Natural Clogging Design for Tailings Pond Filters

Abstract

Filters serve as critical facilities for ensuring the seepage stability of earth-rock dams and tailings dams; their failure poses severe threats to dam safety. Traditional filter design criteria are constrained by the diversity of soil types and fail to account for the influence of pore characteristics (e.g., constriction size) on the soil retention and hydraulic conductivity of filters. Design methods recommended in design codes only provide gradation envelope boundaries without specifying exact gradation curves. This paper proposes a filter design approach based on the natural clogging concept. Using Terzaghi’s interlayer coefficient as the initial parameter, this method induces stable clogging layers of base soil within the filter through sediment-laden seepage, adopting the post-clogging gradation as the design gradation. Experimental results demonstrate that: (1) when the initial interlayer coefficient α of the filter is ≤10.4, the base soil retention rate exceeds 97% (soil loss < 3%), surpassing the conservative limit of α < 4 in Terzaghi’s criterion; (2) the final interlayer coefficient α of filters ZS-2 to ZS-5 ranges between 1.15 and 2.48, with i_b/i_f values between 6.26 and 23.68, simultaneously satisfying Terzaghi’s requirements for soil retention and hydraulic conductivity; (3) this method explicitly defines the specific gradation curve of the filter, with the final gradation curve of ZS-5 largely falling within the envelope recommended by design codes. The proposed method integrates Terzaghi’s interlayer coefficient criterion with the influence of pore characteristics on filter performance, offering a new design strategy for tailings dam filters with fine-grained base soils, preliminarily validated under laboratory conditions.

1. Introduction

The filter layer is a critical structural component for ensuring seepage stability in dam bodies such as earth–rock dams and tailings dams [1]. Failure of the filter can, in minor cases, cause an abnormal rise in the phreatic line within the dam, and, in severe cases, trigger breach accidents, leading to substantial economic losses and serious ecological pollution. Currently, dam seepage disasters caused by improper design of filter materials are frequent [2]. Therefore, developing innovative filter design methods with strong adaptability and well-defined parameters is an urgent engineering need to ensure the safe operation of dam structures.

In 1922, Terzaghi pioneered the first filter design criterion, establishing a new approach for seepage control in dams. After nearly half a century of practice, the dual functions of filters have been further clarified: soil retention and pressure dissipation. Soil retention requires filters to intercept the majority of base soil particles, preventing significant mass loss. Inadequate retention may lead to seepage failure mechanisms, notably piping [3,4,5]. Pressure dissipation necessitates that pore water pressure largely dissipates as seepage enters the filter, ensuring efficient drainage. Compromised dissipation readily elevates phreatic surfaces [6]. However, Terzaghi’s criterion—based on uniform cohesionless soils—exhibits limitations when applied to well-graded cohesionless soils. The control particle size (d₈₅) of base soil is often overestimated, impairing filtration efficacy [7]. Secondly, reliance on characteristic particle sizes (d₁₅, d₈₅) inadequately predicts filtration performance and fails to account for the specific influence of filter gradation curves [8]. Most critically, while Terzaghi’s method permits minor base soil loss for general hydraulic structures (provided overall seepage stability is maintained), this is unacceptable for tailings dams due to the environmental contamination risks posed by migrating tailings particles.

Since the 1980s, advancements in seepage control theory have established filter design as an independent system within dam seepage control frameworks [9]. Given the extensive variety of natural soils, scholars worldwide have expanded Terzaghi’s filter criterion to develop design methods applicable to diverse soil types. These include cohesive soils [10,11,12] and widely graded dispersive soils [13]. The U.S. Bureau of Reclamation incorporated and refined Sherard’s design principles, extending Terzaghi’s criteria to base soils such as sands and gravels with d₈₅ > 5 mm [7]. Locke et al. [14] proposed the reduced PSD method for widely graded soils, leveraging the coarse fraction’s capacity to intercept fine particles (i.e., self-filtration) to optimize filter design. The China Institute of Water Resources and Hydropower Research (IWHR) conducted systematic studies aligned with practical projects [7], broadening the scope of soil materials. Their work introduced filter design methodologies for soils including continuously graded non-uniform cohesionless soils, gap-graded gravels, multi-graded gravelly fine-grained soils, general cohesive soils, fissured clays, and dispersive clays.

In reality, the pore characteristics of filters profoundly govern both soil retention and hydraulic conductivity. Design methods exclusively focused on characteristic particle sizes neglect the influence of pore features on protected soils. Raut et al. [13] demonstrated that comparing the constriction size (D_c35) of filters with the representative particle size (d₈₅) of base soil more accurately represents physical filtration processes than the traditional D₁₅/d₈₅ criterion. Consequently, research priorities shifted from particle-to-particle toward pore-to-particle interactions, catalyzing the emergence of the constriction size distribution (CSD) method. Accurate quantification of CSD in granular media thus became pivotal. Current quantification approaches encompass direct observation or inverse analysis through filtration tests [15], numerical simulations, digital techniques utilizing CT scanning [16,17,18,19], and probabilistic models founded on geometric assumptions [20,21]. Kalore et al. [8] leveraged the CSD–base soil gradation relationship by treating particle and constriction sizes as stochastic variables to establish Probabilistic Assessment Criteria. Indraratna et al. [21] incorporated relative density effects on filter porosity, proposing the combined particle and constriction size distribution (CP-CSD) method that integrates particle size distribution (PSD) with CSD. Rather et al. [22] and Shire et al. [23] further enhanced hydraulic conductivity predictions by embedding CSD and particle shape parameters into granular filter models. Collectively, these advances provide transformative perspectives for modern filter design.

