Research ArticleExperimental Investigation of Unsaturated Silt-SandSoil Permeability

Samad Nazari 1 Mahmoud Hassanlourad2 Elham Chavoshi3 and Ali Mirzaii4

1Department of Civil Engineering Isfahan (Khorasgan) Branch Islamic Azad University Isfahan Iran2Imam Khomeini International University Qazvin Iran3Department of Soil Science College of Agriculture Isfahan (Khorasgan) Branch Islamic Azad University Isfahan Iran4University of Kashan Kashan Iran

Correspondence should be addressed to Samad Nazari samadnazarigmailcom

Received 24 July 2017 Revised 15 October 2017 Accepted 18 October 2017 Published 23 January 2018

Academic Editor Claudio Tamagnini

Copyright copy 2018 Samad Nazari et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e permeability of unsaturated silt-sand soil is important in many geotechnical and geoenvironmental challenges erefore anappropriate method to evaluate silt-sand soil permeability is important particularly in Iran where it received little considerationIn this in vitro research different amounts of fine silt were evaluated on behavior of an unsaturated silt-sand soil with differentgrain size distribution using a new modified triaxial apparatus Permeability was measured against matric suction and volumetricwater content and the results are compared against experimental models e results indicated that the behavior of unsaturatedsandy soil permeability could be determined as a function of matric suction soil void size and percentage of fine aggregateFurthermore the results appeared to imply that an increase of fine contents reduced the permeability specifically at higher valuesof suction is trend for the reduction of soil permeability was related to the increase in the amount of fine contents

1 Introduction

Many geotechnical and geoenvironmental problems includeconsideration of water flow through unsaturated soil isrequires an understanding on the coefficient of permeabilitywithin the soil but features of unsaturated soil are subject toconstant change Changing features of unsaturated soil in-clude slope road and railway embankments dams andtransport of pollutants A wide range of changes in per-meability of unsaturated soil is a major obstacle in analysisere are numerous leaks that give rise to issues that mightdirect engineers to an assumption that it would be impos-sible to find a solution However experience shows thatmany questions relating to evaluation of leakage in un-saturated soil have already been answered

e coefficient of permeability within the soil is a mea-sure of the resistance of the soil against the flow of water [1]In saturated soils the soil permeability is a function of voidspaces However in unsaturated soils both water and airphases affect the flow of water within the soil and thehydraulic conductivity of the soil is related to the amount of

water content and soil void spaces [2] Studies have shownthat water only flows through soil gaps that have beencontinuously filled with water So permeability of un-saturated soil is related to two variables special vertical stressand matric suction that control the water content in un-saturated soil [3] e matric suction has a significant in-fluence on soil water content e decreasing water contentbecause of increased matric suction causes a considerabledecrease in permeability of unsaturated soil e soil per-meability coefficient of unsaturated soil changes more than10 times as the matric suction changes Evaluations showthat permeability of unsaturated soil has a close relation withthe soil-water characteristic curve (SWCC) in drying andwetting processes [4 5] In other words unsaturated soilpermeability has hysteresis behavior as does the soil-watercharacteristic curve which as the restructuring of the soilbecomes minimal or reversible causes decreased hysteresis[2 6 7] So it seems necessary to indicate the permeabilityfunction in front of the matric suction

Fredlund et al [4] reported that the permeability ofunsaturated soil is firstly defined from soil void size

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 4946956 12 pageshttpsdoiorg10115520184946956

distribution and indirectly the permeability coefficient ofsoil is defined by the soil-water characteristic curve Byassessing these aforementioned characteristics it is notnecessary to have an evaluation of the remaining watercontent in order to determine permeability of the un-saturated soil e suggested permeability function is cal-culated from the integral relation between suction and watercontent e suggested relations show good agreement withdata obtained from the laboratory Finally the permeabilitycoefficient function is gained against the matric suction bynormalizing the permeability coefficient Leong andRahardjo [8ndash10] assessed 3 sets of permeability functions inunsaturated soil samples experimental microscopic andstatistical models e theoretical history and operation ofeach set was evaluated against different laboratory dataey concluded that the statistical and experimentalmodels had good compatibility with the laboratory resultsFredlund et al [4] designed a flexible wall permeameterDirect measurement was made on the unsaturated silty sandpermeability coefficient using the combination of matricsuction and special vertical stress ey concluded that thepermeability coefficient in matric suctions lower than that inair-entry value suction is unchangeable Also the perme-ability coefficient in matric suctions above the air-entryvalue suction reduces with a high rate Agus et al [1] re-ported that Singapore has widespread distribution of un-saturated soil so there is a need for permeability coefficientsof soils and due to difficulties in terms of cost and timesome functions have been presented to provide estimationsof permeability of unsaturated soil Results for estimations ofsoil permeability have shown good compatibility with resultsfrom laboratory tests

Gallage et al [7] used a newly developed parameter tomeasure unsaturated soil hydraulic conductivity by applyingthe steady flow method and direct measurement of matricsuction e device was prepared by two tensiometers thatmeasured suction directly For evaluating the new hydraulicconductivity method two types of sand were measured inthe drying and wetting procedures that demonstrated sig-nificant hysteresis behavior against the matric suction Buthysteresis was not apparent when hydraulic conductivitywas drawn against water e results showed good co-ordination with functions of the estimated hydraulic con-ductivity In their opinion the new suggested relation justneeded one extra parameter and this was easily calibratedwith the SWCC To evaluate their studies results of previousexperiments were used and indicated good compatibilitybetween the relation and the experiment results In anotherstudy a modified triaxial device was built to measure thepermeability coefficient and the CD shear strength of 3 typesof unsaturated soil in drying and wetting cycles on a sample[12] e results showed good compatibility with the resultsreported in the literature ere have been many reports onpermeability of unsaturated soil in the literature Resultshave been determined by a variety of different methods andon different sets of samples However little is known aboutthe effect of silty fine-grained soil on the permeability co-efficient e objectives of this study were to measure andcompare the effects of different amounts of silt on the sand

permeability coefficient is was tested using a modifiedtriaxial device

2 Approaches to Determine the Permeability ofUnsaturated Soils

In previous studies the permeability of saturated soil (Ks)was only evaluated in relation to the void ratio while forunsaturated soils the permeability coefficient (kw) was re-lated to both the void ratio (e) and the water content (w) Asthe void ratio (e) degree of saturation (s) and the watercontent (ω) are related to each other kw can be presented asthe following which is a function of two of them

kw f(e w) kw f(s e) kw f(s w) (1)

If soil structure becomes incompressible then the twoparameters in (1) can be separated is means that thesaturated permeability coefficient (Ks) determines the voidratio effect and another function determines the watercontent in soil Direct and indirect methods can be used todetermine permeability in unsaturated soil [10]

Measuring permeability can be done either in a labora-tory or in situ however local measurements are more easilyavailable Laboratory measurements are preferable becauseof accuracy and lower cost [13] In other words the indirectmethod of determining permeability of unsaturated soil isrelated to special characteristics such as SWCC Directmeasurement of permeability of unsaturated soil in a labo-ratory can be conducted using stable and unstable methodse stable method (the fixed head or the fixed flow) useda fixed hydraulic head gradient afloat in the sample [2] Bycreating water flow through the sample matric suction andwater content were fixed However according to Benson andGribb [13] the stable method was more time consumingthan the unstable method but it had more accurate resultsusing the Darcy law Unstable methods such as variablehead penetration techniques and immediate techniques areapplicable in the laboratory and on location but themethodshave some differences e main difference is in the flowprocedure hydraulic head measuring and flow rate [2 14]

e flow procedure can be a wetting procedure in whichthe water flows into a soil sample or it can be a dryingprocedure in which water flows out of a sample When thevariable head method is used to measure permeability it isoften difficult to maintain a stress state during tests [15] Twopermeameter have often been used tomeasure permeability ofunsaturated soil these include a rigid wall permeameter anda flexible wall permeameter [7 16ndash19] ese have been usedto measure permeability of unsaturated soil [15 20ndash22]

e shape of the permeability function is near SWCC [417] Different research studies such as Richards [23] Brooksand Corey [24] Mualem [25] Kunze et al [26] van Gen-uchten [27] and Leong and Rahardjo [10] have produceddifferent functions for estimating permeability of un-saturated soil samples Most functions have been based onthe relation between SWCC and permeability void size andtheir distribution in soil Permeability functions are able toestimate soil permeability very fast However some of these

2 Advances in Civil Engineering

functions ignore permeability in some types of unsaturatedsoil [4 27 28] Hence it is always recommended that al-though the permeability procedure is time consuming itshould be done completely for unsaturated soil [2]

ere are three approaches to determine the perme-ability of unsaturated soil (1) experimental equations (2)microscopic models and (3) statistical models ese threemodels are presented below

