Extreme Compaction Effects on Gas Transport Parametersand Estimated Climate Gas Exchange

for a Landfill Final Cover SoilShoichiro Hamamoto1; Per Moldrup2; Ken Kawamoto3; Praneeth Nishadi Wickramarachchi4;

Masanao Nagamori5; and Toshiko Komatsu6

Abstract: Landfill sites have been implicated in greenhouse warming scenarios as a significant source of atmospheric methane. In this study,the effects of extreme compaction on the two main soil-gas transport parameters, the gas diffusion coefficient (Dp) and the intrinsic airpermeability (ka), and the cumulative methane oxidation rate in a landfill cover soil were investigated. Extremely compacted landfill coversoil exhibited negligible inactive soil-air contents for both Dp and ka. In addition, greater Dp and ka were observed as compared with normalcompacted soils at the same soil-air content (ε), likely because of reduced water-blockage effects under extreme compaction. These phe-nomena are not included in existing predictive models for DpðεÞ and kaðεÞ. On the basis of the measured data, new predictive models forDpðεÞ and kaðεÞ were developed with model parameters (representing air-filled pore connectivity and water-blockage effects) expressed asfunctions of dry density (ρb). The developed DpðεÞ and kaðεÞ models together with soil-water retention data for soils at normal and extremecompaction (ρb ¼ 1:44 and 1:85 g cm�3) implied that extremely compacted soils will exhibit lower Dp and ka at natural field-water content(�100 cm H2O of soil-water matric potential) because of much lower soil-air content. Numerical simulations of methane gas transport,including a first-order methane oxidation rate, were performed for differently compacted soils by using the new predictive DpðεÞ model.Model results showed that compaction-induced difference in soil-air content at a given soil-water matric potential condition is likely the mostimportant parameter governing methane oxidation rates in extremely compacted landfill cover soil. DOI: 10.1061/(ASCE)GT.1943-5606.0000459. © 2011 American Society of Civil Engineers.

CE Database subject headings: Landfills; Coverings; Gas; Parameters; Methane.

Author keywords: Landfill final cover soil; Gas transport parameters; Compaction.

Introduction

Landfill sites are a significant source of methane (CH4), which hasa high global warming potential, estimated to be more than 20 timesthat of carbon dioxide (Lelieveld et al. 1998). The estimated CH4

emissions from landfills are 550–635 Mt CO2-equivalent year�1,corresponding to approximately 9% of global anthropogenic meth-ane emissions (Rogner et al. 2007; Bogner et al. 2008). In addition,the emissions of toxic gases, such as hydrogen sulfide, and volatile

organic chemicals from landfill sites affect surrounding localenvironments (Song et al. 2007).

These greenhouse and toxic gases are typically produced bymicrobiological processes acting on waste materials under anaero-bic conditions and are emitted to the atmosphere through landfillfinal cover soils (Hilger et al. 1999; de Gioannis et al. 2009). There-fore, the optimal landfill final cover soil should promote gas ex-changes between the atmosphere and landfill wastes layer tomaintain aerobic decomposition conditions and high methane ox-idation rates in the landfill cover soil (Vangpaisal and Bouazza2004; Moon et al. 2008). However, the design criteria for the land-fill final cover systems have focused primarily on the hydraulic per-formance for inhibiting water infiltration and geotechnical stabilityfor preventing ground sliding and cracking (Week et al. 1992;Albright et al. 2006; Benson et al. 2007; Moon et al. 2008;McGuire et al. 2009). Generally, landfill final cover soils are highlycompacted to prevent precipitation infiltration (Osinubi andNwaiwu 2006). Weeks et al. (1992) reported dry density (ρb) rang-ing from 1:57–1:74 g cm�3 for differently textured landfill coversoils. Values of ρb ranging from 1.63–1.65 for coarse sand andsandy clay loam used as landfill cover soils have been reportedin Chanton et al. (2009) and references in this paper. Comparedwith the intensive investigations on the hydraulic characteristics,only few studies about gas transport characteristics of landfill coversoils are available.

The gas exchange through the final cover soil is controlled byadvective and diffusive gas transport. The intrinsic air permeabilityðka;m2Þ or the related air conductivity [Ka, m s�1; equal to kaρg=η,where ρ = density of air (kgm�3); η = viscosity of air (Pa s); and

1Assistant Professor, Graduate School of Science and Engineering,Saitama Univ., 225 Shimo-okubo, Sakura-ku, Saitama, 338-8570, Japan(corresponding author). E-mail: hamasyo@mail.saitama-u.ac.jp

2Professor, Environmental Engineering Section, Dept. of Biotechnol-ogy, Chemistry and Environmental Engineering, Aalborg Univ., Sohn-gaardsholmsvej 57, DK-9000 Aalborg, Denmark.

