Modeling of Clay Liner Desiccation

Yafei Zhou1 and R. Kerry Rowe2

Abstract: The potential for the desiccation of clay liner component of composite liners due to temperature field generated by breakdown of organic matter in municipal solid waste landfills is examined using a model proposed by Zhou and Rowe. In these analyses, a set of fully coupled governing equations expressed in terms of displacement, capillary pressure, air pressure, and temperature increase are used, and numerical results are solved by using finite element method with a mass-conservative numerical scheme. The model results are shown to be in encouraging agreement with experimental data for a problem involving heating of a landfill liner. The fully coupled transient fields ͑temperature, horizontal stress change, suction head, and volumetric water content͒ are then examined for two types of composite liner system, one involving a geomembrane over a compacted clay liner ͑CCL͒ and the other involving a geomembrane over a geosynthetic clay liner ͑GCL͒. It is shown that there can be significant water loss and horizontal stress change in both the CCL and GCL liner even with a temperature increase as small as 20°C. The time to reach steady state decreases as boundary temperature increases. Under a 30°C temperature increase, it takes 5 years to reach the steady state water content with a GCL liner but 50 years with a CCL liner. The effects of various parameters, such as hydraulic conductivity and thickness of the liner, on the performance of the liner are discussed. DOI: 10.1061/͑ASCE͒1532-3641͑2005͒5:1͑1͒ CE Database subject headings: Clay liners; Desiccation; Numerical models; Temperature; Unsaturated flow.

Introduction cause sufficient decrease in water content to induce cracks that could substantially increase the hydraulic conductivity of the Due to their low hydraulic conductivity, compacted clay liners cracked liner. ͑CCLs͒ and geosynthetic clay liners ͑GCLs͒ are commonly used The desiccation of landfill liners due to temperature increases in modern waste disposal facilities to minimize advective flow of has previously been modeled using a semicoupled approach ͑Döll leachate from landfills ͑Rowe et al. 2004͒. When placed, these 1997, 1996 and Heibrock 1997͒ that involves the calculation of liners are unsaturated. The biodegradation of organic matter in the suction profile in rigid media and then assessing the effect of this waste body can cause the temperature at the top of the landfill suction profile on horizontal stress and the possibility of tensile liner to increase up to 65°C, although increases up to 40°C are cracking. The limitations of this approach include the fact that no more common ͑Collins 1993; Barone et al. 1997; and Yoshida et consideration is given to the effect of: ͑1͒ stress and deformation al. 1997͒. A change in liner temperature causes a change in soil on fluid flow; ͑2͒ air flow on water and heat transfer; ͑3͒ tempera- properties. Under nonisothermal conditions ͑Fig. 1͒, water vapor ture on the hydraulic conductivity and water retention curve other moves from areas of higher temperature toward areas of lower than due to changes in surface tension and viscosity; ͑4͒ hyster- temperature due to vapor diffusion, while liquid water moves esis; and ͑5͒ temperature on deformations and therefore the ten- from higher capillary pressure toward lower capillary pressure. In sile stress field. In particular, the stress induced by thermal expan- addition, air moves from zones of higher air pressure to those of sion of the medium is an important part of the stress field and may lower air pressure. This air flow can increase or decrease vapor not be negligible. transport due to advection. The combined effect of liquid water, There has been considerable interest in the study of heat and vapor water, and air flow is a redistribution of water in the liner mass transfer in deformable unsaturated porous media ͑Daksha- system; this redistribution has the potential to cause desiccation of namurthy and Fredlund 1981; Geraminegad and Saxena 1986; clay liners. Navarro et al. 1993; Thomas and Sansom 1995; Thomas et al. Desiccation may cause a reduction in void ratio, deformations, 1996; Yang et al. 1998; and Zhou et al. 1998͒. For example, and crack initiation and propagation ͑Abu-Hejleh and Znidarcic Geraminegad and Saxena ͑1986͒ developed a thermoelastic 1995͒. A significant temperature increase has the potential to model for saturated and unsaturated porous media incorporating soil deformation due to change in the flowing phases ͑moisture 1Engineer, CAD/CAE Applications Dept., Climate Control Systems, and air phases͒, but did not include soil deformation due to ex- Visteon Corporation, 45000 Helm St., Plymouth, MI 48170. ternal loading. Thomas and Sansom ͑1995͒ and Thomas et al. 2Professor, Dept. of Civil Engineering, GeoEngineeering Centre at ͑1996͒ presented models for coupled deformations and heat and Queen’s-RMC, Queen’s Univ., Ellis Hall, Kingston ON, Canada K7L moisture flow in unsaturated media using elasticity/ 3N6. E-mail: [email protected] elastoplasticity theory and state surface approach. Yang et al. Note. Discussion open until August 1, 2005. Separate discussions ͑1998͒ proposed a general three-dimensional mathematical model must be submitted for individual papers. To extend the closing date by for coupled heat, moisture, air flow, and deformation problems in one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- unsaturated soils. An elastoplastic framework was used to de- sible publication on July 1, 2002; approved on July 28, 2004. This paper scribe the deformation behavior of the unsaturated soil structure. is part of the International Journal of Geomechanics, Vol. 5, No. 1, Finally, Zhou et al. ͑1998͒ proposed a consistent fully coupled March 1, 2005. ©ASCE, ISSN 1532-3641/2005/1-1–9/$25.00. nonlinear model for heat, moisture, and air transfer in deformable

