles were eroded, resulting in a change in the matrix. Therefore, the deformation caused by erosion is significant, and it is considered as suffosion. Conversely, the value of D’15/d’85 of soils in zone C is relatively higher, indicating that the self-filtration is weak or non-existent. After some fine particles were eroded, the erosion process and stress transfer remained unchanged. Consequently, the deformation caused by erosion is negligible, and it is considered as suffusion.

In Zone D, maximum deformation exceeded 1%, indicating suffosion as the primary mechanism. These soils were overfilled, with fine particles forming the primary load-bearing matrix, while coarse particles were embedded and lacked contact (Fig. 13c). The erosion of fine particles led to significant matrix readjustments and deformation. Li, et al.57 emphasized the critical role of fine particles in the force chain, with coarse particles contributing minimally. Liu, et al.59 observed that in samples with Ff = 35%, suffusion caused sudden changes in the force chain angle and magnitude, collapsing the original load-bearing skeleton and forming a new one. Alnmr61 noted that when fine content exceeded a critical threshold, soil compressibility increased, exhibiting behavior consistent with the Soft Soil model. These findings highlight the vulnerability of overfilled soils to deformation and instability during erosion.

Fig. 13
figure 13

A diagrammatic representation of the composition of mixes with varying amounts of fine components: (a) low fines contents (≤ 20%); (b) medium fines contents (20~35%); (c) high fines contents (≥ 35%).

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Deformation during erosion is influenced by particle type and relative density, factors not considered in this study. Maroof, et al.41 demonstrated that using the same particle size distribution (PSD) but different particle types (e.g., glass beads, rough glass beads, rounded particles, and flaky particles) resulted in deformation ranging from 0.36 to 2.89%. Similarly, Zhou, et al.62 observed variations in deformation under different particle types. Lee, et al.43 studied soil GW at varying relative densities (50, 65, and 80%), reporting deformation ranging from 0.36 to 7.40%, while all tests in this study were conducted under the same relative density. These factors represent limitations of this study and will be addressed in future research to establish a more comprehensive erosion criterion.

Conclusion

This study investigated the particle size distribution (PSD) characteristics of internally unstable soils susceptible to suffusion and suffosion by compiling a dataset of 75 erosion tests, including 49 from published literature and 26 conducted in the laboratory using the uniaxial erosion apparatus. Based on the analysis of these results, several key findings can be summarized:

  1. (a)

    Soils with Ff ≤ 20% (zone A) experience suffusion, where the loss of fine particles causes only minimal deformation due to the moderate contribution of fine particles to the soil matrix and stress transfer.

  2. (b)

    Zone B (20% < Ff < 35% and Ff > 2.73 D’15/d’85 + 0.89) is characterized by susceptibility to suffosion. In this zone, the loss of fine particles destabilizes the self-filtering structure, leading to significant and harmful deformation as the equilibrium state is disrupted.

  3. (c)

    Zone C (20% < Ff < 35% and Ff < 2.73 D’15/d’85 + 0.89) experiences suffusion. The self-filter in this zone is not stable enough to maintain its structure upon the loss of fine particles, but the impact on stress transfer is minimal, resulting in less significant deformation compared to suffosion.

  4. (d)

    Zone D (Ff ≥ 35%) is particularly prone to suffosion. The fine particles play a critical role in maintaining the force chain within the soil matrix. When fine particles are lost, stress redistribution occurs, forming a new load-bearing skeleton. This leads to significant and harmful deformation.

In conclusion, the erosion behavior of internally unstable soils is largely influenced by the fine particle content and the self-filtering properties of the soil. This study provides valuable insights into the specific zones of susceptibility to suffusion and suffosion, contributing to a deeper understanding of the mechanisms of internal erosion in granular soils. The findings of can further inform field practices, offering recommendations for assessing the internal stability of soils in engineering projects. For instance, the erosion susceptibility zones identified in this study can be used as guidelines in the design and evaluation of embankment dams and foundation systems. Engineers can apply these insights to develop tailored preventive measures to mitigate the risks of suffusion and suffosion, thereby enhancing the safety and resilience of geotechnical structures.

Future research should explore the behavior of other soil types under varying environmental and load conditions to extend the applicability of these findings. Investigations into long-term stability assessments, including cyclic loading and environmental changes, would provide a deeper understanding of erosion mechanisms. Additionally, advancing experimental techniques and numerical modeling approaches could further refine our understanding of the interplay between particle size distribution and soil erosion processes.