181

i) Assistant Professor, Laboratoire d'Ondes et Milieux Complexes, Universit áe du Havre, France (Said.Taibi＠univ-lehavre.fr).ii) Associate Professor, Dept. of Civil Engineering, Federal University of Espirito Santo, Brazil.iii) Post-doc Researcher, Laboratoire d'Ondes et Milieux Complexes, Universit áe du Havre, France.iv) Professor, Laboratoire MSS-Mat, Ecole Centrale Paris, France.

The manuscript for this paper was received for review on February 21, 2008; approved on January 29, 2009.Written discussions on this paper should be submitted before November 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.

181

SOILS AND FOUNDATIONS Vol. 49, No. 2, 181–191, Apr. 2009Japanese Geotechnical Society

MEASUREMENTS OF UNSATURATED HYDRAULICCONDUCTIVITY FUNCTIONS OF TWO FINE-GRAINED MATERIALS

SAID TAIBIi), KATIA VANESSA BICALHOii), CHAHIRA SAYAD-GAIDIiii) and JEAN-MARIE FLEUREAUiv)

ABSTRACT

Water unsaturated hydraulic conductivity (kw) functions of two remolded ˆne-grained materials were measured overa wide range of degrees of saturation (Sr) with two methods. The instantaneous proˆle method (IPM) was used for Sr

À50z. An original vapor equilibration method (also known as the vapor equilibrium technique, VET) was used for Sr

º50z. Both materials compacted at the standard Proctor optimum water content and maximum density, have satu-rated hydraulic conductivities (ksat)º10－7 m/s. The VET couples the total soil suction (s) control from desiccators withsaturated salt solutions with water mass measurements from a digital laboratory balance. The kw measurements of thetwo techniques are consistent and complementary. The eŠect of hysteresis on the kw functions at higher s values wasalso investigated. The experimental results suggest that the hysteretic eŠect on the kw-Sr and kw-s relationships cannotbe neglected, and that the measured kw are signiˆcantly dependent on the initial Sr. The VET tests on the specimensthat were initially dried give the lowest values of kw and the tests on the specimens that were initially saturated give thehighest values of kw. The relative hydraulic conductivity values are very small (krwº2×10－5) in this saturation range(Srº50z) for the tested materials.

Key words: drying and wetting paths, instantaneous proˆle method, laboratory tests, unsaturated hydraulic conduc-tivity, vapor equilibrium technique (IGC: D4/E7)

INTRODUCTION

Reliable measurements and predictions of kw functionsfor low permeability soils are essential for describing un-saturated ‰ow in natural or compacted soils that areoften used to construct liners and covers for waste con-tainment. Although several laboratory experimental tech-niques are now available to determine the water and airhydraulic conductivity functions of unsaturated rigid andswelling soils, there are still few experimental data in liter-ature regarding the unsaturated hydraulic properties oflow permeability soils (kwÃ10－9 m/s) over a large Sr

range. In addition, a characteristic of kw that is signiˆcantwhen modeling the hydraulic behavior of earth barriers isthe hysteresis of kw functions (Topp and Miller, 1966;Corey, 1957; Hillel, 1982; Fredlund and Xing, 1994;Meerdink et al., 1996; Fleureau and Taibi, 1995): de-pending on the hydraulic path (wetting or drying) fol-lowed, diŠerent functions can be obtained. As a result,the objectives of this paper are: (i) to show measurementsof the kw functions in a large saturation range for lowpermeability materials by using two laboratory testingtechniques; (ii) to evaluate whether hysteresis exists in thekw-Sr and kw-s relationships at high soil suction values, for

the tested materials.The objectives are attained by performing several

laboratory tests and analyzing the experimental results.Two testing techniques are used for determining the kw

functions over a wide Sr range of a sandy-clay: the instan-taneous proˆle method (IPM) for SrÀ50z and an origi-nal vapor equilibrium technique (VET) for Srº50z. TheVET couples the total soil suction control from desicca-tors with saturated salt solutions with water mass mea-surements from a digital laboratory balance (drying andwetting paths). The VET was also used to verify the eŠectof hysteresis on measured kw functions of two ˆne-grained materials (i.e., a sandy-clay mixture and a mud-cement mixture) under high total soil suctions.

The soil water retention curves, SWRC, (i.e., therelationship between the soil suction and its water con-tent) of the tested materials were also determined by usingthese techniques. In the VET, total suctions are con-trolled by the salts whereas the IPM uses tensiometersthat measure directly matric suctions. In most soils, os-motic suction generally represents only a small fractionof the total suction for water content changes normallyencountered in most engineering problems involving un-saturated soils (Aitchison, 1961; Fredlund and Rahardjo,

182182 TAIBI ET AL.

1993) and the matric and total suction can be consideredas comparable for the tested sand-clay mixture. In thecase of mud-cement samples, osmotic suction can benegligible compared to matric suction only at the verystrong suctions used in the VET, but would certainly notbe it in the ˆeld of weak suctions of the IPM, taking intoaccount the pollutants likely to be in material. For sim-plicity reasons, in this paper, the word ``suction'' is usedsynonymously with soil matric suction. This paperdescribes the two laboratory testing techniques and ana-lyzes the experimental results of the two tested materials.

