Performance-based design of land ll liners

Engineering Geology 60 2001) 139±148 www.elsevier.nl/locate/enggeo Performance-based design of land ll liners T. Katsumi a,1, *, C.H. Benson b, G.J. Foose c, M. Kamon d a Department of Civil Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan b Department of Civil and Environmental Engineering, University of Wisconsin-Madison, Madison, WI 53705, USA c Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45221, USA d Disaster Prevention Research Institute DPRI), Kyoto University, Uji, Kyoto 611-0011, Japan Accepted for publication 15 April 2000 Abstract Factors affecting chemical transport in geomembrane, clay and composite liners are reviewed, and a simpli ed performancebased method for evaluating land ll bottom liners is presented. For single geomembrane liners, mass transport of inorganic chemicals is calculated from the leakage rate from holes for an assumed frequency of hole occurrence. Transport of organic chemicals is obtained by accounting for molecular diffusion through the intact geomembrane. Migration of inorganic and organic chemicals in compacted clay liners is calculated using a solution of the 1D advection±dispersion-reaction equation. For composite liners consisting of a geomembrane and a clay liner, 3D ow and transport of inorganic chemicals is approximated using an equivalent 1D model for transport through an effective area of transport. The approximation is based on results from 3D analyses that have been conducted for a variety of cases. Migration of organic chemicals through composite liners is calculated using a 1D diffusion model. Applicability of the method is illustrated by using it to evaluate the relative performance of several different liner systems. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Land ll liner; Performance-based design; Geomembrane; Clay; Mass ux 1. Introduction Bottom lining systems consisting of a geomembrane, a clay layer, or both are commonly used to contain wastes in land lls in many countries. To compare the effectiveness of different liner systems or alternatives to a regulatory prescribed liner, a performance-based analysis is necessary. Performance-based analysis is dif cult, however, because chemical transport in land ll liners is complex and * Corresponding author. Fax: 181-77-561-2667. E-mail addresses: tkatsumi@se.ritsumei.ac.jp T. Katsumi), benson@engr.wisc.edu C.H. Benson). 1 Formerly, Research Associate, Disaster Prevention Research Institute DPRI), Kyoto University, Uji, Kyoto 611-0011, Japan. dif cult to model. Nevertheless, simpli ed methods can be used that have suf cient accuracy for making engineering judgments, such as choosing an appropriate type of liner from several possible options. There are several criteria that may be used to evaluate the performance of land ll liners with respect to chemical migration. Leakage rate and solute ux are two possible criteria. Foose et al. 1996) compared three performance criteria rate of leakage, concentration of chemical, solute ux of chemical), and indicated that the effectiveness of the liner depends on the performance criterion selected. For the case in which environmental impact due to chemicals contained in the waste leachate needs to be evaluated, solute ux or the concentration of the speci c chemical should be selected as a performance criterion. 0013-7952/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S0013-7952 00)00096-X

140 T. Katsumi et al. / Engineering Geology 60 2001) 139±148 Nomenclature A e Equivalent area a Area of a geomembrane hole C B Dimensionless coef cient c e Concentration of the referred chemical beneath the geomembrane c 0 Concentration of the referred chemical in waste leachate above the liner D Dispersion coef cient in liner clay D g Diffusion coef cient in a geomembrane d Diameter of the geomembrane defect h w Water head of the waste leachate above the liner i Average vertical hydraulic gradient for 1D ow K g Partition coef cient for a geomembrane K P Partition coef cient for liner clay L Thickness of clay liner N Geomembrane defects per area n Porosity of liner clay P L Peclet number ˆ v s L/D Q Leakage rate through a hole in a geomembrane Q e Equivalent rate of leakage R Retardation factor ˆ 1 1 r d K P /n r Radius of the geomembrane defect T R Time factor ˆ v s t/rl t Time t g Thickness of a geomembrane v s Seepage velocity w Width of the geomembrane defect x Vertical downward coordinate with origin at the surface of the liner r d Dry density of liner clay r w Density of the waste leachate above the liner m Viscosity of the waste leachate In this paper, factors affecting chemical transport in geomembrane, clay, and composite liners are reviewed, and a simpli ed performance-based method for evaluating land ll bottom lining systems is presented. The proposed method is readily applied by engineering practitioners; calculations are made using typical spreadsheet applications, such as Microsoft Excel w. The proposed method considers only solute transport. Multiphase phase ow of organic chemicals is not considered. 