3Associate Professor, Graduate School of Science and Engineering,Saitama Univ., 225 Shimo-okubo, Sakura-ku, Saitama, 338-8570, Japan.

4Ph.D. Student, Graduate School of Science and Engineering, SaitamaUniv., 225 Shimo-okubo, Sakura-ku, Saitama, 338-8570, Japan.

5Senior Scientist, Center for Environmental Science, 914 Kamitanadare,Kisai, Kitasakitama, Saitama 347-0115, Japan.

6Professor, Graduate School of Science and Engineering, SaitamaUniv., 225 Shimo-okubo, Sakura-ku, Saitama, 338-8570, Japan.

Note. This manuscript was submitted on July 23, 2009; approved onOctober 8, 2010; published online on October 20, 2010. Discussion periodopen until December 1, 2011; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, Vol. 137, No. 7, July 1, 2011. ©ASCE,ISSN 1090-0241/2011/7-653–662/$25.00.

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g = gravitational acceleration (m s�2)] govern the advective gastransport induced by a soil-air pressure gradient. The soil-gasdiffusion coefficient (Dp, m2 s�1) governs diffusive gas transportinduced by a soil-gas concentration gradient. Soil compaction isexpected to highly affect gas transport characteristics and param-eters. From the Dp data for volcanic ash soils at different ρb(0:4–0:71 g cm�3), Resurreccion et al. (2008) showed a decreaseof threshold soil-air content (where diffusive transport is negligiblebecause of disconnected air-filled pore networks) and lower incre-mental increase of Dp with increasing soil-air content for highlycompacted volcanic ash soil. Hamamoto et al. (2009b) suggestedthat soil compaction simultaneously caused reduced water-blockage effects and reduction of larger-pore spaces, resulting ingreater Dp but lower ka on the basis of the Dp and ka measurementsfor differently compacted sandy soils (ρb from 1:4–1:6 g cm�3).Both studies showed significant effects of soil compaction ongas transport parameters for soils under natural compaction levels.However, gas transport characteristics for extremely compactedlandfill cover soils have not yet been investigated.

Understanding the effects of soil compaction levels in landfillfinal cover soils on the soil-gas transport parameters is essentialfor accurately simulating greenhouse and toxic gas emissions fromlandfill sites and for optimizing the design of landfill covers to re-duce undesired gas emissions. In this study, we focus on the effectsof extreme soil compaction on the main gas transport parameters(Dp and ka) and the gas transport characteristics in landfill coversoil. The objectives of this study are (1) to measure the soil-gastransport parameters at different moisture conditions using differ-ently compacted landfill cover soils and evaluate the effects of soilcompaction on the gas transport parameters; (2) to develop predic-tive models for the soil-gas transport parameters, consideringmodel parameters as functions of dry density; and (3) to performa sensitivity analysis of the effects of the gas transport parameters,tortuosity of soil-pore networks, and estimated methane oxidationrate for differently compacted landfill cover soils by using the de-veloped predictive models.

Model Development

Most existing predictive models for Dp and ka are based on power-law functions of soil-air content (ε, m3 m�3, ratio of volume of soil-air to the total soil volume) (Buckingham 1904; Marshall 1959;Millington 1959; Millington and Quirk 1961; Currie 1960b;Moldrup et al. 2000, 2001, 2003; Kawamoto et al. 2006a).Power-law type models for Dp=D0 and ka can be written in generalform (Troeh et al. 1982; Ball et al. 1988) as

Dp

D0¼ αpεXP ð1a Þ

ka ¼ αaεXa ð1b Þwhere D0 = gas diffusion coefficient in free air (m2 s�1); αp andαa = pore connectivity-tortuosity parameters for Dp=D0 and ka,respectively; and Xp and Xa = water-blockage parameters forDp=D0 and ka, respectively.

The widely used Millington and Quirk (1961) model for Dp canbe written as

Dp

D0¼ ε10=3

Φ2 ¼ 1Φ2 ε

10=3 ð2Þ

where Φ = total porosity (m3 m�3, ratio of volume of void to thetotal soil volume). In the Millington and Quirk (1961) model,

(1=Φ2) and 10=3 are identical to αp and Xp in Eq. (1a), respectively.Moldrup et al. (2004) showed a good model performance of theMillington and Quirk (1961) model for sandy European soils.

Moldrup et al. (2000) suggested the water-induced linear reduc-tion (WLR) model based on and extending the classical Dp modelsfor dry soil by Penman (1940), Marshall (1959), and Millington(1959). The WLR-type DpðεÞ model can be written in generalform as

Dp

D0¼ εXdry

�εΦ

�N¼ 1

ΦN εXdryþN ð3Þ

where Xdry and N = pore structure parameters. In the WLR-typeDpðεÞ model, (1=ΦN) and (Xdry þ N) are identical to αp and Xpin Eq. (1a), respectively. The WLR (Millington) and the WLR(Marshall) models by Moldrup et al. (2000) are given byEq. (3) with Xdry ¼ 1:33 and N ¼ 1:0, and Xdry ¼ 1:5 andN ¼ 1:0, respectively. The WLR (Marshall) model showed theoverall best performance for sieved and repacked soils (Moldrupet al. 2000). In addition, recent studies showed that the WLR(Marshall) model described DpðεÞ=D0 effectively for differentlytextured, intact soils (Werner et al. 2004).