3 Experimental Equations

e experimental equations of unsaturated soil permeabilityare gained based on laboratory data e relation betweenpermeability matric suction (ψ) and water content (θw) is asfollows

kw f(ψ) kw f θw( 1113857 (2)

where ψ is the matric suction and θw is the water contentAccording to Leong and Rahardjo [8ndash10] the SWCC is

similar to the suction-permeability curve (water contentpermeability) Some experimental permeability equationssuggested from different researchers are shown in Table 1

According to Table 1 for the kw f(ψ) equation dif-ferent relations are suggested such as the linear function ofRichards [23] the single power function from Weeks andRichards [28] and an exponential function from Philip [43]And also for kw f(θw) power functions from Gardner[29] Campbell [30] and Gillham et al [33] exponentialfunctions from Davidson et al [36] and Dane and Klute [37]were suggested Comparison of this research on suggestedfunctions for unsaturated soil permeability suggests thefollowing relation

Kr Θp (3)

where Kr is the relative permeability coefficient or the Kw toKs ratio Θ is the normalized volumetric water contentor(θw minus θr)(θs minus θr) in which s and r suffixes show saturatedand remaining respectively and P is constant

e power p in (3) covers an expanded domain of dryingand wetting curves and the fit curve in all states except forlow volumetric waters seems to be fair Leong and Rahardjo[8ndash10] in a critical review has assumed the Kr Θp relation asa function of ψ and has modified [44] the relation andpresented it as the following

Kr 1

ln e +ψa

1113872 1113873b

1113874 11138751113882 1113883cd

(4)

where a b c and d are fixed amounts and a has a similar unitas ψ (matric suction)

e mentioned relation shows good fitness with dryingand wetting lab procedurese writers of (4) concluded thatKw can be determined directly from the soil-water charac-teristic curve is method significantly decreases the errorsof Kw measuring and finally the following equation ispresented [8ndash10]

Kr 1

ln e +ψA

1113872 1113873B

1113874 11138751113882 1113883C

(5)

where A B and C are fixed amounts

31 Microscope Models Firstly microscopic models arepresented based on a mechanistic view representing the

Table 1 Empirical permeability functions and soil-water characteristic and permeability coefficient curve equations

Type Permeability functions

k f(θw)

kw aθbw Gardner [29]

kw ks1113874θw

θs1113875

b

b ΔlogφΔlogω

Campbell [30]Ahuja [31 32]Gillham [33]

Zachmann et al [34]Hillel [35]

Davidson [36]

kw ksexp[b(θw minus θs)]Davidson [36]

Dane and Klute [37]

k f(ψ)

kw a + bφ Weeks and Richards [38]

kw aφminusbWind [39]

Weeks and Richards [38]Gardner [29]

Kw Ks1113896(ua minus uw)b

(ua minus uw)1113897

η

η 2 + 3λBrooks and Corey [24]

Kw Ks for ua minus uw le (ua minus uw)b

kw ks

1+ a(φ

ρωg1113857b

Arbhabhirama and Kridakorn [40]

kw a exp(bφ) Christensen [41]kw k for φleφb Rijtema [42]

kw ks exp[b(φminusφb)] for φgtφb Phillip [43]Note a and b are constants k is coefficient of permeability where subscripts w and s denote unsaturated and saturated respectively S is the effective degree ofsaturation ψ is the matric suction θw is the volumetric water content

Advances in Civil Engineering 3

fluid-filled pores as bundles of various sized capillary tubes[8ndash10 24] e goal was to conclude a permeability functionanalysis In a microscopic scale the liquid flow is consideredas a slow flow showing the general flow in the soil Whenunsaturated soils are considered as a set of simple capillarytubes the flow can be defined by using flow medium ratehydraulic gradient hydraulic radius and permeability ehydraulic radius measures efficiency of the flow channeleflow rate along the channel depends on the cross-sectionarea more than any other factor e magnitude of thehydraulic radius shows high efficiency and results in higherflow volume [8ndash10]

According to assumptions in the mentioned paragraphBrooks and Corey [24] recommended a microscopic modelfor the relative permeability ratio which is defined as theunsaturated soil permeability coefficient to the saturatedpermeability coefficient

Kr Sr minus Sresr( 1113857

1minus Sresr( 1113857

1113938Sres

0 sminus2dSr

111393810 sminus2dSr

(6)

where (Sr minus Sresr )(1minus Sresr ) is the curvature factor due to thedifference between the natural rate and the real rate of voidswith the pressure real and natural gradient Sr and Sresr arethe degree of saturation and the remaining degree ofsaturation respectively Also (Sr minus Sresr )(1minus Sresr ) is namedthe effective degree of saturation (Se) 1113938

Sres

0 sminus2dSr 111393810 sminus2dSr

is the hydraulic radius which is gained from the integral ofthe SWCC e effective permeability coefficient like thesuction powered function could be presented as thefollowing

Kr Sδe (7)

where δ is a constant number and can change due to theassumptions Different researchers have recommendeddifferent numbers such as 35 by Averjanov [45] 2 by Yuster[46] 3 by Irmay [47] and 4 by Corey [48]

emain criticism of the microscopic models is that theyignore the effect of void size distribution [24 49] Brooks andCorey [24] showed that δ for a soil with a uniform voiddistribution is equal to 3 and generally recommended thefollowing relation δ 2 + 3λλ where λ is the distributionindex of void shape and is a positive number

e experimental and microscopic models seem to bethe same but they each have a different theoretical base andexcavation procedure e experimental models are gainedfrom the curve fitting on experimental data due to re-gression but microscopic models are determined fromliquid flow in a porous environment which is based on fluidmechanics Also many microscopic models are related tosoilndashwater retention behavior [8ndash10]

4 Statistical Models

Statistical models have been built based on statistical co-operation of void size changes on the permeability co-efficient e statistical perspective of void size distributionand the probability of the connections of pores are discussedin this part Statistical models are known to be very accurate

for calculating permeability of unsaturated soil [8ndash10] Inthis model the permeability coefficient function is gainedusing the SWCC ree assumptions are required to extractthe statistical model [8ndash10]

(1) It is assumed that the soil is a system composedof interconnected collection and pore distribu-tion is random and the pore characteristics aregained by r and f(r) which is the same throughoutthe soil

(2) e HagenndashPoiseuille equation is valid which is usedto calculate the permeability of a unique porechannel and general permeability is calculatedaccording to integration of water-filled pores

(3) Due to the Calvin capillary model the SWCC used togain the permeability equation is the representativeof the soil pore distribution function

According to technical literature the statistical modelscan be presented as follows

Kr θw( 1113857 Φx1113938θw

0 dθwSy( 11138571113874 1113875

1113938θs

0 dθwSy( 11138571113874 1113875

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

z

(8)

Kr θw( 1113857 Φx1113938θw

0 d θwminus ξ1113872 1113873Sy1113872 1113873dξ1113876 1113877

1113938θs

0 d θw minus ξ( 1113857Sy( 1113857dξ1113876 1113877

⎧⎪⎪⎨

⎪⎪⎩

⎫⎪⎪⎬

⎪⎪⎭

Z

(9)

whereΦ is the curvature factor and it is representative of thevoid size effect of pores on the permeability function and itis shown that it improves the permeability coefficientfunctionrsquos estimation factor (Kr) without a correctionfactor e curvature facture is gained from normalizing(Φ (θw minus θr)(θs minus θr)) the water content in which θs andθr are the water content in the saturated state andremaining state respectively In (8) ξ is the integrationartificial variable and x y and z are the constants of themodel For example in the recommended model ofBurdine [50] x 2 y 2 and z 1 for (7) while x

05 y 1 and z 2 for Mualem [25] For the Childs andCollis-George [49] model (CCG model) x 0 y 2 andz 1 in (8) were recommended while for the modifiedCCG model the numbers were x 0 y 0 and z 2 byusing Agus et al [15]

5 Material Properties and Testing Methods

A series of hydraulic conductivity tests were performed toexamine the influence of silt fine content on the hydraulicconductivity of clean sand taken from the Firouzkouh areain the north of Iran [51]

A new modified suction-controlled double-walled tri-axial apparatus was used for this purpose with the detailsillustrated in Figure 1 As shown pore air and pore waterpressures were applied throughout separate lines from bothtop and bottom of the specimens Two one bar ceramicdisks were installed at both top and bottom pedestals to

4 Advances in Civil Engineering

control or measure the pore water pressure independentlye rate of inflow and outflow of the water was measured bymeans of two automatic pressurevolume change con-trollers e Firouzkouh sand was mixed with the range ofsilt contents that were 0 10 20 30 and 40 (ie FK0FK10 FK20 FK30 and FK40 resp)e basic properties ofthe five types of sand-silt mixtures considered in this studyare summarized in Table 2 Accordingly the variationmaximum and minimum void ratio for the range of soilmixtures are illustrated in Figure 2 Also Figure 3 repre-sents the soil aggregation curve for the sand-silt mixturesconsidered

Cylindrical triaxial samples with the same height anddiameter (7 cm) and a relative density (Dr) based on theASTM D4254-16 code [52] were prepared in a specifieddried special weight e dry weight of each sample wascalculated and the samples were poured into a mold in somelayers with the same weight Table 3 shows the densityproperties of preparing the samples