2. Principle of performance-based design method Design methods can be generally classi ed as construction-based design, product-based design, and performance-based design. Regulations are generally based on product-based design where properties of the materials are prescribed e.g. hydraulic conductivity and thickness of a clay liner). Performance-based design considers the surrounding environment i.e. use of the land and water and its impact on the ef uent standard), and is a more logical way to design land ll liners. Fig. 1 is a schematic showing how performance-based design can be used to select an appropriate land ll liner. In this case, a maximum permissible concentration at the groundwater well would be the basis for the performancebased design. Possible performance criteria include: 1) a speci- ed value for the rate of leakage, Q; 2) a speci ed maximum value for the solute ux of an individual solute species, J; 3) a speci ed maximum value for the concentration of the chemical, C; 4) time to reach a speci ed leakage rate, T Q ; 5) time to reach a speci- ed solute ux, T J ; and 6) time to reach a speci ed solute concentration, T C : Regardless of the criterion selected, the basis for specifying the criterion is to maintain groundwater quality. A liner is then selected that ensures that the criterion selected is met. 3. Simpli ed performance-based method Using performance-based design methods to design and evaluate land ll liners can be cumbersome because chemical transport in land ll liners can be dif cult to model. However, one of the purposes of performance-based methods is to make rational engineering judgments such as choosing an appropriate type of liner from several possible options. In such cases, a simpli ed method for performance-based design can be used effectively. A simpli ed method is proposed below. The calculations can be done using a spreadsheet application such as Microsoft Excel w.

T. Katsumi et al. / Engineering Geology 60 2001) 139±148 141 Fig. 1. Basic concept of performance-based design of land ll liners. 3.1. Geomembrane liners Two primary mechanisms for contaminant transport through geomembranes are ªleakageº through holes and molecular ªdiffusionº through the intact geomembrane. Holes and defects in geomembranes are caused by defects in geomembrane seams, punctures caused by sharp materials beneath the geomembrane liner and installation tools, tension forces induced by placing waste on the liner, and material failure induced by creep or cyclic loading. Giroud and Bonaparte 1989) investigated the occurrence of defects in geomembrane liners, and concluded that 8±10 holes/ha are usually present with good quality assurance and 17 holes/ha are typically present when quality assurance is poor. Even if quality assurance is excellent, 1±2 holes/ha are unavoidable. Equations for calculating the rate of leakage from geomembrane defects have been proposed by Giroud and Bonaparte 1989) and Giroud et al. 1998). The leakage rate, Q, can be obtained in two different ways. If the hole is small enough such that the diameter of the hole is less than the thickness of geomembrane, the leakage rate is a function of the viscosity and Q can be expressed using Poiseuille's equation Giroud and Bonaparte 1989): Q ˆ pr wh w d 4 1 128mt g where r w is the density of the leachate, m the viscosity of the leachate, h w the water head above the geomembrane, t g the thickness of the geomembrane and d the diameter of the hole. From a practical perspective, r w and m for water can be used in Eq. 1). If the hole diameter is larger than the thickness of geomembrane, Bernoulli's equation for free ow through an ori ce can be used Giroud and Bonaparte 1989) p Q ˆ C B a 2gh w 2 where C B is a dimensionless coef cient which can be obtained empirically, a is the area of the hole and g the acceleration due to gravity. Experiments conducted by Benson et al. 1995) indicate that C B ˆ 0:6 is appropriate for most geomembrane holes. In Eqs. 1) and 2), a constant water head above the geomembrane h w ) is assumed to simplify the calculation. If it is appropriate to consider changing water head, an equation for calculating the rate of leakage through a geomembrane overlain and underlain by permeable media proposed by Giroud et al. 1998) can be used. The solute ux, J a, due to leakage can be calculated by Fig. 2) J a ˆ NQc 0 3 where N is the number of the geomembrane holes per area and c 0 the concentration of the solute in the leachate above geomembrane. The number of the holes, N, depends on the level of quality assurance as mentioned previously. Fig. 2. Leakage through defects in a geomembrane.