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 / 1 strain, ͑3͒ thermal equilibrium between different phases, ͑4͒ liquid water and air flow follows Darcy’s law, ͑5͒ vapor flow is due to diffusion and convection, and ͑6͒ heat flow is due to conduction, convection, and latent heat transfer. Plasticity, creep, and long term volume change related to the possible development of non- reversible shear strains are not considered and the initial strain is considered to be zero. Due to limited data, the effects of thermo- osmosis and thermal filtration are not considered in this study. ͑ ͒ ͑ ͒ ͑ ͒ Displacements ui , capillary pressure pc , air pressure pa , and temperature increase ͑T͒ are chosen as the basic variables in the formulation of the fully coupled model. The following is a brief ͑ ͒ Fig. 1. Heat and mass fluxes in unsaturated medium under geomem- summary of the model proposed by Zhou and Rowe 2003 based brane due to temperature gradient on the assumptions described above. To establish a fully coupled model, the following two constitutive relationships ͑in general form͒ relating void ratio ͑e͒ and unsaturated media based on two general constitutive relationships liquid water content ͑␪͒ to net mean stress ͑␴*͒, capillary pres- ͑ ͒ ͑ ͒ relating void ratio and liquid water content to stress, capillary sure pc , and temperature increase T are introduced pressure, and temperature change. The governing equations are ͑␴ ͒͑͒ explicitly expressed in terms of deformation, capillary pressure, e = f *, pc,T 1 air pressure, and temperature. ␪ ͑␴ ͒͑͒ Mass balance error is a problem often encountered in numeri- = f *, pc,T 2 cal modeling of mass transport phenomenon using capillary po- where p =p −p ; ␴*=p +(␴ +␴ +␴ )/3; p ϭpore water pres- tential ͑or suction͒ as a basic variable, especially for transient c l a a 1 2 3 l sure; p ϭair pressure; and ␴ (i=1,..,3)ϭthree principal stresses analysis where the error may accumulate to an unacceptable level a i ͑tension positive͒. ͑Celia et al. 1990͒. Unfortunately, this error has often been ig- The complete stress–strain relationship for a nonlinear ther- nored in previous models of heat and mass transfer in deformable moporoelastic medium can be established from Eq. ͑1͒ in incre- media. mental form and written as Recently, Zhou and Rowe ͑2003͒ presented a thermal- hydromechanical coupled model for the simulation of heat and ␮ moisture transfer in landfill liner systems and the evaluation of d␴ =2Gͩd␧ + ␦ d␧ ͪ − KB ␦ dp − ␦ dp − KB ␦ dT ij ij ij1−2␮ kk 1 ij c ij a 2 ij the potential for desiccation cracking by examining the consequent stress field. This fully coupled model overcomes the limi- ͑3͒ tations of previous attempts to model liner desiccation and, in ␴ ϭ ␧ ϭ ␦ ϭ where ij stress tensor; ij strain tensor; ij Kronecker’s delta; particular, considers both the effect of temperature on stresses and Gϭshear modulus; ␮ϭPoisson’s ratio; Kϭbulk modulus of the the effect of air flow on moisture redistribution. Thus, to facilitate ϭ soil medium; B1 compressibility of the soil medium due to cap- the study of desiccation cracking of liners, the stress and defor- ϭ illary pressure change; and B2 thermal expansion coefficient mation are calculated simultaneously. This approach uses a mass- ͑Zhou and Rowe 2003͒. conservative finite element scheme to ensure mass balance and The equation for force equilibrium in the soil can be written in obtain accurate solutions. The advantages of this model include incremental form as the theoretical consistency of incorporating the coupled effects of heat transfer, fluid flow, and mechanical deformation in the gov- ͑ ␴ ͒ ͑ ͒ d ij ,j + dbi =0 4 erning equations, and the numerical accuracy gained due to its ϭ mass conservative solution technique. where bi body force in i direction. ͑ ͒ The objectives of this paper are threefold. First, to further vali- The mass balance for water in both liquid and vapor phases date the model of Zhou and Rowe ͑2003͒ by simulating a field in a deformable unsaturated soil is given by experiment involving heating a landfill liner system. Second, to ␳ ͑1+e͒␪ + ␳ ͓e − ͑1+e͒␪͔͖͕ ץ gain insight into the potential for desiccation cracking by exam- l v =− ٌ ͑q + q ͒͑5͒ l v ץ ͒ ͑ ining the consequent stress field in the liners for several practical 1+e0 t problems involving nonisothermal water and heat transport where e ϭinitial void ratio; tϭtime, ␳ and ␳ ϭdensities of liquid ͑ ͒ 0 l v through two types of liner systems CCL and GCL liners . Third, water and vapor water depending on temperature and capillary to evaluate the effect of parameters such as the: hydraulic con- ϭ pressure; and ql and qv fluxes of liquid water due to Darcy’s ductivity of the attenuation layer, clay liner thickness, magnitude flow and vapor water due to diffusion and convection of boundary temperature change, and type of liner system on the ٌ potential for cracking. ␳ ␬ ٌ ͑ ␳ ͒ ٌ ␳ ␳ ␬ ql =− l l pc + pa + lgz ; qv =−D * v − v a pa ͑6͒ ␬ ϭ Development of Theoretical Model l mobility coefficient for liquid water associated with Darcy’s ͓␬ ͑␳ ͔͒ ϭ flow l =Kl / lg ; Kl hydraulic conductivity of the soil me- ϭ ␬ ϭ In a deformable nonisothermal soil medium, mechanical deforma- dium; g gravitational acceleration; a mobility coefficient of tion, fluid flow, and heat transfer are three coupled processes. To air; zϭvertical coordinate; D*ϭeffective molecular diffusivity of ϭ ␬ ␬ study the interactions between these different physical processes, water vapor; and va velocity of air. Both l and a depend on the a set of governing equations are established assuming: ͑1͒ an intrinsic permeability of the soil material, degree of saturation, isotropic soil medium, ͑2͒ small deformation and infinitesimal and temperature.