Despite the significant advances achieved by the aforementioned methods, existing approaches still share a common limitation in that they primarily focus on static assessment of the soil-retention capacity of filters or passively utilize the inherent properties of soil to prevent particle migration, both regarding clogging as a failure mechanism to be avoided. The Natural Clogging Method (NCM) proposed in this study adopts a different design logic in that NCM does not statically evaluate whether a filter can retain the protected soil but dynamically simulates the clogging evolution process under real seepage conditions and adopts the steady-state gradation as the design output. Unlike the Constriction Size Distribution method which relies on tedious geometric or probabilistic characterizations of pore structure, NCM bypasses complex CSD calculations through physical infiltration tests, with the final filter structure determined by the natural interaction between particles and pores. Furthermore, unlike the self-filtering method which passively optimizes the gradation based on the inherent soil properties, NCM actively induces controllable clogging and transforms the clogging process traditionally regarded as a seepage failure mechanism into a design resource. A comparative analysis of various existing filter design methods is presented in

Table 1. Comparison of various filter design methods.

Comparison Dimension	Terzaghi’s Criterion	CSD Method	Simplified Particle Gradation Method	Natural Clogging Method (NCM)
Core Principle	Interlayer coefficient (D15/d85)	Matching between constriction size distribution and soil gradation	Utilization of the inherent self-retention capacity of coarse particle skeletons	Induction of controllable clogging by sediment-laden seepage with steady-state gradation as the design output
Key Assumptions	Soil is uniform and cohesionless, and arching occurs at particle contact points	Pore structure can be geometrically defined, and particle–pore matching can be probabilistically characterized	Coarse skeleton is self-stable, and fine particles can be internally retained	Clogging can reach steady state, and steady-state gradation possesses self-filtering capacity
Input Parameters	D15 and d85	Gradation curve, constriction size distribution, and relative density	Gradation of wide-gradation soil	Initial interlayer coefficient α, sediment concentration, and protected soil gradation
Design Output	Gradation envelope range	Probabilistic soil retention criterion and gradation envelope	Interlayer coefficient criterion as a design envelope or criterion	Specific gradation curve measured after clogging
Main Advantages	Simple and classical, with wide engineering application	Considers pore characteristics, and the physical process is explicit	Concise theory that relaxes filter requirements for self-filtering soils without complex testing	Outputs a unique specific curve, integrates interlayer coefficients and pore evolution, and transforms clogging into a design resource
Main Limitations	Ignores pore geometry, is conservative for gap-graded soils, and provides no specific curve	Calculation is tedious, and pore definition is highly subjective	Provides only criteria or envelopes, exhibits strong soil-type dependence, and lacks an explicit final-state gradation curve	Currently verified only for tailings sand, requires physical tests, and long-term stability remains to be verified

.

In conclusion, this study conceptualizes the filter and base soil as an integrated system during seepage, fully leveraging the self-filtration effect during soil clogging to propose a filter design approach based on the natural clogging concept. This method takes the interlayer coefficient of Terzaghi’s filter criterion as the design starting point, uses coarse particles with different gradations as the initial medium for filter design, and prepares the protected soil (tailings sand) as sediment-laden water at a specific concentration. This process forms a stable clogging layer within the filter, where coarse particles retain the base soil, amplifying its self-filtration capacity to achieve effective protection. The post-clogging gradation is then adopted as the finalized filter design. This research provides an innovative framework for designing filters in earth–rock dams and tailings ponds, offering both theoretical insights and practical guidance for enhancing anti-seepage performance and ensuring dam stability.

2. Clogging Seepage Trial of Tailings Pond Filters via Natural Clogging Method

2.1. Objectives and Methodology

For a filter layer in service, an excessively small characteristic particle size fails to achieve the pressure reduction objective, whereas an excessively large characteristic particle size fails to satisfy the soil retention requirement. If the filter layer and the protected soil are regarded as an integrated system, a portion of the protected soil particles are allowed to enter the filter layer during the preliminary design stage to form clogging and thereby reach an overall stable state, enabling both the filter layer and the protected soil to jointly perform the filtering function. This gradation is adopted as the design gradation curve of the filter layer, representing the result of natural selection by the protected soil under sediment-laden seepage. Meanwhile, this method accounts for the influence of pore characteristics of the filter layer on both soil retention and permeability, and only requires a limited number of coarse particle gradation combinations at the initial stage of testing. The steady-state clogging gradation is determined through laboratory sediment-laden seepage tests and can be directly adopted as the design gradation curve for field construction.

The base soil for this experiment comprised medium sand from the Lixi Tailings Pond of Jinduicheng Molybdenum Industry, with its gradation detailed in

Table 2. Initial Gradation Design Scheme for Coarse Filter Materials.

Conditions	Initial Grain Composition (mm) of Filter (%)				D15 (mm)	Dry Density of Filter(g/cm3)	Grain Composition (mm) of Base Soil (%)				d85 (mm)	Interlayer Coefficient α
	10~20	5~10	2~5	1~2			0.5~1	0.25~0.5	0.075~0.25	<0.075
ZS-1	85	5	5	5	10.0	1.72	10	65	20	5	0.48	20.8
ZS-2	80	10	5	5	7.5	1.79	10	65	20	5	0.48	15.6
ZS-3	70	15	10	5	5.0	1.85	10	65	20	5	0.48	10.4
ZS-4	60	20	15	5	4.0	1.86	10	65	20	5	0.48	8.3
ZS-5	40	30	20	10	2.8	1.88	10	65	20	5	0.48	5.7

Note: D₁₅ denotes the particle size corresponding to 15% finer by mass in the filter (unit: mm). d₈₅ denotes the particle size corresponding to 85% finer by mass in the tailings sand (unit: mm).