MATERIALS AND METHODS

MaterialsTwo ˆne-grained remolded materials with diŠerent

hydrodynamic properties were tested: a sandy-clay and a`mud-cement' mixture. The sandy-clay consists of a mix-ture of 90z of kaolin, 5z of sand and 5z of silica basedon dry weights. The liquid limit of the sand-clay is 38z,the plastic limit is 19z, clay fraction is 53z, Casagrandeclassiˆcation is CL, speciˆc gravity is 2.63, Proctor opti-mum water content is about 18z and the correspondingdry density, gd, normalized with the unit weight of thewater at 49C, gw, (i.e., gd/gw) is 1.67. The mud-cementmixtures consist of mixtures of an organic mud and aCPA cement. The mud is classiˆed as organic high plas-ticity silt based on the USCS. X-ray diŠraction showedthat the mud is predominantly made of quartz (30–40z),calcite (20–30z), feldspar (3–7z), dolomite (2–3z), andthe clay fraction (about 10z) is mixed layers of smectite(20z), kaolinite (10z) and illite (7z). The organic mat-ter content varies from 5 to 10z. The liquid limit is118z, the plastic limit is 58z, and speciˆc gravity of thesolids is 2.5. Further details regarding the properties andmineralogical compositions of the `mud-cement' mixtureare provided by Boutouil (1998).

The saturated water hydraulic conductivity, ksat, of thematerials, measured under steady state and unsteadystate conditions by means of constant pressure head andpulse tests (Brace et al., 1968; Hsieh et al., 1981; Taibi etal., 2003) are about 1.5×10－10 m/s for the sandy-claycompacted at the standard Proctor optimum water con-tent and 10－8 m/s for the `mud-cement' mixture, respec-tively.

Water Unsaturated Hydraulic Conductivity (kw) Func-tions

Two laboratory experimental techniques were used fordetermining the kw functions of ˆne-grained materials:IPM (inˆltration in a vertical column of soil) and anoriginal VET that couples suction control from desicca-tors with saturated salt solutions with water mass mea-surements from a digital laboratory balance. The IPMwas used to determine kw functions for the compactedsandy-clay in the Sr range of 50z to approximately 90zwith corresponding total (or matric) soil suction range of6 MPa to 30 kPa whereas the VET was used to determinekw functions for low degrees of saturation (Srº50z) with

relatively high total soil suctions (4 MPaºsº345 MPa).VET tests were performed on the sandy-clay and the`mud-cement' mixtures, following the drying and wettingpaths to evaluate the eŠect of hysteresis on kw functionsof these materials.

IPM (Inˆltration in a Vertical Column of Soil)The IPM applied to diŠerent surface water ‰ow condi-

tions (evaporation and inˆltration) has been used bymany researchers (Wind, 1968; Vachaud et al., 1974;Hamilton et al., 1981; Daniel, 1983; Ed Diny, 1993;Tamari et al., 1993; Chiu and Shackelford, 1998; Gaidi,2002; Arya 2002) to estimate the retention and conductiv-ity curves for diŠerent soils in a large water contentrange. The IPM is an unsteady-state method. It uses acylindrical specimen of soil that is subjected to a continu-ous water ‰ow from one end of the specimen. Thehydraulic head gradient and ‰ow rate at various pointsalong the specimen can be obtained using one of severalprocedures (Klute, 1972; Fredlund and Rahardjo, 1993).Using the ˆrst procedure, the water content and pore-water pressure head distributions can be measured in-dependently. The water content distribution can be usedto compute the ‰ow rates. The pore-water pressure headgradient can be calculated from the measured pore-waterpressure head distribution. The gravitational headgradient is obtained from the elevation diŠerence. Usingthe second procedure, the water content distribution ismeasured while the pore-water pressure head is inferredfrom the soil-water characteristic curve.

Unsaturated hydraulic conductivity is derived fromDarcy's law using the pressure head gradient and mean‰ow between two measurement points. Morath et al.(1997) observed that the calculated hydraulic conductivi-ty using the IPM is very sensitive to errors of calibrationand position of the tensiometers in the column of soil,and to sample non-homogeneity. All the variations of theIPM are based on the same theoretical principles, andprimarily diŠer in the method used to remove or addwater and in the technique of suction or moisture mea-surements (Bicalho et al., 2007).