2 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 The mass balance for air in a deformable unsaturated soil ͑in- Eqs. ͑4͒,͑12͒–͑14͒ are a set of fully coupled governing equa- cluding the effect of solubility of air into water͒ can be expressed tions of the thermohydromechanical behavior of unsaturated soils as that can only be solved numerically due to the nonlinear nature of the properties. ␳ ͓e − ͑1−H͒͑1+e͒␪͔͖͕ ץ da =− ٌ q ͑7͒ Zhou and Rowe ͑2003͒ proposed a mass conservative finite da ץ ͒ ͑ 1+e0 t element model to evaluate the parameters in the equations, de- where Hϭcoefficient of solubility of air into water defined by scribed a method for solving the equations, and demonstrated the ͑ ͒ ␳ ϭ applicability and accuracy of the model through various ex- Henry’s law Sisler et al. 1953 , da density of dry air; and q ϭflux of dry air due to solubility and convection amples. This approach is used to obtain the results presented in da the following discussion. ͔͒͑ ٌ ␳ ͓ ␬ ٌ ͑ ␳ ͒ ␬ qda =− da H l pc + pa + lgz + a pa 8 The heat energy balance can be described by Results ␧ ץ ⌽ ץ T + T ͒KB v =− ٌ q ͑9͒͑ − T ץ 2 0 ץ ͒ ͑ 1+e0 t t Three examples are presented in this section to illustrate the applications of the theory described above. The first is a simulation where T ϭreference temperature in °C. The second term in Eq. 0 of a field experiment involving heating a landfill liner system. The ͑9͒ is the heat sink due to thermal expansion of the medium; and second and third are simulations of fully coupled fields of two ⌽ϭheat content of a representative element ͑specific volume=1 types landfill barrier systems ͑CCLs and GCLs͒ and evaluations +e͒ of the medium and can be expressed as of effects of various parameters on the potential for cracking. ⌽ ͕␳ ␳ ͑ ͒␪ ␳ ͓ ͑ ͒␪͔ ␳ ͓ ͑ ͒ = sCs + lCl 1+e + vCv e − 1+e + daCda e − 1−H ϫ͑ ͒␪͔͖ ␳ ͓ ͑ ͒␪͔ ␳ ͑ ͒␪ ͑ ͒ 1+e T + L0 v e − 1+e + l 1+e W 10 Field Experiment ␳ ϭ ϭ where s density of soil grains; Cs , Cl , Cv, and Cda gravimetric This section considers the Karlsruhe field test reported by Got- specific heats of soil grains, liquid water, water vapor, and dry air, theil and Brauns ͑1995͒. In this test, a 0.9–1 m thick layer of ϭ respectively; L0 latent heat of evaporation at reference tempera- Karlsruhe silt loam liner was placed over a 0.3 m thick layer of ϭ ture T0; and W differential heat of wetting associated with the coarse gravel resting on the natural Karlsruhe loess. The entire exothermic process of wetting of the medium ͑Milly 1984͒. liner was covered with geomembrane. Heating equipment was The total heat flux due to heat conduction, heat convection and installed in a sand layer above the geomembrane. Matric poten- latent heat transfer qT is given by tial, volumetric water content, temperature, and gas pressure were measured at various locations in the liner and in the subsurface. ͒ ͑ ٌ ␭Ј qT =− T + qlClT + qvCvT + qdaCdaT + L0qv 11 The water retention curve and hydraulic conductivity for clay ͑ ͒ where ␭ЈϭFourier thermal conductivity of the unsaturated me- liners in landfills at reference temperature T0 =20°C can be de- dium. scribed by van Genuchten–Mualem functions ͑Döll 1997; The manipulation of the balance equations and substitution of Mualem 1976; and van Genuchten 1980͒ as related basic relationships results in the following system of bal- ␪ − ␪ ance equations written in terms of the basic unknowns displace- ␪ ␪ s r ␪ ഛ␪ഛ␪ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ = r + n m , r s 15 ments ui , capillary pressure pc , air pressure pa , and tempera- ͑1+͉␣␺͉ ͒ ture increase ͑T͒ ץ ץ ␧ ץ v pc pa ͓͑ ͉␣␺͉n͒m ͉␣␺͉n−1͔2 ͑L + L ͒ + ͑L + L ͒ + ͑L + L ͒ 1+ − ␬ = ␬ ͑16͒ ץ 23 13 ץ 22 12 ץ 21 11 t t t l sat ͑1+͉␣␺͉n͒m͑l+2͒ T ץ ͑ ͒ ␪ ϭ ␪ ϭ + L14 + L24 where r residual water content; s saturated water content; t ϭ ␺ ␳ ϭ ץ l, m, and n fitted parameters; m=1−1/n, (=pc / lg) capillary ␳ ␬ *͒ ٌ ͔ ٌ ͓␳ ␬ ␳ ␬ *͒ ٌ potential head at the reference temperature T ; and ␬ ϭsaturated͓͑ ٌ = l l + D1 pc + l l + v a + D2 pa 0 sat mobility of liquid water. ͒ ͑ ͔͒ ␳ ␬ ٌ ͑␳ ͓ ٌ ͒ ٌ * ͑ ٌ + D3 T + H l l lgz 12 Due to limited experimental data, in this analysis the effect of temperature on the water retention curve is considered through T ץ p ץ p ץ ␧ ץ L v + L c + L a + L matric potential head correction. Therefore, for nonisothermal .t conditions the water retention curve can still be described by Eq ץ t 34 ץ t 33 ץ t 32 ץ 31 ͑15͒, except that the variable ␺ is replaced by ⌿ which represents ͔ H␳ ␬ ٌ p ͒ + ٌ ͓␳ ͑␬ + H␬ ͒ ٌ p͑ ٌ = da l c da a l a a temperature corrected potential head and is assumed to be a ␳ ␬ ٌ ͑␳ ͔͒ ͑ ͒ ␺ ͓ ٌ + H da l lgz 13 function of capillary potential head and temperature increase T ͑above reference temperature in °C͒͑Milly 1984͒ ץ ץ ץ ␧ ץ v pc pa T L41 + L42 + L43 + L44 t ⌿ = ␺ exp͓− C␺T͔͑17͒ ץ t ץ t ץ t ץ ϭ ͑ −1͒ ٌ * ٌ * ٌ * ͓ ٌ = Dc2 pc + Da2 pa + DT2 T where C␺ temperature coefficient of water retention °C .In −1 the present analysis, C␺ =−0.0068°C ͑Scalon and Milly 1994͒. C ␳ + C ␳ H͒␬ T ٌ ͑␳ gz͔͒ ͑14͒͑ + l l da da l l Considering the effect of matric potential correction and the * * * * * * where Lij, D1 , D2 , D3 , Dc2 , Ta2, and DT2 are given by Zhou and change in water viscosity, the mobility coefficient of water due to Rowe ͑2003͒. temperature change is given by ͑Döll 1997͒