. Initially, filters were designed using varying coarse-particle contents based on the interlayer coefficient α = D₁₅/d₈₅, where D₁₅ denotes the particle size corresponding to 15% finer in the filter, and d₈₅ represents the size for 85% finer in the base soil. Tailings material was then prepared as a sediment-laden water at a concentration of 121 g/L, consistent with Lixi tailings transport specifications. This concentration is the measured average mass concentration of tailings slurry transported through the Lixi Gully pipeline during normal operation of the Lixi tailings dam, representing the transport state of tailings sand under the actual discharge conditions of this facility. Hydraulic conductivity trends were monitored throughout testing, while post-experiment analysis quantified the mass and gradation of tailings deposited on the filter surface, trapped internally, and discharged.

Experiments employed a custom-built sediment-laden seepage system (Figure 1) developed by Xi’an University of Technology’s Geotechnical Institute. The prepared suspension was poured into a water supply tank, with a pump transferring it to a surge tank. Stirrers installed atop both tanks prevented particle sedimentation. Upon achieving steady water levels in the surge tank, valves were opened to initiate gravity-fed flow into the seepage cylinder, allowing natural clogging of tailings within the filter.

2.2. Experimental Procedure

The experiments were conducted in a temperature-controlled environment at 20 ± 2 °C under boundary conditions of constant water supply level and natural clogging. The initial hydraulic head difference for sediment-laden seepage was set at ΔH = 50 cm, with the water supply level kept constant by an overflow weir in a constant-head tank, and the sediment-laden water infiltrated naturally under gravity. As clogging progressed, the permeability resistance of the filter increased and the hydraulic gradient adjusted naturally in response to the evolving seepage state. The flow rate was measured by the volumetric cylinder and stopwatch method with readings recorded at 5-min intervals during the sediment-laden seepage stage. The test was terminated when the outflow transitioned from turbid to clear and the coefficient of variation of the flow rate was less than 5% for three consecutive measurements, indicating that clogging had reached steady state. The detailed experimental procedure is described in the following text.

(1)

Filter installation: A 10 cm-thick coarse-grained buffer was placed and saturated with water. The 20 cm-thick filter was then compacted in four successive lifts (L₁~L₄). Each lift underwent saturation prior to subsequent compaction. Final achieved dry densities of the filter under each test condition are provided in Table 2.

(2)

Apparatus assembly: The water supply tank, surge tank, seepage cylinder, and piezometer tube were interconnected. Clean water was added to the supply tank. Valves were opened to initiate flow until piezometric heads stabilized, marking the formal commencement of the test.

(3)

Test initiation: Prior to sediment-laden water seepage, vacuum saturation was applied to the filter. A 30-min clean water seepage phase ensued, during which piezometric heads were monitored for stability and flow rates were recorded at 5-min intervals. Upon confirmation of stable seepage field establishment within the filter, tailings sand particles were introduced into the supply tank to initiate sediment-laden water seepage. Continuous agitation prevented particle sedimentation throughout this phase.

(4)

Data collection: During sediment-laden water seepage, piezometric head readings were recorded concurrently with flow rate measurements.

(5)

Post-test sampling: Upon test completion, stratified sampling of the filter was conducted at designated elevations. Samples were oven-dried, followed by physical separation of filter material from tailings particles prior to individual mass measurements.

In addition, the measurement precision of the experiments is addressed herein. The uncertainty in retention ratio determination is primarily attributed to the weighing error of the electronic balance with a precision of 0.01 g, standard sieve analysis losses, mass losses during oven drying, operational errors in flow rate measurement by the volumetric cylinder and stopwatch method, and errors associated with layered sampling operations. These factors represent the main sources of error in retention ratio determination and should serve as a reference for evaluating data reliability in the subsequent analysis of results.

3. Analysis of Natural Clogging Seepage Results for Tailings Pond Filters

Upon completion of each test, tailings sand deposited on the upper surface of the filter, retained within the filter (sampled at four distinct elevations), and exfiltrated through the filter was separately collected. These samples underwent oven-drying, sieving, and weighing to determine the particle size distribution of tailings sand at different locations for each test scenario.

3.1. Clogging Mode Classification

Whether tailings sand, serving as the base soil, can penetrate the filter and induce clogging depends on the ratio of the effective opening size of the filter to the characteristic particle size of the tailings sand, as expressed by Equation (1) [24].

$$\lambda =D_0/d_{\mathrm{et}}$$

(1)

where λ denotes the clogging coefficient, D₀ represents the effective opening size of the filter, and d_et signifies the equivalent particle size of the tailings sand, defined herein as d₂₀ [25].

In the above equation the effective pore diameter D₀ is determined by the empirical formula proposed by Liu [26] based on extensive hydraulic filling tests on cohesionless soils, as expressed by Equation (2).

$$D_0=0.63n{D}_{20}$$

(2)

where n denotes the porosity of the filter, and D₂₀ represents the particle size at which 20% of the filter material mass is finer by mass. The coefficient 0.63 in the formula originates from the empirical formula proposed by Liu [26], which was derived from systematic statistical analysis of extensive hydraulic filling test data on non-uniform cohesionless soils including experimental data from B.C. Istomina(B.C. Иcтoминa) and the China Institute of Water Resources and Hydropower Research, and reflects the statistical relationship between the effective pore diameter and the product of the equivalent particle size D₂₀ and the porosity n.