51 Determination of Water Permeability Coefficient epermeability of an unsaturated soil can be calculated fromthe Darcy law [2 49]

qt VA KwiA Kw

h

LA (10)

where qt is the water flow rate in the cross section v is theflow speed A is the area Kw is the Darcy permeabilitycoefficient (water permeability coefficient) i is the hydraulicgradient which is equal to hL h is the missed head and L isthe height of soil sample

e high air-entry ceramic plate permeability is con-sidered in analyzing the results gained from the perme-ability test with the modified triaxial device e soilpermeability (or the water permeability) was determined inthree layers plate soil and plate [15] e flow speed (v)was the same in all three layers while the general missedhead (ht) is equal to the summary of the missed head ineach layer (the upper plate the soil sample and the lower

Load cellDifferential transformer

Cell top

Loading ram

Top port

Lucite cylinder

O-Rings

1-Bar high air entryRubber membraneWater compartmentPorous metal

Cell base

Soilspacemenϕ 70 mmH 70 mm

Pore air pressure line

Pore air pressure transducer

Cell pressure line

Cell pressure transducer

Top cap

Pore water pressure line

Pore water pressure line (top cap)

Flushing line (top cap)

Flushing linePore_water pressure transducer

Figure 1 Schematic diagram of modified triaxial apparatus for permeability measurement

Advances in Civil Engineering 5

plate) e flow speed and the missed head have relations asfollows

v vt vs vb (11)

hT ht + hs + hb (12)

where vt is the flow speed passing the upper ceramic plate vs

is the flow speed passing the soil sample vb is the flow speedpassing the lower ceramic plate ht is the missed head alongthe upper ceramic plate hs is the missed head along the soil

sample and hb is the missed head along the lower ceramicplate

By substituting relation (10) in relation (12) the fol-lowing relation is gained

vTlT

kT

vtlt

kt

+vsls

kw

+vblb

kb

(13)

where Kw is the water permeability coefficient of the soilsample kT is the permeability coefficient of the plate-soil-plate

Table 2 Basic properties of the studied soil samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Sand content (by dry weight) () 100 90 80 70 60Silt content (by dry weight) () 0 10 20 30 40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum dry density cdmax (grcm3) 1594 1719 1797 1799 167Minimum dry density cdmin (grcm3) 1385 1423 1424 1402 1356Saturated permeability coefficient Ks (ms)cdmax (grcm3) constant 14 841eminus2 326eminus2 942eminus3 363eminus3 313eminus4

Plasticity index PI NP NP NP NP NPMaximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531D10 (mm) 0151 0069 0019 0012 00069D30 (mm) 0194 0174 0156 0077 0032D50 (mm) 025 0233 0214 0191 0164D60 (mm) 0285 0269 0253 0229 0203Cu (D60D10) 1887 3899 13316 19083 2942Cc ((D30)2(D60lowastD10)) 0875 1631 5063 2158 0731Soil classification (USCS) SP SP-SM SM SM SM

030

040

050

060

070

080

090

100

110

120

00 100 200 300 400 500

Voi

d ra

tio (e

max

e min

e)

Fine content ()

emax

emin

e (Dr = 55)

Figure 2 Void ratio curve for the prepared samples

N 2

00

N 1

00

N 5

0N

40

N 3

0

N 1

6

00

100

200

300

400

500

600

700

800

900

1000

0001 001 01 1 10Grain size (mm)

Sand(100)-Silt(00)

Sand(90)-Silt(10)

Sand(80)-Silt(20)

Sand(70)-Silt(30)

Sand(60)-Silt(40)

Perc

ent b

y w

eigh

t fine

r (

)

Figure 3 Grain size distribution of soil samples used in this study

6 Advances in Civil Engineering

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

functions ignore permeability in some types of unsaturatedsoil [4 27 28] Hence it is always recommended that al-though the permeability procedure is time consuming itshould be done completely for unsaturated soil [2]

ere are three approaches to determine the perme-ability of unsaturated soil (1) experimental equations (2)microscopic models and (3) statistical models ese threemodels are presented below

3 Experimental Equations

e experimental equations of unsaturated soil permeabilityare gained based on laboratory data e relation betweenpermeability matric suction (ψ) and water content (θw) is asfollows

kw f(ψ) kw f θw( 1113857 (2)

where ψ is the matric suction and θw is the water contentAccording to Leong and Rahardjo [8ndash10] the SWCC is

similar to the suction-permeability curve (water contentpermeability) Some experimental permeability equationssuggested from different researchers are shown in Table 1

According to Table 1 for the kw f(ψ) equation dif-ferent relations are suggested such as the linear function ofRichards [23] the single power function from Weeks andRichards [28] and an exponential function from Philip [43]And also for kw f(θw) power functions from Gardner[29] Campbell [30] and Gillham et al [33] exponentialfunctions from Davidson et al [36] and Dane and Klute [37]were suggested Comparison of this research on suggestedfunctions for unsaturated soil permeability suggests thefollowing relation

Kr Θp (3)

where Kr is the relative permeability coefficient or the Kw toKs ratio Θ is the normalized volumetric water contentor(θw minus θr)(θs minus θr) in which s and r suffixes show saturatedand remaining respectively and P is constant

e power p in (3) covers an expanded domain of dryingand wetting curves and the fit curve in all states except forlow volumetric waters seems to be fair Leong and Rahardjo[8ndash10] in a critical review has assumed the Kr Θp relation asa function of ψ and has modified [44] the relation andpresented it as the following

Kr 1

ln e +ψa

1113872 1113873b

1113874 11138751113882 1113883cd

(4)

where a b c and d are fixed amounts and a has a similar unitas ψ (matric suction)

e mentioned relation shows good fitness with dryingand wetting lab procedurese writers of (4) concluded thatKw can be determined directly from the soil-water charac-teristic curve is method significantly decreases the errorsof Kw measuring and finally the following equation ispresented [8ndash10]

Kr 1

ln e +ψA

1113872 1113873B

1113874 11138751113882 1113883C

(5)

where A B and C are fixed amounts

31 Microscope Models Firstly microscopic models arepresented based on a mechanistic view representing the

Table 1 Empirical permeability functions and soil-water characteristic and permeability coefficient curve equations

Type Permeability functions

k f(θw)

kw aθbw Gardner [29]

kw ks1113874θw

θs1113875

b

b ΔlogφΔlogω

Campbell [30]Ahuja [31 32]Gillham [33]

Zachmann et al [34]Hillel [35]

Davidson [36]

kw ksexp[b(θw minus θs)]Davidson [36]

Dane and Klute [37]

k f(ψ)

kw a + bφ Weeks and Richards [38]

kw aφminusbWind [39]

Weeks and Richards [38]Gardner [29]

Kw Ks1113896(ua minus uw)b

(ua minus uw)1113897

η

η 2 + 3λBrooks and Corey [24]

Kw Ks for ua minus uw le (ua minus uw)b

kw ks

1+ a(φ

ρωg1113857b

Arbhabhirama and Kridakorn [40]

kw a exp(bφ) Christensen [41]kw k for φleφb Rijtema [42]

kw ks exp[b(φminusφb)] for φgtφb Phillip [43]Note a and b are constants k is coefficient of permeability where subscripts w and s denote unsaturated and saturated respectively S is the effective degree ofsaturation ψ is the matric suction θw is the volumetric water content

Advances in Civil Engineering 3

fluid-filled pores as bundles of various sized capillary tubes[8ndash10 24] e goal was to conclude a permeability functionanalysis In a microscopic scale the liquid flow is consideredas a slow flow showing the general flow in the soil Whenunsaturated soils are considered as a set of simple capillarytubes the flow can be defined by using flow medium ratehydraulic gradient hydraulic radius and permeability ehydraulic radius measures efficiency of the flow channeleflow rate along the channel depends on the cross-sectionarea more than any other factor e magnitude of thehydraulic radius shows high efficiency and results in higherflow volume [8ndash10]

According to assumptions in the mentioned paragraphBrooks and Corey [24] recommended a microscopic modelfor the relative permeability ratio which is defined as theunsaturated soil permeability coefficient to the saturatedpermeability coefficient

Kr Sr minus Sresr( 1113857

1minus Sresr( 1113857

1113938Sres

0 sminus2dSr

111393810 sminus2dSr

(6)

where (Sr minus Sresr )(1minus Sresr ) is the curvature factor due to thedifference between the natural rate and the real rate of voidswith the pressure real and natural gradient Sr and Sresr arethe degree of saturation and the remaining degree ofsaturation respectively Also (Sr minus Sresr )(1minus Sresr ) is namedthe effective degree of saturation (Se) 1113938

Sres

0 sminus2dSr 111393810 sminus2dSr

is the hydraulic radius which is gained from the integral ofthe SWCC e effective permeability coefficient like thesuction powered function could be presented as thefollowing