The IPM used is an instrumented vertical column ofsoil with HMS 9000 probes and tensiometers measuring,respectively, the resulting volumetric water content andpore water pressure in the soil column at several depthsand time intervals under inˆltration conditions imposedat the bottom of the soil column (z＝0) and zero-‰owcondition imposed at the top of the soil column (z＝l ). Aschematic of the experimental equipment used is illustrat-ed in Fig. 1. The equipment consists of an acrylic cylinder(220 mm in length and 50 mm in inner diameter) contain-ing the compacted soil specimen, four sets of soilmoisture sensors (HMS 9000 probes) placed along the soilspecimen at diŠerent depths (15 mm from the bottomface (probe a), 95 mm (probe b), 155 mm (probe c), and195 mm (probe d)) for the measurement of the volumetricwater content at the given position and time, a set of ten-siometers inserted in the soil specimen, connected to apressure transducer and recorded on a personal com-

183

Fig. 1. Schematic diagram of the experimental IPM equipment

Fig. 2. Schematic diagram of the experimental VET equipment (a)sample during vapor equilibrium in desiccators, (b) sample duringthe weighing, (c) hydraulic boundary conditions of the sample, (d)details of the diametrical sealing of the sample and (e) several desic-cators with diŠerent salt solutions

183UNSATURATED HYDRAULIC CONDUCTIVITY

puter-based data acquisition system, and a water sourcefor wetting the soil column with a digital water pressure-volume controller connected to one end of the specimencolumn (at z＝0). The vertical column has small holes lo-cated at four depths in which the probe and tensiometersare inserted. Each set of tensiometers and probe is placedat the same elevation along the column so that the porewater pressure and volumetric water content recordeddata can be directly correlated. The HMS 9000 probes arebased on the principle of electrical capacity measure-ments and were calibrated for the tested sandy-clay soil.The tests were conducted on specimens of the sandy-claycompacted directly in the test column at the standardProctor optimum water content and corresponding dryunit weight using a static compaction press.

VET (Desiccators with Saturated Salt Solutions and aDigital Balance)

For higher suctions and continuous air interface phasethe transfer of water occurs in the vapor phase, and desic-cators with saturated salt solutions are routinely used todetermine the SWRC data for total suction values rang-ing from 3 to 400 MPa (Fleureau et al., 1993; Delage etal., 1998; Tang and Cui, 2005; Taibi et al., 2005). Thisrelatively low cost laboratory technique consists in plac-ing the soil specimens in a totally closed desiccator thatcontains a given saturated salt solution at the bottom.The saturated salt solutions are used to control the rela-tive humidity of the atmosphere in the desiccators con-taining the soil specimens. The imposed total soil suctionis related to the relative humidity (H ) of the vapor spacewhere the specimen is equilibrated by the following equa-tion, which is derived from Kelvin's law (Fredlund andRahardjo, 1993):

s＝－RT

Mw(1/rw)ln (H ) (1)

where R＝universal gas constant [8.31432 J/mol K]; T＝absolute temperature [K]; Mw＝molecular weight of

water [18.016 g/mol]; rw＝density of water [Mg/m3] as afunction of T; and H＝measured relative humidity de-ˆned as uv/uvo, where uv＝the partial pressure of pore-water vapor in the soil specimen and uvo＝the saturationpressure of water vapor above a ‰at surface of water attemperature T. The value of H depends on the tempera-ture, type and concentration of the used salt solution(Tang and Cui, 2005). Therefore, the accuracy of thistechnique depends on the calibration used to determinethe H generated by the used salt solution at the measuredtemperature. All the measurements were performed atconstant temperature (about 209C±29C).

The laboratory experimental technique used for deter-mining the kw functions of low permeability soils couplesthe total soil suction control from desiccators with satu-rated salt solutions with water mass measurements from adigital balance (precision 10－3 g). The basic experimentalsetup consists of several desiccators with diŠerent satu-rated salt solutions at the bottom and a digital laboratorybalance (Fig. 2). The suction diŠerence (Ds) between thesoil specimen (s) and that imposed by the relative humidi-ty generated by the saturated salt solution in the desicca-tor (s0) causes the water to ‰ow in or out of the soil speci-men until the potential equilibrium is reached. During thewetting or drying paths, the balance monitors the porewater gain (wetting path) or loss (drying path). The soilspecimens are laterally sealed with para‹n for creatingone-dimensional ‰ow condition. During the unsteady

184184 TAIBI ET AL.

state ‰ow in the sample, one measures the variation of theaverage water content with time by weighing the soilspecimen until the specimen's ˆnal suction reachesequilibrium. At this time, the ‰ow stops (hydraulic ‰owrate (v) is equal to zero).