Theoretically, tailings sand is retained by the filter when its effective pore size D₀ is smaller than the characteristic particle size d_et of the tailings, whereas tailings penetrate the filter if D₀ > d_et. However, during actual experiments, the pores formed by filter particles exhibit size variability, and tailings particles are inherently non-uniform. Consequently, when the clogging coefficient λ > 1, internal clogging may still occur. The classification criteria for this phenomenon are defined in

Table 3. Clogging Mode Classification for Coarse-Grained Soils [24].

Mode	Surface Siltation	Surface-Internal Siltation	Internal Siltation	Non-Siltation
λ	<1	1~2	2~4	>4

.

The calculated clogging coefficients λ for the tested soils are presented in

Table 4. Calculation of Clogging Coefficients for Filters.

Conditions	Dry Density (g/cm3)	Specific Gravity	Void Ratio	Porosity	D20 (mm)	D0 (mm)	det (mm)	λ
ZS-1	1.72	2.72	0.58	0.37	10.59	2.45	0.48	5.11
ZS-2	1.79	2.72	0.52	0.34	9.58	2.06	0.48	4.30
ZS-3	1.85	2.72	0.47	0.32	6.67	1.34	0.48	2.80
ZS-4	1.86	2.72	0.46	0.32	5.00	1.00	0.48	2.07
ZS-5	1.88	2.72	0.45	0.31	3.51	0.68	0.48	1.42

. According to the classification criteria in Table 3, conditions ZS-1 to ZS-2 with λ > 4 exhibit non-siltation behavior, while ZS-3 to ZS-4 with 2 < λ < 4 demonstrate pore constriction-induced internal siltation. Condition ZS-5 with 1 < λ < 2 displays surface-internal siltation.

3.2. Particle Migration Patterns of Tailings Sand

Figure 2 illustrates the deposition of tailings sand on filter surfaces and their infiltration states during experiments. Red lines indicate the initial top and bottom boundaries of filters during sample preparation, while yellow dashed lines demarcate infiltration depths of tailings sand; yellow arrows and numbers further annotate the deposition thickness and infiltration depth. As shown in Figure 2a, filter ZS-1 (α = 20.8) contained the coarsest particles and its initial pore structure was excessively open. During testing, fine tailings sand particles penetrated directly through the filter layer and discharged from the base; internal pores were filled by fine particles, with only a thin clogging layer approximately 1 cm thick forming at the top surface. This indicates that when the initial interlayer coefficient is excessively large, the skeleton pore size of the filter layer is significantly larger than the tailings sand particles, such that effective internal retention cannot be established and fine particles predominantly penetrate through and are lost. This phenomenon validates the determination in the preceding section that for case ZS-1 the clogging coefficient λ exceeds 4, indicating that tailings sand particles penetrated through the filter layer and failed to form effective internal clogging. Excessive fine-particle migration through ZS-1 compromised tailings protection, deeming this filter ineffective. Thus, an interlayer coefficient α = 20.8 fails to satisfy the soil retention criterion for filter design.

Figure 2b shows that a substantial quantity of tailings sand particles entered and were retained within the filter layer, with clogging distributed over a relatively wide range such that traces of tailings sand clogging were clearly observable throughout the entire depth of the filter layer and the internal pores were essentially filled with fine particles. However, a markedly non-uniform distribution occurred along the depth direction, with the fine particle content in the upper portion significantly exceeding that in the lower portion, indicating that the filter layer was capable of establishing a certain degree of internal retention. Simultaneously, a thick clogging layer approximately 5.7 cm thick formed at the top surface of the filter layer, further inhibiting the migration of fine particles toward deeper regions. During the initial stage of testing, the relatively large initial pores of filter ZS-2 allowed a small number of tailings sand particles to penetrate through the filter layer and discharge from the base, yet as the upper and internal pores were gradually filled with fine particles, the seepage channels progressively narrowed and impeded the continued migration of upstream tailings sand particles toward the lower portion of the filter layer, causing the clogging state to eventually tend toward stability. Further analysis in conjunction with Figure 3 indicates that the clogging coefficient λ of filter ZS-2 slightly exceeds the critical value of 4, with λ equal to 4.30 as presented in Figure 4, and although this value approaches the boundary for the non-clogging classification, the actual seepage process did not exhibit sustained characteristics of penetration and loss. This is attributable to the fact that although a portion of fine particles penetrated during the early infiltration stage, the majority of particles were retained and deposited internally, and as clogging in the upper pores developed, the seepage resistance increased rapidly, ultimately achieving a stable clogging state dominated by internal filling and thick-layer deposition at the top surface. This demonstrates that filter ZS-2 possesses effective soil retention capacity, and its soil retention mechanism is manifested in that a small quantity of fine particles are allowed to penetrate during the initial stage, followed by rapid stabilization through internal self-clogging and thick-layer deposition at the top surface.

