Linear Model to Predict Soil-Gas Diffusivity from Two Soil-Water Retention Points in Unsaturated Volcanic Ash Soils

SOILS AND FOUNDATIONS Vol. 48, No. 3, 397–406, June 2008 Japanese Geotechnical Society

LINEAR MODEL TO PREDICT SOIL-GAS DIFFUSIVITY FROM TWO SOIL-WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS

AUGUSTUS C. RESURRECCIONi),TOSHIKO KOMATSUii),KEN KAWAMOTOii), MASANOBU ODAii),SEIKO YOSHIKAWAiii) and PER MOLDRUPiv)

ABSTRACT Risk assessment and design of remediation methods at soil sites polluted with gaseous phase contaminant require an accurate description of soil-gas diŠusion coe‹cient (Dp) which is typically governed by the variations in soil air-ˆlled porosity (va). For undisturbed volcanic ash soils, recent studies have shown that a linear Dp(va) model, taking into ac- count inactive air-ˆlled pore space (threshold soil-air content, va, th), captured the Dp data across the total soil moisture range from wet to completely dry conditions. In this study, we developed a simple, easy to apply, and still accurate linear Dp(va) model for undisturbed volcanic ash soils. The model slope C and intercept (interpreted as va, th) were der- X ived using the classical Buckingham (1904) Dp(va) power-law model, va ,attwosoil-watermatricpotentialsofpF2 (near ˆeld capacity condition) and pF 4.1 (near wilting point condition), and assuming the same value for the Buckin- gham exponent (X＝2.3) in agreement with measured data. This linear Dp(va) prediction model performed better than the traditionally-used non-linear Dp(va) models, especially at dry soil conditions, when tested against several indepen- dent data sets from literature. Model parameter sensitivity analysis on soil compaction eŠects showed that a decrease in slope C and va, th due to uniaxial reduction of air-ˆlled pore space in between aggregates markedly aŠects the magnitude of soil-gas diŠusivity. We recommend the new Dp(va) model using only the soil-air contents at two soil-water matric potential conditions (ˆeld capacity and wilting point) for a rapid assessment of the entire Dp-va function.

Key words: air-ˆlled porosity, soil-gas diŠusion coe‹cient, soil-gas diŠusivity, soil-water retention, volcanic ash soil (IGC: D4/E14)

Several predictive models for soil-gas diŠusivity, INTRODUCTION Dp/Do (where Do is the gas diŠusion coe‹cient in free 3 －3 The movement of gaseous phase contaminants in soil air), as a function of soil-air content (va,m soil-air m (e.g., volatile organic chemicals as a result of spills or soil) have been proposed. These include both empirical, leaks from underground tanks) is generally controlled by soil-type independent models and some recent and more gas diŠusion through tortuous air-ˆlled pathways in be- conceptual soil-water retention (pore-size distribution) tween soil particle-water complexes (Hers et al., 2002). dependent models. The early Dp/Do models of Buckin- An accurate prediction of the soil-gas diŠusion coe‹cient gham (1904) and Penman (1940) require only va to esti-

(Dp) and its dependency on the soil moisture conditions in mate Dp, whereas the later Millington and Quirk (1960, the unsaturated zone are, therefore, essential to realisti- 1961) Dp/Do models also include the soil total porosity cally simulate the migration of soil-gaseous contaminants (F,m3 pore space m－3 soil). These soil-type independent and to quantify the associated risk from soil contamina- Dp/Do models performed poorly when tested against Dp tion(Petersenetal.,1996).Thisisespeciallythecasefor measurements on soils with diŠerent texture (including soils in urban areas where the degree of soil compaction volcanic ash soils) and across a wide interval of soil below buildings will additionally in‰uence the magnitude moisture conditions (Moldrup et al., 1999, 2000, 2003). of Dp. Since measurements of Dp are highly time consum- However, the Millington and Quirk (1961) Dp/Do model ing and require specialized measurement apparatus (Rol- is still today the most widely used model when investigat- ston and Moldrup, 2002) that is not available in most ing the diŠusion of gaseous phase contaminants in soil soils and geotechnical laboratories, a prediction model (e.g., Jury et al., 1983; H äohener and Surbeck, 2004). for Dp requiring easily obtainable input parameters To take into account the eŠect of soil type on Dp,Mol- without sacriˆcing prediction accuracy is needed. drup et al. (1996, 1999, 2000) developed the soil-water

i) Dept. of Engineering Sciences, University of the Philippines-Diliman, Philippines (acresurrecci＠up.edu.ph). ii) Graduate School of Science and Engineering, Saitama University, Japan. iii) Department of Hilly Land Agriculture, National Agricultural Research Center for Western Region, Kagawa, Japan. iv) Environmental Engineering Section, Dept. of Biotechnology, Chemistry and Environmental Engineering, Aalborg University, Denmark. The manuscript for this paper was received for review on May 25, 2007; approved on February 5, 2008. Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

397 398 RESURRECCION ET AL.

characteristic (SWC)-based Dp/Do models. These SWC- MATERIALS AND METHODS based Dp/Do models performed superior to the soil-type independent models when estimating Dp for diŠerent soil Data from Literature types (Moldrup et al., 1999, 2000, 2004). For well-ag- We considered 24 Dp/Do data sets for undisturbed vol- gregated volcanic ash soils, however, the SWC-based canic ash soils from Osozawa (1998) and Resurreccion et 3 Dp/Do models had a tendency to underestimate Dp at in- al. (2007a, b) where Dp wasmeasuredon100cm core termediate soil moisture conditions (soil-water matric samples. Each undisturbed (intact) soil sample was col- potentials between pF 2 and pF 4.2; where pF＝log (－c, lected by inserting a 100-cm3 core into the soil. The soil soil-water matric potential in cm H2O)) and largely sample was removed using a hand shovel, trimmed, overestimated Dp at air- and oven-dry conditions (Mol- sealed with a vinyl tape, and stored at 2¿59Cbefore drup et al., 2003; Resurreccion et al., 2007a, b). laboratory analyses. Measurements of Dp were conducted

The SWC-based Dp/Do models do not consider the at a wide range of soil moisture conditions and with a eŠect of isolated air-ˆlled pore space entrapped by inter- number of intact samples measured for Dp at air- and connected water ˆlms in between soil aggregates. This in- oven-dry conditions. Some of the data sets from Osoza- active air-ˆlled pore space governs the magnitude of Dp at wa (1998) in this study were also used by Moldrup et al. very high soil-water content, as reported by several (2003) in testing the performance of SWC-based Dp/Do authors (Call 1957; Troeh et al., 1982; Freijer, 1994). models.