The governing equation for one-dimensional ‰ow,neglecting gravity, is:

&c&t

＝D&2c&z2 (2)

where c＝suction head [(length)]; t＝time, z＝distanceand D＝diŠusivity. In general, Eq. (2) is non-linear anddi‹cult to solve analytically. However, if the incrementsof s are su‹ciently small, it is possible to assume that D isconstant and that the s-u relationship is linear betweentwo steps, which makes it possible to linearize Eq. (2) andobtain its analytical solution. Considering the initial andboundary conditions as:

c(z, 0)＝c (soil specimen initial suction) (3)c(0, t)＝c(l, t)＝c0

(imposed suction in the desiccator) (4)

Using the method suggested by Gardner (1956), the solu-tion of Eq. (2) is:

c(z, t )＝c0＋4Dc

p

/

Sn＝1

1n

sinnpl

z exp «－Øn2p2

l 2 »Dt$ (5)

Vw(t)＝VwT «1－ 8p2 exp Ø－p2

l 2 Dt»$ (6)

ln [VwT－Vw(t)]＝Ln Ø8VwT

p2 »－Øp2

l2D»t (7)

D＝l 2mp2 (8)

where Vw(t)＝change in water volume at time t, VwT＝total change in water volume, l＝length of the soil speci-men, and m＝slope of the straight line in [t, ln (VwT-Vw(t)]space.

The coe‹cient of diŠusivity D is related to the hydraul-ic conductivity kw by (Child and Collins, 1950; Klute,1952): D＝kw(&c/&u), with c: the capillary potential andu: volumetric water content, deˆned as the ratio of porewater volume Vw to the total volume of sample VT, (u＝(Vw/VT)). When the sample is placed in the desiccator, itscapillary potential varies from c1 (initial capillary poten-tial) to c2 (imposed capillary potential in the desiccator),then Dc＝c2－c1, and its volumetric water content va-ries from u1 to u2, then Du＝u2－u1.

The chosen Dc must be small enough to meet the con-sidered assumption (&c/&u)§(Dc/Du), but large enoughto provide a measurable volume of ‰ow. The mean diŠu-sivity is then written as: D＝kw (Dc/Du), or kw＝D(Dc/Du). The volume of pore water Vw is related to itsmass Ww by Vw＝(Ww/rw), where rw is the water density.The variation of the volumetric water content Du can berelated to the variation of the total change in water massof the sample WwT by: Du＝(WwT/rwVT) and the kw-D

relationship is deˆned by:

kw＝D&c&u

＝D

DcWwT

rwVT(9)

This method assumes that kw is constant during the‰ow process. The mass measurements throughout the testand the dry mass and total volume of the soil specimenmeasured at the end of the test are used to back-calculatethe mean specimen volumetric water content at each step.The external total volume of the specimens (between 1cm3 and 3 cm3) was determined by immersing the speci-mens for 2 hours in a non-wetting oil (commercial Ker-dane, BP) to ˆll the largest pores without swelling andweighing them before and after imbibition (Fleureau etal., 1993).

The kw is determined for each increment of suction andthe experiment is repeated for diŠerent magnitudes ofsuction or water content to yield a water hydraulic con-ductivity-suction (kw-s) relationship. On wetting path, thekw-s relationship is obtained by proceeding through aseries of steady states with smaller and smaller suctions.The method is also used for obtaining the drying kw-srelationship (i.e., series of steady states with increasingsuction). The same soil specimen was continuouslymoistened/dried so that there is no hysteresis associatedwith alternately wetting and drying a soil.

The time required to reach equilibrium for the soilspecimen is obtained by taking the mass measurementsthroughout the test. The frequency of weighing variesfrom 1 per day at the beginning of the test, to 3 per day atthe end. Equilibrium is reached when the relative varia-tion of the weight of the sample Dm/m0 versus time (Figs.6(a) and 7(a)) does not exceed 0.01z per day, m0 is the in-itial weight of the sample. Taibi et al. (2005) mention thatthe equilibrium time depends on the soil properties, thesoil specimen size and the suction diŠerence. In order todecrease the equilibrium time, the tests are carried out onvery small soil specimens (10 mm in height and 35 mm indiameter).

The samples used in the VET for the measurement ofkw functions were ˆrst statically compacted in a mold atthe standard Proctor optimum water content (or satura-tion Srp) and corresponding density. To evaluate whetherhysteresis exists in the kw-Sr and kw-s relationships for thesandy-clay, three procedures were used to prepare the soilspecimens: (i) for the drying path starting from the initialdegree of saturation Sr0＝Srp, some of the specimens wereused `as compacted', (ii) for the wetting path startingfrom Sr0＝0z, some of the compacted specimens were al-lowed to dry in the oven at 1059C±59C for 24 hours, and(iii) for the drying path starting from Sr0＝100z, some ofthe specimens were saturated by applying vacuum and‰ushing de-aired water into the specimen for a period of120 minutes. VET tests were also conducted using speci-mens of `mud-cement' mixtures, either saturated (for thedrying path starting from Sr0＝100z) or dried in the ovenat 1059C±59C for 24 hours (for the wetting path startingfrom Sr0＝0z).

