Centrifuge Modeling of Chloride Ions Completely Breakthrough Kaolin Clay Liner

Abstract

The 2 m thick compacted clay liner with a permeability coefficient of 1 × 10⁻⁷ cm/s is required in the Chinese technical specifications about landfills. The processes of chloride ion completely breakthrough low permeability barriers (k ≤ 1 × 10⁻⁷ cm/s) were modeled at 50 g in a geo-centrifuge. A measuring system was used to monitor solute velocity and conductivity. The entire process of chloride ion completely breaking through 2 m Kaolin clay liner was modeled successfully, which provided a valuable testing technology for centrifuge modeling of contaminant transport through low-permeable clay. The analyses results indicated the breakthrough time of conservative pollutant for the 2 m clay liner with a hydraulic conductivity of 1.0 × 10⁻⁹ m/s under Δh_w of 40 m was 1.6 years. As for strongly adsorptive pollutants, the breakthrough time t_0.1 increased by 9 times when R_d increased from 1 to 10, which indicates that the effect of R_d on the performance of the liner was significant.

1. Introduction

With the gradual increase in the number of old-type landfill sites in China, the transport of pollutants in landfills has been concerned widely [1,2,3]. When the monitoring results of pollutants transport cannot be obtained from field tests, the centrifugal model is also an approach to figure out pollution [4]. The primary mechanisms for pollutants transport in porous media include advection, hydrodynamic dispersion (molecular diffusion and mechanical dispersion), and adsorption [5,6], which are usually described by an advection–dispersion equation [5,6,7]:

$$R_d\frac{\partial C}{\partial t}=\frac{\partial }{\partial z}\left(D_h\frac{\partial C}{\partial z}\right)-v_s\frac{\partial C}{\partial z}$$

(1)

where v_s is the actual pore-water velocity, and D_h is the hydrodynamic dispersion coefficient. D_h = D_d^* + D_m, D_d^* = τD_d, and D_m = αv_s, D_d^* is the coefficient of effective diffusion, τ is the tortuosity factor, D_d is the molecular diffusion coefficient of the pure solution, D_m is the mechanical dispersion coefficient, and α is the dispersivity. R_d is the retardation factor, C is the pore-water concentration, t is the time, and z is the migration distance. It is important to obtain pollutant transport parameters for evaluating the service life of anti-pollution barrier.

In the late 1980s, researchers began to use centrifuge modeling technology to study the transport of pollutants in soils. It is tremendously advantageous to use geotechnical centrifuge to simulate the long-term transport of long-lived pollutants. The simulation principle is as follows: a high-speed rotating long-arm centrifuge is used to produce hundreds of times the acceleration and the scaling relationships are shown in

Table 1. Centrifuge scaling relationships [8].

Physical Quantity	Unit	Similarity Scaling (Model: Prototype)
Acceleration of gravity	m/s2	N
Size	m	1/N
Stress	kPa	1
Density	kg/m3	1
Porosity	1	1
Viscosity coefficient	Pa·s	1
Permeability coefficient	m/s	N
Concentration	mg/L	1
Time (advection and molecular diffusion)	s	1/N2
Velocity	m/s	N
Molecular diffusion coefficient	m2/s	1

.

