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).