142 T. Katsumi et al. / Engineering Geology 60 2001) 139±148 Fig. 3. Schematic of concentration pro les for organic transport through geomembranes. Organic chemicals diffuse at the molecular level through geomembranes Park et al., 1996). The basic chemical transport mechanisms are illustrated in Fig. 3. An organic chemical having concentration, c 0, rst partitions into the geomembrane K g c 0 ), then diffuses downward, and then partitions back into the pore water at the base of the liner c e ). Park et al. 1996) illustrate that molecular diffusion of organic chemicals is more signi cant than leakage through geomembrane defects. Since geomembranes are thin enough such that steady-state conditions are quickly reached, the concentration gradient can be assumed to be constant throughout the geomembrane, and the mass ux of organic chemical can be expressed as Park et al., 1996) J d ˆ D g K g c 0 2 c e t g 4 where D g is the diffusion coef cient for the solute in the geomembrane, K g the solute±geomembrane partition coef cient and c e the concentration of the organic chemical beneath the geomembrane. Conservative estimates of the ux can be obtained by assuming c e ˆ 0: Foose 1997) and Rowe 1998) have summarized diffusion and partition coef cients for several organic chemicals in geomembranes. that accounts for adsorption can be expressed as: 1 1 r dk p n 2c 2t ˆ D 22 c 2x 2 2 v 2c s 2x 5 where c is the concentration of the solute, r d the dry density of the clay, n the porosity of the clay, K P the clay±solute partition coef cient, D the dispersion coef cient for the solute and v s the seepage velocity. The term 1 1 r d K P =n in Eq. 5) is called the retardation factor, R. Clay liners placed above the groundwater table are generally unsaturated. However, if seepage is assumed to be steady-state and suction existing at the bottom of the liner is ignored Fig. 4, i.e. the level of the groundwater table is at the bottom of the liner), the transport calculations can be performed relatively easily. These assumptions generally result in conservative predictions. If the soil properties i.e. r d, n, K P, D) are assumed to be homogenous and time invariant, and no chemical reactions occur, then the concentration c) and the mass ux J) of the solute at the bottom of the liner at time, t, can be obtained by Ogata and Banks, 1961; Shackelford, 1990): c x ˆ L; t c 0 ˆ 0:5 " 1 2 TR erfc p 2 T R =P L # " #) 1 1 TR 1 exp P L erfc p 2 T R =P L and J t 1 2 T ˆ 0:5 erfc p R v s nc 0 2 T R =P L " 1 1 p exp 2 1 2 T # R 2 pp L T R 4T R =P L 6 7 3.2. Clay liners Because clay liners generally have low hydraulic conductivity, dispersive and advective transport must be considered. The 1D advection±dispersion equation Fig. 4. Concept of chemical transport through clay liner.

T. Katsumi et al. / Engineering Geology 60 2001) 139±148 143 Fig. 5. Conceptual diagram of simpli ed analysis of inorganic chemical transport through composite liners. In Eqs. 6) and 7), L is the thickness of the clay liner and x is the vertical downward coordinate with origin at the surface of the liner. The parameter T R is the dimensionless time factor: T R ˆ vst 8 RL and P L is the Peclet number: P L ˆ vsl 9 D The Peclet number represents the relative magnitudes of advective and dispersive transport, with dispersion becoming more important as P L becomes smaller. The initial and boundary conditions used to obtain Eqs. 6) and 7) are c 0; t ˆc 0 ; c x; 0 ˆ0 for x. 0 ; and 2c 1; t 2=x ˆ 0: The last boundary condition implies that the concentration gradient 2c=2x is negligible for distances far x ˆ 1 from the source. Calculations can be made using Eqs. 6) and 7) with applications where the error function is available, such as Microsoft Excel w, or using an electronic calculator if a table of the error function is available. Shackelford and Daniel 1991)and Foose 1997) have summarized dispersion coef cients for several chemicals in clay. 3.3. Composite liners A composite liner exploits the advantages of geomembrane and clay liners; the geomembrane restricts the area through which leakage