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 / 3 Table 1. Material Parameters for Field Experiment ͑Reprinted with Permission from Döll 1997͒ ␪ ␪ ␣ ͑ ͒ ␪ Soil np r s (1/m)N1 Ksat m/s f0 k Karlsruhe silt loam 0.365 0 0.35 0.0000015 1.25 −4 5ϫ10−10 0.3 0.1 Karlsruhe gravel 0.38 0 0.38 0.003 2.00 0.5 1.0ϫ10−2 0.5 0.1 Karlsruhe loess 0.385 0 0.37 0.00003 1.40 −1.5 1.5ϫ10−7 0.3 0.1

͓͑1+͉␣⌿͉n͒m − ͉␣⌿͉n−1͔2 impermeable top boundary and relative permeable bottom inter- ␬ ␬ ␬T ͑ ͒ l = sat ͑ ͒ e 18 face with the gravel layer. As time progresses, the area near the ͑1+͉␣⌿͉n͒m l+2 top loses more water than the bottom. The present prediction where ␬ϭtemperature coefficient of hydraulic conductivity, a cor- agrees with the trend evident from the field data. rection factor on hydraulic conductivity due to temperature Döll ͑1997͒ predicted that the water content would increase increase. most in the middle of the gravel layer. In contrast, the present The properties of liner and subsurface material are given in model predicts that water content increase will be greatest near Table 1 and thermal properties are given by Döll ͑1997͒. The the bottom of the gravel layer. Considering the high permeability initial conditions involved a uniform temperature of ͑14°C͒ and of the gravel layer, the present solution is more realistic than matric potential heads that varied with depth ͑−5.8 m at top, Döll’s. −5.0 m at 0.15 m depth, −3.8 m at 0.45 m depth, −3.0 m at 0.75 The encouraging agreement between the observed field behav- m depth, −2.2 m at −1.5 m depth͒. The top boundary is imperme- ior and the prediction by the present model provides an incentive able. Starting approximately 1.5 years after the emplacement of to numerically investigate the potential implication of heating on the geomembrane, the surface of the mineral liner was heated to the behavior of a 0.6 m thick CCL or a GCL used as part of a approximately 40°C. Measured data from the first 616 days of the composite liner overlying a 4 m thick unsaturated medium sand. nonisothermal phase were evaluated. Throughout this time period, the boundary conditions vary. Temperature on the top was main- Nonisothermal Water and Heat Transport through tained at 30°C during the first 21 days, and then increased to Compacted Clay Liners and Geosynthetic 41°C. At the bottom, capillary pressure was maintained at Clay Liners −2.2 m, but the bottom temperature varied with time ͑17°C for 1–13 days; 22°C for 14–38 days; 28°C for 38–83 days; 31°C for Based on the literature, the following form of state surface gives 83–120 days; 33°C for 120–616 days͒. It is assumed that air an accurate description of the behavior of deformable unsaturated pressure is constant in the medium. soils ͑Lloret and Alonso 1985 and Thomas et al. 1996͒ The measured and calculated volumetric water content decreases along the depth are presented at five different times in Fig. ͑ ␴ ͒ ͑ ͒ ͑ ␴ ͒ ͑ ͒ e = a + b ln − * + c ln − pc + d ln − * ln − pc 2. The calculated results are obtained using a vapor transport ͑ ͒␣ ͑ ͒ enhancement factor ͑F␯ =8.2͒. It can be seen ͑Fig. 2͒ that the + 1+e0 TT 19 calculated results agree very well with the field data at 77, 441, ϭ ϭ and 616 days. However, at 168 and 252 days, the calculated re- where pc capillary potential. a, b, c, and d model parameters. ͑ ͒ sults show less water loss than field data. The calculated trends of Eq. 19 indicates the effect of stress, capillary potential, and volumetric water content decreases in layered soil medium agree temperature change on void ratio, and it can be used to derive the ͑ ͒ with what might be expected. nonlinear elastic stress strain law in the form of Eq. 3 . The ␣ It is noted that Döll ͑1997͒ used a semicoupled model to simu- thermal coefficient of volume change T can be expressed as ͑Thomas et al. 1996͒ late the same problem using F␯ =4.5. Her solution showed that the water losses at the bottom of the liner are always more than those at the top. But this trend is not in agreement with the field data. ␴* ␣ = ␣ + ␣ T + ͑␣ + ␣ T͒lnͫ ͬ ͑20͒ ͑ ͒ T 0 2 1 3 ␴* The field data shows that initially at 77 days there is more water 0 loss at the bottom of the liner than that at the top due to the ␴*ϭ ␣ ␣ ␣ where 0 reference net mean stress; and 0 , 1 , 2, and ␣ ϭ 3 model parameters. The water retention curve for isothermal deformable unsaturated soils can be described by ͑Lloret and Alonso 1985͒

e ␪ ͕ ͓ ͑ ͔͒͑ ␴ ͖͒ ͑ ͒ = aЈ − 1 − exp − bЈpc cЈ − dЈ * 21 1+e0

where aЈ, bЈ, cЈ, and dЈϭmodel parameters. ͑ ͒ The hydraulic conductivity Kl of the deformable unsaturated soil under isothermal conditions is given by ͑Alonso et al. 1988͒

3 Sl − Slu ␣ ␬ ␳ ͫ ͬ ke ͑ ͒ Kl = l lg = A 10 22 1−Slu Fig. 2. Measured and calculated water content decrease under plastic ϭ ␣ ϭ where Sl degree of saturation; and A, Slu, and k constants. liner The conductivity of air is given by

4 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 Table 2. Parameters for Deformable Unsaturated Soil abcdaЈ bЈ Clay liner 5.5 −0.4 −0.25 0.02 1.0 0.8 Sand layer 0.9312 −0.02 −0.002 0.0001 −500 2.41 Geosynthetic clay liner 3.7555 −0.1965 −0.1297 0.0086 1.0 0.595

cЈ dЈ ABSlu Clay liner −1.0ϫ10−8 1.0ϫ10−5 6.0ϫ10−14 1.8ϫ10−12 0.05 — Sand layer −0.5714 1.5ϫ10−13 1.0ϫ10−10 28.061 — Geosynthetic clay liner 0 0.94ϫ10−8 1.2ϫ10−16 3.0ϫ10−9 0.05 — ␣ ␤ ␭ ␭ ␮ k k dry sat Clay liner 5 4 0.3 1.3 0.35 — Sand layer −12.235 4 0.256 2.804 0.35 — Geosynthetic clay liner 5 4 0.3 1.3 0.35 —