Resurreccion et al. (2007a, b) showed that a linear Dp/Do The undisturbed volcanic ash soils were taken from model, proposed by Moldrup et al. (2005a) and taking diŠerent locations in Japan, and are labeled according to into account the inactive pore space (threshold soil-air the sampling location (name of the local area). The data content, va, th) well captured the observed linear Dp(va)be- from Osozawa (1998) consist of 20 soils collected from havior of undisturbed, unsaturated volcanic ash soils. Tsumagoi (10 soils), Kyushu (5 soils), and Miura (5 soils).

The two model parameters (slope C and intercept va, th), Measurements of Dp and soil-water retention at soil- however, have yet to be linked to measurable soil physical water matric potential intervals between pF 1 and 4.2 characteristics (e.g., soil-water retention). were conducted on triplicate samples and the mean value Alternatively, Moldrup et al. (2005b) revisited the was used in the analysis. Tsumagoi and Kyushu soils were X Buckingham (1904) power-law model (va )andsuggested characterized as humic to highly humic volcanic ash soils the possibility of linking the exponent X with soil from agricultural and grass lands, respectively; while moisture condition in terms of the soil-water matric Miura soils were characterized as light clay volcanic ash potential c or pF. Moldrup et al. (2005b) showed that X soil. Two Tsumagoi soils were also measured for Dp at is expected to vary between 2 for drier soil and gradually air-dry condition. increases to 2.5 or more for wetter soil, based on data for The remaining four volcanic ash soils are from Resur- 44 diŠerently textured undisturbed soils. In this study, we reccion et al. (2007a, b) and were sampled from Nishi- will combine the approaches of Moldrup et al. (2005a, b) Tokyo (1 soil) and Fukushima (3 soils). Nishi-Tokyo soil to arrive at a simple and easy applicable model for soil- data represent 12 intact soil samples collected along a gas diŠusivity taking into account both inactive air-ˆlled transect in a pasture ˆeld and characterized as highly or- pore space and soil-water retention. ganic loam with approximately 11z organic matter con- Volcanic ash soil diŠers from normal mineral soils be- tent, while 36 intact soil samples from Fukushima were cause this soil usually possesses dual porosity aggregated taken from a forest site at three depths (12 intact soil sam- structure including high amounts of Allophane, a clay ples per depth) with a steep organic matter gradient. Mea- mineral with a hollow particle structure. These allophanic surements of Dp and soil-water retention were done at the volcanic ash soils have unique physical and chemical soil-water matric potential intervals between pF 1 and properties, including high water retention, good 4.1. Dp was measured for 19 samples at air-dry condition drainage, and high nutrient availability that make them and for 10 samples at oven-dry condition out of the 48 suitable for agricultural production (Shoji et al., 1993). samples in total. The remaining soil samples collapsed In Japan, it extends to most of the Kanto region in East during the drying process and therefore did not allow

Japan (Takahashi and Shoji, 2002) including highly ur- measurements of Dp at air- and oven-dry conditions. We banized areas within the Tokyo metropolis. adopted the value of pF 6 as the soil-water matric poten- The objectives of this study are (1) to develop a simple, tial at air-dry condition following Poulsen et al. (2006). predictive Dp/Do model for unsaturated volcanic ash soils The soil physical and geotechnical indices of all un- based on only two well-deˆned points on the soil-water disturbed volcanic ash soils in this study are given in retention curve, (2) to test the performance of this new Table 1. Data on texture, liquid, and plastic limits of

Dp/Do model against independent soil-gas diŠusivity data soils from Osozawa (1998) were obtained from similar from literature covering a wide range of soil-moisture soil series at diŠerent places from the sampling points of conditions, soil texture, and bulk densities, hereunder Osozawa (1998); whereas data on texture, liquid, and comparing model performance with that of existing plastic limits of Nishi-Tokyo and Fukushima Andisols predictive Dp/Do models, and (3) to evaluate the eŠects of were results of direct measurements on samples taken bulk density on the sensitivity Dp/Do based on the new from the actual sampling location. model and supporting measurements. TWO SOIL-WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS 399

Table 1. Soil properties for the 24 Andisols used in this study including soil-air content data at pF 2 and 4.1 (4.2). Data from Osozawa (1998), Resurreccion et al. (2007a, b), and this study

Soil-Air Content, e Gas diŠusivity, Particle Bulk Sand* Silt* Clay* Gravel* Total Liquid Plastic (m3 m－3) D /D Soil density density Porosity p o －3 －3 (z) (z) (z) (z) 3 －3 limit limit (Mg m ) (Mg m ) (m m ) pF 2 pF 4.1 (4.2)† pF 2 pF 4.1 (4.2)†