185

Fig. 3. (a) Volumetric water content and (b) suction proˆles within the sandy-clay specimen a-1

Fig. 4. Measured kw functions for tested sandy-clay specimen a-1 (wetting path, Sr0＝Srp) versus (a) degree of saturation and (b) suction

185UNSATURATED HYDRAULIC CONDUCTIVITY

RESULTS AND DISCUSSION

Measured Unsaturated Hydraulic ConductivityIPM (Inˆltration in a Vertical Column of Soil) Results

Examples of the resulting volumetric water content andpore water pressure proˆles at various time intervals forthe sandy-clay due to a pressure of 20 kPa applied at thebottom of the soil column are presented in Figs. 3(a) and(b), respectively.

Plotting the measured inˆltration velocity against timeshows that the steady state (v＝3×10－4 cm/s) wasreached after about 6 days for the tested clay. The soilspecimen's height was measured during the tests by usinga dial gauge and a negligible change in the height of thesample was observed (i.e., e＝Dl/l0º1z).

Figures 4(a) and (b) present the measured kw-Sr and kw

-s relationships, respectively, for the tested sandy-clay(wetting path, Sr0＝Srp). The measured kw values range

from 6×10－11 m/s to 10－14 m/s for the tested sandy-clay.The corresponding s values change from 3 kPa to 16MPa. The tensiometers used in the IPM were designed tomeasure matric suctions ranging from 3 kPa to approxi-mately 90 kPa. However, problems were met with thesedevices and eventually suctions were derived from theSWRC, using the correspondence between water contentsand suctions. The data of the SWRC of the sandy-claywere determined independently using diŠerent methods(i.e., tensiometric plates (1–20 kPa), osmotic technique(0.05–1.5 MPa) and vapor equilibrium technique withsaturated salt solutions (4–300 MPa)) to control the soilsuction (Fig. 5). Details of these methods are provided byFleureau et al. (1993). The SWRC data for the sandy-clayobtained from the VET tests discussed in this paper arealso presented in Fig. 5. The experimental results derivedfrom these diŠerent techniques are consistent and com-plementary.

186

Fig. 5. SWRC data for the sandy-clay (Legend: [VET method speci-mens: specimen b-1, VET wetting path (Sr0＝0%); ~ specimenc-1, VET drying path (Sr0＝Srp); specimen d-1, VET drying path(Sr0＝100%)]; [Tensiometric plates (Sr0＝Srp): % wetting path]; [Os-mosis (Sr0＝Srp): wetting path; # drying path]; [salt solutions (Sr0

＝Srp): drying path])

Fig. 6. VET experimental results (drying path) for the ``mud-cement'' specimen f-1: (a) variation of the water mass vs. time, (b) variation of thewater volume vs. time and (c) the resulting ln (VwT-Vw(t)) vs. time

186 TAIBI ET AL.

The IPM technique cannot adequately capture condi-tions close to or at saturation, therefore, the saturatedhydraulic conductivity (ksat＝1.5×10－10 m/s) was in-dependently measured under steady state and unsteadystate conditions by means of constant pressure head andpulse tests.

VET (Desiccators with Saturated Salt Solutions and aDigital Balance) Results

Some examples of the variation of the water mass,water volume and the resulting ln (VwT-Vw(t)) against timefor the tested `mud-cement' (drying path) and sandy-clay(wetting path) are presented in Figs. 6 and 7, respectively.The initial (Sr0, s0) and ˆnal (Srf, sf) conditions for eachstage of imposed suction are also presented in the ˆgures.The values of suction are determined by using the VETand the corresponding saturation values by using a non-wetting oil (commercial Kerdane, BP) to determine theexternal total volume of the specimens (Fleureau et al.,1993). Equilibrium time was reached after about 12 daysfor the small tested `mud-cement' specimens (10 mm inheight and 35 mm in diameter) and the used salt solutions(Fig. 6). In the case of the sandy-clay (wetting tests), the

187

Fig. 7. VET experimental results (wetting path) for the sandy-clay specimen b-1: (a) variation of the water mass vs. time, (b) variation of the watervolume vs. time and (c) the resulting ln (VwT-Vw(t)) vs. time

Fig. 8. Measured kw functions (VET) for the mud-cement specimen f-1; specimen e-1

187UNSATURATED HYDRAULIC CONDUCTIVITY

equilibrium time was reached after about 30 days (Fig.7).

For each soil specimen, the hydraulic conductivity is

analytically determined from the graph of ln (VwT-Vw(t))versus time. Examples of the resulting plot for the dryingpath of the saturated `mud-cement' mixture and wetting

188

Fig. 9. Measured kw functions (VET) for the sandy-clay; ~ specimen c-1; specimen d-1; specimen b-1

Fig. 10. Measured (IPM and VET) and predicted krw-Sr functions ondrying and wetting paths (Legend: sandy-clay (C); mud-cement(M); $ C-IPM wetting path (Sr0＝Srp), specimen a-1; ~ C-VETdrying path (Sr0＝Srp), specimen c-1 C-VET drying path (Sr0＝

100%), specimen d-1; C-VET wetting path (Sr0＝0%), specimenb-1; M-VET drying path (Sr0＝100%), specimen f-1; M-VETwetting path (Sr0＝0%), specimen e-1; continuous line) (Bicalho etal., 2000)

188 TAIBI ET AL.

path of the sandy-clay are presented in Figs. 6(c) and7(c), respectively. The experimental results presented inFigs. 6(c), and 7(c) conˆrm the assumed linearity of theln (VwT-Vw(t))-time relationship (coe‹cient of determina-tion R-squaredÀ0.87) for the tested materials.