Figure 2c–e demonstrate that as the initial interlayer coefficient α decreases, the clogging depth of fine tailings sand particles within the filter interior progressively diminishes while the deposition depth above the filter layer increases correspondingly. Specifically, the clogging depth for ZS-3 (α = 10.4) is approximately 3.3 cm with an overlying deposition depth of approximately 8.8 cm, for ZS-4 (α = 8.3) the clogging depth is approximately 2.8 cm with an overlying deposition depth of approximately 12.4 cm, and for ZS-5 (α = 5.7) the clogging depth is approximately 1.9 cm with an overlying deposition depth of approximately 14.6 cm. This phenomenon is consistent with the clogging mode classification in Table 3 in that as α decreases, the initial pore structure of the filter layer becomes denser, reducing the number of tailings sand particles capable of entering internal pores, and more fine particles are intercepted at the filter surface and shallow layers, thereby decreasing the clogging depth while increasing the surface deposition thickness. During the clogging stabilization stage, the effluent at the outlet was observed to transition gradually from an initially turbid state containing substantial fine particles to a clear state, indicating that the filter layer achieves effective retention of tailings sand particles through the synergistic action of internal clogging and surface interception, thereby providing satisfactory soil retention performance, which demonstrates that the soil retention criterion for filter design is satisfied when α ≤ 10.4. Whereas Terzaghi’s criterion requires α to be less than 4, the results for ZS-3 permit a preliminary determination that the soil retention criterion in Terzaghi’s method is relatively conservative.

It is important to note that the proposed threshold of α ≤ 10.4 is derived from a limited dataset comprising five discrete initial gradation conditions. The interval between α = 10.4 (ZS-3) and α = 15.6 (ZS-2) represents a transition zone wherein the true critical value may reside; finer gradation increments within this range (e.g., α = 12, 13, 14) were not tested in the present study. Consequently, α = 10.4 should be regarded as the upper bound of the effective retention domain observed under the current experimental conditions, rather than a universally applicable design constant.

3.3. Particle Size Distribution of Tailings Sand Across Filter Zones

Upon completion of the sediment-laden seepage tests, the mass of tailings sand deposited on the filter surface, retained within the filter interior, and lost through penetration was statistically analyzed, and the results are presented in Figure 3. As the interlayer coefficient α decreased, the deposited mass of tailings sand particles on the filter surface increased progressively while the internal clogging quantity decreased correspondingly, indicating that the retention location of fine particles gradually concentrated toward the surface layer. For ZS-1 (α = 20.8), the excessively large interlayer coefficient resulted in an overly open internal pore structure, allowing fine tailings sand particles to penetrate directly through the filter layer and discharge from the base, with the retention mass on the top surface and within the interior accounting for only approximately 30% and the loss fraction approaching 70%, thereby rendering the filter nearly ineffective. For ZS-2 to ZS-5, the interlayer coefficients were relatively small, and the overall retention rate of tailings sand particles exceeded 97% with the loss controlled within 3%. However, the steady-state clogging characteristics differed among these conditions. ZS-2 (α = 15.6) achieved a final retention rate of 97% yet exhibited minor fine-particle penetration during the initial testing stage with a relatively delayed clogging stabilization process, representing a transitional state of initial leakage followed by stabilization, while ZS-3 to ZS-5 (α ≤ 10.4) achieved rapid retention from the initial seepage stage without obvious fine-particle penetration, representing a secure steady state. The 1% to 3% difference in retention rates among ZS-2 to ZS-5 essentially reflects the physical trend of clogging efficiency converging toward a limiting value as α decreases. From an engineering safety perspective, α ≤ 10.4 can serve as the upper bound of the effective retention domain, and this limit ensures that the filter layer possesses reliable soil retention performance from the initial service stage and avoids the early penetration risk manifested in ZS-2. In comparison, the qualitative transition in retention performance between ZS-2 to ZS-5 and ZS-1, from 70% loss to over 97% retention, clearly demonstrates that the filter layer experiences penetration failure when the initial interlayer coefficient α is excessively large (e.g., 20.8). Further comparison of the steady-state characteristics between ZS-2 (α = 15.6) and ZS-3 to ZS-5 (α ≤ 10.4) indicates that the filter layer enters a secure soil retention state from the initial seepage stage when α decreases to 10.4 and below. Under conditions ZS-2 to ZS-5, tailings sand particles were jointly retained on the filter surface and within the interior, achieving a total retention rate exceeding 97%, with surface deposition accounting for 71% to 93% and internal clogging accounting for 7% to 26%. This indicates that as α decreases, the retention mechanism gradually shifts from internal filling dominance to surface interception dominance, and the integrated filter–clogging layer system provides effective protection for upstream tailings sand particles. Specifically, ZS-4 and ZS-5 achieved surface deposition rates of 88% and 93% respectively, demonstrating that when α is relatively small, the soil retention requirement in Terzaghi’s criterion for protecting at least 85% of the protected soil particles from loss is satisfied.