A number of studies on simulating pollutant migration using centrifuge have been conducted. Celorie et al. [9] simulated the migration of NaCl solution in Kaolin clay with a small laboratory centrifuge. During the test, the leachate was been collected after the centrifuge was stopped at intervals. The process of the start up and shut down of the centrifuge would cause unstable seepage, which made the actual breakthrough time smaller. Arulanandan et al. [10] deduced eight linearly independent dimensionless groups and proved the feasibility of simulation of pollutants with centrifuge tests. In the test, the concentration was determined by measuring the resistance through the resistance sensor embedded in the model. Hensley et al. [11] determined the concentration of chloride ion in silt by measuring the resistance change through the resistance sensor embedded in the model of soil, and proved that the centrifuge modeling technology could provide effective test data for the verification of the mathematical model. Depountis et al. [12] used an assessment of miniaturised electrical imaging equipment to monitor the chloride ion pollution plume’s evolution in models during centrifuge tests. In the above experiments, the concentrations of pollutant in model were determined by measuring resistivity of the model soil. Mckinley et al. [13] carried out centrifuge modeling of the transport of chloride ion in saturated Kaolin clay layer. In the test, the model was sliced into pieces. The profile concentration along depth of the model was obtained, and a series of pollutant transport parameters were obtained. The permeability coefficient of the silt model was 12 × 10⁻⁷ cm/s. Nakajima et al. [14] used a geo–centrifuge to simulate the migration of sodium chloride solution in silica sand and clay models. In the experiment, the embedded resistance sensor was used to determine the conductivity change so that the concentration of chloride ion is obtained. The permeability coefficients of the silica and clay model was 2.3 × 10⁻³ cm/s and 1.4 × 10⁻⁶ cm/s, respectively. Lo et al. [15] carried out the centrifuge modeling of Cd transport in saturated and unsaturated soils. A time-division collection device with a rotatable bottom was proposed in this paper. Timms et al. [16] used a small indoor centrifuge to simulate the sodium chloride transported in clay. The pollutant solution was collected at different times after the machine stopped so that a breakthrough curve was obtained. Zeng et al. [17] carried out centrifuge modeling of lead(Ⅱ) transport in compacted clay liner. In the test, three different adsorption isotherms were considered to analyze the performance of clay liner. Therefore, there was large quantity of works about modelling pollutant transport in centrifuge that focused on pollutant breaking through the barrier with high permeability coefficients. The resistance sensor was usually used to obtain the profile concentration [10,11,12,14]. The effluent concentration was difficult to monitor in real time. Therefore, it was urgent to find a method to monitor the flux and concentration of effluents in centrifuge in real time.

The 2 m thick compacted clay liner with a permeability coefficient of 1 × 10⁻⁷ cm/s is required in the Chinese technical specifications for landfill. However, centrifuge modeling tests for pollutant transport in low permeability barriers (k ≤ 1 × 10⁻⁷ cm/s) have been reported rarely. A concentration measurement is a technical difficulty in pollutant transport centrifugal tests. It can be observed from the report that the methods to obtain profile concentration include testing conductivity to deduce concentration in soil, directly testing the actual concentration by slicing, and the methods for obtaining bottom outflows include collecting by stopping the machine (for small laboratory centrifuges) and time-division collection devices with bottom rotation. The applicability of these methods is relevant to the type of soil, the permeability coefficients of the models, and the test conditions.

In this paper, a centrifuge modeling test of 4 cm thick kaolin clay liner was carried out at 50 g centrifugal accelerations. Moreover, the entire process of 2 m thick clay liner prototype being broken through by chloride ion at high water head was simulated. A set of real-time monitoring device for seepage flow and effluent concentration was used in the geo–centrifuge, which provided an effective centrifuge modeling test technology for the study of pollutants breaking through low-permeability coefficient barriers.

2. Test Scheme

2.1. Model Materials

Commercial kaolin clay was used for preparing the soil column models. Kaolin clay was named Jiangsu kaolin clay for its origin.

Table 2. Physical parameters of Jiangsu kaolin clay [18].

Soil Type	Specific Gravity Gs	Clay Content (%)	Liquid Limit wL(%)	Plasticity Index Ip(%)	Mean Particle Size d (mm)
Jiangsu kaolin clay	2.61	67.8	67.1	34.6	0.003

lists the physical properties of this kaolin clay [18]. Figure 1 presents the gradation curve of the kaolin clay. It shows that this kaolin clay had a high clay-crumb content and its mean particle diameter was 0.003 mm. According to the 17 mm plasticity chart, the Jiangsu kaolin clay was classified as high liquid-limit clay. In this study, inert chloride ion was used as a tracer pollutant, and its absorbability can be ignored [9,10].

2.2. Test Equipment and Apparatus

Figure 2 presents a photograph of the clay model set up in a model cylinder. The model cylinder, including a top cover and a bottom pedestal, was made of polymethyl methacrylate. The inner diameter, wall thickness, and height of the model cylinder were 10 cm, 1 cm, and 25 cm, respectively. Both the top cover and bottom pedestal can be detached from the model cylinder. When they are set up, a rubber washer was used for sealing at their connections to the cylinder. A shallow, cross-shaped slot was produced on the pedestal, and effluent holes were created at the ends of the slot. A hole was also created at the center of the top cover and connected to a Mariotte bottle that was used to maintain a constant hydraulic head.

A custom-built reaction frame for loading was used to consolidate the model. A pressure dial was installed on the reaction frame to control the load. A dial indicator with a measuring range of 5 cm and a minimum reading of 0.01 mm was installed on the pressure rod to monitor the consolidation settlement of liner models.