B ␤ lems. This is because of the mechanical–thermalhydraulically K = ͑eS ͒ k ͑23͒ a ␩ g coupled nature of the problem and the need for stress calculation a in an area with a high stress gradient. ␩ ϭ ␤ ϭ In the first year ͑Fig. 3͒, the temperature steadily increased where a viscosity of the air; and B and k constants. The thermal conductivity of the unsaturated media can be approximated everywhere in the liner and attenuation layer and approached the by steady state distribution. However, the temperature then started to decrease in the middle of the medium. This interesting phenom- ␭ = ␭ ͑1−S ͒ + ␭ S ͑24͒ enon can be explained by the decrease in thermal conductivity of dry l sat l the materials due to the decrease in water content. It took about ␭ ␭ ϭ 50 years to truly approach the steady state temperature distribu- where dry and sat coefficients of thermal conductivity at the statuses of complete dry and fully saturated, respectively. tion. In this example, temperature effects on water retention curve When a drying soil is restrained such that there can be no ͑ ͒ and hydraulic conductivity are considered using the same ap- volume change i.e., when free shrinkage is not allowed , soil proach described in “Field Experiment”. The material parameters suction can lead to development of tensile stresses in the re- ͑ ͒ used in the following examples for the clay liner and attenuation strained direction Kodikara et al. 1999 . There are several theo- ͑e.g., sand͒ layer are given in Table 2. These parameters are se- ries that can be used to predict desiccation cracking. One ap- lected based on typical properties reported in the literature. proach is based on tensile strength theory. When the tensile stresses exceed the tensile strength of the soil, clay soils tend to Heat-Moisture Transfer and Stress Field in Compacted Clay crack ͑i.e., primary cracking͒ releasing the strain energy devel- Liner oped in the soil. In this example, a geomembrane, overlying a two-layered unsat- Fig. 4 shows that the horizontal compressive stress in the clay urated soil ͑0.6 m thick CCL liner overa4msand attenuation liner is reduced due to heating, with maximum decrease of 15 kPa layer͒ is subjected to a sudden increase of temperature. The satu- near the top of the liner after 50 years. In contrast, the horizontal rated hydraulic conductivities of CCL and sand attenuation layer stress in the sand layer increased with a maximum value of 40 are 4.3ϫ10−11 and 7.5ϫ10−5 m/s, respectively. The initial conditions are constant vertical compressive stress ͑200 kPa͒, uniform temperature ͑10°C͒, uniform air pressure ͑100 kPa͒, and uniform capillary potential ͑2.8 kPa͒. Under these initial conditions, the degree of water saturation is over 98% in clay liner, and 5% in the sand layer. The boundary conditions are no displacement ͑fixed͒, constant capillary potential, air pressure and temperature at the bottom, impermeable to water, constant air pressure, and 30°C temperature increase on the surface of the top layer. This problem was analyzed using three different finite element meshes ͑150, 300, and 450 elements͒. It was found that the 300 element mesh was most appropriate since the 150 element mesh was not refined enough to give accurate results, while there was negligible difference between solutions from 300 element and 450 element meshes. The 300 element mesh had 60 elements in the top 0.25 m, followed by 60 elements in the next 0.35 m clay. In the attenuation layer, there were 120 elements for the top 2 m, followed by 60 elements for the bottom 2 m. In each region, the elements were uniformly distributed. The number of elements Fig. 3. Temperature profiles at different time due to 30°C tempera- used in this analysis is more than that required for diffusion prob- ture increase

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 / 5 Fig. 6. Water content proﬁles at different times due to 30°C tempera- Fig. 4. Horizontal stress change at different times due to 30°C tem- ture increase perature increase ͑tensile change positive͒

years͒, the predicted volumetric water content had decreased from 0.35 to 0.07 in the clay liner, and from 0.05 to less than 0.01 in kPa near top of the attenuation layer at 1 year. The decrease in most of the sand layer. horizontal compressive stress in clay liner could cause cracking of Due to the temperature increase, the air pressure in the clay the liner and affect its performance if the initial horizontal stresses liner ͑Fig. 7͒ initially increased to a maximum of 118 kPa after 4 were sufficiently low. However in practical applications involving days. As the temperature decreased from the maximum value that a significant amount of waste above the liner, the initial horizontal resulted from the nonhomogeneous thermal conductivity change stresses would be expected to exceed 15 kPa, and in this case in the barrier, the air pressure also decreased. After 5 years, the cracking would not be anticipated. minimum air pressure in the liner dropped from 100 to 78 kPa. The suction distribution curves ͑Fig. 5͒ were continuous with Thereafter, there was a gradual dissipation in air pressure in the depth and moved towards higher suction with time. In the first 20 liner and after 10 years the air pressure profile was very close to years, the suction at both the top and bottom of clay liner are steady state. higher than those in the middle due to the higher temperature at The above problem and results described above will be used as the top, the low hydraulic conductivity of the clay liner, and the a base case and in the following subsections the effect of varying high hydraulic conductivity in the sand layer. The suction head a number of parameters will be explored. distribution reached steady state at about 50 years, and gradually Effect of Hydraulic Conductivity of Attenuation Layer. To decreased with depth. The steady state suction head was 500 m at evaluate the effect of hydraulic conductivity of sand layer on the the top and 50 m at the bottom of the clay liner. performance of clay liner, the problem was also studied using a The volumetric water content ͑Fig. 6͒ decreased with time in hydraulic conductivity for the underlying layer 1/100th of that both the clay liner and the sand layer. The pattern of water content examined above ͑with all other parameters remaining un- distribution closely followed the suction distribution profiles. In changed͒. In this case the temperature varied more significantly the first 20 years, there was more water loss at both the top and than in the previous case ͑compare Figs. 3 and 8͒. With the lower the bottom of the clay liner than in the middle. At steady state ͑50 hydraulic conductivity, it is predicted that it would take more than

Fig. 5. Suction proﬁles at different times due to 30°C temperature Fig. 7. Air pressure proﬁles at different times due to 30°C tempera- increase ture increase

6 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 Fig. 10. Water content distribution due to different temperature in- Fig. 8. Temperature proﬁles at different times due to 30°C tempera- creases ͑after 10 years͒ ture increase ͑lower hydraulic condictivity in bottom layer͒

