# Centrifuge Modeling of Chloride Ions Completely Breakthrough Kaolin Clay Liner

^{1}

^{2}

^{*}

## Abstract

**:**

^{−}

^{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

_{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.

^{−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.

^{−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.

## 2. Test Scheme

#### 2.1. Model Materials

#### 2.2. Test Equipment and Apparatus

_{W}) and conductivity (S): C

_{W}< 40, C

_{W}= 0.1183S and C

_{W}≥ 40, C

_{W}= 0.2652S − 48 (see Figure 4).

#### 2.3. Model Preparation

#### 2.4. Test Process

_{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.

## 3. Model Parameters and Result Analyses

#### 3.1. Permeability Coefficient Analysis of Model

^{−}

^{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

_{0}fluctuated around 1.

_{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.

_{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}m

^{2}/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

^{−}

^{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}m

^{2}/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.

_{d}of pollutants in clay, t

_{0.1}of three pollutants with different adsorption in liner with different Δh

_{w}was simulated below.

_{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

- (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}m^{2}/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.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Xu, H.; Zhan, L.-T.; Li, H.; Lan, J.-W.; Chen, Y.-M.; Zhou, H.-Y. Time- and stress-dependent model for predicting moisture retention capacity of high-food-waste-content municipal solid waste: Based on experimental evidence. J. Zhejiang Univ. A
**2016**, 17, 525–540. [Google Scholar] [CrossRef] [Green Version] - Zhan, L.-T.; Xu, H.; Chen, Y.-M.; Lan, J.-W.; Lin, W.-A.; Xu, X.-B.; He, P.-J. Biochemical, hydrological and mechanical behaviors of high food waste content MSW landfill: Liquid-gas interactions observed from a large-scale experiment. Waste Manag.
**2017**, 68, 307–318. [Google Scholar] [CrossRef] [PubMed] - Zhan, L.-T.; Xu, H.; Jiang, X.-M.; Lan, J.-W.; Chen, Y.-M.; Zhang, Z.-Y. Use of electrical resistivity tomography for detecting the distribution of leachate and gas in a large-scale MSW landfill cell. Environ. Sci. Pollut. Res.
**2019**, 26, 20325–20343. [Google Scholar] [CrossRef] - Shu, S.; Zhu, W.; Fan, X.; Wu, S.; Li, Y.; Ng, C.W.W. Effect of competitive adsorption on the transport of multiple pollutants through a compacted clay liner. Waste Manag. Res.
**2021**, 39, 368–373. [Google Scholar] [CrossRef] - Zheng, C.M.; Bennett, G.D. Applied Contaminant Transport Modeling, 2nd ed.; Higher Education Press: Beijing, China, 2009. [Google Scholar]
- Sharma, H.D.; Reddy, K.R. Geoenvironmental Engineering: Site Remediation, Waste Containment, and Emerging Waste Management Technologies; HarperCollins: New York, NY, USA, 2004; pp. 170–172. [Google Scholar]
- Shackelford, C.D. Critical concepts for column testing. J. Geotech. Eng.
**1994**, 120, 1804–1828. [Google Scholar] [CrossRef] - Zeng, X. Similitude for Centrifuge Modelling of Heavy Metal Migration in Clay Barrier and Method for Evaluating Breakthrough Time. Ph.D. Thesis, Zhejiang University, Hangzhou, China, 2015. (In Chinese). [Google Scholar]
- Celorie, J.A.; Vinson, T.S.; Woods, S.L.; Istok, J. Modeling Solute Transport by Centrifugation. J. Environ. Eng.
**1989**, 115, 513–526. [Google Scholar] [CrossRef] - Arulanandan, K.; Thompson, P.Y.; Kutter, B.L.; Meegoda, N.J.; Muraleetharan, K.K. Centrifuge Modeling of Transport Processes for Pollutants in Soils. J. Geotech. Eng.
**1988**, 114, 185–205. [Google Scholar] [CrossRef] - Hensley, P.J.; Schofield, A.N. Accelerated Physical Modelling of Hazardous-waste Transport. Geotechnique
**1991**, 41, 447–465. [Google Scholar] [CrossRef] - Depountis, N.; Harris, C.; Davies, M. An assessment of miniaturised electrical imaging equipment to monitor pollution plume evolution in scaled centrifuge modelling. Eng. Geol.