As the centrifuge modeling tests were performed under a high-speed rotation condition, an effluent collection device was developed to automatically monitor the flux and concentration of effluent from the model’s bottom, as shown in Figure 3. The collection device consisted of a pair of twin cylinders that were made of acrylic and both were opened on the top. One of the cylinders was connected to the pedestal of the model cylinder for collecting effluent, and the other was partially filled with a constant head of water acted as a reference cylinder. The twin cylinders were connected to a high-solution differential pressure transducer through the holes produced on the sidewall near the bottom of each cylinder. During the test, the change of hydraulic pressure between the effluent collection cylinder and the reference cylinder was recorded by the differential pressure transducer. The effluent volume and flux could be calculated according to the recorded data and inner diameter of the twin cylinders. An electrical conductivity sensor was installed at the bottom of the effluent collection cylinder to measure the concentration of the accumulated effluent. Both the differential pressure transducer and the electrical conductivity sensor were calibrated in advance. A mathematical analysis was provided to calculate the relationship between concentration (C_W) and conductivity (S): C_W < 40, C_W = 0.1183S and C_W ≥ 40, C_W = 0.2652S − 48 (see Figure 4).

Centrifuge modeling tests were carried out at the 400 gton geotechnical centrifuge facility [19,20]. The maximum acceleration of the centrifuge was 150 g and the rotation arm diameter was 4.5 m. The acceleration of the centrifuge increased from 0 to 50 g took 8 min, and the stop time was the same.

2.3. Model Preparation

The model was prepared through the compression and consolidation of remolded clay. To ensure the full saturation, homogeneity, and reproducibility of soil samples, The dried kaolin clay powder was mixed with deionized (DI) water and was stirred in a vacuum mixture for an initial water content of 180%, which was 2 times higher than the measured liquid limit of the kaolin clay. The mixture was vacuum pumped during the mixing process for 2 h. The kaolin clay slurry exhibited good liquidity. A corresponding mass of slurry was loaded into the custom-built PMMA sample cylinder. The slurry was liquid with high water contents and the saturation of the slurry reached 99%. Because of its extremely low strength, the slurry could not be compressed and consolidated directly. Therefore, the slurry was allowed to drain and consolidate for 1d under self-weight stress naturally. After the strength of the slurry increased a certain degree, two 1.275 kg weights were used to preload the soil sample for 1 day. A custom-built compression and consolidation device was used to compress and consolidate the soil sample step-by-step with a series of pressure levels (25 kPa, 50 kPa, 100 kPa, 200 kPa, and 400 kPa) afterward. To effectively monitor the conductivity of the effluent from the bottom of the model, it was necessary to reduce interference from the background conductivity of the model’s material. Therefore, after the model consolidated, DI water with a high hydraulic head was used to leach the model to reduce the conductivity of the effluent until it became stable, which was at approximately 40 μm/cm (Figure 5).

2.4. Test Process

After the preparation of a soil column, the model cylinder was connected to the hydraulic head controlling device, and the permeability coefficient of the soil column was measured. Thereafter, the weight and height of the soil column were measured. Prior to each centrifuge modeling test, the model cylinder was filled with sodium chloride solution (chloride ion concentration: 1050 mg/L) and then connected with a Mariotte bottle filled with the same solution. The Mariotte bottle was used to keep the required hydraulic head. The hydraulic head difference Δh_w applied on the soil column was set as 80 cm (40 m as corresponding prototype hydraulic head difference) by adjusting the elevation of the Mariotte bottle. The discharge hole at the bottom of the model cylinder was connected to the effluent collection device. The entire setup of test apparatus, including the model cylinder, the Mariotte bottle, and the effluent collection device, was installed on the centrifuge (see Figure 6). The test was started by opening both the two control valves for inflow and outflow, and then the centrifuge was spined to the specified acceleration (50 g). The test was running at 50 g for 24 h. At the end of the test, the centrifuge was turned down, and both the valves for the inflow and outflow were turned off. Then, the residual solution on the soil column was removed, and the soil column was pushed out and weighed. The effluent collection device was weighed to determine the total volume of the effluent.