100 years for the temperature to reach steady state ͑compared to 50 years in the base case͒. The decrease in compressive stress was bottom of the liner, but almost no water loss in the middle of the more than 22 kPa near the top of the liner at 100 years ͑compared liner. After 50 years, the degree of saturation over a major portion with 15 kPa at 50 years in the base case͒, while the suction head of the liner was still at more than 50%. After 100 years, both the in the clay liner was more than 1,000 m at 100 years ͑compared to clay liner and attenuation layer became very dry, and approached 500 m at 50 years in the base case͒. The volumetric water content steady state with a volumetric water content of about 0.06 in the reached steady state in the clay liner at 50 years. In the bottom CCL. layer, the water content increased in the first 20 years but water Effect of Boundary Temperature Change. The effects of was then driven towards the bottom. It took more than 100 years boundary temperature change on desiccation was studied by con- for bottom layer to reach steady state; this is again much longer sidering the following four different increases in boundary tem- than in the base case. The air pressure profiles were almost the perature ͑above original ambient temperature͒: 20°C ͑Case 1͒, same as those in the base case, except for a small variation in the 30°C ͑Base case 2͒, 40°C ͑Case 3͒, and 50°C ͑Case 4͒. sand layer. As in the base case, the decrease in horizontal stress Fig. 10 shows the water content distributions in the barrier at due to the temperature field would be unlikely to cause cracking 10 years for the four cases. In the first year only areas near the for the parameters considered. boundary of the liner experienced water losses in all the cases, Effect of Clay Liner Thickness. To evaluate the effect of the including that where the temperature increased by 50°C at the top thickness of clay liner on the performance of the barrier, the of the clay liner ͑Case 4͒ and the results were generally very thickness was increased from 0.6 to 1.5 m. In this case it took similar to those shown in Fig. 6. However, after 10 years ͑Fig. much longer than for the base case to reach steady state ͑more 10͒, significant differences in the water content distribution were than 100 years compared to about 50 years for the base case͒. The predicted for the four cases. The simulated results indicated that it maximum stress reduction increased from 15 to 18 kPa ͑Fig. 9͒, would take 20 years to reach steady state for a 50°C increase and and maximum suction head in the liner increased from 800 to more than 100 years for water content to reach steady state for 1,000 m. At 20 years, there were water losses at both the top and Case 1 ͑20°C boundary temperature increase͒. The final water contents in the liner were almost the same ͑0.06͒ for the range of the boundary temperature increases ͑20–50°C͒ studied. Thus, it can be concluded that the magnitude of temperature increase on top of the liner will have a significant effect on the rate of desiccation, but a negligible effect on the final steady-state water content distribution for the parameters considered here.

Heat-Moisture Transfer and Stress Field in Geosynthetic Clay Liner Geosynthetic clay liners are growing in popularity as an alterna- tive to compacted clay liners. To the authors’ knowledge, the performance of this material under nonisothermal conditions has not been previously studied. In this section, the effect of temperature on the performance of a GCL liner is simulated. The material parameters for the GCL are given in Table 2. The saturated hydraulic conductivity of GCL is 7.6ϫ10−11 m/s. The conﬁguration of the barrier system includes a 1.0 cm thick GCL liner on top of a 4.0 m thick attenuation ͑sand͒ layer. The initial and boundary Fig. 9. Horizontal stress change at different times due to 30°C tem- conditions imposed on the medium are the same as those in the ͑ ͒ perature increase with 1.5 m thick clay liner previous section.