Kr Sδe (7)

where δ is a constant number and can change due to theassumptions Different researchers have recommendeddifferent numbers such as 35 by Averjanov [45] 2 by Yuster[46] 3 by Irmay [47] and 4 by Corey [48]

emain criticism of the microscopic models is that theyignore the effect of void size distribution [24 49] Brooks andCorey [24] showed that δ for a soil with a uniform voiddistribution is equal to 3 and generally recommended thefollowing relation δ 2 + 3λλ where λ is the distributionindex of void shape and is a positive number

e experimental and microscopic models seem to bethe same but they each have a different theoretical base andexcavation procedure e experimental models are gainedfrom the curve fitting on experimental data due to re-gression but microscopic models are determined fromliquid flow in a porous environment which is based on fluidmechanics Also many microscopic models are related tosoilndashwater retention behavior [8ndash10]

4 Statistical Models

Statistical models have been built based on statistical co-operation of void size changes on the permeability co-efficient e statistical perspective of void size distributionand the probability of the connections of pores are discussedin this part Statistical models are known to be very accurate

for calculating permeability of unsaturated soil [8ndash10] Inthis model the permeability coefficient function is gainedusing the SWCC ree assumptions are required to extractthe statistical model [8ndash10]

(1) It is assumed that the soil is a system composedof interconnected collection and pore distribu-tion is random and the pore characteristics aregained by r and f(r) which is the same throughoutthe soil

(2) e HagenndashPoiseuille equation is valid which is usedto calculate the permeability of a unique porechannel and general permeability is calculatedaccording to integration of water-filled pores

(3) Due to the Calvin capillary model the SWCC used togain the permeability equation is the representativeof the soil pore distribution function

According to technical literature the statistical modelscan be presented as follows

Kr θw( 1113857 Φx1113938θw

0 dθwSy( 11138571113874 1113875

1113938θs

0 dθwSy( 11138571113874 1113875

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

z

(8)

Kr θw( 1113857 Φx1113938θw

0 d θwminus ξ1113872 1113873Sy1113872 1113873dξ1113876 1113877

1113938θs

0 d θw minus ξ( 1113857Sy( 1113857dξ1113876 1113877

⎧⎪⎪⎨

⎪⎪⎩

⎫⎪⎪⎬

⎪⎪⎭

Z

(9)

whereΦ is the curvature factor and it is representative of thevoid size effect of pores on the permeability function and itis shown that it improves the permeability coefficientfunctionrsquos estimation factor (Kr) without a correctionfactor e curvature facture is gained from normalizing(Φ (θw minus θr)(θs minus θr)) the water content in which θs andθr are the water content in the saturated state andremaining state respectively In (8) ξ is the integrationartificial variable and x y and z are the constants of themodel For example in the recommended model ofBurdine [50] x 2 y 2 and z 1 for (7) while x

05 y 1 and z 2 for Mualem [25] For the Childs andCollis-George [49] model (CCG model) x 0 y 2 andz 1 in (8) were recommended while for the modifiedCCG model the numbers were x 0 y 0 and z 2 byusing Agus et al [15]

5 Material Properties and Testing Methods

A series of hydraulic conductivity tests were performed toexamine the influence of silt fine content on the hydraulicconductivity of clean sand taken from the Firouzkouh areain the north of Iran [51]

A new modified suction-controlled double-walled tri-axial apparatus was used for this purpose with the detailsillustrated in Figure 1 As shown pore air and pore waterpressures were applied throughout separate lines from bothtop and bottom of the specimens Two one bar ceramicdisks were installed at both top and bottom pedestals to

4 Advances in Civil Engineering

control or measure the pore water pressure independentlye rate of inflow and outflow of the water was measured bymeans of two automatic pressurevolume change con-trollers e Firouzkouh sand was mixed with the range ofsilt contents that were 0 10 20 30 and 40 (ie FK0FK10 FK20 FK30 and FK40 resp)e basic properties ofthe five types of sand-silt mixtures considered in this studyare summarized in Table 2 Accordingly the variationmaximum and minimum void ratio for the range of soilmixtures are illustrated in Figure 2 Also Figure 3 repre-sents the soil aggregation curve for the sand-silt mixturesconsidered

Cylindrical triaxial samples with the same height anddiameter (7 cm) and a relative density (Dr) based on theASTM D4254-16 code [52] were prepared in a specifieddried special weight e dry weight of each sample wascalculated and the samples were poured into a mold in somelayers with the same weight Table 3 shows the densityproperties of preparing the samples

51 Determination of Water Permeability Coefficient epermeability of an unsaturated soil can be calculated fromthe Darcy law [2 49]

qt VA KwiA Kw

h

LA (10)

where qt is the water flow rate in the cross section v is theflow speed A is the area Kw is the Darcy permeabilitycoefficient (water permeability coefficient) i is the hydraulicgradient which is equal to hL h is the missed head and L isthe height of soil sample

e high air-entry ceramic plate permeability is con-sidered in analyzing the results gained from the perme-ability test with the modified triaxial device e soilpermeability (or the water permeability) was determined inthree layers plate soil and plate [15] e flow speed (v)was the same in all three layers while the general missedhead (ht) is equal to the summary of the missed head ineach layer (the upper plate the soil sample and the lower

Load cellDifferential transformer

Cell top

Loading ram

Top port

Lucite cylinder

O-Rings

1-Bar high air entryRubber membraneWater compartmentPorous metal

Cell base

Soilspacemenϕ 70 mmH 70 mm

Pore air pressure line

Pore air pressure transducer

Cell pressure line

Cell pressure transducer

Top cap

Pore water pressure line

Pore water pressure line (top cap)

Flushing line (top cap)

Flushing linePore_water pressure transducer

Figure 1 Schematic diagram of modified triaxial apparatus for permeability measurement

Advances in Civil Engineering 5

plate) e flow speed and the missed head have relations asfollows

v vt vs vb (11)

hT ht + hs + hb (12)

where vt is the flow speed passing the upper ceramic plate vs

is the flow speed passing the soil sample vb is the flow speedpassing the lower ceramic plate ht is the missed head alongthe upper ceramic plate hs is the missed head along the soil

sample and hb is the missed head along the lower ceramicplate

By substituting relation (10) in relation (12) the fol-lowing relation is gained

vTlT

kT

vtlt

kt

+vsls

kw

+vblb

kb

(13)

where Kw is the water permeability coefficient of the soilsample kT is the permeability coefficient of the plate-soil-plate

Table 2 Basic properties of the studied soil samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Sand content (by dry weight) () 100 90 80 70 60Silt content (by dry weight) () 0 10 20 30 40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum dry density cdmax (grcm3) 1594 1719 1797 1799 167Minimum dry density cdmin (grcm3) 1385 1423 1424 1402 1356Saturated permeability coefficient Ks (ms)cdmax (grcm3) constant 14 841eminus2 326eminus2 942eminus3 363eminus3 313eminus4

Plasticity index PI NP NP NP NP NPMaximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531D10 (mm) 0151 0069 0019 0012 00069D30 (mm) 0194 0174 0156 0077 0032D50 (mm) 025 0233 0214 0191 0164D60 (mm) 0285 0269 0253 0229 0203Cu (D60D10) 1887 3899 13316 19083 2942Cc ((D30)2(D60lowastD10)) 0875 1631 5063 2158 0731Soil classification (USCS) SP SP-SM SM SM SM

030

040

050

060

070

080

090

100

110

120

00 100 200 300 400 500

Voi

d ra

tio (e

max

e min

e)

Fine content ()

emax

emin

e (Dr = 55)

Figure 2 Void ratio curve for the prepared samples

N 2

00

N 1

00

N 5

0N

40

N 3

0

N 1

6

00

100

200

300

400

500

600

700

800

900

1000

0001 001 01 1 10Grain size (mm)

Sand(100)-Silt(00)

Sand(90)-Silt(10)

Sand(80)-Silt(20)

Sand(70)-Silt(30)

Sand(60)-Silt(40)

Perc

ent b

y w

eigh

t fine

r (

)

Figure 3 Grain size distribution of soil samples used in this study

6 Advances in Civil Engineering

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

fluid-filled pores as bundles of various sized capillary tubes[8ndash10 24] e goal was to conclude a permeability functionanalysis In a microscopic scale the liquid flow is consideredas a slow flow showing the general flow in the soil Whenunsaturated soils are considered as a set of simple capillarytubes the flow can be defined by using flow medium ratehydraulic gradient hydraulic radius and permeability ehydraulic radius measures efficiency of the flow channeleflow rate along the channel depends on the cross-sectionarea more than any other factor e magnitude of thehydraulic radius shows high efficiency and results in higherflow volume [8ndash10]

According to assumptions in the mentioned paragraphBrooks and Corey [24] recommended a microscopic modelfor the relative permeability ratio which is defined as theunsaturated soil permeability coefficient to the saturatedpermeability coefficient