Tsumagoi 1 2.47 0.57 30.6§ 35.2§ 34.2§ 0§ 0.770 88‡ 59‡ 0.342 0.523 0.103 0.231 Tsumagoi 2 2.46 0.73 nm nm nm nm 0.705 135‡ 75‡ 0.084 0.292 0.002 0.059 Tsumagoi 3 2.41 0.61 26.5§ 38.4§ 35.2§ 0§ 0.745 172‡ 83‡ 0.061 0.237 0.001 0.040 Tsumagoi 4 2.39 0.40 nm nm nm nm 0.834 nm nm 0.279 0.489 0.069 0.243 Tsumagoi 5 2.82 0.69 nm nm nm nm 0.756 nm nm 0.171 0.255 0.026 0.057 Tsumagoi 6 2.57 0.57 nm nm nm nm 0.778 nm nm 0.353 0.517 0.115 0.212 Tsumagoi 7 2.57 0.76 nm nm nm nm 0.706 nm nm 0.170 0.341 0.015 0.089 Tsumagoi 8 2.55 0.72 nm nm nm nm 0.717 nm nm 0.134 0.276 0.010 0.064 Tsumagoi 9 2.56 0.63 nm nm nm nm 0.754 nm nm 0.357 0.539 0.090 0.202 Tsumagoi 10 2.56 0.77 nm nm nm nm 0.700 nm nm 0.165 0.300 0.012 0.064

Miura 1 2.51 0.79 nm nm nm nm 0.687 nm nm 0.224 0.377 0.029 0.135 Miura 2 2.50 0.71 nm nm nm nm 0.715 nm nm 0.267 0.446 0.059 0.191 Miura 3 2.68 0.49 nm nm nm nm 0.819 nm nm 0.230 0.387 0.034 0.129 Miura 4 2.66 0.67 nm nm nm nm 0.750 nm nm 0.321 0.458 0.082 0.194 Miura 5 2.52 0.62 nm nm nm nm 0.753 nm nm 0.284 0.460 0.074 0.201

Kyushu 1 2.45 0.74 33.1§ 36.3§ 30.6§ 4.4§ 0.697 100‡ 70‡‡ 0.141 0.332 0.020 0.110 Kyushu 2 2.59 0.56 48.0§ 28.3§ 23.7§ 3.2§ 0.783 158‡ 126‡‡ 0.087 0.161 0.012 0.040 Kyushu 3 2.62 0.52 31.2§ 28.9§ 39.9§ 8.1§ 0.802 163‡ 128‡‡ 0.103 0.207 0.014 0.051 Kyushu 4 2.58 0.81 18.8§ 37.6§ 43.6§ 0.6§ 0.685 86‡ 58‡‡ 0.195 0.320 0.029 0.080 Kyushu 5 2.58 0.75 16.6§ 46.8§ 36.6§ 0§ 0.708 94‡ 65‡‡ 0.196 0.347 0.032 0.091 Nishi-Tokyo 2.63 0.77 25.6 52.1 22.3 0 0.710 72 53 0.140 0.370 0.019 0.120

Fukushima 1 2.35 0.51 31.6 47.2 20.9 0.5 0.780 127 84 0.290 0.460 0.050 0.150 Fukushima 2 2.56 0.65 43.0 36.6 19.6 0.8 0.740 97 76 0.260 0.410 0.060 0.150 Fukushima 3 2.71 0.64 49.2 41.5 8.8 0.9 0.760 106 71 0.210 0.360 0.040 0.130

† Measurements of soil-water retention and Dp were done at pF 4.1 for Nishi-Tokyo and Fukushima volcanic ash soils, and at pF 4.2 for Tsumagoi, Miura, and Kyushu volcanic ash soils. * Sand, silt and clay fractions of Nishi-Tokyo and Fukushima soils were classiˆed according to Japan Geotechnical Society (JGS) while other soils were classiˆed according to International Society of Soil Science (ISSS). § Data from the Department of Environmental Chemistry, National Institute of Agro-Environmental Sciences (1976). ‡ Data from Wada (1986). ‡‡ Data from Osozawa (1998). nm＝not measured

New Data Representing DiŠerent Compaction Levels were kept for 5 to 7 days at a constant water level around In the present study, disturbed soil was also collected at 2¿5 mm below the upper edge of the soil core. After the same soil site in Nishi-Tokyo. The disturbed soil was saturation, the soil samples were then drained subse- 3 passed through a 2-mm sieve and repacked onto 100 cm quently to diŠerent pF conditions where Dp was measured soil cores (in triplicate) at bulk densities of 0.6, 0.7, and at each drainage step. Before measurements of Dp,soil 0.73 Mg m－3, thus representing three diŠerent levels of samples were weighed to determine the soil-water content uniaxial compaction. Soil-water retention and Dp were at each pF. For soil samples successfully measured for Dp measured on these repacked samples at pF 1, 1.5, 1.8, 2, at air- and oven-dry conditions, the samples were placed 2.3, 3, 4.1, and 6 (air-dry condition). inside a convective air-‰ow oven which was set at 209C for 5 to 7 days for air-dry condition, and at 1059Cfor2 Measurement Methods days for oven-dry condition.

For all data sets, the same experimental methods for The soil-gas diŠusion coe‹cients (Dp)weremeasured measurements of soil-water retention and Dp were used. by the method of Currie (1960) as recommended by Rol- Soil-water retention was measured using a draining ston and Moldrup (2002). The apparatus uses a diŠusion curve, using either a hanging water column for pFÃ2 chamber with oxygen as the experimental gas at 209C(see

(i.e., cÆ－100 cm H2O) or a pressure plate extractor for Fig. 1). The diŠusion chamber was ‰ushed with 100z pFÀ2(i.e.,cº－100 cm H2O). Resurreccion et al. nitrogen gas while the upper end of the soil core was ex- (2007a, b), however, used only the pressure plate extrac- posed to the atmosphere. Once the slide plate is opened to tor across the entire pF interval. Firstly, soil core samples establish contact between soil sample and diŠusion cham- were immersed in a basin containing water (treated with ber, oxygen from the atmosphere diŠuses through the soil sodium azide, NaN3, to prevent fungal growth) to sample into the diŠusion chamber while nitrogen gas saturate the soil samples by capillary action. Soil samples diŠuses through the soil sample into the atmosphere. The 400 RESURRECCION ET AL.