**2001**, 60, 83–94. [Google Scholar] [CrossRef] - Mckinley, J.D.; Price, A.; Lynch, R.J.; Schofield, A.N. Centrifuge modelling of the transport of a pulse of two contaminants. Geotechnique
**1998**, 48, 421–425. [Google Scholar] [CrossRef] - Nakajima, H.; Hirooka, A.; Takemura, J.; Marino, M.A. Centrifuge Modeling of One-Dimensional Subsurface Contamination. J. Am. Water Resour. Assoc.
**1998**, 34, 1415–1425. [Google Scholar] [CrossRef] - Lo, I.M.C.; Zhang, J.H.; Hu, L.M. Centrifuge Modeling of Cadmium Migration in Saturated and Unsaturated Soils. Soil Sediment Contam.
**2005**, 14, 417–431. [Google Scholar] [CrossRef] - Timms, W.A.; Hendry, M.J. Long-Term Reactive Solute Transport in an Aquitard Using a Centrifuge Mode. Groud Water
**2008**, 46, 616–628. [Google Scholar] [CrossRef] [PubMed] - Zeng, X.; Wang, H.; Yao, J.; Li, Y. Analysis of Factors for Compacted Clay Liner Performance Considering Isothermal Adsorption. Appl. Sci.
**2021**, 11, 9735. [Google Scholar] [CrossRef] - Zhong, X.L.; Zhan, L.T.; Gong, B.; Zeng, X.; Chen, Y.M. Consolidation permeability and adsorption properties of three kinds of typical kaolin clays in china. J. Zhejiang Univ. (Eng. Sci. Ed.)
**2014**, 48, 1947–1954. [Google Scholar] - Chen, Y.M.; Han, C.; Ling, D.S.; Kong, L.G.; Zhou, Y.G. Development of geotechnical centrifuge ZJU400 and performance assessment of its shaking table system. Chin. J. Geotech. Eng.
**2011**, 33, 1887–1894. [Google Scholar] - Zhan, L.T.; Zeng, X.; Li, Y.C.; Zhong, X.L.; Chen, Y.M. Centrifuge Modeling for Chloridion Breaking Through Kaolin Clay Liner with High Hydraulic Head. J. Yangtze River Sci. Res.
**2011**, 33, 1887–1894. [Google Scholar] - Van, G.M.T.; Parker, J.C. Boundary conditions for displacement experiments through short laboratory soil columns. Soil Sci. Soc. Am. J.
**1984**, 48, 703–708. [Google Scholar] - Parker, J.C.; Van, G.M.T. Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport. Water Resour. Res.
**1984**, 20, 866–872. [Google Scholar] [CrossRef] - Zeng, X.; Zhan, L.T.; Chen, Y.M. Applicability of boundary conditions for analytical modelling of advection-dispersion transport in low-permeability clay column tests. Chin. J. Geotech. Eng.
**2017**, 39, 636–644. [Google Scholar] - CJJ 113-2007; Technical Code for Liner System of Municipal Soil Waste Landfill. China Building Industry Press: Beijing, China, 2007.
- CJJ176-2012; Technical Code for Geotechnical Engineering of Municipal Soil Waste Sanitary Landfills. China Building Industry Press: Beijing, China, 2012.
- GB 50869-2013; Technical Code for Municipal Soil Waste Sanitary Landfills. China Planning Press: Beijing, China, 2013.
- Zeng, X.; Zhan, L.T.; Zhong, X.L.; Chen, Y.M. Similarity of centrifuge modeling of chloride dispersion in low-permeability clay. J. Zhejiang Univ. A
**2016**, 50, 241–249. [Google Scholar] - Zhan, L.T.; Guan, C.; Xie, H.J.; Chen, Y.M. Vertical migration of leachate pollutants in clayey soils beneath an uncontrolled landfill at Huainan, China: A field and theoretical investigation. Sci. Total Environ.
**2014**, 470, 290–298. [Google Scholar] [CrossRef] - Xie, Y.; Xie, H.J.; Chen, Y.M.; Lou, Z.H. Comparisons of measurements of contaminant concentration in landfill bottom soils with theoretical solutions. J. Nat. Disasters
**2009**, 18, 62–69. [Google Scholar] - Lewis, T.W.; Pivonka, P.; Fityus, S.G.; Smith, D.W. Parametric sensitivity analysis of coupled mechanical consolidation and contaminant transport through clay barriers. Comput. Geotech.
**2009**, 36, 31–40. [Google Scholar] [CrossRef] - Shackelford, C.D. Transit-time design of earthen barriers. Eng. Geol.
**1990**, 29, 79–94. [Google Scholar] [CrossRef] - Malusis, M.A.; Maneval, J.E.; Barben, E.J.; Shackelford, C.D.; Daniels, E.R. Influence of adsorption on phenol transport through soil–bentonite vertical barriers amended with activated carbon. J. Contam. Hydrol.
**2010**, 116, 58–72. [Google Scholar] [CrossRef] - Zeng, X.; Liu, X.; Li, Y.H. The Breakthrough Time Analyses of Lead Ions in CCL considering Different Adsorption Isotherms. Adv. Civ. Eng.
**2020**, 2020, 8861866. [Google Scholar] [CrossRef] - Zhang, J.; Loirene, M.C.; Li, H.U. Centrifuge modeling of moisture and contaminant migration in unsaturated soils. Chin. J. Geotech. Eng.
**2002**, 24, 622–625. [Google Scholar]