The measured kw values (drying and wetting pathsstarting from diŠerent initial degrees of saturation, Sr0)for the mud-cement mixture and the compacted sandy-clay are plotted as a function of saturation and suction inFigs. 8(a), 9(a), and 8(b), 9(b), respectively. Taking intoaccount the experimental conditions, hydraulic conduc-tivity was given with an uncertainty of about 10z. Theexperimental results suggest that the hysteretic eŠect onthe kw-Sr and kw-s relationships cannot be neglected in thissaturation range (Srº50z), and that the kw-s relation-ship appears to exhibit less hysteresis than the kw-Sr

relationship at relatively high suctions (4 MPaºsº330MPa).

Figure 10 presents a dimensionless plot of thelogarithm of the relative hydraulic conductivity, krw＝kw

/ksat, versus Sr for the IPM and VET tests conducted onthe sandy-clay mixture (C) soil and the VET tests con-ducted on the ``mud-cement'' mixture (M). Figure 10shows that the values of kw measured by these tests aresigniˆcantly dependent on the initial degree of saturationof the specimens. The VET tests (wetting path) on thespecimens which were initially dried (Sr0＝0z) give thelowest values of kw and the VET tests (drying path) on thespecimens which were initially saturated (Sr0＝100z) givethe highest values of kw. The trend observed in the meas-ured kw values is:

kw [for tests on initially dry samples]ºkw [for tests onsamples at the initial optimum water content]ºkw [fortests on initially saturated samples].

The IPM test results on the sandy-clay (C), followingthe wetting path starting from the initial degrees of satu-ration corresponding to the standard Proctor optimumwater content (Sr0＝Srp), indicate that krw has a small

value (krw§0.05) while the saturation is relatively high (Sr

§0.8). These results are consistent with the measured krw

values presented in previous studies (Taibi, 1994; Bi-calho, 1999) for ˆne-grained soils. The VET test resultsof the sandy-clay mixture (C) and the mud-cement mix-ture (M) indicate that krwº2×10－5 m/s for Srº50z.

The predicted results for the tested clay obtained by anempirical expression proposed originally by Bicalho et al.(2000) for deˆning krw-Sr relationship at higher Sr on thewetting cycle of a compacted silt is also presented in Fig.10. The expression was determined by curve ˆtting to theexperimental results and is given by:

189

Table 1. Summary of the specimen preparation for the hydraulic conductivity tests (initial values)

Testmethods Material Initial state Number of

specimens

Diameter/Height(mm)

Mean drydensity

Mean initial degreeof saturation

Sr0 (z)

Mean initialwater content

w0 (z)

I.P.M Sandy-clay CSPOW (*) 01(a-1) 50/220 1.67 72 16

V.E.T

Sandy-clay

CSPOW (*)and dried in the oven at

105/1109C

01(b-1)

35/10

¿1.7 ¿0 ¿0

CSPOW (*) 02(c-1, c-2) 1.67 81 18

CSPOW (*)and saturated

01(d-1) ¿1.6 ¿100 ¿25

Mud-cement

compacted then driedin the oven at

105/1109C

01(e-1)

35/10

1.1 ¿0 ¿0

compacted andsaturated

01(f-1) 1.1 100 58

(*)CSPOW＝Compacted at the standard Proctor optimum water content

Table 2. The used saturated salt solutions: (1) K2SO4; (2) CuSO4; (3) ZnSO4, 7H2O; (4) KCl; (5) NH4, Cl; (6) NaCl; (7) NaNO2; (8) Ca(NO3)4H2O; (9)KCNS; (10) CaCl2, 6H2O; (11) H2SO4

189UNSATURATED HYDRAULIC CONDUCTIVITY

krw(Sr)＝a＋(1－a) «(Sr－b)(1－b) $

n

(10)

where a, b and n are empirical parameters. Although theEq. (10) has been proposed for soils with a discontinuousair phase, it was included to illustrate an approximatetrend observed on the experimental data due to the ‰ex-ibility of the exponentional equation with a small numberof parameters. The obtained empirical parameters for thekrw-Sr function for the sandy-clay are: a＝0.00000006, b＝0.001 and n＝11. The results of the experimental inves-tigation indicate that the expression proposed by Bicalhoet al. (2000) is in reasonable agreement with the values ofmeasured krw derived from both the IPM and VET tests(drying and wetting paths starting from the same initialdegree of saturation, Srp) for the tested sandy-clay.