10/3 Dp (va) ＝ 2 (5) Do F Soil-Water Characteristic (SWC) Based Models

The recent Dp(va)/Do models developed by Moldrup et al. (1996, 1999, 2000, 2005a) linked soil-gas diŠusivity to soil type through the pore size distribution (PSD) parameter b by using the Campbell (1974) soil-water retention model, c u －b ＝Ø » (6) ce us Fig. 1. Schematic diagram of the experimental apparatus used to where c is the soil-water matric potential (cm H2O), ce is measure soil-gas diŠusion coe‹cient, Dp the air-entry potential (cm H2O), u is the volumetric soil- 3 －3 water content (m m ), us is the soil-water content at saturation (m3 m－3), and b (À0) is the slope of the SWC oxygen concentration inside the diŠusion chamber was curve in a log (－c) versus log (u) plot. The SWC-based measured using an electrode sensor. Oxygen consump- Dp(va)/Do models include the Buckingham-Burdine-Cam- tion in the soil samples was considered negligible for the pbell (BBC) model (Moldrup et al., 1999), the va, 100-de- short measurement time (Schjønning, 1985). Mixing of pendent (macroporosity-dependent) model (Moldrup et air within the small diŠusion chamber was assumed to oc- al., 2000), and the Three-Porosity Model (TPM, Mol- cur instantly. The calculation of the soil-gas diŠusion drup et al., 2004). coe‹cient, Dp, was done according to Rolston and Mol- The BBC Dp(va)/Do model (Moldrup et al., 1999) is, 3 drup (2002). 2＋ D v b p＝F2 Ø a » (7) Do F MODELS FOR SOIL-GAS DIFFUSIVITY where the expression, F2, is a reference gas diŠusivity at Soil-Type Independent Models completely dry conditions, following Buckingham Buckingham (1904) suggested that the soil-gas diŠu- (1904). The exponent 2＋3/b is analogous to the Burdine sion coe‹cient depends on soil-air content following a (1953) capillary tube model for unsaturated hydraulic power-function, conductivity.

The va, 100-dependent Dp(va)/Do model (Moldrup et al., Dp X ＝(va) (1) 2000) is, Do 3 2＋ b Dp 3 va Buckingham suggested the Buckingham exponent X ap- ＝(2va, 100＋0.04va, 100)Ø » (8) Do va, 100 proximately equals to 2 based on measurements of Dp on sand, loam, and clay soils. where va, 100 is reference soil-air content equal to the The Penman (1940) model assumed a linear variation amount of pore space at soil-water matric potential of of Dp/Do with soil-air content, c＝－100 cm H2O. In Eq. (8), an empirical relation D between gas diŠusivity at c＝－100 cm H2Oandthe p＝0.66v (2) macroporosity (v ) replaces the Buckingham expres- D a a, 100 o sion in the BBC model (F2 in Eq. (7)). Call (1957) modiˆed the Penman model by assuming Moldrup et al. (2004) combined the BBC (Eq. (7)) and

10z of the total soil volume consisted of isolated (inac- the macroporosity-dependent (Eq. (8)) Dp/Do models to tive) air-ˆlled pores. This model successfully described reduce the necessary parameter input from soil-water the diŠusion of ethylene dibromide in a sandy loam soil. retention data yielding the Three-Porosity Model (TPM).

The Call (1957) Dp/Do model is given as, The TPM is given as,

XT Dp Dp 2 va ＝0.66(va－0.1) (3) ＝F Ø » (9) Do Do F

Millington and Quirk (1960, 1961) used a mechanistic ap- where XT is a tortuosity-connectivity factor calculated as, proach to develop non-linear Dp(va)/Do models. The Mil- 3 2va, 100＋0.04va, 100 lington and Quirk (1960) Dp(va)/Do model is given as, log Ø 2 » 2 F Dp (va) XT＝ (10) ＝ 2/3 (4) va, 100 Do F log Ø F » where F is the soil total porosity (m3 pore space m－3 soil).

The Millington and Quirk (1961) Dp(va)/Do model is, TWO SOIL-WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS 401

New Two-Retention-Point (2RP) Model va, th is the threshold soil-air content below which soil-gas To develop a simpler and easily applicable gas diŠusivi- diŠusivity becomes negligible (ceases due to the inactive ty model, we consider a linear so-called Penman-Call or remote air-ˆlled pore space created by inter-connected type Dp(va)/Do model (Moldrup et al., 2005a), water ˆlms). Both C and va, th are likely dependent on soil pore size distribution (i.e., soil-water retention) and soil Dp structure(e.g.,aggregation)(Moldrupetal.,2005a). ＝C(va－va, th)ifvaÆva, th (11a) Do Figure 2 shows measurements of Dp on two un-

Dp disturbed soil samples from Nishi-Tokyo and Tsumagoi, ＝0ifvaºva, th (11b) supporting a highly linear relation between Dp/Do and va, Do starting from the threshold soil-air content (va, th)upto where C is the slope of the linear Dp(va)/Do model, and the air-dry soil moisture condition. This linear behavior

of Dp(va)/Do was also observed for all Nishi-Tokyo and Fukushima undisturbed soils, as already reported by Resurreccion et al. (2007a, b), and on the 20 data sets from Osozawa (1998).

Since the Penman-Call type Dp(va)/Do model

represents a linear function of va, only two points (i.e.,

va–Dp/Do coordinates) on the prediction line are su‹cient to derive the model parameters (slope C and intercept

va, th). In order to deˆne the prediction line, it is necessary to estimate the gas diŠusivities at two appropriately

selected values of va based on the soil-water retention curve. In this study, the Buckingham (1904) power func- X tion va ,isusedtoestimatetheDp/Do values at the two chosen values of soil-air content. For the classical Buckingham (1904) power-law model

to accurately estimate Dp/Do the Buckingham exponent

X has to vary with va and, thus, with soil-water matric potential (pF), as illustrated in Fig. 3(a) for the soil moisture conditions at pF 3 and 6. Data for three Fig. 2. Plot of the soil-gas diŠusivity against soil-air content for Tsumagoi and Nishi-Tokyo volcanic ash soils. A linear ˆt to each Fukushima soils with Dp measured up to air-dry condi- tion suggested that X has to vary symmetrically with soil- Dp/Do data set and the Millington and Quirk (MQ, 1961) model, Eq. (5), are also shown water matric potential (expressed as pF) with a minimum

Fig. 3. (a) Plot of Dp/Do against soil-air content for 13 intact volcanic ash soil samples from Fukushima 0–5 cm, 15–20 cm and 55–60 cm depths at

soil-water matric potentials of pF 3 and 6 (air-dry, as ˆlled out symbols). The Buckingham (1904) Dp/Do power-law model ˆtted to the Dp/Do data at pF 3 and 6 is also shown. (b) Plot of the average of Buckingham exponent (X) values at each pF measurement for three Fukushima soil layers. The symmetric X(pF) function ˆtted to the average X-pF data (excluding data at pF 1) in this study (solid line) and to individual soil from Fukushima are also shown. Data from Resurreccion et al. (2007b) 402 RESURRECCION ET AL.