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 / 7 Fig. 11. Horizontal stress changes at different times in barrier with Fig. 12. Horizonal stress changes at different times in barrier with −2 geosynthetic clay liner due to 30°C temperature increase geosynthetic clay liner ͑10 lower hydraulic conductivity͒ due to 30°C temperature increase

The temperature increased with time in both GCL liner and liner due to hydraulic conductivity change. The liner desiccates attenuation layers in the first year. After that, the temperature in faster and reaches steady state a little quicker than the previous the middle of the attenuation layer experienced a decrease and case. then an increase as it approached steady state. The increase– decrease–increase phenomenon for temperature in the attenuation layer was due to a variation in its thermal conductivity that is Conclusion related to water content. It took 20 years for temperature to reach steady state in the attenuation layer, while for the CCL liner it The fully coupled model of Zhou and Rowe ͑2003͒ was used to took 50 years. analyze a field experiment involving heating a landfill liner and it The horizontal stress changes ͑Fig. 11͒ in the GCL liner was was found that the model provided very encouraging agreement almost uniform with depth and increases ͑less compressive͒ with with the observed field behavior, providing additional validation time up to 20 years. The maximum horizontal stress change ͑de- of the model. The model was then utilized to analyze the heat– crease in compressive stress͒ in the liner was over 43 kPa. How- moisture–air transport in two types of deformable landfill barrier ever, in many base liner applications the horizontal stress is likely systems due to an increase in surface temperature. Each liner was to exceed 43 kPa and hence no crack would be expected. In the a composite with a geomembrane overlying a clay liner, one case first year, the horizontal stress in the sand layer becomes more involving a CCL and the other a GCL. The profiles of tempera- compressive due to thermal expansion caused by the temperature ture, volumetric water content, horizontal stress variation, and increase. After 1 year, the stress in the sand layer starts to reduce suction head at different times were presented. The temperature due to the increase in suction. The final horizontal stress change increases on top of the liner gave rise to a decrease in water in the sand layer is close to linear distribution along the depth content, and a reduction in horizontal compressive stress ͑less with the maximum value of −30 kPa ͑more compressive͒ at the compressive͒ for the cases examined. The volumetric water con- top after 20 years. The sign difference in stress change between tent in the compacted clay liner reduced from an initial value 0.35 the GCL layer and sand layer is attributed to their differences in bulk modulus. If thermal expansion were neglected, the resulting stress variation would be less compressive in both the GCL liner and sand layer. The suction increased with time in the medium, was continuously distributed with depth, and reached steady state after 20 years. The maximum suction head in the liner was 60 m. The volumetric water content in the GCL liner was essentially linearly distributed with the depth and approached steady state (␪=0.2͒ after 5 years, while in the sand layer the top portion continued to experience water loss until after 20 years. To evaluate the effect of hydraulic conductivity of the GCL liner on the performance of the barrier, the problem was also studied using a hydraulic conductivity for GCL 1/100th of that examined above ͑with all other properties remaining unchanged͒. The temperature profiles and the time to reach steady state were almost the same as in the previous case, but the horizontal stress increase ͑Fig. 12͒, suction head, and water content distributions ͑Fig. 13͒ become obviously nonlinear along the depth. The maximum stress change increased from 43 to 55 kPa near the top, and Fig. 13. Water content profiles at different times in barrier with geo- ͑ −2 ͒ maximum suction head increased from 60 to 80 m. It is of interest synthetic clay liner 10 lower hydraulic conductivity due to 30°C to note the different patterns in water content distribution in the temperature increase