Kr Sr minus Sresr( 1113857

1minus Sresr( 1113857

1113938Sres

0 sminus2dSr

111393810 sminus2dSr

(6)

where (Sr minus Sresr )(1minus Sresr ) is the curvature factor due to thedifference between the natural rate and the real rate of voidswith the pressure real and natural gradient Sr and Sresr arethe degree of saturation and the remaining degree ofsaturation respectively Also (Sr minus Sresr )(1minus Sresr ) is namedthe effective degree of saturation (Se) 1113938

Sres

0 sminus2dSr 111393810 sminus2dSr

is the hydraulic radius which is gained from the integral ofthe SWCC e effective permeability coefficient like thesuction powered function could be presented as thefollowing

Kr Sδe (7)

where δ is a constant number and can change due to theassumptions Different researchers have recommendeddifferent numbers such as 35 by Averjanov [45] 2 by Yuster[46] 3 by Irmay [47] and 4 by Corey [48]

emain criticism of the microscopic models is that theyignore the effect of void size distribution [24 49] Brooks andCorey [24] showed that δ for a soil with a uniform voiddistribution is equal to 3 and generally recommended thefollowing relation δ 2 + 3λλ where λ is the distributionindex of void shape and is a positive number

e experimental and microscopic models seem to bethe same but they each have a different theoretical base andexcavation procedure e experimental models are gainedfrom the curve fitting on experimental data due to re-gression but microscopic models are determined fromliquid flow in a porous environment which is based on fluidmechanics Also many microscopic models are related tosoilndashwater retention behavior [8ndash10]

4 Statistical Models

Statistical models have been built based on statistical co-operation of void size changes on the permeability co-efficient e statistical perspective of void size distributionand the probability of the connections of pores are discussedin this part Statistical models are known to be very accurate

for calculating permeability of unsaturated soil [8ndash10] Inthis model the permeability coefficient function is gainedusing the SWCC ree assumptions are required to extractthe statistical model [8ndash10]

(1) It is assumed that the soil is a system composedof interconnected collection and pore distribu-tion is random and the pore characteristics aregained by r and f(r) which is the same throughoutthe soil

(2) e HagenndashPoiseuille equation is valid which is usedto calculate the permeability of a unique porechannel and general permeability is calculatedaccording to integration of water-filled pores

(3) Due to the Calvin capillary model the SWCC used togain the permeability equation is the representativeof the soil pore distribution function

According to technical literature the statistical modelscan be presented as follows

Kr θw( 1113857 Φx1113938θw

0 dθwSy( 11138571113874 1113875

1113938θs

0 dθwSy( 11138571113874 1113875

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

z

(8)

Kr θw( 1113857 Φx1113938θw

0 d θwminus ξ1113872 1113873Sy1113872 1113873dξ1113876 1113877

1113938θs

0 d θw minus ξ( 1113857Sy( 1113857dξ1113876 1113877

⎧⎪⎪⎨

⎪⎪⎩

⎫⎪⎪⎬

⎪⎪⎭

Z

(9)

whereΦ is the curvature factor and it is representative of thevoid size effect of pores on the permeability function and itis shown that it improves the permeability coefficientfunctionrsquos estimation factor (Kr) without a correctionfactor e curvature facture is gained from normalizing(Φ (θw minus θr)(θs minus θr)) the water content in which θs andθr are the water content in the saturated state andremaining state respectively In (8) ξ is the integrationartificial variable and x y and z are the constants of themodel For example in the recommended model ofBurdine [50] x 2 y 2 and z 1 for (7) while x

05 y 1 and z 2 for Mualem [25] For the Childs andCollis-George [49] model (CCG model) x 0 y 2 andz 1 in (8) were recommended while for the modifiedCCG model the numbers were x 0 y 0 and z 2 byusing Agus et al [15]

5 Material Properties and Testing Methods

A series of hydraulic conductivity tests were performed toexamine the influence of silt fine content on the hydraulicconductivity of clean sand taken from the Firouzkouh areain the north of Iran [51]

A new modified suction-controlled double-walled tri-axial apparatus was used for this purpose with the detailsillustrated in Figure 1 As shown pore air and pore waterpressures were applied throughout separate lines from bothtop and bottom of the specimens Two one bar ceramicdisks were installed at both top and bottom pedestals to

4 Advances in Civil Engineering

control or measure the pore water pressure independentlye rate of inflow and outflow of the water was measured bymeans of two automatic pressurevolume change con-trollers e Firouzkouh sand was mixed with the range ofsilt contents that were 0 10 20 30 and 40 (ie FK0FK10 FK20 FK30 and FK40 resp)e basic properties ofthe five types of sand-silt mixtures considered in this studyare summarized in Table 2 Accordingly the variationmaximum and minimum void ratio for the range of soilmixtures are illustrated in Figure 2 Also Figure 3 repre-sents the soil aggregation curve for the sand-silt mixturesconsidered

Cylindrical triaxial samples with the same height anddiameter (7 cm) and a relative density (Dr) based on theASTM D4254-16 code [52] were prepared in a specifieddried special weight e dry weight of each sample wascalculated and the samples were poured into a mold in somelayers with the same weight Table 3 shows the densityproperties of preparing the samples

51 Determination of Water Permeability Coefficient epermeability of an unsaturated soil can be calculated fromthe Darcy law [2 49]

qt VA KwiA Kw

h

LA (10)

where qt is the water flow rate in the cross section v is theflow speed A is the area Kw is the Darcy permeabilitycoefficient (water permeability coefficient) i is the hydraulicgradient which is equal to hL h is the missed head and L isthe height of soil sample

e high air-entry ceramic plate permeability is con-sidered in analyzing the results gained from the perme-ability test with the modified triaxial device e soilpermeability (or the water permeability) was determined inthree layers plate soil and plate [15] e flow speed (v)was the same in all three layers while the general missedhead (ht) is equal to the summary of the missed head ineach layer (the upper plate the soil sample and the lower

Load cellDifferential transformer

Cell top

Loading ram

Top port

Lucite cylinder

O-Rings

1-Bar high air entryRubber membraneWater compartmentPorous metal

Cell base

Soilspacemenϕ 70 mmH 70 mm

Pore air pressure line

Pore air pressure transducer

Cell pressure line

Cell pressure transducer

Top cap

Pore water pressure line

Pore water pressure line (top cap)

Flushing line (top cap)

Flushing linePore_water pressure transducer

Figure 1 Schematic diagram of modified triaxial apparatus for permeability measurement

Advances in Civil Engineering 5

plate) e flow speed and the missed head have relations asfollows

v vt vs vb (11)

hT ht + hs + hb (12)

where vt is the flow speed passing the upper ceramic plate vs

is the flow speed passing the soil sample vb is the flow speedpassing the lower ceramic plate ht is the missed head alongthe upper ceramic plate hs is the missed head along the soil

sample and hb is the missed head along the lower ceramicplate

By substituting relation (10) in relation (12) the fol-lowing relation is gained

vTlT

kT

vtlt

kt

+vsls

kw

+vblb

kb

(13)

where Kw is the water permeability coefficient of the soilsample kT is the permeability coefficient of the plate-soil-plate

Table 2 Basic properties of the studied soil samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Sand content (by dry weight) () 100 90 80 70 60Silt content (by dry weight) () 0 10 20 30 40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum dry density cdmax (grcm3) 1594 1719 1797 1799 167Minimum dry density cdmin (grcm3) 1385 1423 1424 1402 1356Saturated permeability coefficient Ks (ms)cdmax (grcm3) constant 14 841eminus2 326eminus2 942eminus3 363eminus3 313eminus4

Plasticity index PI NP NP NP NP NPMaximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531D10 (mm) 0151 0069 0019 0012 00069D30 (mm) 0194 0174 0156 0077 0032D50 (mm) 025 0233 0214 0191 0164D60 (mm) 0285 0269 0253 0229 0203Cu (D60D10) 1887 3899 13316 19083 2942Cc ((D30)2(D60lowastD10)) 0875 1631 5063 2158 0731Soil classification (USCS) SP SP-SM SM SM SM

030

040

050

060

070

080

090

100

110

120

00 100 200 300 400 500

Voi

d ra

tio (e

max

e min

e)

Fine content ()

emax

emin

e (Dr = 55)

Figure 2 Void ratio curve for the prepared samples

N 2

00

N 1

00

N 5

0N

40

N 3

0

N 1

6

00

100

200

300

400

500

600

700

800

900

1000

0001 001 01 1 10Grain size (mm)

Sand(100)-Silt(00)

Sand(90)-Silt(10)

Sand(80)-Silt(20)

Sand(70)-Silt(30)

Sand(60)-Silt(40)

Perc

ent b

y w

eigh

t fine

r (

)