Several models for intrinsic air permeability (ka) have been de-veloped on the basis of the soil-air content at a selected moisturecondition (reference point). In most of these models, the pF 2[ψ ¼ �100 cm H2O; where ψ = soil-water matric potential incm H2O and pF = logð�ψÞ] was chosen as the reference point be-cause ka measurements under very dry conditions are practicallyimpossible without soil shrinkage away from the cylinder walls(Blackwell et al. 1990; Loll et al. 1999; Moldrup et al. 2003).By using the measured ka;pF2 (ka at pF 2) and εpF2 (ε at pF 2)as reference point values, the reference point power law (RPL)kaðεÞ model can be written in general form as

ka ¼ ka;pF2

�ε

εpF2

�η¼ ka;pF2

ðεpF2Þηεη ð4Þ

where η = water-blockage parameter for the RPL kaðεÞ model. Inthe RPL kaðεÞ model, (ka;pF2=ε

ηpF2) and η are identical to αa and Xa

in Eq. (1b), respectively. Moldrup et al. (1998) suggested η ¼ 2:0for sandy soils.

Materials and Methods

A waste landfill site in Saitama Prefecture, Japan, was selected asthe sampling location. A 2.5-m-thick soil covers the waste layer asa final cover soil. The final cover soil at the sampling site isextremely compacted, exhibiting an in situ dry density (ρb) of ap-proximately 1:90 g cm�3 and a total porosity (Φ) of only 0.29(Table 1). Undisturbed soil samples to depths of ∼50 cm weretaken from the final cover soil, and the soil samples were sieved

Table 1. Physical Properties of Landfill Cover Soil

Property Unit Value

Gravel (75� 4:75 mm) Percent 36

Sand (4:75� 0:075 mm) Percent 42

Silt (75� 5 μm) Percent 13

Clay (< 5 μm) Percent 9

Dry density ρb g cm�3 ≈1:90

Specific gravity of soil Gs 2.66

Total porosity Φ m3 m�3 ≈0:29

Loss of ignition Li Percent 2.1

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through 2-mm mesh to eliminate effects of gravel and coarse sandsize fractions (75–2.0 mm) on gas transport and obtain homo-geneous soil physical properties. The soil texture of the soil sample(size fraction less than 2 mm) was silty sand (ASTM 2008a). Thephysical properties of the soil samples are shown in Table 1.

Compaction tests were performed for soil samples at differentwater contents by using modified (ASTM 2008b) and standard(ASTM 2008c) methods. Water contents of soil samples were ad-justed by adding water to air-dried soil samples. In the compactiontests, the soil samples were repacked into large soil cores (innerdiameter 15 cm, length 12 cm) at two different compaction levels(high: 2;700 kJ=m3; low: 600 kJ=m3) (Fig. 1). The falling height(H) and weight of the rammer (M) for high and low compactionlevels were 45.7 and 30.5 cm and 4.5 and 2.5 kg, respectively.To obtain each compaction level for the large soil cores used inthis study, 56 blows were applied per layer (high compaction: 5layers; low compaction: 3 layers). The results of the compac-tion tests are shown in Fig. 2. The dry density (ρb) rangedfrom 1:8–2:0 g cm�3 for the greater compaction level and1:7–1:9 g cm�3 for the lesser compaction level. The two

compaction curves did not exhibit the expected lower optimummoisture content for the high compaction tests because of the lackof experimental data. The optimum moisture content for both com-paction levels was around 11% (Fig. 2) and the void ratio for theoptimum dry density was around 0.30.

After compaction tests, two 100 cm3 core samples (inner diam-eter 5.1 cm, length 4.1 cm) were taken inside each repacked largecore. The 100 cm3 core samples were classified into two differentρb ranges: 1:80–1:90 g cm�3, labeled as extreme compaction (EC),and 1:70–1:80 g cm�3, labeled as high compaction (HC). The bot-tom end of the 100 cm3 core samples was submerged into a vesselcontaining free water, and the water level was kept near the top endof the core samples to saturate them. After the core samples werewater-saturated, they were drained at different matric suctions, andthe gas diffusion coefficient (Dp) and intrinsic air permeability (ka)were measured. Two different methods, according to the matricsuction ranges, were used for adjusting the matric suction of thesamples. A hanging water suction method was used for low matricsuctions up to pF 2 (�100 cm H2O) and a pressure plate apparatusfor medium suctions (pF 2 to pF 4, i.e., �100 cm H2O to�10;000 cm H2O). Finally, the repacked soil cores were air-driedand the pF value of the samples was measured using a dew pointpotentiometer (WP4-T, Decagon Devices, Pullman, Washington)(Hamamoto et al. 2009a). For comparison, disturbed soil samplesat different water contents were repacked into 100 cm3 cores at drydensity of 1:55 g cm�3, representing normal compacted soils(labeled as normal compaction, NC), and the Dp and ka were mea-sured on the repacked soil samples at different soil-air contents (ε).