The soil column was sliced into pieces at about 5 mm thick to determine the distribution of pollutants along the transport direction, i.e., the depth. The mass of soil-sample sections was recorded. Approximately 10 g of each soil sample was dried to measure water content. Approximately 1 g of soil sample was separated from the remained sections and then mixed with 50 mL of DI water. The mixture was oscillated for 24 h. After the mixture was centrifuged, 1 mL of the supernatant was collected, which was then diluted to 100 mL using DI water. An ion chromatograph was used to analyze the concentration of chloride ion in the diluted solution, and the corresponding concentration of chloride ion inside the soil-sample section was then determined. Then, the concentration profile of chloride ion was acquired.

3. Model Parameters and Result Analyses

3.1. Permeability Coefficient Analysis of Model

Before the centrifugal test, the permeability coefficient of the model can be measured by leaching the model. After the centrifugal model test, the permeability coefficient of the model can also be obtained according to the reduced water volume of the Mariotte bottle, the effluent volume of the collection cylinder, and the differential pressure sensor. The centrifuge modeling test was conducted at 11 °C at the beginning and 15 °C one hour later. The room temperature in the centrifuge chamber was stable at 19.6 °C, and the temperature correction coefficient of permeability coefficient was 1.012. The permeability coefficient can be calculated from the velocity. Figure 7 shows the real-time velocity obtained by the differential pressure sensor during the centrifuge test. The centrifugal model is consolidated under high osmotic pressure, and there was unstable seepage flow in the model in the meantime, which had influence on the pollution transport and pore-water velocity [20]. Therefore, the pore-water’s velocity increased with time. After a period of maximum centrifugal acceleration, the model was no longer consolidated and the pore-water velocity was steady almost. The pore water velocity fluctuated slightly in the later stage of centrifugal model test. It may be influenced by temperature rising during centrifugation. The permeability coefficients obtained in different stages and approaches are shown in

Table 3. The permeability coefficients obtained by different methods at different stages.

Different Method	Before the Centrifugal Test	During the Centrifugal Test
	Leaching	From Mariotte Bottle	From Collection Cylinder	From Differential Pressure Sensor
k20 (× 10−9 m/s)	0.950	0.913	0.929	0.962

. It can be found that the average of permeability coefficients obtained by the three methods in the centrifugal test is 0.935 × 10⁻⁹ m/s, which decreased by 1.6% than the penetration coefficient determined before the test. In the centrifugal test, the permeability coefficients obtained by the three methods are also slightly different, with an error rate of less than 3% relative to the mean. It can be seen that the permeability coefficient of the model remains basically stable on the whole. On the other hand, it showed that the differential pressure sensor can effectively monitor real-time velocity at the bottom of the model. The average of permeability coefficients in centrifugal test is used in the analysis.

3.2. Analyses of Model Concentration

After the centrifugal test, the concentration of chloride ion in the collection cylinder was measured as 336.4 mg/L, and the volume of effluent was 1329.33 mL, so the total mass of chloride ion was 447.1863 mg. The transport parameters of the model are shown in

Table 4. The parameters of the model.

	H (cm)	Void Ratio e	Moisture Content w	Δhw (cm)	k20 (m/s)	vs (m/s)	Dh (m2/s)
M1	4.08	1.614	61.8%	80	9.35 × 10−10	1.45 × 10−6	20.65 × 10−10

. The values of height, hydraulic head, permeability coefficient, and velocity of the model were measured, and the value of the hydrodynamic dispersion coefficient was fitted. Details are as follows.

The apparent real-time variation in conductivity was detected in the collection device at the bottom during the centrifugal test, and the cumulative effluent concentration of the model was acquired. The results are presented in Figure 8. The chloride ion concentration profile of the model was acquired by section analysis at the end of the test, and the results were shown in Figure 9. The model is completely broken through, and the profile concentration value C/C₀ fluctuated around 1.

The one-dimensional transport problems in the abovementioned models can be described using Equation (1) (the advection–dispersion equation); its definite conditions are as follows.

$$\mathrm{Initial}\mathrm{condition:}{C}_r\left(x,0\right)=0$$

(2)

$$\mathrm{Inflow}\mathrm{boundary:}\left[v_s{C}_r(0^{+},t)-D_h\frac{\partial C_r\left(0^{+},t\right)}{\partial x}\right]=v_s{C}_0$$

(3)

$$\mathrm{Outflow}\mathrm{boundary:}\frac{\partial C_r\left(\infty ,t\right)}{\partial x}=0$$

(4)