Figure 3 Grain size distribution of soil samples used in this study

6 Advances in Civil Engineering

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

control or measure the pore water pressure independentlye rate of inflow and outflow of the water was measured bymeans of two automatic pressurevolume change con-trollers e Firouzkouh sand was mixed with the range ofsilt contents that were 0 10 20 30 and 40 (ie FK0FK10 FK20 FK30 and FK40 resp)e basic properties ofthe five types of sand-silt mixtures considered in this studyare summarized in Table 2 Accordingly the variationmaximum and minimum void ratio for the range of soilmixtures are illustrated in Figure 2 Also Figure 3 repre-sents the soil aggregation curve for the sand-silt mixturesconsidered

Cylindrical triaxial samples with the same height anddiameter (7 cm) and a relative density (Dr) based on theASTM D4254-16 code [52] were prepared in a specifieddried special weight e dry weight of each sample wascalculated and the samples were poured into a mold in somelayers with the same weight Table 3 shows the densityproperties of preparing the samples

51 Determination of Water Permeability Coefficient epermeability of an unsaturated soil can be calculated fromthe Darcy law [2 49]

qt VA KwiA Kw

h

LA (10)

where qt is the water flow rate in the cross section v is theflow speed A is the area Kw is the Darcy permeabilitycoefficient (water permeability coefficient) i is the hydraulicgradient which is equal to hL h is the missed head and L isthe height of soil sample

e high air-entry ceramic plate permeability is con-sidered in analyzing the results gained from the perme-ability test with the modified triaxial device e soilpermeability (or the water permeability) was determined inthree layers plate soil and plate [15] e flow speed (v)was the same in all three layers while the general missedhead (ht) is equal to the summary of the missed head ineach layer (the upper plate the soil sample and the lower

Load cellDifferential transformer

Cell top

Loading ram

Top port

Lucite cylinder

O-Rings

1-Bar high air entryRubber membraneWater compartmentPorous metal

Cell base

Soilspacemenϕ 70 mmH 70 mm

Pore air pressure line

Pore air pressure transducer

Cell pressure line

Cell pressure transducer

Top cap

Pore water pressure line

Pore water pressure line (top cap)

Flushing line (top cap)

Flushing linePore_water pressure transducer

Figure 1 Schematic diagram of modified triaxial apparatus for permeability measurement

Advances in Civil Engineering 5

plate) e flow speed and the missed head have relations asfollows

v vt vs vb (11)

hT ht + hs + hb (12)

where vt is the flow speed passing the upper ceramic plate vs

is the flow speed passing the soil sample vb is the flow speedpassing the lower ceramic plate ht is the missed head alongthe upper ceramic plate hs is the missed head along the soil

sample and hb is the missed head along the lower ceramicplate

By substituting relation (10) in relation (12) the fol-lowing relation is gained

vTlT

kT

vtlt

kt

+vsls

kw

+vblb

kb

(13)

where Kw is the water permeability coefficient of the soilsample kT is the permeability coefficient of the plate-soil-plate

Table 2 Basic properties of the studied soil samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Sand content (by dry weight) () 100 90 80 70 60Silt content (by dry weight) () 0 10 20 30 40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum dry density cdmax (grcm3) 1594 1719 1797 1799 167Minimum dry density cdmin (grcm3) 1385 1423 1424 1402 1356Saturated permeability coefficient Ks (ms)cdmax (grcm3) constant 14 841eminus2 326eminus2 942eminus3 363eminus3 313eminus4

Plasticity index PI NP NP NP NP NPMaximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531D10 (mm) 0151 0069 0019 0012 00069D30 (mm) 0194 0174 0156 0077 0032D50 (mm) 025 0233 0214 0191 0164D60 (mm) 0285 0269 0253 0229 0203Cu (D60D10) 1887 3899 13316 19083 2942Cc ((D30)2(D60lowastD10)) 0875 1631 5063 2158 0731Soil classification (USCS) SP SP-SM SM SM SM

030

040

050

060

070

080

090

100

110

120

00 100 200 300 400 500

Voi

d ra

tio (e

max

e min

e)

Fine content ()

emax

emin

e (Dr = 55)

Figure 2 Void ratio curve for the prepared samples

N 2

00

N 1

00

N 5

0N

40

N 3

0

N 1

6

00

100

200

300

400

500

600

700

800

900

1000

0001 001 01 1 10Grain size (mm)

Sand(100)-Silt(00)

Sand(90)-Silt(10)

Sand(80)-Silt(20)

Sand(70)-Silt(30)

Sand(60)-Silt(40)

Perc

ent b

y w

eigh

t fine

r (

)

Figure 3 Grain size distribution of soil samples used in this study

6 Advances in Civil Engineering

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

plate) e flow speed and the missed head have relations asfollows

v vt vs vb (11)

hT ht + hs + hb (12)

where vt is the flow speed passing the upper ceramic plate vs

is the flow speed passing the soil sample vb is the flow speedpassing the lower ceramic plate ht is the missed head alongthe upper ceramic plate hs is the missed head along the soil

sample and hb is the missed head along the lower ceramicplate

By substituting relation (10) in relation (12) the fol-lowing relation is gained

vTlT

kT

vtlt

kt

+vsls

kw

+vblb

kb

(13)

where Kw is the water permeability coefficient of the soilsample kT is the permeability coefficient of the plate-soil-plate

Table 2 Basic properties of the studied soil samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Sand content (by dry weight) () 100 90 80 70 60Silt content (by dry weight) () 0 10 20 30 40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum dry density cdmax (grcm3) 1594 1719 1797 1799 167Minimum dry density cdmin (grcm3) 1385 1423 1424 1402 1356Saturated permeability coefficient Ks (ms)cdmax (grcm3) constant 14 841eminus2 326eminus2 942eminus3 363eminus3 313eminus4

Plasticity index PI NP NP NP NP NPMaximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531D10 (mm) 0151 0069 0019 0012 00069D30 (mm) 0194 0174 0156 0077 0032D50 (mm) 025 0233 0214 0191 0164D60 (mm) 0285 0269 0253 0229 0203Cu (D60D10) 1887 3899 13316 19083 2942Cc ((D30)2(D60lowastD10)) 0875 1631 5063 2158 0731Soil classification (USCS) SP SP-SM SM SM SM

030

040

050

060

070

080

090

100

110

120

00 100 200 300 400 500

Voi

d ra

tio (e

max

e min

e)

Fine content ()

emax

emin

e (Dr = 55)

Figure 2 Void ratio curve for the prepared samples

N 2

00

N 1

00

N 5

0N

40

N 3

0

N 1

6

00

100

200

300

400

500

600

700

800

900

1000

0001 001 01 1 10Grain size (mm)

Sand(100)-Silt(00)

Sand(90)-Silt(10)

Sand(80)-Silt(20)

Sand(70)-Silt(30)

Sand(60)-Silt(40)

Perc

ent b

y w

eigh

t fine

r (

)

Figure 3 Grain size distribution of soil samples used in this study

6 Advances in Civil Engineering

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

system kt is the water permeability coefficient of the upperplate kb is the water permeability coefficient of the lowerplate ls is the soil sample length lt is the upper ceramic platethickness lb is the lower ceramic plate thickness and lT is thethickness of the plate-soil-plate system that is lT ls + lt + lb

When v is the same in all layers (13) can be rewritten asthe following

Kw ls

lTkT( 1113857minus ltkt( 1113857 + lbkb( 11138571113858 1113859 (14)

So the soil permeability coefficient can be calculatedfrom (14) e permeability coefficient of the plate-soil-platesystem (KT) can be calculated through permeability testsfrom the following equation

kT Qw

iAt (15)

where Qw is the volume of water passing through the soilsample and t is the time

e properties of the porous plate used in this study arepresented in Table 4

In this study the hydraulic conductivity tests wereperformed after drying and wetting of samples to a range ofmatric suctions between 1 and 60 kPa A pore air pressure of100 kPa was applied to the specimens and the pore waterpressure was varied to reach the target matric suctions alongdrying and wetting paths e hydraulic conductivity ofsamples was consequently measured within a steady stateflow of water in the flow head of 30 kPa Using a similarapproach to Pavlakis [20] and Mirzaii amp Yasrobi [3] theaverage matric suction of specimens remained unchangedduring the infiltration of water is was experimentallyachieved by 15 kPa increment of sample bottom pore waterpressure and 15 kPa decrement of sample top pore waterpressure while the average pore water pressure was un-changed e rates of inflow and outflow of water werereached to analogous constant values in a steady statecondition within 30 to 50 hours

6 Results and Discussion

In this part the test results of this study are discussed basedon experiments and the presented models [44] e un-saturated soil permeability coefficient is presented accordingto (4) and (5) e results are presented in two parts (1)permeability coefficient changes against the matric suctionand (2) permeability coefficient changes against the volu-metric water content

61 Permeability Coefficient Changes against Matric Suctione general scheme of the matric suction-permeabilitycoefficient curve for different types of soil is shown in

Table 4 Porous ceramic plate properties (porous ceramic plate4mm thickness 1 bar high flow)

Ceramic info ickness (mm) K Capacity (bar)High flow 4 693eminus7 1

Zone 1

Zone 2

Zone 3

solid

water

Air

Ks1

Ks2

Hyd

ranl

ic co

nduc

tivity

(log

ms

)