(v )2.3－(v )2.3 C＝ a, 4.1 a, 2 (12) va, 4.1－va, 2

where va, 2 and va, 4.1 are soil-air content values at pF 2 and

4.1, respectively. The threshold soil-air content, va, th,is calculated as, (v )1.3 v ＝v 1－ a, 4.1 (13) a, th a, 4.1 Ø C » where the expression inside the parenthesis in Eq. (13) is the fraction of air-ˆlled pores less than 0.2 mm that con- stitutes the threshold soil-air content for soil-gas diŠu- sion.

In order to use the 2RP Dp/Do model, values of va, 2 and

va, 4.1 have to be either measured or estimated. When mea- surements are not available, the soil-air content at pF 2 Fig. 4. Model concept for the two-retention-point (2RP) soil-gas (va, 2) can be deduced from the soil-water content at ˆeld diŠusivity model, Eq. (11). The Dp/Do values at the two soil-water capacity. The ˆeld water capacity is the remaining soil- retention points are estimated from the Buckingham (1904) power- X water content in the soil drained a few days after rainfall law model, va , assuming the same value of X＝2.3 at both reten- tion points or irrigation (when free drainage is negligible). On the other hand, measurement of the soil-air content at pF 4.1 would require a pressure plate apparatus to drain the soil X value occurring at around pF 3 (Fig. 3(b)). This soil- to near wilting point conditions. However, with limited water matric potential (pF 3) was suggested as the soil- data, the soil-air content at pF 4.1 can be estimated using water retention point where separation between inter- pedotransfer functions from clay, silt, and sand fractions and intra-aggregate pore space region takes place (Givietal.,2004). (Kawamoto and Aung, 2004). At this pF condition, maxi- The soil-water retention hysteresis aŠects the calcula- mum continuity (connectivity) of air-ˆlled pore space tion of the soil-air content both at pF 2 and pF 4.1. likely occurs because voids between aggregates are almost However, in this study, the new 2RP model is developed completely drained eliminating the inter-connected water based on the soil-air content calculated from the main ˆlms between water-ˆlled aggregates resulting in a mini- drying curve of soil-water retention. The eŠect of hystere- mum water blocking eŠect (and, therefore, minimum X sis on the conˆguration of the air-ˆlled pore connectivity value). This is in agreement with the Dp/Do data of Mol- is outside the scope of this paper and should be further drup et al. (2005b) for 44 diŠerently textured undisturbed studied. soils.

Figure 4 illustrates the proposed linear Dp/Do model Statistical Analyses named as the Two-Retention-Point (2RP) Dp/Do model. To compare the diŠerent predictive Dp/Do models, the

Two va values from the soil-water retention curve were root mean square error (RMSE, Eq. (14)) was used for selected at the soil-water matric potential conditions of the best overall ˆt compared to measured data. ＝－ ＝－ pF 2 (c 100 cm H2O) and pF 4.1 (c 12600 cm 1 n H O). The soil-moisture condition at pF 2, where large RMSE＝ (d )2 (14) 2 n S i pores larger than 30 mm are likely to be drained, is close i＝1 to the natural ˆeld capacity for a wide range of soils where di is the diŠerence between the predicted and the (Beukes, 1987). The soil-moisture condition at pF 4.1 is measured values of Dp/Do at a given soil-air content, and close to the wilting point condition where water becomes n is the number of measurements. unavailable for the plants to use (Hillel, 1998; So, 1998). The two pF values near ˆeld capacity and wilting point RESULTS AND DISCUSSION conditions typically correspond to va values that are far from each other. This reduces the prediction error propa- Model Tests gated across the entire va values when the Dp/Do values at The performances of the soil-type independent (Eqs. pF 2 and 4.1 are slightly under or over-estimated by the (1) to (5)), the SWC-based (Eqs. (7) to (10)) and the 2RP X Buckingham Dp/Do power-law model, va . Following the (Eq. (11) with Eqs. (12) and (13)) Dp(va)/Do models tested ˆtted symmetric X-pF function in Fig. 3(b), the same X against the Dp measurements in this study (24 volcanic values (＝2.3) at both pF 2 and 4.1 were used in the Buck- ash soils with a total of 424 data points) are shown in Fig. ingham (1904) power-law model leading to the derivation 5 and Table 2. For the 20 soils from Osozawa (1998), the of the expression for the slope C of the 2RP Dp/Do model soil-aircontentatpF4.2wasusedinEqs.(12)and(13)as as, va, 4.1 since measurements at pF 4.1 were not available. In general, the traditional soil-type independent and

SWC-based Dp(va)/Do models largely overestimated TWO SOIL-WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS 403

Fig. 5. Scatterplot comparison of predicted and measured gas diŠusivities (24 soils, 424 data points). Test of (a) Buckingham(1904), Eq. (1), (b) Penman (1940), Eq. (2), (c) Call (1957), Eq. (3), (d) Millington and Quirk (MQ, 1960), Eq. (4), (e) Millington and Quirk (MQ, 1961), Eq. (5), (f) the Buckingham-Burdine-Campbell (BBC), Eq. (7), (g) Macroporosity-dependent, Eq. (8), (h) TPM, Eq. (9 and 10), and (i) the two-retention-

point (2RP), Eq. (11, 12, 13), Dp/Do models. Data are from Osozawa (1998) and Resurreccion et al. (2007a, b)