The water retention curves obtained for EC and HC soil sampleswere fitted by a unimodal lognormal distribution model (Kosugi1996). The unimodal lognormal distribution model (Kosugi1996) is

θ ¼ θr þ ðθs � θrÞiQ�lnðψ=ψmÞ

σ

�ð5Þ

where θ = soil-water content (m3 m�3, ratio of volume of soil-waterto the total soil volume); ψmi and σ = fitting parameters; QðxÞ =complementary cumulative normal distribution function; θs isthe saturated water content (m3 m�3); and θr = residual water con-tent (m3 m�3). The pore-size density (PSD) is defined as the deriva-tive of the water content with respect to pF (Durner 1994; Seki2007):

PSD ¼ lnð10Þ θs � θrffiffiffiffiffiffi2π

pσexp

�� ½lnðψ=ψmÞ�2

2σ2i

�ð6Þ

TheDp was measured on the repacked 100 cm3 soil cores with adiffusion chamber method (Osozawa 1987; Rolston and Moldrup2002). Oxygen was used as tracer gas and measured as a function oftime in the diffusion chamber. The Dp was calculated according toOsozawa (1987). In this study, the gas diffusion coefficient of oxy-gen in free air (D0) at 20°C was taken as 0:20 cm2 s�1 (Glinski andStepniewski 1985; Currie 1960a). Following Iversen et al. (2001),the ka was measured by blowing air through a repacked 100 cm3

soil core at three flow rates (where each flow rate falls within theinterval 0.2–2.3, 1.7–10.3, and 5:7–60 dm3 min�1, respectively).The ka was calculated from the Darcy’s equation on the basis ofthe pressure difference across the core and the viscosity of theair (1:86 × 10�5 Pa s) (Iversen et al. 2001).

In addition to the Dp and ka measurements for the repackedlandfill cover soils at the EC, HC, and NC levels, we consideredliterature data for Dp=D0 and ka for differently compacted sandysoils [sands with fines (< 75 μm)]; the Mammen (ρb ¼ 1:50)and Jyndevad (ρb ¼ 1:43–1:46) sandy soils from Kawamoto et al.

Fig. 1. Schematic design of experimental setup for laboratory compac-tion test

Fig. 2. Compaction curves of landfill cover soil at different compactionlevels

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(2006a, b), sands with 15% fines (ρb ¼ 1:49) from Shimamura(1992), and Skellingsted sandy landfill cover soil (ρb ¼ 1:71) fromPoulsen et al. (2001).

Results and Discussion

Effects of Soil Compaction on Gas Diffusivity andIntrinsic Air Permeability

Fig. 3(a) shows the measured Dp=D0 values for repacked soilsamples at ρb ¼ 1:80–1:90 (EC) and 1.55 (NC). The total porositiesfor soil samples at EC and NC are 0.30 and 0.42, respectively.The Dp=D0 increased with increasing ε. At the same ε, greaterDp=D0 for the EC soil were observed, indicating less water-blockage effects on gas diffusion for the EC soil because of lowervolumetric water content ðθ;m3 m�3Þ as compared to NC soil [e.g.,compare at ε ¼ 0:20 in Fig. 3(a)]. All Dp=D0 data for differentlycompacted soils are shown in Fig. 3(b). The solid lines show thefitted model curves by a power-law type DpðεÞ model [Eq. (1a)]against soil samples at ρb ¼ 1:80–1:90 (EC), 1.70–1.80 (HC),

1.49–1.55 (NC, including reference data), and 1.43–1.46 (LC,Jyndevad). The difference of Dp=D0 in EC and HC soils was minor.The power-law type DpðεÞ models fit the measured DpðεÞ well fordifferently compacted soils.