Figure 4 presents the mass content of tailings sand particles clogged within the filter across all tests. For conditions ZS-2 to ZS-5, the internally retained tailings mass progressively decreased with infiltration depth. Specifically, in layers L₁ to L₄, the percentage of fine tailings particles clogged in the uppermost layer (L₁) accounted for 48.9, 65.6, 86.8, and 84.5 percent of total internal clogging mass respectively, indicating predominant accumulation near the surface. This distribution arises from kinetic energy dissipation during particle migration through filter pores. Under consistent gravitational and hydraulic driving forces, the probability of individual particles traversing successive filters diminishes with depth [27], resulting in exponential attenuation of particle retention along the depth profile [28]. Concurrently, finer filter gradations increase collision frequency between particles and pore walls, amplifying kinetic energy loss per layer. Consequently, the mass of internally retained fine particles sequentially decreased from ZS-2 to ZS-5. Figure 4b,c elucidate the operational mechanism: partial particle ingress into the filter fills pores to establish stability, thereby preventing subsequent particle exfiltration and promoting surface deposition. Notably, finer filter gradations require less internally retained mass to achieve stabilization. As Figure 3 data confirm, ZS-4 and ZS-5 satisfied Terzaghi’s soil retention criterion solely through surface deposition (88% and 93% retention respectively). In contrast, ZS-2 and ZS-3 achieved compliance (97% and 99% total retention) only by combining surface accumulation with internal particle retention. This substantiates that effective filtration is not attributable to the filter alone but emerges from the joint filtration effect achieved by the filter and its retained particle matrix.

3.4. Hydraulic Conductivity Analysis of Filter

The preceding section established that over half of retained tailings particles clogged within the L₁ layer in effective filters ZS-2 to ZS-5. This implies that the void ratio and hydraulic conductivity of L₁ must be lower than those of underlying layers (L₂~L₄). To investigate filter hydraulic conductivity, the surface-deposited tailings layer (L₀) and the uppermost filter (L₁) were examined (as illustrated in Figure 1). Hydraulic conductivities and hydraulic gradients at L₀ and L₁ during testing were calculated through statistical analysis of piezometric readings and seepage flow rates.

Figure 5a–d present the temporal variations in hydraulic conductivity for layers L₀ and L₁ during sediment-laden seepage in test conditions ZS-2 to ZS-5, and the time axis is normalized to facilitate analysis. It can be observed that during the initial stage of sediment-laden seepage, a substantial quantity of tailings sand entered the filter interior to cause clogging and rapidly accumulated on the filter surface, resulting in sharp decreases in the hydraulic conductivities of both L₁ and L₀. Specifically, the hydraulic conductivity of the filter layer K₀ in ZS-2 decreased from an initial value of 23.92 cm/min to a steady-state value of approximately 0.14 cm/min, representing a reduction of 99.4%, while the hydraulic conductivity of the tailings sand deposition layer K₁ decreased from an initial value of approximately 36.79 cm/min to a steady-state value of approximately 3.27 cm/min, representing a reduction of approximately 91.11%. Similar trends were observed for ZS-3 to ZS-5, with K₀ reductions of 98.6%, 99.2%, and 98.6%, and K₁ reductions of 91.6%, 94.5%, and 92.4%, respectively. As tailings sand continuously accumulated on the filter surface, the overall permeability of the specimen gradually became controlled by the tailings sand in layer L₀, and the piezometric levels and flow rates stabilized at this stage, indicating that clogging had entered a stable phase and the hydraulic conductivity had tended toward a constant value. Under steady-state conditions, the hydraulic conductivity of the filter layer K₀ for all test conditions decreased to the order of 0.1 cm/min, while the hydraulic conductivity of the deposition layer K₁ was maintained in the range of 0.42 to 3.27 cm/min, and the hydraulic conductivity of the filter layer remained consistently higher than that of the tailings sand deposition layer by a factor of approximately 6.2 to 23.7, which indicates that the filter skeleton retained relatively high permeability after clogging while the surface deposition layer provided the primary seepage resistance.

Figure 6a–d present the temporal variations in hydraulic gradients for layers L₀ and L₁ during sediment-laden seepage in test conditions ZS-2 to ZS-5. Unlike the trends shown in Figure 5, the hydraulic gradient of layer L₀ increased significantly and tended toward stabilization as infiltration progressed, whereas the hydraulic gradient of layer L₁ exhibited varying degrees of initial elevation due to pore pressure accumulation and subsequently decreased rapidly to reach a stable state. Specifically, the steady-state hydraulic gradient values i₀ for ZS-2 to ZS-4 were concentrated in the range of 11.5 to 12.8, representing increases of approximately 0.8 to 3.1 times the initial values, while for ZS-5 the steady-state i₀ value was approximately 9.1 with an increase of approximately 1.9 times due to its relatively dense initial skeleton. The hydraulic gradient i₁ of the filter layer exhibited an opposite trend, decreasing from an initial value of approximately 3.7 to a steady-state value of 0.5 for ZS-2 with a reduction exceeding 85%, and to approximately 0.9, 1.2, and 1.4 for ZS-3 to ZS-5 respectively. At steady state, the i₀/i₁ ratios for all test conditions ranged between 6.3 and 23.7 and decreased with decreasing initial interlayer coefficient α, which is consistent with the variation pattern of the permeability margin of each filter layer and indicates that a smaller α results in the surface thick deposition layer bearing more head loss while the filter skeleton still maintains sufficient drainage capacity. This is because during the initial infiltration stage, fine tailings sand particles entering layer L₁ formed clogging within the pores, causing pore pressure in L₁ to be unable to dissipate in time and thus producing an initial elevation of the hydraulic gradient. During the middle and late stages, the natural release of pore pressure through the underlying filter layer and the redistribution of fine tailings sand particles within the filter layer under seepage forces caused the pore pressure in L₁ to gradually decrease and eventually stabilize. The tailings sand layer deposited on the filter surface possesses lower permeability relative to the filter layer, preventing the dissipation of pore pressure in L₀ and causing its hydraulic gradient to increase rapidly and ultimately stabilize at a relatively high level.