occurs and the clay liner beneath the geomembrane minimizes leakage from the geomembrane defects. As a result, leakage from composite liners is often orders of magnitude less than leakage from single geomembrane liners and clay liners. Several equations for calculating the rate of leakage through geomembrane defects in composite liners have been proposed Giroud and Bonaparte 1989; Giroud et al., 1989; Giroud et al., 1994; Giroud, 1997; Foose, 1997; Giroud et al., 1998; Rowe, 1998). To calculate the leakage rate, contact between the geomembrane and clay liner, the size and the shape of geomembrane hole, and the thickness of clay liner must be considered. Good contact minimizes leakage since a smaller area of the clay liner is exposed to the ow, whereas poor contact permits greater leakage because liquid can freely penetrate in the space between the geomembrane and clay. Poor contact can be caused by geomembrane wrinkles or an uneven surface of the clay liner beneath the geomembrane. When analyzing transport of inorganic chemicals through composite liners, leakage through geomembrane defects is the primary transport mechanism. This ow and transport process Fig. 5a) is threedimensional 3D), which makes it dif cult to simulate. However, the 3D system can be analyzed readily if it is approximated as an equivalent one-dimensional 1D) system having ow rate Q e ) through an area A e Fig. 5b). The transport calculations are then made using the 1D advection±dispersion equation. The effective area A e is de ned by assuming the area of transport is equal to the average area of leakage. Under this assumption, A e is calculated using Darcy's Law: A e ˆ Qe 10 ki where i is the average vertical gradient for 1D ow

144 T. Katsumi et al. / Engineering Geology 60 2001) 139±148 Table 1 Equations to calculate ow factors after Foose 1997) Contact condition Circular defect F r Long defect F w Perfect contact F r ˆ 4 1 3.35 r/l) F w ˆ 1/ 0.52 2 0.76 log w/l)) Good contact F r,g ˆ 168.5r 20.85 F r F w,g ˆ 6.45F w Poor contact F r,p ˆ 5.48F r,g F w,p ˆ 2.35F w,g i.e. i ˆ 1 1 h w =L). The magnitude of Q e depends on the shape of the defects, contact between the soil and geomembrane, and the depth of leachate. Equations by Giroud et al. 1998), Rowe 1998) or Foose 1997) can be used to calculate Q e. For a circular defect, Q e can be calculated as Foose, 1997): Q e ˆ F r kh t r 11 and for linear defects, Q e can be calculated as Foose, 1997): Q e ˆ F w kh t 12 where h t is the total head drop across the composite liner, r the radius of the defect and F r and F w are ow factors obtained from 3D nite-difference analysis and analysis of equations shown in Giroud et al. 1998) and Foose 1997). A list of ow factors is shown in Table 1. The mass ux and the concentration can be calculated by Eqs. 6) and 7). Because the mass ux, J e, corresponds to the area A e instead of the total area, the mass ux for the liner is obtained as: J total ˆ J e NA e 13 For organic chemicals, the following assumptions are made: 1) the contribution of leakage through the geomembrane defects is negligible because molecular diffusion through the geomembrane is far more significant; 2) diffusion through the geomembrane is ignored because the geomembrane is signi cantly thinner than the clay liner; and 3) advection is zero because the geomembrane limits leakage to very small quantities. As a result, only diffusion in the clay layer is considered. Eqs. 6) and 7) are used for the calculations. Because v s ˆ 0; Eqs. 6) and 7) can be simpli ed as follows: c x ˆ L; t c 0 ˆ erfc 1 p 2 Dt=L 2 R 14 J t nc 0 ˆ 1 p exp 2 1 pt=dr 4Dt=L 2 R 15 Calculations made using this method are in excellent agreement with the results from a more exact 3D nite difference analysis Foose et al., 1999). 