The Dp=D0 (log scale) for differently compacted soils is shownas a function of ε in Fig. 4(a). The power-law type DpðεÞ modelsalso represented the low Dp=D0 values well for all soils at low ε.Again, Fig. 4(a) documents greater Dp=D0 values for HC and ECsoils as compared with less compacted soils (NC and LC) becauseof reduced water-blockage effects. Especially under wetter condi-tions (e.g., compare at ε ¼ 0:1), the reduced water-blockage ef-fects dramatically enhance gas diffusion for the HC and EC soils.Fig. 4(b) shows ka (log scale) for differently compacted soils as afunction of ε. The power-law type model for ka [Eq. (1b)] was fittedto data for each soil sample at different ranges of dry density: ρb ¼1:80–1:90 (EC), 1.70–1.80 (HC, including Skellingsted), 1.50–1.55 (NC, including Mammen), and 1.43–1.46 (LC, Jyndevad).At dry conditions, the ka for the LC soil showed greater valuesas compared with highly compacted soils (NC, HC, and EC) be-cause of enhanced advective flow through larger-pore networks. Atlower ε, greater ka values for HC and EC soils were observed as

Fig. 3. (a) Dp=D0 as a function of ε for soils at ρb ¼ 1:80� 1:90 and 1.55; (b) Dp=D0 as a function of ε for differently compacted soils; solid linesrepresent fitted model curves using the power-law type model [Eq. (1a)] against each soil group at different ρb ranges

Fig. 4. Solid lines represent fitted model curves using the power-law type model [Eqs. (1a) and (1b)] against each soil group at different ρb ranges;regression coefficient (R2) for each fitted curve ranged from 0.89–0.97 and from 0.70–0.78, respectively: (a) Dp=D0 (log scale); (b) ka (log scale) as afunction of ε for differently compacted soils

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compared with NC and LC soils; this is similar to what wasobserved for gas diffusivity.

Schjønning et al. (2003) suggested that Dp=D0 ¼ 10�4 can betaken as an indication of the point at which no effective gas diffu-sion through continuous air-filled pore spaces takes place becausethe diffusion in air is approximately 104 times higher than that inwater. Based on this, the soil-air content at Dp=D0 ¼ 10�4 was de-fined as a threshold soil-air content (εth) at which gas diffusion insoil is negligible because of disconnectivity of the remaining air-filled pore spaces [Fig. 4(a)]. For ka, we defined the soil-air contentat ka ¼ 0:1 μm2 as a threshold soil-air content (εth) for gas advec-tion because ka measurements generally have a lower detectionlimit of 0:1 μm2. Table 2 shows the obtained εth for Dp=D0 andka for differently compacted soils. Lower εth values for bothDp=D0 and ka were found for highly compacted soils. This is be-cause soil compaction causes an increased volumetric surface area(soil surface area per soil volume), resulting in a reduction of theconnected water phase (water bridges between particles); this re-duction then promotes both gas diffusion and advection. In addi-tion, slightly lower εth values for ka were observed as compared tothose for Dp=D0, implying that water-blockage effects on diffusivegas transport are more pronounced as compared to advective gastransport.

Fig. 5(a) shows the fitted parameter values for the power-lawtype DpðεÞ model [Eq. (1a)] against measured Dp data for differ-ently compacted soils. A linear decrease of water-blockage param-eters (Xp) with increasing dry density (ρb) was observed. Thisindicates that increased volumetric surface area reduced thewater-blockage effects on Dp=D0 for highly compacted soils.The Xp values for the HC and EC soils were close to 1.0, repre-senting an almost linear increase of Dp=D0 with ε [Fig. 3(b)]. Thus,these significantly lower water-blockage effects should be takeninto account when simulating gas transport through extremely

compacted landfill cover soils. The fitted αp values for thepower-law typeDpðεÞmodel [Eq. (1a)] also linearly decreased withincreasing ρb [Fig. 5(a)]. This indicates that the reduction of larger-pore-size networks because of soil compaction caused decreasedsoil-pore connectivity and reduced gas diffusion.

Fig. 5(b) shows the fitted αa and Xa values for the power-lawtype kaðεÞmodel [Eq. (1b)] against measured ka data for differentlycompacted soils. Similar to Dp=D0, both αa and Xa values de-creased linearly with increasing ρb, indicating reduced pore tortuos-ity and water-blockage effects on ka for HC and EC soils. Thedecrease of αa with increasing ρb was more significant than thedecrease of αp for Dp=D0 because ka (representing gas advection)is primarily governed by pore-size distributions and the continuityof larger-pore networks (Osozawa 1998).

Model Tests of ρb-Dependent Predictive Models forGas Diffusivity and Intrinsic Air Permeability

The following predictive DpðεÞ models were tested against themeasured Dp data for differently compacted soils: the Millingtonand Quirk (MQ) model [Eq. (2), Millington and Quirk 1961],the WLR type model [Eq. (3), Moldrup et al. 2000] with N ¼1:0 and either Xdry ¼ 1:33 (Milligton 1959) or 1.5 (Marshall1959), and the power-law type model [Eq. (1a)] with both αpand Xp taken as a linear function of ρb obtained from Fig. 5(a).Scatter plot comparisons of predicted and measured Dp=D0and the root-mean-square error (RMSE) for these models areshown in Figs. 6(a)–6(d). The MQ model predicted well thedata for the LC and NC soils but highly underestimated Dp=D0for the HC and EC soils. This indicates that the MQ model couldnot express the reduced water-blockage effects for HC and ECsoils. This is because the MQ model was originally derived fora porous medium with randomly distributed particles of uniformsize, implicitly exhibiting a large reduction of gas transportparameters under wetter conditions. Although the original WLRmodels performed better than the MQ model for all soils[Figs. 6(b) and 6(c)], both models overestimated Dp=D0 for theLC soil, and the WLR (Marshall) underestimated Dp=D0 for theEC soil. The new power-law type DpðεÞ model generally predictedDp=D0 well across all compaction levels (LC, NC, HC, EC), asshown in Fig. 6(d).