Beyond soil retention, filters must simultaneously satisfy hydraulic conductivity requirements to reduce internal pore pressures and control phreatic surfaces within embankments. Terzaghi stipulates that filter hydraulic conductivity should be governed by Equation (3) [26]. Post-clogging measurements for ZS-2 to ZS-5 yielded i_b/i_f ratios of 23.68, 13.16, 10.68, and 6.26 respectively, confirming compliance with drainage-induced pore pressure reduction requirements.

$${\displaystyle \frac{i_b}{i_f}}={\displaystyle \frac{K_f}{K_b}}\ge 4~16$$

(3)

where K_b and i_b denote the hydraulic conductivity and prevailing hydraulic gradient of the base soil, respectively, and K_f and i_f represent the hydraulic conductivity and prevailing hydraulic gradient of the filter, respectively.

3.5. Optimum Gradation Curve for the Filter

Section 3 demonstrates that filter designs ZS-2 to ZS-5 satisfy both soil retention and hydraulic conductivity criteria, with fine tailings particles predominantly clogged in layer L₁. Consequently, the gradation of L₁ after sediment-laden seepage defines the optimal filter design curve under self-clogging conditions, as illustrated in Figure 7. Here, D_max and D_min represent the upper and lower boundary envelopes specified in the Design Code for Rolled Earth-Rock Dams (NB/T 10872-2021), hereafter referred to as the Code [29]. The filter design method in this Code is based on Terzaghi’s filter criterion (α < 4) and the permeability criterion as theoretical foundations, combined with empirical corrections. Compared to the Code’s envelope method, the Natural Clogging Method explicitly defines the filter gradation curve. Final gradation curves of ZS-2 to ZS-5 align with the Code’s envelopes, where gradations ZS-2 to ZS-4 exhibit marginally higher coarse fraction content (5~20 mm range) than the upper boundary D_max, indicating that moderate relaxation of coarse particle limits does not compromise soil retention. ZS-5’s curve fully complies with the envelope, with characteristic particle sizes D₁₅ = 1.19 mm and D₈₅ = 15.75 mm (as shown in

Table 5. Final Gradation Parameters of Filters.

Conditions	D15	D85	d85	Interlayer Coefficient α
ZS-2	0.554	17.68	0.48	1.15
ZS-3	0.87	17.35	0.48	1.81
ZS-4	1.13	16.98	0.48	2.35
ZS-5	1.19	15.75	0.48	2.48

Note: D_n denotes the particle size at which particles finer than this size constitute n% by mass of the filter material (unit: mm). d₈₅ represents the particle size at which particles finer than this size account for 85% by mass of the tailings sand (unit: mm).

), and the corresponding steady-state interlayer coefficient α = 2.48, satisfying and substantially falling below the safety limit of Terzaghi’s criterion α < 4. This confirms that filters designed by Natural Clogging Method satisfy the Code’s requirements and simultaneously meet both soil retention and hydraulic conductivity demands. Fundamentally, ZS-5’s gradation evolved through physical self-organization rather than empirical estimation, as natural clogging during infiltration formed a stable composite structure with retained particles. This demonstrates that leveraging soil’s self-filtration capability aligns with the Code’s safety principles, establishing the method’s scientific validity and engineering rationality.

The characteristic particle size parameters of the final gradation curves for ZS-2 to ZS-5, designed via the Natural Clogging Method, are presented in Table 5. It can be observed that for the filter gradation curves of ZS-2 to ZS-5, D₁₅ progressively increases while D₈₅ gradually decreases. Filters with smaller initial interlayer coefficients develop enhanced uniformity during advanced clogging stages. The interlayer coefficients α for all four filters range between 1.15 and 2.48, all significantly below the conservative limit of α < 4 recommended by Terzaghi’s criterion, indicating that the post-clogging gradation possesses an adequate safety margin within the Terzaghi framework. In summary, the filters designed by the Natural Clogging Method proposed in this study satisfy both soil retention and hydraulic conductivity requirements.

Comparison with Terzaghi’s criterion and the conventional envelope method further elucidates the advantages of NCM proposed in this study. In terms of soil retention, the filters designed by NCM (ZS-2 to ZS-5) achieved measured retention rates of 97% to 99% for the protected soil, with steady-state interlayer coefficients stabilized between 1.15 and 2.48, which are substantially lower than the conservative limit of 4 in Terzaghi’s criterion, indicating that the post-clogging gradation possesses a considerable safety margin against piping. Regarding permeability, the measured i_b/i_f ratios ranged from 6.26 to 23.68, satisfying and exceeding the permeability requirements of Terzaghi’s criterion (typically i_b/i_f ≥ 4 to 16). Unlike conventional methods that merely provide a gradation envelope range, NCM delivers a specific gradation curve under real seepage conditions, transforming the design process from empirical selection within an envelope into a deterministic output. Furthermore, NCM permits an initial interlayer coefficient of 10.4, whereas Terzaghi’s criterion strictly requires α to be less than 4, which reduces the demand for intermediate particle sizes and broadens the selection range of coarse filter materials. It should be noted that a complete quantitative comparison involving material costs, construction volume, and full life-cycle economic assessment remains to be addressed in future research.

4. Discussion and Limitations

Despite the design potential demonstrated by the Natural Clogging Method (NCM) proposed in this study under experimental conditions, this research remains at the proof-of-concept stage and is subject to several limitations.