Table 2. Test of ten predictive gas diŠusivity models against Dp/Do measured Dp values at air- and oven-dry conditions (Fig. data for 24 soils (424 data points) used in this study. Root Mean 5(a)–(h)). At pFº4.2, the classical Penman (1940), Call Square Error (RMSE, Eq. (14)) is given for each model for all data (1957), and Millington and Quirk (1960) D (v )/D as well as for data divided into pFÃ3andpFÀ3 p a o models overestimated Dp/Do data (Fig. 5(b)–(d)) while Equation RMSE the commonly applied Millington and Quirk (1961) Dp/Do Model Number All data pFÃ3pFÀ3 Dp(va)/Do model underestimated measured gas diŠusivi- ties (Fig. 5(e)). (1) with Buckingham (1904) 0.060 0.021 0.108 The original Buckingham D (v )/D model, Eq. (1), X＝2 p a o Penman (1940) (2) 0.111 0.098 0.137 performed surprisingly well in predicting Dp/Do values Call (1957) (3) 0.055 0.043 0.077 (RMSE＝0.060, Fig. 5(a) and Table 2). When X was mo- Millington and Quirk (1960) (4) 0.091 0.031 0.163 diˆed to 2.3, signiˆcant improvement in the prediction Millington and Quirk (1961) (5) 0.081 0.033 0.143 performance of the Buckingham Dp(va)/Do model was Buckingham-Burdine-Campbell, BBC (7) 0.056 0.017 0.101 obtained, reducing the RMSE to 0.048. The performance Moldrup et al. (1999) X Macroporosity-dependent of the Buckingham va model, with X＝2.3, became com- (8) 0.052 0.017 0.094 Moldrup et al. (2000) parable to the performance of the SWC-based Dp(va)/Do Three-Porosity Model, TPM ＝ (9, 10) 0.058 0.017 0.105 models (BBC with RMSE 0.056, the va, 100-dependent Moldrup et al. (2004) model with RMSE＝0.052, and TPM with RMSE＝ Modiˆed Buckingham (1) with 0.048 0.018 0.085 0.058; see Fig. 5(f)–(h) and Table 2). (this study) X＝2.3 Two-Retention-Point, 2RP The 2RP Dp(va)/Do model well captured the linear (11, 12, 13) 0.026 0.017 0.042 (this study) Dp(va)/Do behavior across the entire soil moisture condi- tions (RMSE＝0.026, Fig. 5(i) and Table 2). In contrast

to the non-linear, SWC-based Dp/Do models, no large 404 RESURRECCION ET AL.

Fig. 6. Plot of gas diŠusivity against soil-air content for individual undisturbed samples from (a) Tsumagoi, (b) Fukushima 0–5 cm depth and (c) Nishi-Tokyo having decreasing soil total porosity values. The Millington and Quirk (MQ, 1961) model (Eq. (5)), the Buckingham-Burdine- Campbell (BBC) model (Eq. (7)), and the two-retention-point (2RP) model, Eqs. (11), (12), (13), are also shown prediction errors at high soil-air content were observed. Resurreccion et al. (2007a) suggested that the much lower measured Dp values at pFÀ4.1 compared to those predicted by the SWC-based power law Dp/Do models were due to an increase in tortuosity for soil-gas diŠusion in the remote air-ˆlled pore space within the soil ag- gregates when soil samples were drained past pF 3.

EŠects of Soil Compaction on Gas DiŠusivity Three individual undisturbed volcanic ash soils from Tsumagoi, Fukushima, and Nishi-Tokyo shown in Fig. 6(a)–(c) diŠer in bulk density and porosity due to diŠer- ent soil compaction conditions. The 2RP Dp/Do model performed better than the MQ (1961) and the SWC-based

BBC Dp/Do models, as also suggested in Fig. 5. Further, the values of the threshold soil-air content, v , were ob- a, th Fig. 7. EŠect of uniaxial compaction on soil-gas diŠusivity at pF 6 served to increase with increasing slope C, consistent with (air-dry). The compaction was assumed to aŠect only the macro the derived expression for va, th (Eq. (13)). pores, va, 2, between aggregates An increase in bulk density due to soil compaction reduces the amount of total pore space, and consequently decreases the continuity of air-ˆlled pores primarily in the r inter-aggregate pore space region. Osozawa (1998) has F＝1－ d (15) shown for a volcanic ash soil compacted at 50, 100, and rs

200 kPa that uniaxial compaction mainly reduces typical- The analysis assumes that the increase in bulk density (rd) ly larger pores (macropores) À30 mm, i.e., mainly due to uniaxial compaction reduces the total porosity cal- reduces inter-aggregate pores without reducing the intra- culated following Eq. (15). The change in the total pore aggregate porosity. This results in water blocking eŠects space, F, is re‰ected only on the reduction of larger inter- between aggregates at wet conditions, giving low values aggregate pores, va, 2. Further, since the intra-aggregate of slope C and va, th at high bulk density, in agreement pores are not likely aŠected by soil compaction, the with data for the three diŠerently compacted soils in Fig. diŠerences between va, 4.1 and va, 2 and between va, 6 (air- 6(a)–(c). ˆlled porosity at pF 6) and va, 4.1 were kept constant and To illustrate the eŠect of soil compaction, a model sen- assumed equal to 0.2 m3 m－3 (i.e., from the initial diŠer- sitivity analysis using the 2RP model to predict Dp at air- ence in soil-air content in between pF 2 and pF 4.1 and in dry condition under increasing soil dry bulk density (rd) between pF 4.1 and pF 6 for the Tsumagoi sample). The by using a Tsumagoi sample (particle density, rs,of2.41 analysis showed that the slope C and intercept va, th －3 －3 Mg m , bulk density of 0.4 Mg m , and macroporosi- decreased with increase in rd, and consequently decreased 3 －3 ty, va, 2,of0.28m m ; see Table 1) is shown in Fig. 7. the calculated value of Dp at pF 6, in full agreement with The relation between soil dry bulk density (rd)andsoil the measurements for the three volcanic ash soils in Fig. total porosity (F)isgivenby 6(a)–(c).