Matric suction (log kPa)

Figure 4e general scheme of the matric hydraulic conductivity-matric suction curve for different types of soil

Table 3 Density properties of samples

SpecificationSample

FK0 FK10 FK20 FK30 FK40Specific gravity Gs (grcm3) 2658 2663 2684 2671 2652Maximum void ratio emax 0883 0839 0844 0871 0924Minimum void ratio emin 0633 0517 0459 0481 0531Dr () 55 55 55 55 55e (Dr 55) 077 0694 0671 0696 0747cd (grcm3) 1473 1543 1576 1545 1489

10E minus 1010E minus 0910E minus 0810E minus 0710E minus 0610E minus 0510E minus 0410E minus 0310E minus 0210E minus 0110E + 00

01 1 10 100

Rela

tive c

oeff

of p

erm

eabi

lity k r

Expt

Equation 4

Equation 5

Specimen FK0σ0 = 15 kPaDr = 55

Matric suction ψ (Kpa)

Equation 4a = 321b = 438c = 121d = 594

Equation 5A = 346B = 479C = 735

Figure 5 Permeability coefficient changes against matric suctionfor soil FK0

Advances in Civil Engineering 7

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Figure 4 is figure demonstrates that the general schemewas the same in different soil types but the matric suctionperiod and permeability coefficient evaluations were dif-ferent according to soil type According to continuity of thewater and air phases in soil pores the curve had 3 zones andeach zone had different soil behaviors In the first zone thevoids were filled completely with water or distributed in thesoil voids as discontinuous bubbles and the soil behaviorwas just a function of water in the pores and demonstratedthe same behavior as saturated soil In the second zone thesoil pore was filled continuously with air and water and thesoil behavior was a function of the air and water inside porese third zone of the curve was similar to dry or nearly drysituations of the soil in which water was located in the thin

layers between the soils In this condition most spaces in thevoids were filled with air and the capillary water distributionbetween layers is discontinuous

In this study the matric suction was applied between 01and 60 kPa depending on the soil type Figures 5ndash9 show thesoil permeability behavior of FK0 FK10 FK20 FK30 andFK40 against the matric suction respectively

e curves have been drawn from the data gained frompermeability coefficients using relations and parameters ofLeong and Rahardjo [8ndash10] e amounts related to theseparameters (a b c d andA BC) are presented on the curvesand shown separately in Tables 5 and 6

In low suction amounts between 01 and 5 kPadepending on the soil type the soil permeability behavior is

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08Relat

ive c

oeff

of p

erm

eabi

lity

k r

10E minus 10

10E minus 09

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 396b = 472c = 1025d = 557

Equation 5A = 421B = 477C = 584

Specimen FK10σ0 = 15 kPaDr = 55

Figure 6 Permeability coefficient changes against matric suctionfor soil FK10

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

10E minus 05

Equation 4a = 579b = 528c = 075d = 510

Equation 5A = 637B = 498C = 422

Specimen FK20σ0 = 15 kPaDr = 55

Figure 7 Permeability coefficient changes against matric suctionfor soil FK20

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 744b = 569c = 069d = 479

Equation 5A = 653B = 577C = 324

Specimen FK30σ0 = 15 kPaDr = 55

Figure 8 Permeability coefficient changes against matric suctionfor soil FK30

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

Relat

ive c

oeff

of p

erm

eabi

lity

k r

01 1 10 100Matric suction ψ (Kpa)

Expt

Equation 4

Equation 5

Equation 4a = 798b = 671c = 049d = 435

Equation 5A = 764B = 447C = 258

Specimen FK10σ0 = 15 kPaDr = 55

Figure 9 Permeability coefficient changes against matric suctionfor soil FK40

8 Advances in Civil Engineering

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

different Considerable changes happened by increasing thesuction As shown in Figures 5ndash9 by increasing the amountof silt permeability was reduced in higher amounts ofsuction e intensity of these changes for amounts of 2030 and 40 is shown in Figure 10 as a comparison

Generally the soil behavior in two relations 5 and 6 is thesame So the previous graph is presented for (6) e resultsshow that the permeability coefficient was the same for allsoils at low level suction (lower than 15 kPa) But thepermeability coefficient showed difference as the matricsuction increased And as the suction increased and timepassed this difference became bigger and bigger Accordingto Figure 10 it can be seen that at the same amount ofsuction more than 6 kPa FK40 had the highest permeabilitycoefficient and FK0 had the lowest It can be said that

increasing the amount of silt caused a reduction in soil poresize and produced a denser and stable network for water toexit which caused a reduction in general permeability of thesoil So water neededmore time to get out of the soil Hencethe disconnection of waterways happened later so the di-agram was stretched higher is behavior was seen inamounts of silt more than 10 In the second zone the curveslope increased as the silt amount decreased So the FK40had the least slope and FK0 has the steepest slope isbehavior showed that in samples with higher amounts ofsilt water exited for a longer time

62 Permeability Coefficient Changes against the VolumetricWater Amount In this part the permeability behavior wasevaluated in different soil samples in this test against thevolumetric water content e behavior of these changes indifferent soils is shown in Figures 11ndash15

Table 5 Parameters a b c and d for permeability function of soilspecimens for (4)

Specimen a (kPa) b c dFK0 321 438 1211 594FK10 396 472 1025 557FK20 579 528 0754 510FK30 744 569 0696 479FK40 798 671 0494 435

Table 6 Parameters A B and C for permeability function of soilspecimens for (5)

Specimen A (kPa) B CFK0 346 479 735FK10 421 477 584FK20 637 498 422FK30 653 577 324FK40 764 447 258

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

Relat

ive c

oeff

of p

erm

eabi

lity

k r

010 100 1000 10000Matric suction ψ (Kpa)

FK0 minus Equation 5FK10 minus Equation 5FK20 minus Equation 5FK30 minus Equation 5FK40 minus Equation 5

FK0 minus ExptFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 10 A comparison graph for permeability changes againstmatric suction for different soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Expt

Equation 3

Specimen FK0σ0 = 15 kPaDr = 55p = 547

Figure 11 Permeability changes against volumetric water contentfor FK0 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03Volumetric water content θw

Specimen FK10σ0 = 15 kPaDr = 55p = 744

Expt

Equation 3

Figure 12 Permeability changes against volumetric water contentfor FK10 soils

Advances in Civil Engineering 9

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

According to Figure 16 it is clear that by increasing thevolumetric water content through the sample the perme-ability coefficient increased in all soils e point is that theintensity of these changes increased as the silt amount in-creased So samples with 40 silt had a lower permeabilitycoefficient and with a decreasing amount of silt the per-meability coefficient increased e pure sand sample FK0had the highest permeability coefficient is behavior wasbecause of aggregation change in soil and the effect of poresize changes due to silt changes As the soil pore size de-creased soil permeability also decreased

7 Conclusion

is study considered in vitro evaluations and permeabilitybehavior comparisons of unsaturated silty sand samples withdifferent aggregations with relative density against matric

suction and volumetric water content using a modifiedtriaxial device e results were compared with differentexperimental models such as Leong and Rahardjo [8ndash10]e results of this study are presented as follows

(i) By increasing the amount of fine-grained aggregatethe permeability started to reduce at higher suctionis amount increased faster in soil samples withmore silt

(ii) An increase in fine grain caused a reduction of soilpore size and built a more stable and dense networkfor the water to exit So the water needed more timeto exit the soil and permeability decrease happenedat a higher level of suction

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

Specimen FK20σ0 = 15 kPaDr = 55p = 1171

Expt

Equation 3

0 01 02 03 04Volumetric water content θw

Figure 13 Permeability changes against volumetric water contentfor FK20 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 01 02 03 04Volumetric water content θw

Expt

Equation 3

Specimen FK30σ0 = 15 kPaDr = 55p = 1489

Figure 14 Permeability changes against volumetric water contentfor FK30 soils

100E + 00

100E minus 01

100E minus 02

100E minus 03

100E minus 04

100E minus 05

Relat

ive c

oeff

of p

erm

eabi

lity k r

0 005 01 015 02 025 03 035 04Volumetric water content θw

Expt

Equation 3

Specimen FK40σ0 = 15 kPaDr = 55p = 1935

Figure 15 Permeability changes against volumetric water contentfor FK40 soils

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

10E minus 06

10E minus 07

10E minus 08

10E minus 09

10E minus 10

Relat

ive c

oeff

of p

erm

eabi

lity k r

000 005 010 015 020 025 030 035 040Volumetric water content θw

FK0 minus Equation 3FK10 minus Equation 3FK20 minus Equation 3FK30 minus Equation 3FK40 minus Equation 3

FK0 minus ExpFK10 minus ExptFK20 minus ExptFK30 minus ExptFK40 minus Expt

σ0 = 15 kPaDr = 55

Figure 16 Comparison of figures of permeability changes againstvolumetric water content