First, this study employed only the medium tailings sand from the Lixi tailings dam as the protected soil, and proposed a soil retention threshold of α ≤ 10.4 based on five discrete initial gradations (α = 20.8, 15.6, 10.4, 8.3, and 5.7). This threshold currently represents an experimental observation with a restricted validation range, and its statistical significance is constrained by the limited sample size. Meanwhile, given the absence of intermediate gradation increments between α = 10.4 and 15.6, the comparison between ZS-2 (α = 15.6) and ZS-3 (α = 10.4) indicates that a transition zone may exist within this interval: the filter layer approaches failure when α exceeds approximately 15.6, whereas it tends toward a secure retention state when α decreases to the vicinity of 10.4 and below. Therefore, α = 10.4 represents only the upper bound of the effective retention domain observed under the current experimental conditions, rather than a universal design constant. This threshold is currently applicable only to fine-grained cohesionless soils similar to the tested tailings sand, and the applicability boundaries for cohesive soils, wide-gradation gravels, and other tailings materials with different mineral compositions, particle shapes, or gradation characteristics remain to be verified through future experiments with expanded soil sources and intermediate gradation increments (e.g., α = 12, 13, 14).

Second, it should be noted that all tests were conducted as single-run experiments without replication. The primary uncertainties in this test originate from the measurement error of the electronic balance (precision 0.01 g), standard sieve analysis losses, mass fluctuations during oven drying at 105 °C, flow rate measurement errors by the volumetric cylinder and stopwatch method, and operational errors in stratified sampling. These measurement errors primarily affect the precise values of the retention ratio, yet their cumulative effect is far from sufficient to alter the qualitative distinction between ZS-1 (approximately 70% loss, representing filter failure) and ZS-2 to ZS-5 (retention ratio > 97%, representing effective filtration). The 1% to 3% difference in retention rates among ZS-2 to ZS-5 falls within the superimposed range of measurement uncertainty and material inherent response variability under different gradation conditions, and should be interpreted as the physical trend of clogging efficiency converging with decreasing α, rather than a statistically significant quantitative distinction. The core conclusion of this study, namely that α ≤ 10.4 serves as the upper bound of the effective retention domain, does not depend on these minor differences but is based on the qualitative distinction between failure and effectiveness. Future research will conduct replicate tests targeting the transition zone (α = 10~16) to separate measurement errors from material inherent variability and establish the statistical confidence interval for this threshold.

Furthermore, the Natural Clogging Method proposed in this paper represents a promising laboratory-scale design method, and its broader engineering applicability remains to be validated through large-scale model tests or field measurement studies. This test aimed to determine the steady-state clogging gradation as a material design parameter, which falls within the scope of gradation characterization. The seepage apparatus adopted a diameter of 10 cm, approximately five times the maximum particle size, satisfying the dimensional requirements for seepage tests on coarse-grained soils, and existing literature [2] has also commonly employed this scale to investigate filter performance. It should be noted that when applying the laboratory-determined gradation curve to full-scale tailings dams, field factors such as overburden stress, multidimensional seepage paths, and construction heterogeneity may influence the service evolution of the clogging layer, yet they do not alter the basic material gradation determined by standardized testing. The extent to which these field factors affect long-term applicability remains to be further investigated through field trials or centrifuge modeling.

Finally, the design gradation obtained in this study represents only the material parameter for the initial design stage. During decades of service in actual tailings dams, long-term factors such as cyclic hydraulic loading, chemical precipitation, and biological action may cause the permeability of the clogging layer to deviate from design expectations. Therefore, the method proposed in this paper is currently applicable primarily to the initial gradation design of filter layers, and the degradation patterns of long-term performance, maintenance cycles, and replacement criteria remain to be further investigated through long-term monitoring.

In summary, this study has preliminarily established a promising laboratory-scale filter design method through natural clogging tests, and its effectiveness has been validated under experimental conditions. Future work will focus on verification across multiple soil types, long-term progressive clogging evolution mechanisms, durability assessment of the design gradation, and validation of field-scale applicability, to advance this method from the laboratory design stage toward complete engineering application.

5. Conclusions

This study fully exploits the self-filtering effect during soil clogging to propose a filter design method based on the natural clogging concept. The method adopts the Terzaghi interlayer coefficient as the initial design parameter, forms a stable clogging layer within the filter through laboratory sediment-laden water infiltration tests, and adopts the measured post-clogging gradation as the design gradation. This approach integrates the combined influence of the interlayer coefficient and pore characteristics on both soil retention and permeability, resolves the inability of conventional envelope methods to specify a precise gradation curve, and provides a new technical approach for the design of filters for fine-grained tailings sand. The principal conclusions are presented in the subsequent discussion.

• An initial interlayer coefficient α ≤ 10.4 achieves base soil retention > 97% (loss ≤ 3%), satisfying soil retention criteria.
• Filters designed via the Natural Clogging Method concurrently meet soil retention and hydraulic conductivity requirements. Final α values for ZS-2–ZS-5 range between 1.15~2.48, complying with Terzaghi’s retention threshold, while i_b/i_f ratios of 6.26~23.68 fulfill hydraulic conductivity requirements.
• Unlike traditional envelope-based approaches, this method explicitly defines specific filter gradation curves. The final curve for ZS-5 largely aligns with the gradation envelope recommended in the Code.

The Natural Clogging Method provides theoretical innovation and technical support for filter design in earth–rock dams and tailings ponds. Its core contribution is overcoming the limitation of “gradation-by-characteristic-size” conventions through natural gradation optimization via simulated seepage-clogging processes.