The power-law type model for ka [Eq. (1b)] with both αa and Xataken as a linear function of ρb [Fig. 5(b)] was tested in comparisonwith the RPL kaðεÞ model with η ¼ 2:0 [Eq. (4), Moldrup et al.

Table 2. Estimated Threshold Soil-Air Contents for Dp and ka

ρb (g cm�3) εth for Dp (m3 m�3) εth for ka (m3 m�3)

1.85 0.004 0.001

1.75 0.003 0.002

1.55 0.017 0.015

1.40 0.034 0.032

Fig. 5. (a) Pore connectivity parameter [αp in Eq. (1a)] and water-blockage parameter [Xp in Eq. (1a)] for Dp, as a function of dry density (ρb);(b) pore connectivity parameter [αa in Eq. (1b)] and water-blockage parameter [Xa in Eq. (1b)] for ka as a function of dry density (ρb)

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1998] against the measured ka data for differently compacted soils.For the RPL kaðεÞ model, both measured εpF2 and ka;pF2 valueswere used for all soils except for the landfill cover soil at ρb ¼1:55 (where, because of lack of water retention data, the highestε and ka values were instead used as the reference point). Scatter

plot comparisons of predicted and measured ka and RMSE [Eq. (5)]for these models are shown in Figs. 7(a) and 7(b). Both RPL andpower-law type models predicted ka values well for the LC and NCsoils, but the new power-law type kaðεÞ model gave better predic-tions of ka for the HC and EC soils.

Fig. 6. Scatter plot comparison of model performances: (a) Millington and Quirk (MQ) model [Eq. (2)]; (b) WLR (Millington) model [Eq. (3)] withXdry ¼ 1:33 and N ¼ 1:0; (c) WLR (Marshall) model [Eq. (3)] with Xdry ¼ 1:5 and N ¼ 1:0; (d) power-law type model [Eq. (1a)] with modelparameters (αp and Xp) taken as a function of ρb [from Fig. 5(a)]

Fig. 7. Scatter plot comparison of model performances: (a) RPL model [Eq. (4)] with measured ka;pF2, εpF2, and η ¼ 2:0; (b) power-law type model[Eq. (1b)] with model parameters (αa and Xa) taken as a function of ρb [from Fig. 5(b)]

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Sensitivity Analysis of Gas Diffusivity and Intrinsic AirPermeability for Differently Compacted Soils

A sensitivity analysis of the effects of soil compaction and moisturelevel on Dp=D0 and ka for differently compacted soils was per-formed on the basis of the power-law type models for Dp=D0[Eq. (1a)] and ka [Eq. (1b)]. For the analysis, pore connecti-vity and water-blockage parameters were expressed as linear func-tions of ρb (Fig. 5). Fig. 8 showsDp=D0 and ka as a function of ε forsoils at ρb ¼ 1:40, 1.60, and 1.80. The extremely compacted soil(ρb ¼ 1:80) showed greater Dp=D0 across the ε interval (ε < 0:3)because of the reduced water-blockage effects as compared withless compacted soils. For ka, the extremely compacted soil showedgreater ka at wetter conditions (ε < 0:15) but lower at greater ε ascompared with less compacted soils, indicating the effects ofreduced larger-pore networks because of soil compaction moremarkedly affected gas advection at greater ε. Both DpðεÞ andkaðεÞ behaviors become more linear with increasing compaction,in agreement with Shimamura (1992), which found linear DpðεÞfor compacted sands with varying contents of fine particles< 75 μm.