4. Parametric study Results for several liner systems obtained using the above analysis are summarized in Table 2. Although a single geomembrane liner may have leakage 1.44 10 6 l/ha/y) similar to that from a single 60-cm-thick clay liner having hydraulic conductivity of 10 27 cm/s 4.73 10 5 l/ha/y), the geomembrane liner releases a much greater mass of organic chemicals because molecular diffusion occurs across the entire area of the thin geomembrane liner. Increasing the thickness of clay liner from 60 to 120 cm decreases the release of chemicals 4.73 10 21 to 3.94 10 21 kg/ha/y for both inorganic and organic chemicals), and increases the retardation effect. However, placing a geomembrane above the 60-cm-thick clay liner has a more signi cant effect on decreasing the release of chemicals 4.73 10 21 to 1.36 10 23 kg/ha/y for inorganics; 4.73 10 21 to 2.03 10 22 kg/ha/y for organics). In addition, adding the geomembrane increases the retardation effect. Even the composite liner consisting of geomembrane and clay liner having higher hydraulic conductivity of 10 26 cm/s releases a smaller mass of inorganic chemicals than a single clay liner having a lower hydraulic conductivity of 10 27 cm/s. Results for inorganic transport through a composite liner are shown in Fig. 6 for three different values of D, two different hydraulic conductivities, k, and R ˆ 2 for the clay liner. Thickness of the clay liner is 60 cm, and the other assumptions are

T. Katsumi et al. / Engineering Geology 60 2001) 139±148 145 Table 2 Calculated results of leakage and chemical release from liners it was assumed that c 0 ˆ 1mg=l and h w ˆ 30 cm for leachate above liner, circular defect, N ˆ 10 holes/ha, d ˆ 2 mm, D g ˆ 2 10 28 cm 2 =s; K g ˆ 130 and t g ˆ 0:1 cm for geomembrane, and D ˆ 2 10 26 cm 2 =s and R ˆ 2 for inorganics), R ˆ 1 for organics), and n ˆ 0:4 for clay liner. T 0.1 and T 0.9 stand for the time to reach 0.1 c 0 and 0.9 c 0 concentrations of leaked water, respectively) Type of liner Geomembrane Clay layer Leakage Release of inorganics Release of organics Thickness cm) Hydraulic conductivity cm/s) Thickness cm) l/ha/y) T0.1 y) T0.9 y) Jmax kg/ha/y) T0.1 y) T0.9 y) Jmax kg/ha/y) Geomembrane liner 0.1 ± 1.44 10 6 ± ± 1.44 10 0 ± ± 8.34 10 1 Clay liner ± 1 10 27 60 4.73 10 5 5.6 16 4.73 10 21 2.8 7.9 4.73 10 21 Clay liner ± 1 10 27 120 3.94 10 5 16 35 3.94 10 21 7.7 18 3.94 10 21 Composite liner 0.1 1 10 27 60 1.36 10 3 5.6 16 1.36 10 23 11 1808 2.03 10 22 Composite liner 0.1 1 10 26 60 1.36 10 4 0.85 1.2 1.36 10 22 11 1808 2.03 10 22

146 T. Katsumi et al. / Engineering Geology 60 2001) 139±148 Fig. 6. Contaminant release at the bottom of a composite liner for different dispersion coef cients and hydraulic conductivities. similar to those shown in Table 2. The hydraulic conductivity of 10 26 cm/s represents the composite liner prescribed by the Japanese government in 1998 although the prescribed thickness in Japan is 50 cm instead of 60 cm), while 10 27 cm/s corresponds to the liner prescribed by the US and some European governments. When the hydraulic conductivity is 10 27 cm/s, the effect of the dispersion coef cient is signi cant. The largest value of D 1 10 25 cm 2 /s) results in an increase in concentration and mass ux in only 2 years, whereas release does not occur until 7 years for the smallest value of D 4 10 27 cm 2 /s). In contrast, if the hydraulic conductivity of the clay liner is 10 26 cm/ s, c=c 0 reaches 1 in only two years regardless of the dispersion coef cient. The mass ux also directly re ects the hydraulic conductivity; the mass ux is a one-order of magnitude higher when the hydraulic conductivity is 10 26 cm/s. Results for three different values of R, D ˆ 2 10 26 cm 2 =s; and k ˆ 10 26 or 10 27 cm/s are shown in Fig. 7. When the hydraulic conductivity is 10 27 cm/s, R signi cantly affects the release of inorganic chemicals. Chemicals are released in 2 years and c=c 0 reaches almost 1 after 12 years when R ˆ 1 no adsorption). When R ˆ 5; chemicals are not released for 10 years because of the adsorptive capacity of the soil. However, if the hydraulic conductivity of clay liner is 10 26 cm/s, c=c 0 reaches 1 in only 3 years even if R ˆ 5; and in one year if R ˆ 1: The magnitude of the mass ux is similarly re ected by the hydraulic conductivity. Much lower mass ux is obtained when the hydraulic conductivity is 10 27 cm/s.