8 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MARCH 2005 to 0.07 at steady status ͑80% reduction͒ due to 30°C temperature temperature gradients: desiccation of mineral liners below landfills.” increase. A 15–24 and 43–55 kPa reduction in compressive stress PhD thesis, Technical Univ. of Berlin, Berlin. was calculated for CCL and GCL, respectively, for the problem Döll, P. ͑1997͒. “Desiccation of mineral liners below landfills with heat studied. This reduction would be less than the expected horizontal generation”. J. Geotech. Geoenviron. Eng. 123͑11͒, 1001–1009. ͑ ͒ stress in many practical applications and in these cases cracking van Genuchten, M. T. 1980 . “A closed-form equation for predicting the would not be anticipated. It takes much less time for the noniso- hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44, 892–898. thermal process to reach steady state in the GCL liner than in the Geraminegad, M., and Saxena, S. K. ͑1986͒. “A coupled thermoelastic CCL liner. This study suggests that temperature generated in land- model for saturated-unsaturated porous media.” Geotechnique, 36, fill waste body could cause significant loss of water content in 539–550. clay liners and warrants more study and consideration in landfill Gottheil, K.-M., and Brauns, J.͑1995͒. “Thermische einflusse auf die design. Reduction in hydraulic conductivity of the attenuation dichtwirkung von kombinationsdichtungen—Messungen an einem layer, increase in clay liner thickness, and reduction in boundary testfeld.” BMBF-Verbundforschungsvorhaben Weiterentwicklung von temperature change all reduced the rate of desiccation. Deponieabdichtungssystemen, H. August, U. Holzlohner, and T. Meg- Unfortunately, very little data are available in the literature gyes, eds. Vol. 3, Bundesanstalt fur Materialforschung und -Prufung relating to the problem examined in this paper. The results sug- Berlin, Berlin, 175–184. gest the need for more experimental studies to be conducted to Heibrock, G. ͑1997͒. “Desiccation cracking of mineral sealing liners.” allow calibration and confirmation of the model findings. Further- Proc., 6th Int. Landfill Symp. Vol. 3, 101–113. more, to take full advantage of this model for simulation of the Kodikara, J., Barbour, S. L., and Fredlund, D. G. ͑1999͒. “Changes in landfill barrier system, more work is needed in determining the clay structure and behavior due to wetting and drying.” liner material properties ͑constitutive relationship, water charac- Lloret, A., and Alonso, E. E.͑1985͒. “State surface for partially saturated teristic curve, hydraulic conductivity, thermal properties, tensile soils.” Proc., 11th ICSMFE, Vol. 2, San Francisco, 557–562. strength, etc.͒, taking into consideration the effects of tempera- Milly, P. C. D. ͑1984͒. “A simulation analysis of thermal effects on ture, stress, and suction. evaporation from soil.” Water Resour. Res., 20, 1087–1098. Mualem, Y. ͑1976͒. “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res., 12, 1248– Acknowledgments 1254. Navarro, V., Gens, A., Lloret, A., and Alonso, E. E. ͑1993͒. “Develop- ment of a computer code for the analysis of coupled thermo-hydro- The financial support of the Natural Sciences and Engineering mechanical boundary value problems.” Proc., 3rd Int. Workshop on Research Council of Canada ͑NSERC͒, Terrafix Geosynthetics Clay Barriers, Bergamo, Italy. Inc, the Centre for Research in Earth and Space Technology ͑ ͒ Rowe, R. K., Quigley, R. M., Brachman, R. W. I, and Booker, J. R. CRESTech , and Naue Fasertechnik GmbH & Co. are gratefully ͑2004͒. Barrier systems for waste disposal facilities, Taylor & Francis acknowledged. ͑E&FN Spon͒, London. Scanlon, B. R., and Milly, P. C. 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