CONCLUSIONS

Very small kw values of two ˆne-grained materials (i.e.,

a sandy-clay mixture, and a `mud-cement' mixture) weremeasured using two laboratory testing techniques: (i)VET (vapor equilibrium technique) that couples the totalsoil suction control from desiccators with saturated saltsolutions with water mass measurements from a digitallaboratory balance (on drying and wetting paths); theVET was used for measuring kw values under very highsuctions 4 MPaºsº345 MPa where the corresponding Sr

º50z. (ii) IPM (inˆltration in a vertical column of soil)used for measuring kw at SrÀ50z for the sandy-clay mix-ture. The kw results of the two techniques are consistentand complementary in terms of suction ranges. Themeasured kw values range from 10－9 to 10－17 m/s. TheVET is able to measure very small kw values (10－15ºkw

º10－17 m/s). The IPM test results on the sandy-clay (C)following the wetting path starting from Sr0＝Srp indicatethat krw has a small value (krw§0.05) while the Sr is rela-tively high (Sr§0.8), and the VET test results on the san-dy-clay (C) and the mud-cement mixture show that krw

values are very small (krwº2×10－5) at Srº50z.

190190 TAIBI ET AL.

The VET on drying and wetting paths is used to evalu-ate the eŠect of hysteresis on the kw functions under highsuction values for the tested materials. This study showsthat the measured kw (VET tests) of the two materials issigniˆcantly dependent on the initial S. The VET tests(wetting path) on initially dried specimens give the lowestvalues of kw and the tests (drying path) on the initiallysaturated specimens give the highest values of kw. The ex-perimental results suggest that the kw-s relationship ex-hibits less hysteresis than the kw-Sr relationship at rela-tively high suctions (4 MPaºsº330 MPa) where the cor-responding degrees of saturation are Srº50z for thetested material. However, the eŠect of hysteresis on thekw-Sr and kw-s relationships in a large Sr range for lowpermeability soils is still a matter of debate.

NOTATION

IPM＝instantaneous proˆle method;VET＝vapor equilibrium technique;

SWRC＝soil water retention curves;C＝sandy-clay mixture;M＝``mud-cement'' mixture;kw＝water unsaturated hydraulic conductivity;krw＝relative water hydraulic conductivity;ksat＝saturated water hydraulic conductivity;

a, b and n＝Bicalho et al. (2000) empirical parametersfor kr (Sr) function;

Sr＝degree of saturation;Sr0＝initial Sr;Srp＝Sr at optimum water content;

e＝Dl/l, axial strain;Dl＝soil specimen height change;l0＝initial soil specimen height;s＝soil suction;sp＝soil suction at optimum water content;H＝relative humidity;R＝the universal gas constant (i.e., 8.31432

J/mol K);T＝the absolute measured temperature in K;

Mw＝the molecular weight of water (i.e., 18.016g/mol);

rw＝density of water in kg/m3 as a function ofT;

c＝suction head [(length)];u＝volumetric water content, it represents the

fraction of the total volume of soil that isoccupied by the water contained in the soil;u＝(Vw/VT)

REFERENCES

1) Aitchison, G. D. (1961): Proc. Conference on Pore Pressure andSuction in Soils, Butterworths, London, 47–52.

2) Arya, L. M. (2002): Wind and hot-air methods, Methods of SoilAnalysis-Part 4: Physical Methods (eds. by J. H. Dane and G. C.Topp), Soil Science Society of America, Madison, WI, 916–926.

3) Bicalho, K. V. (1999): Modeling water ‰ow in an unsaturated com-pacted soil, Ph.D. Dissertation, University of Colorado, Boulder,Colo.

4) Bicalho, K. V., Znidarcic, D. and Ko, H.-Y. (2000): Air entrap-ment eŠects on hydraulic properties, ASCE Geotechnical SpecialPublication, 99, 517–528.

5) Bicalho, K. V., Znidarcic, D. and Fleureau, J. M. (2007): Determi-nation of water hydraulic conductivity functions of unsaturatedsoils, 3rd Asian Conference on Unsaturated Soils, China.

6) Boutouil, M. (1998): Traitement des vases de dragage parsolidiˆcation/stabilisation a base de ciment et additifs, Th àese deDoctorat, Universite du Havre.

7) Brace, W. F., Walsh. J. B. and Frangos, W. T. (1968): Permeabil-ity of granite under high pressure, Journal of GeophysiqueResearch, 73(6), 2225–2236.

8) Chiu, T.-F. and Shackelford, C. D. (1998): Unsaturated hydraulicconductivity of compacted sand-kaolin mixtures, J. Geotech.Engrg, ASCE, 124(2), 160–170.

9) Corey, E. C. (1957): Measurement of water and air permeability inunsaturated soils, Soil Science Society of America Proc., 21(1),7–11.