T. Katsumi et al. / Engineering Geology 60 2001) 139±148 147 Fig. 7. Contaminant release at the bottom of a composite liner for different retardation factors and hydraulic conductivities. 5. Conclusions Transport mechanisms relevant to the performance of land ll liners are summarized in this paper and a simpli ed performance-based method to design land ll liners has been introduced. The discussion was presented based on results obtained using the simpli ed design method. The proposed method can be readily used to compare the effectiveness of different liner systems geomembrane liner, clay liner, and composite liner) based on a performance measure such as the mass ux of a chemical of concern. The signi cant advantage of the composite liner relative to geomembrane liners and clay liners was illustrated by comparing the mass ux of chemicals. The dispersion coef cient and retardation factor affect the performance of liners when the hydraulic conductivity of the clay liner is low 10 27 cm/s), whereas these parameters have much smaller effect when the hydraulic conductivity is higher 10 26 cm/s) Acknowledgements Financial support for Dr Katsumi was provided by The Kajima Foundation, which supported his leave at the University of Wisconsin-Madison from Kyoto University from January to December 1998. The Wisconsin Groundwater Research Advisory Council

148 T. Katsumi et al. / Engineering Geology 60 2001) 139±148 GRAC) provided support for Dr Foose and Dr Benson. Support from The Kajima Foundation and GRAC is gratefully acknowledged. References Benson, C.H., Tinjum, J.M., Hussin, C.J., 1995. Leakage rates from geomembrane liners containing holes. Geosynthetics'95, IFAI 2, 745±758. Foose, G.J., 1997. Leakage rates and chemical transport through composite land ll liners. PhD thesis. University of Wisconsin- Madison. Foose, G.J., Benson, C.H., Edil, T.B., 1996. Evaluating the effectiveness of land ll liners. In: Kamon, M. Ed.), Environmental Geotechnics, 1. Balkema, Rotterdam, pp. 217±221. Foose, G.J., Benson, C.H., Edil, T.B., 1999. Equivalency of composite geosynthetic clay liners as a barrier to volatile organic compounds. Geosynthetics'99, IFAI, 321±334. Giroud, J.P., 1997. Equations for calculating the rate of liquid migration through composite liners due to geomembrane defects. Geosynthetics International 4 3/4), 335±348. Giroud, J.P., Bonaparte, R., 1989. Leakage through liners constructed with geomembranes. Geotextiles and Geomembranes 8, 27±67 see also pp. 71±111). Giroud, J.P., Khatami, A., Badu-Tweneboah, K., 1989. Evaluation of the rate of leakage through composite liners. Geotextiles and Geomembranes 8 4), 337±340. Giroud, J.P., Badu-Tweneboah, K., Soderman, K.L., 1994. Evaluation of land ll liners. Proceedings of the Fifth International Conference on Geotextiles, Geomembranes and Related Products, pp. 981±986. Giroud, J.P., Soderman, K.L., Khire, M.V., Badu-Tweneboah, T., 1998. New development in land ll liner leakage evaluation. Proceedings of the Sixth International Conference on Geosynthetics, IFAI, vol. 1, pp. 261±268. Ogata, A., Banks, R.B., 1961. A solution of the differential equation of longitudinal dispersion in porous media. US Geologic Survey Professional Paper, 441-A. Park, J.K., Sakti, J.P., Hoopes, J.A., 1996. Transport of aqueous organic compounds in thermoplastic geomembranes. II: Mass ux estimates and practical implications. Journal of Environmental Engineering, ASCE 122 9), 807±813. Rowe, R.K., 1998. Geosynthetics and the minimization of contaminant migration through barrier systems beneath solid waste. Proceedings of the Sixth International Conference on Geosynthetics, IFAI, vol. 1, pp. 27±102. Shackelford, C.D., 1990. Transit-time design of earthen barriers. Engineering Geology 29, 79±94. Shackelford, C.D., Daniel, D.E., 1991. Diffusion in saturated soil. II: Results for compacted clay. Journal of Geotechnical Engineering, ASCE 117 3), 485±506.