To investigate the effects of soil compaction on Dp=D0 and ka asa function of soil-water matric potential, the soil-water retentiondata for landfill cover soil at ρb ¼ 1:85 (EC) and Jyndevad sandysoils at ρb ¼ 1:43–1:46 (average ρb ¼ 1:44, LC) from Kawamotoet al. (2006b) were used. The soil-water retention curves and PSDfor each soil are shown in Figs. 9(a) and 9(b). The unimodal log-normal distribution model (Kosugi 1996) represented the soil-waterretention curves well for each soil [Fig. 9(a)]. The LC soil showed arapid decrease of volumetric water content with increasing pF[Fig. 9(a)]. The water content at pF 2 (ψ ¼ �100 cm H2O) isclosely related to a natural field capacity water content (Kawamotoet al. 2006b). The EC soil exhibited greater water content at thenatural field condition (pF ¼ 2) as compared to the LC soil[Fig. 9(a)]. The calculated PSD showed that the LC soil had a peakvalue of PSD at pF ¼ 1:2, corresponding to pore diameterðdÞ≈ 200 μm, as calculated from the capillary rise equation (Hillel1980) [Fig. 9(b)]. The EC soil showed a peak value at pF ¼ 4:2(d ≈ 2 μm). Thus, high compaction will likely remove a major partof the larger-pore-size volume and shift this toward smaller poreswith a broader range of small pore sizes for the low-compacted soil,as illustrated by the arrow in Fig. 9(b). This explains the greaterwater retention for the EC soil at pF 2 [Fig. 9(a)].

Power-law type models for Dp=D0 and ka as a function of ε[Eqs. (1a) and (1b)] with pore connectivity and water-blockageparameters taken as linear functions of ρb (Fig. 5) were modifiedto represent Dp=D0 and ka as a function of pF by using soil-waterretention data [Fig. 9(a)]. Sensitivity analysis of Dp=D0 and ka fortwo differently compacted soils (LC and EC) as a function of pF isshown in Fig. 9(c). The LC soil showed a rapid increase of bothDp=D0 and ka at low pF (pF < 2) and maintained relatively con-stant values at pF > 2, and the EC soil showed a gradual increase ofboth Dp=D0 and ka with increasing pF because of more uniformand larger-pore networks for the LC soil and a wider size distribu-tion of smaller-pore networks for the EC soil [Fig. 9(b)]. At naturalfield-water conditions (pF 2), the EC soil exhibited lower Dp=D0and ka than the LC soil because the soil compaction causedmarkedly increased water retention [i.e., lower soil-air content atpF 2, Fig. 9(a)] and thus greater water-blockage effects on gastransport.

The air-filled pore network tortuosity (τ ) was calculated fromthe measured Dp=D0 and ε (Currie 1960b; Ball 1981; Epstein1989; Moldrup et al. 2001) as

τ ¼ LeL

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiεDp=D0

rð7Þ

where tortuosity = ratio of the average capillary tube length (Le) tothe length of the porous media (soil sample length) (L) along themajor flow (diffusion) axis, in a tortuous capillary tube of uniformdiameter (τ ¼ Le=L). Eq. (7) hereby assumes diffusion in a porousmedium with pores consisting of tortuous and nonconstricted tubeswith uniform and similar diameter. Fig. 9(d) shows the calculated τas a function of pF. Although the LC soil showed greater τ than theEC soil at wetter conditions (around pF 1), the τ values for the LCsoil rapidly decreased with increasing pF. This suggests that thewater-blocked pore spaces at wetter conditions causes highlytortuous pathways for gas diffusion (i.e., greater water-blockageeffects on Dp=D0) and that the drained larger-pore networks athigher pF allows for the formation of more continuous pathwaysfor gas transport. The reduced water-blockage effects and widerpore-size distribution for the EC soil caused a gradual decreaseof τ with increasing pF [Fig. 9(d)]. At pF 2, the EC soil showedgreater soil-pore tortuosity (i.e., greater τ) as compared to the LCsoil because the larger soil-water content (θ) caused more tortuouspathways for gas diffusion.

Numerical Simulation of Methane Oxidation inDifferently Compacted Landfill Final Cover Soil

One-dimensional (1D) methane (CH4) gas transport through twodifferently compacted landfill cover soils (LC and EC) at differentpF conditions was simulated. Only diffusive gas transport was con-sidered because previous studies suggested that gas diffusion is theonly quantitatively important gas transport process in a shallow va-dose zone under natural conditions (Buckingham 1904; Xu et al.1992; Freijer 1994). Assuming that methane oxidation followsfirst-order kinetics (Koschorreck and Conrad 1993; Kruse et al.1996), the governing equation for 1D methane gas transport in soilcan be written as

∂Cg

∂t ¼ Dp

ε∂2Cg

∂z2 � k1Cg ð8Þ

where Cg = methane gas concentration in soil (mol CH4 m�3);k1 = first-order rate constant (s�1); t = time (s); and z = soildepth (m). In this study, a total soil depth of 0.3 m was considered,which is representative of the oxidation zone as suggested byde Visscher et al. (1999), and a k1 of 0:5 h�1 from Kruse et al.