10) Daniel, D. E. (1983): Permeability test for unsaturated soil, Geo-technical Testing Journal, GTJODJ, 6(2), 81–86.

11) Delage, P., Howat, M. D. and Cui, Y. J. (1998): The relationshipbetween suction and swelling properties in a heavily compacted un-saturated clay, Engineering Geology, 50, 31–48.

12) Ed Diny, S. (1993): Etude experimentale des transferts hydriques etdu comportement m áecanique d'un limon non satur áe, Th àese de Doc-torat, Institut National Polytechnique de Lorraine, Nancy, 177p.

13) Fleureau, J. M., Kheirbeck-Saoud, S., Soemitro, R. and Taibi, S.(1993): Behaviour of clayed soils on drying-wetting paths, Canadi-an Geotechnical Journal, 30(2), 287–296.

14) Fleureau, J. M. and Taibi, S. (1995): Water-air permeabilities ofunsaturated soils, 1st Int. Conf. on Unsaturated Soils, Paris, 2,479–484.

15) Fredlund, D. G. and Rahardjo, H. (1993): Soil Mechanics for Un-saturated Soils, John Wiley & Sons, NY.

16) Fredlund, D. G. and Xing, A. (1994): Predicting the permeabilityfunction for unsaturated soils using the soil-water characteristiccurve, Canadian Geotechnical. J., 31, 533–546.

17) Gaidi, A. (2002): Transfert par inˆltration de l'eau et du solut áe dansles sols non satur àes–Utilisation de la methode TDR, Th àese de Doc-torat, INSA de Lyon, 243p.

18) Gardner, W. R. (1956): Calculation of capillary conductivity frompressure plate out‰ow data, Soil Science Society of America Proc.,20, 317–320.

19) Hamilton, J. M., Daniel, D. E. and Olson, R. E. (1981): Measure-ment of hydraulic conductivity of partially saturated soilspermeability and groundwater contaminant transport, ASTM,STP, 746, 182–196.

20) Hillel, D. (1982): Introduction to Soil Physics, Academic, NewYork.

21) Hsieh, P. A., Tracy, J. V., Neuzil, C. E., Bredehoeft, J. D. and Sil-liman, S. E. (1981): A transient laboratory method for determiningthe hydraulic properties of `Tight' rocks–I. Theory, InternationalJournal of Rock Mechanics and Mining Science & Geomechanics,18(3), 245–252.

22) Meerdink, J., Benson, C. and Khire, M. (1996): Unsaturatedhydraulic conductivity of two compacted barrier soils, J. Geotech.Eng., ASCE, 122(7), 565–576.

23) Morath, D., Bruckler, L., Bertuzzi, V, Gaudu, J. C. and Bourlet,M. (1997): Error analysis of an evaporation method for determin-ing hydrodynamic properties in unsaturated soil, Soil Sci. Soc. Am.J., 61, 725–735.

24) Philip, J. R. and De Vries, D. A. (1957): Moisture movement inporous materials under temperature gradients, Trans. Am. Geo-phys. Union, 38, 222–232.

25) Taibi, S. (1994): Comportement m áecanique et hydraulique des solssoumis àa une pression interstitielle n áegative–Etude exp áerimentale etmod áelisation, Th àese de Doctorat, Ecole Centrale de Paris, 374p.

26) Taibi, S., Sayad, C., Kheirbek-Saoud and Fleureau, J. M. (2003):Perm áeabilit áe satur áee et non satur áee d'une barri àere en argile com-pact áee, 13th European Conference on SMGE, Prague.

191191UNSATURATED HYDRAULIC CONDUCTIVITY

27) Taibi, S., Ghembaza, M. S. and Fleureau, J. M. (2005): On the suc-tion control techniques in studying the THM behavior of unsaturat-ed soils, Proc. Int. Symp. on Advanced Experimental UnsaturatedSoil Mechanics, Balkema, 69–75.

28) Tamari, S., Bruckler, L., Halbertsmama, J. and Chadoeuf, J.(1993): A simple method for determining soil hydraulic propertiesin the laboratory, Soil Sci. Soc. Am. J., 57, 642–651.

29) Tang, A. M. and Cui, Y. J. (2005): Controlling suction by thevapour equilibrium technique at diŠerent temperatures, applicationin determining the water retention properties of MX80 clay, Cana-

dian Geotechnical Journal, 42(1), 287–296.30) Topp, G. C. and Miller, E. E. (1966): Hysteretic moisture charac-

teristics and hydraulic conductivities for glass beads media, SoilSci. Soc. Amer. Proc., 30, 156–162.

31) Vachaud, G., Gaudet and Kuraz (1974): Air and water duringponded inˆltration in a vertical bounded column of soil, J. Hydro-logy, 22, 89–108.

32) Wind, G. P. (1968): Capillary conductivity data estimated by a sim-ple method, Water in the unsaturated zone, Proc. WageningenSymposium (ed. by Rijtema and Wassink), 1, 181–191.