**Figure 1.**Gradation curve of Jiangsu kaolin clay [18].

**Figure 6.**Setup of apparatus for centrifuge model tests: (

**a**) diagram of the model; (

**b**) actual figure of the model.

**Table 1.**Centrifuge scaling relationships [8].

Physical Quantity | Unit | Similarity Scaling (Model: Prototype) |
---|---|---|

Acceleration of gravity | m/s^{2} | N |

Size | m | 1/N |

Stress | kPa | 1 |

Density | kg/m^{3} | 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/N^{2} |

Velocity | m/s | N |

Molecular diffusion coefficient | m^{2}/s | 1 |

**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 |

Different Method | Before the Centrifugal Test | During the Centrifugal Test | ||
---|---|---|---|---|

Leaching | From Mariotte Bottle | From Collection Cylinder | From Differential Pressure Sensor | |

k_{20} (× 10^{−}^{9} m/s) | 0.950 | 0.913 | 0.929 | 0.962 |

H (cm) | Void Ratio e | Moisture Content w | Δh_{w} (cm) | k_{20} (m/s) | v_{s} (m/s) | D_{h} (m^{2}/s) | |
---|---|---|---|---|---|---|---|

M1 | 4.08 | 1.614 | 61.8% | 80 | 9.35 × 10^{−}^{10} | 1.45 × 10^{−}^{6} | 20.65 × 10^{−10} |

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**MDPI and ACS Style**

Zeng, X.; Su, J.; Wang, H.; Gao, T.
Centrifuge Modeling of Chloride Ions Completely Breakthrough Kaolin Clay Liner. *Sustainability* **2022**, *14*, 6976.
https://doi.org/10.3390/su14126976

**AMA Style**

Zeng X, Su J, Wang H, Gao T.
Centrifuge Modeling of Chloride Ions Completely Breakthrough Kaolin Clay Liner. *Sustainability*. 2022; 14(12):6976.
https://doi.org/10.3390/su14126976

**Chicago/Turabian Style**

Zeng, Xing, Jia Su, Hengyu Wang, and Tong Gao.
2022. "Centrifuge Modeling of Chloride Ions Completely Breakthrough Kaolin Clay Liner" *Sustainability* 14, no. 12: 6976.
https://doi.org/10.3390/su14126976