Fig. 8. Sensitivity analysis showing effects of compaction on Dp=D0

and ka as a function of ε for differently compacted soils

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(1996) was used [Fig. 10(a)]. Atmospheric CH4 concentration(7:08 × 10�5 mol CH4 m�3) and a CH4 flux boundary (1:52×10�4 mol CH4 m�2 s�1 from de Visscher and van Cleemput(2003) were used as the upper (soil surface) and lower boundary

conditions, respectively [Fig. 10(a)]. The predicted Dp as a functionof pF for soils at ρb ¼ 1:44 and 1.85 [Fig. 9(c)] was used as aninput parameter. Eq. (8) at steady state was solved by a finite-element method using COMSOL multiphysics Ver. 3.4 (Keisoku

Fig. 9. Arrows indicate the changing conditions from low-compacted (LC) to high-compacted (HC) soil: (a) soil-water retention curves; (b) pore-sizedensities for Jyndevad sandy soil (ρb ¼ 1:44) and landfill cover soil (ρb ¼ 1:85); (c) sensitivity analysis showing effects of compaction on Dp=D0

and ka; (d) pore network tortuosity [Eq. (7)] as a function of pF for differently compacted soils

Fig. 10. (a) Boundary conditions and parameter values for numerical simulations; (b) simulated cumulative methane oxidation rate for differentlycompacted soils

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Engineering System Co., Japan). The total methane oxidation ratein the cover soil (RCH4, mol m�2 h�1) was calculated by accumu-lating the methane oxidation with soil depth following Koschorreckand Conrad (1993) and Kruse et al. (1996):

RCH4¼

Z0:3

0k1Cgzεdz ð9Þ

Fig. 10(b) shows the calculated cumulative methane oxidationrate (RCH4) for the LC and EC soils as a function of pF. GreaterRCH4 values for the LC soil were obtained across the pF rangeas compared to the EC soil, indicating greater CH4 accessibilityfor the CH4 oxidation because of greater soil-air content. However,the RCH4 values for the EC and LC soils at pF 3 were 3.7 and 1.7times higher than those at pF 1, respectively. Hence, the increase ofCH4 accessibility with increasing pF (i.e., increase of ε) is greaterfor the EC soil. Thus, technologies for better control of the methaneoxidation in the landfill final cover soils under extreme compactionlevel should address the physical conditions in the cover soils, es-pecially dry density and void ratio as related to water retention.A high air-filled porosity is especially key for optimizing aerobicconditions in the cover soils and thereby enhancing the methaneoxidation.

Conclusions

Extreme soil compaction dramatically influenced both diffusiveand convective gas transport parameters. The compaction causedreduced water-blockage effects on both ka and Dp=D0 under wetterconditions, resulting in lower threshold soil-air content (εth) forboth Dp=D0 and ka. The highly and extremely compacted landfillcover soil (ρb ¼ 1:70–1:80 and 1.80–1.90) showed negligible εthfor both Dp=D0 and ka and an almost linear increase of Dp=D0 withsoil-air content (ε). Soil compaction also caused the reduction oflarger-pore networks, thereby markedly reducing the increase inka with ε under dry conditions.

Power-law type models for Dp=D0 an ka considering both poreconnectivity parameters ðαp;αaÞ and water-blockage parameters(Xp, Xa) as a function of ρb described the measured Dp=D0 andka well for differently compacted and variably saturated soils. Asensitivity analysis using the new power-law type models to re-presentDp=D0 and ka as a function of pF revealed that at the naturalfield-water condition (pF 2), relatively lower ε for the extremelycompacted soil caused lower Dp=D0 and ka values as comparedwith less-compacted soils. Thus, at the same ε value, the Dpand ka will be greater for extremely compacted soil becauseof the reduced water-blockage effects, but at the same pF value(e.g., pF 2), much greater water retention will still cause lowerDp and ka values for extremely compacted soils.

Numerical simulations of one-dimensional methane gas trans-port through differently compacted soils showed that increasedmethane accessibility with increasing pF is a major control forthe total methane oxidation rate in highly compacted landfill coversoil. The findings in this study are very promising for simulatinggreenhouse gas emissions from landfill sites and designing landfillcover soil to optimize gas uptake and prevent gas emissions. Theeffects of gravel contents or coarse size fractions on Dp=D0 and kaand the scale dependency of Dp=D0 and ka for extremely com-pacted landfill cover soils should be investigated for further under-standing of the in situ gas transport and retainment or removal atlandfill sites.

Acknowledgments

This study was made possible by the grant-in-aid for Scientific Re-search No. 206192 and No. 18360224 from the Japan Society forthe Promotion of Science (JSPS) and by a research grant from theInnovative Research Organization, Saitama University. This studywas in part supported by the projects Gas Diffusivity in Intact Un-saturated Soil (“GADIUS”) and Soil Infrastructure, Interfaces, andTranslocation Processes in Inner Space (“Soil-It-Is”) from the Dan-ish Research Council for Technology and Production Sciences. Weespecially acknowledge the careful and dedicated laboratory workby former B.S. student Yoshiharu Fujiwara and M.S. student YuichiSugimoto, Saitama University.

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