The solution of the above problem is as follows:

$$\frac{C_r\left(x,t\right)}{C_0}=\frac{1}{2}efrc\left(\frac{R_{d}x-v_{s}t}{2\sqrt{D_h{R}_{d}t}}\right)+\sqrt{\frac{v_s{}^{2}t}{\pi D_h{R}_d}}\exp \left[-\frac{{\left(R_{d}x-v_{s}t\right)}^2}{4D_h{R}_{d}t}\right]-\frac{1}{2}(1+\frac{v_{s}x}{D_h}+\frac{v_s{}^{2}t}{D_h{R}_d})\exp \left(\frac{v_{s}x}{D_h}\right)erfc\left(\frac{R_{d}x+v_{s}t}{2\sqrt{D_h{R}_{d}t}}\right)$$

(5)

The inflow boundary described in Equation (3) represents continuous flux, which is suitable for the analysis of the pore-water concentration profile in a model [21,22,23]. For models in which complete breakthrough occurs.

$$C_e=\frac{J\left(L^{-},t\right)}{v_s}=C_r(L^{-},t)-\frac{D_h}{v_s}\frac{\partial C_r\left(L^{-},t\right)}{\partial x}$$

(6)

where C_e is generally defined as the effluent concentration [21,22,23]; its detailed expression was calculated by using the common Ogata solution, which is obtained by substituting Equation (5) into Equation (6). Therefore, the expression of the effluent concentration at the bottom of the soil column test is as follows.

$$\frac{C_e}{C_0}=\frac{1}{2}\left[erfc\left(\frac{z{R}_d-v_{s}t}{2{(D_h{R}_{d}t)}^{1/2}}\right)+\exp \frac{v_{s}z}{D_h}erfc\left(\frac{z{R}_h+v_{s}t}{2{\left(D_h{R}_{d}t\right)}^{1/2}}\right)\right]$$

(7)

The effluent breakthrough curve and the cumulative curve can be calculated based on Equation (7).

In the transport process, the pore velocities of the models were measured values, and the adsorption of chloride ion was not considered: R_d = 1. Therefore, only one parameter (the hydrodynamic dispersion coefficient, D_h) needed to be fitted based on the concentration curve. In general, according to Equation (5), the concentration profile points obtained in the test can be fitted, and the hydrodynamic dispersion coefficient D_h can be obtained. However, the model is completely broken through, and the theoretical concentration profile should be a vertical line. Thus, D_h cannot be obtained through profile fitting, and the conductivity curve of the accumulated effluent obtained in the test should be used. According to the relationship between calibrated conductivity and concentration, the conductivity curve can be transformed into a cumulative concentration curve and effluent concentration (7). The theoretical accumulative concentration curve can be acquired, so D_h = 2.065 × 10⁻⁹ m²/s can be fitted (see Table 4). The fitting curve was shown in Figure 8. The measured curve was identical with the theoretical curve. The final total accumulated chloride ion mass in the collection cylinder obtained through theoretical calculation was 446 mg, which basically coincided with the measured value (447.186 mg). The corresponding theoretical concentration profile was shown in Figure 9, which was indeed a vertical line and coincided with the measured data points. It showed that the curve of cumulative concentration measured coincided with the profile concentration data, and the test data were valid. The electrode can effectively monitor the cumulative conductivity of the outflow under centrifugal state.

4. Prediction of Clay Liner Breakthrough Time

As the 2 m thick compacted clay liner with permeability coefficient of 1 × 10⁻⁹ m/s is required in the Chinese technical specifications for landfills [24,25,26], the performances of this compacted clay liner were analyzed at different hydraulic heads. The effective molecular diffusion coefficient D_d^* can be taken as 6.88 × 10⁻⁹ m²/s [27]. According to the fitted D_h, α can calculated as 0.00095. According to the on-site investigation, the hydraulic head of landfill in China is high, which can reach a few tens of meters [28,29], while the landfill specifications require that the height of the hydraulic head on the liner should not exceed 30 m [25]. Therefore, in the analyses, the hydraulic head differences between the upstream and the downstream of clay liner were considered in several cases: 40 m, 20 m, 10 m, 2 m, and 0.3 m. The relative breakthrough time can be defined when the effluent concentration reaches the threshold value [30,31,32,33]. Ten percent of the source concentration was defined as the threshold value in this paper [33], and time can be expressed as t_0.1. According to the calculation results (see Figure 10), under the hydraulic heads of 40 m, 20 m, 10 m, 2 m, and 0.3 m, the pollutants broke through the 2 m thick clay liner in about 1.6 years, 2.98 years, 5.38 years, 18.64 years, and 72.47 years, respectively. Therefore, under a high hydraulic head, the leachate in the landfill is easy to break through in the liner; when the hydraulic head was 0.3 m, meeting the specification, the liner can prevent the pollutant from the well.