The variation of C and va, th with bulk density and the decrease in Dp at pF 6 (air-dry condition) shown in Fig. 7 TWO SOIL-WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS 405

Fig. 8. Plot of gas diŠusivity against soil-air content for three repacked volcanic ash soils from Nishi-Tokyo at (a) 0.6, (b) 0.7 and (c) 0.73 Mg m－3 dry bulk densities. The Millington and Quirk (MQ, 1961) model (Eq. (5)), the Buckingham-Burdine-Campbell (BBC) model (Eq. (7)), and the two-retention-point (2RP) model, Eqs. (11), (12), (13), are also shown

is supported by the measurements of Dp on repacked for prediction of gas diŠusivity and calculation of gas Nishi-Tokyo volcanic ash soil compacted at three bulk diŠusive transport in volcanic ash soils, especially under densities, seen in Fig. 8. Similar to the observations in dry moisture conditions where the 2RP model is sig- Fig. 6(a)–(c) and what is suggested by the model sensitivi- niˆcantly more accurate than previous models while req- ty analysis in Fig. 7, the slope C and va, th decreased as uiring the same or less data input. bulk density increased. The decrease of C and va, th with theincreaseinrd implies that at a given soil-air content within intermediate soil-moisture conditions (i.e., except ACKNOWLEDGEMENT at high soil-air contents) the soil-gas diŠusivity increased This study was made possible by the Grant-In-Aid for with a decrease in bulk density. This is in agreement with Scientiˆc Research no. 18360224 from the Japan Society Currie (1984) and further supported by the ˆndings of for the Promotion of Science (JSPS) and by a grant from Fujikawa and Miyazaki (2005) based on measurements the Innovative Research Organization, Saitama Universi- on repacked volcanic ash soil within the range of soil-air ty. This study was in part supported by the projects Gas 3 －3 content vaº0.4 m m . DiŠusivity in Intact Unsaturated Soil (``GADIUS'') and Lastly, the new 2RP model predicted excellently the Soil Infrastructure, Interfaces, and Translocation measured Dp values on repacked Nishi-Tokyo volcanic Processes in Inner Space (``Soil-it-is'') from the Danish ash soils at three diŠerent bulk densities (Fig. 8), while Research Council for Technology and Production the widely used MQ (1961) and BBC Dp/Do models per- Sciences. We would like to acknowledge the support formed poorly. Thus, the new 2RP model seems promis- from the University of the Philippines-Diliman. ing for predicting gas diŠusivities across moisture condi- tions (from wet to dry) in both non-compacted and com- pacted volcanic ash soils. REFERENCES 1) Beukes, D. J. (1987): Comparison between hydraulic conductivity and related properties of a ˆne sand and a ˆne sandy loam during CONCLUSIONS in-situ drainage, South African J. Plant and Soil, 4, 151–158 (in Afrikaans with English summary). In this study, we developed an easily applicable, linear 2) Buckingham, E. (1904): Contributions to our knowledge of the aer- soil-gas diŠusivity model that uses only two points on the ation of soils, USDA.Bur.SoilBul., 25,U.S.Gov.Print.O‹ce, soil-water retention curve. The performance of this so- Washington, DC. 3) Burdine, N. T. (1953): Relative permeability calculations from called 2RP Dp/Do model proved superior to the widely used Millington and Quirk (1961) and to nonlinear D /D pore-size distribution data, Trans. AIME, 198, 71–78. p o 4) Call, F. (1957): Soil fumigation: V, DiŠusion of ethylene dibromide models that require the full range of soil-water retention through soils, J. Sci. Food Agric., 8, 143–150. data. 5) Campbell, G. S. (1974): A simple method for determining unsatu- The 2RP model was tested for Japanese Andisols wi- rated conductivity from moisture retention data, Soil Sci., 117, thin the following parameter intervals: 0.68¿0.78 total 311–314. porosity (m3 pore space m－3 soil), 0.57¿0.81 bulk den- 6) Currie, J. A. (1960): Gaseous diŠusion in porous media: Part 1, A －3 nonsteady state method, Br.J.Appl.Phys., 11, 314–317. sity (Mg dry soil m soil), and less than 20 percent soil 7) Currie, J. A. (1984): Gas diŠusion through soil crumbs: the eŠect of organic matter. compaction and wetting, J. Soil Sci., 35, 1–10. As illustrated by both the new model and gas diŠusivity 8) Department of Environmental Chemistry, National Institute of measurements, soil compaction has a large eŠect on gas Agro-Environmental Sciences (1976): National and prefectural diŠusivity in volcanic ash soils because of a decrease in agricultural technology center: Soil proˆle examination, physical and chemical analysis, and soil classiˆcation, 252–253, 398–403. the void space, mainly taking place between aggregates. 9) Freijer, J. I. (1994): Calibration of jointed tube model for gas diŠu- We recommend the use of the new 2RP Dp/Do model 406 RESURRECCION ET AL.

sion coe‹cient in soils, Soil Sci. Soc. Am. J., 58, 1067–1076. A. M. and Rolston, D. E. (2005a): Predictive-descriptive models 10) Fujikawa, T. and Miyazaki, T. (2005): EŠect of bulk density and for gas and solute diŠusion coe‹cients in variably saturated porous soil type on the gas diŠusion coe‹cient on repacked and un- media coupled to pore-size distribution: III, Inactive pore space in- disturbed soils, Soil Sci., 170, 892–901. terpretations of gas diŠusivity, Soil Sci., 170, 867–880. 11) Givi, J., S., Prasher, O. and Patel, R. M. (2004): Evaluation of the 25) Moldrup, P., Olesen, T., Yoshikawa, S., Komatsu, T. and Rolston, pedotransfer functions in predicting the soil water contents at ˆeld D. E. (2005b): Predictive-descriptive models for gas and solute capacity and wilting point, Agric. Water Mgt., 70, 83–96. diŠusion coe‹cients in variably saturated porous media coupled to 12) Hers, I., Zapf-Gilje, R., Evans, D. and Li, L. (2002): Comparison, pore-size distribution: II, Gas diŠusivity in undisturbed soil, Soil validation, and use of models for predicting indoor air quality from Sci., 170, 854–866. soil and groundwater contamination, Soil and Sediment Contami- 26) Osozawa, S. (1998): Bulletin of National Institute for Agro-En- nation, 11, 491–527. vironmental Sciences, (15), Natl. Inst. of Agro-Environmental Sci., 13) Hillel, D. (1998): Environmental Soil Physics, Academic Press. Ibaraki, Japan. 14) H äohener, P. and Surbeck, H. (2004): Radon–222 as a tracer for 27) Penman, H. L. (1940): Gas and vapor movements in soil: The diŠu- nonaqueous phase liquid in the vadose zone, Vadose Zone J., 3, sion of vapors through porous solids, J. Agric. Sci., 30, 437–462. 1276–1285. 28) Petersen, L. W., El-Farhan, Y. H., Moldrup, P., Rolston, D. E. 15) Jury, W. A., Spencer, W. F. and Farmer, W. J. (1983): Behavior and Yamaguchi, T. (1996): Transient diŠusion, adsorption, and assessment model for trace organics in soil: I, Model description, J. emission of volatile organic vapors in soils with ‰uctuating low Environ. Qual., 12(4), 558–564. water contents, J. Environ. Qual., 25, 1054–1063. 16) Kawamoto, K. and Aung, B. (2004): Experimental study on soil 29) Poulsen, T., Moldrup, P., Yoshikawa, S. and Komatsu, T. (2006): water repellency of volcanic ash soils: EŠects of organic matter con- Bimodal probability law model for uniˆed description of water tent and initial water content, Trans. Jpn. Soc. Irrig. Drain. retention, air and water permeability, and gas diŠusivity in variably Reclam. Engrg., 230, 75–83. saturated soil, Vadose Zone J., 5, 1119–1128. 17) Millington, R. J. and Quirk, J. M. (1960): Transport in porous me- 30)Resurreccion,A.C.,Kawamoto,K.,Komatsu,T.,Moldrup,P., dia, Transactions of the 7th International Congress of Soil Science Ozaki, N. and Rolston, D. E. (2007a): Gas transport parameters (eds. by Van Beren, F. A. et al.), 1, Madison, WI. 14–24 Aug. along ˆeld transects of a volcanic ash soil, Soil Sci., 172, 3–16. Elsevier, Amsterdam. 97–106. 31)Resurreccion,A.C.,Kawamoto,K.,Komatsu,T.,Moldrup,P., 18) Millington, R. J. and Quirk, J. M. (1961): Permeability of porous Sato, K. and Rolston, D. E. (2007b): Gas diŠusivity and air solids, Trans. Faraday Soc., 57, 1200–1207. permeability in a volcanic ash soil proˆle: EŠects of organic matter 19) Moldrup, P., Kruse, C. W., Rolston, D. E. and Yamaguchi, T. and water retention, Soil Sci., 172, 432–443. (1996): Modeling diŠusion and reaction in soils: III, Predicting gas 32) Rolston, D. E. and Moldrup, P. (2002): Gas DiŠusivity,in:Dane, diŠusivity from the Campbell soil water retention model, Soil Sci., J. H. and Topp, G. C. (eds.). Methods of Soil Analysis, Part 4, 161, 366–375. SSSA Book Ser. 5, ASA and SSSA, Madison, WI, 1113–1139. 20) Moldrup, P., Olesen, T., Yamaguchi, T., Schjønning, P. and Rol- 33) Schjønning, P. (1985): A laboratory method for the determination ston, D. E. (1999): Modeling diŠusion and reaction in soils: IX, of gas diŠusion in soil, Rep. S1773, Danish Institute of Agricultural The Buckingham-Burdine-Campbell equation for gas diŠusivity in Sciences, Jyndevad, Denmark (in Danish with English summary). undisturbed soil, Soil Sci., 164, 542–551. 34) Shoji, S., Nanzyo, M. and Dahlgren, R. (1993): Volcanic ash soils: 21) Moldrup, P., Olesen, T., Schjønning, P., Yamaguchi, T. and Rol- Genesis, properties and utilization, Developments in Soil Science, ston, D. E. (2000): Predicting the gas diŠusion coe‹cient in un- 21, Elsevier, Amsterdam. disturbed soil from soil water characteristics, Soil Sci. Soc. Am. J., 35) So, E. K. (1998): Statistical correlation between Allophane content 64, 94–100. and index properties for volcanic cohesive soil, Soils and Founda- 22) Moldrup, P., Yoshikawa, S., Olesen, T., Komatsu, T. and Rolston, tions, 38(4), 85–94. D. E. (2003): Gas diŠusivity in undisturbed volcanic ash soils: Test 36) Takahashi, T. and Shoji, S.(2002): Distribution and classiˆcation of soil-water-characteristic based prediction models, Soil Sci. Soc. of volcanic ash soils, Global Environmental Research, 6, 83–97. Am. J., 67, 41–51. 37) Troeh, F. R., Jabro, J. D. and Kirkham, D. (1982): Gaseous diŠu- 23) Moldrup, P., Olesen, T., Yoshikawa, S., Komatsu, T. and Rolston, sion equations for porous materials, Geoderma, 27, 239–253. D. E. (2004): Three-porosity model for predicting the gas diŠusion 38) Wada, K. (1986): Ando Soils in Japan, Kyushu University Press, coe‹cient in undisturbed soil, Soil Sci. Soc. Am. J., 68, 750–759. Japan, 168–203. 24) Moldrup, P., Olesen, T., Yoshikawa, S., Komatsu, T., McDonald,