Chloride ion was chosen as the target pollutant in this study. The actual breakthrough time should be longer for strong adsorptive ions such as heavy metals [34]. According to the value of common retardation factor R_d of pollutants in clay, t_0.1 of three pollutants with different adsorption in liner with different Δh_w was simulated below.

Figure 11 shows that t_0.1 decreases as Δh_w increases. The data in the figure show linear relationships in a semi-logarithmic coordinate system, and the formulas are presented. Figure 12 shows variations of breakthrough time of liner with different retardation factors. An exact linear relationship exists between t_0.1 and R_d. The breakthrough times increase by nine times when the retardation factor R_d increases from 1 to 10, which indicates that the effect of R_d on the performance of the liner is significant. For strongly adsorptive pollutants, t_0.1 becomes longer with the increase in R_d. Therefore, the absorbability of the liner material to the corresponding pollutants should be considered for breakthrough time predictions.

5. Conclusions and Prospects

The centrifugal model test of 4 cm thick kaolin clay model with 50 g centrifugal acceleration was presented. A uniform and saturated kaolin clay remodeling model was prepared by the kaolin slurry consolidation method. A set of real-time monitoring device for seepage flow and effluent concentration was used to monitor a volume of the effluent and real-time conductivity of the cumulative effluent under hypergravity conditions. In this test, chloride ions completely broke through the kaolin clay model. The permeability coefficient and concentration of model had been predicted. The entire process of 2 m thick clay liner prototype being broken through by chloride ion at high water head was successfully simulated, which provides an effective test technology for centrifugal model tests of pollutant migration in low permeability soil. Important conclusions were drawn as follows.

(1)

In this paper, a complete set of kaolin model preparation method was provided. The soil sample was homoplasmic and repeatable in this method. Kaolin was mixed with an initial water content of 180% and vacuum pumped during the mixing process for enough time (vacuum level: 0.1 MPa). The saturation of the slurry reached 99% and had uniformity and fluidity after mixed. The slurry was allowed to stand for 1 d to allow self-weight drainage and consolidation to occur naturally. The soil sample could be consolidated step-by-step with a series of pressure levels.

(2)

After the centrifugal model test, the permeability coefficient of the model can be obtained according to the reduced water volume of the Mariotte bottle, the effluent volume of the collection cylinder, and the differential pressure sensor. The permeability coefficients are 0.913 × 10⁻⁹ m/s, 0.929 × 10⁻⁹ m/s, and 0.962 × 10⁻⁹ m/s, respectively. The average of three permeability coefficients is 0.935 × 10⁻⁹ m/s, which is slightly smaller than that before the centrifugal test, reduced by 1.6%, and complies with the Chinese technical specifications the 2 m thick compacted clay liner with permeability coefficient of 1.0 × 10⁻⁹ m/s. Therefore, it is feasible to use the real-time monitoring device for seepage flow and effluent concentration to monitor the volume of the effluent and real-time conductivity of the cumulative effluent under hypergravity conditions.

(3)

The measured cumulative concentration curve was consistent with the measured profile concentration data, the test data were valid, and the electrode can effectively monitor the cumulative conductivity of the outflow under centrifugal state. According to the values of height, hydraulic head, permeability coefficient, and the velocity of the model, the value of the hydrodynamic dispersion coefficient was fitted, as D_h = 2.065 × 10⁻⁹ m²/s.

(4)

t_0.1 decreases as Δh_w increases, and an exact linear relationship exists between t_0.1 and R_d. The breakthrough time of a conservative pollutant for the 2 m clay liner with a hydraulic conductivity of 1.0 × 10⁻⁹ m/s under Δh_w of 40 m was 1.6 years. As for strongly adsorptive pollutants, the breakthrough time t_0.1 increase by 9 times when R_d increases from 1 to 10, which indicates that the effect of R_d on the performance of the liner is significant.

(5)

This study is applicable to pollutants without absorbability that break through the kaolin clay liner. The adsorption of pollutant by kaolin has not been considered. The accuracy of the experimental results under this condition is unknown.