10 Advances in Civil Engineering

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(iii) e permeability against suction decreased as thefine grain increased is shows that at highersuction the water exited the soil later and thisindicated that in fine-grained soil the permeabilityreduction rate was slower

(iv) e permeability coefficient increased with differentfine-grained percentages as the volumetric waterincreased and the permeability coefficient de-creased as the fine grains increased in a fixedamount of water is behavior caused changes inaggregate percentage and pore size

Conflicts of Interest

e authors declare that there are no conflicts of interest

References

[1] R D Holtz and W D Kovacs An Introduction to Geo-technical Engineering Prentice-Hall Upper Saddle River NJUSA 1981

[2] D G Fredlund and H Rahardjo Soil Mechanics forUnsaturated Soils John Wiley amp Sons New York NY USA1993

[3] A Mirzaii and S S Yasrobi ldquoEffect of net stress on hydraulicconductivity of unsaturated soilsrdquo Transport in Porous Mediavol 95 no 3 pp 497ndash505 2012

[4] D G Fredlund A Xing and S Huang ldquoPredicting thepermeability function for unsaturated soils using the soilndashwater characteristic curverdquo Canadian Geotechnical Journalvol 31 no 4 pp 533ndash546 1994

[5] A Mirzaii S S Yasrobi and N Khalili ldquoExperimentalinvestigation of hydraulic conductivity in unsaturatedcompressible soilsrdquo in Proceedings of the 2nd EuropeanConference on Unsaturated Soils pp 205ndash212 Napoli ItalyJune 2012

[6] D G Fredlund ldquoUnsaturated soil mechanics in engineeringpractiserdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 132 no 3 pp 286ndash321 2006

[7] C Gallage J Kodikara and T Uchimura ldquoLaboratorymeasurement of hydraulic conductivity functions of twounsaturated sandy soils during drying and wetting processesrdquoSoils and Foundations vol 53 no 3 pp 417ndash430 2013

[8] E C Leong and H Rahardjo ldquoA review on soil-watercharacteristic curve equationsrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 123 no 12 pp 1106ndash11171997b

[9] E C Leong and H Rahardjo ldquoDiscussion of Unsaturatedhydraulic conductivity of two compacted barrier soilsrdquoJournal of Geotechnical Engineering vol 123 no 12pp 1186ndash1188 1997c

[10] E C Leong and H Rahardjo ldquoPermeability functions for un-saturated soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 123 no 12 pp 1118ndash1126 1997a

[11] S S Agus E C Leong and H Rahardjo ldquoEstimating per-meability functions of Singapore residual soilsrdquo EngineeringGeology vol 78 no 1-2 pp 119ndash133 2005

[12] S G Goh H Rahardjo and E C Leong ldquoShear strength ofunsaturated soils under multiple drying-wetting cyclesrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 140 no 2 p 06013001 2014

[13] C H Benson and M M Gribb ldquoMeasuring unsaturatedhydraulic conductivity in the laboratory and fieldrdquo in

Unsaturated Soil Engineering Practice Geotechnical SpecialPublication No 68 pp 113ndash168 American Society of CivilEngineers New York NY USA 1997

[14] H Krisdani H Rahardjo and E C Leong ldquoUse of in-stantaneous profile and statistical methods to determinepermeability functions of unsaturated soilsrdquo CanadianGeotechnical Journal vol 46 no 7 pp 869ndash874 2009

[15] S S Agus E C Leong and H Rahardjo ldquoA flexible wallpermeameter for measurements of water and air coefficient ofpermeability of residual soilrdquo Canadian Geotechnical Journalvol 40 no 3 pp 559ndash574 2003

[16] A Klute ldquoLaboratory measurement of hydraulic conductivityof unsaturated soilsrdquo in Method of Soil Analysis C A BlackD D Evans J L White L E Esminger and F E Clark Edsvol 1 pp 253ndash261 Merican Society of Agronomy MadisonWI USA 1965

[17] J K M Gan and D G Fredlund ldquoA new laboratory methodfor the measurement of unsaturated coefficient of perme-ability of soilsrdquo in Proceedings of the Asian Conference onUnsaturated SoilsndashFrom Eeory to Practise pp 381ndash386Singapore May 2000

[18] N Lu A Wayllace J Carrera W J Likos L David Suits andT C Sheahan ldquoConstant flow method for concurrentlymeasuring soilndashwater characteristic curve and hydraulicconductivity functionrdquo Geotechnical Testing Journal vol 29no 3 p 12637 2006

[19] S K Vanapalli V K Garga and P Brisson ldquoA modifiedpermeameter for determination of unsaturated coefficient ofpermeabilityrdquo Geotechnical and Geological Engineeringvol 25 no 2 pp 191ndash202 2007

[20] C H Barden and G Pavlakis ldquoAir and water permeability ofcompacted unsaturated cohesive soilsrdquo Journal of Soil Sciencevol 22 no 3 pp 302ndash318 1971

[21] S Huang D G Fredlund and S L Barbour ldquoMeasurement ofthe coefficient of permeability for a deformable unsaturatedsoil using a triaxial permeameterrdquo Canadian GeotechnicalJournal vol 35 no 3 pp 426ndash432 1998

[22] M P HMoncada and TM P Campos ldquoA new permeameterfor the determination of the unsaturated coefficient of per-meabilityrdquo in Proceedings of the Fifth International Conferenceof Unsaturated Soil UNSAT 2010 pp 701ndash706 BarcelonaSpain September 2010

[23] L A Richards ldquoCapillary conducting of liquids throughporous mediumrdquo Physics vol 1 no 5 pp 318ndash333 1931

[24] R H Brooks and A T Corey Hydraulic Properties of PorousMedia Hydrology Paper no 3 Colorado State UniversityFort Collins CO USA 1964

[25] Y Mualem ldquoA new model for predicting the hydraulicconductivity of unsaturated porous mediardquo Water ResourcesResearch vol 12 no 3 pp 513ndash522 1976

[26] R J Kunze G Uehera and K Graham ldquoFactors important inthe calculation of hydraulic conductivityrdquo Soil Science Societyof America Journal vol 32 no 6 pp 760ndash765 1968

[27] M T van Genuchten ldquoA closed form equation predictingthe hydraulic conductivity of unsaturated soilsrdquo Soil Sci-ence Society of America Journal vol 44 no 5 pp 892ndash8981980

[28] T Chiu and C D Shack el ford ldquoUnsaturated hydraulicconductivity of compacted sandndashkaolin mixturesrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 2 pp 160ndash170 1998

[29] W R Gardner ldquoCalculation of capillary conductivity frompressure plate outflow datardquo Soil Science Society of AmericaProceedings vol 20 no 3 pp 317ndash320 1956

Advances in Civil Engineering 11

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[30] G S Campbell ldquoA simple method for determining un-saturated conductivity from moisture retention datardquo SoilScience vol 117 no 6 pp 311ndash314 1974

[31] L R Ahuja ldquoA numerical and similarity analysis of in-filtration into crusted soilsrdquo Water Resource Research vol 9no 4 pp 987ndash994 1973

[32] L R Ahuja ldquoUnsaturated hydraulic conductivity from cu-mulative inflow datardquo Proceedings of Soil Science Society ofAmerica vol 36 pp 695ndash699 1974

[33] R W Gillham A Klute and D F Heermann ldquoHydraulicproperties of a porous medium measurement and empiricalrepresentationrdquo Soil Science Society of America Journalvol 40 no 2 pp 203ndash207 1976

[34] D W Zachmann P C Ducthateau and A Klute ldquoecalibration of the Richards flow equation for a drainingcolumn by parameter identificationrdquo Journal of Soil ScienceSociety of America vol 45 pp 1012ndash1015 1981

[35] D Hillel Introduction to Soil Physics Academic Press NewYork NY USA 1982

[36] J M Davidson L R Stone D R Nielsen and M E LarueldquoField measurement and use of soilndashwater propertiesrdquo WaterResources Research vol 5 no 6 pp 1312ndash1321 1969

[37] J H Dane and A Klute ldquoSalt effects on the hydraulicproperties of a swelling soilrdquo Soil Science Society of AmericaJournal vol 41 no 6 pp 1043ndash1049 1977

[38] L V Weeks and S J Richards ldquoSoil-water properties com-puted from transient flow datardquo Soil Science Society ofAmerica Journal vol 31 no 6 pp 721ndash725 1967

[39] G P Wind ldquoField experiment concerning capillary rise ofmoisture in heavy clay soilrdquo Netherlands Journal of Agri-cultural Science vol 3 pp 60ndash69 1955

[40] A Arbhabhirama and C Kridakorn ldquoSteady downward flowto water tablerdquo Water Resource Research vol 4 no 6pp 1249ndash1257 1968

[41] H R Christensen Permeability-Capillary Potential Curves forEree Prairie Soils Journal Paper No J-1167 Project 504Agricultural Experiment Station Ames IA USA pp 381ndash901943

[42] P E Rijtema ldquoAn analysis of actual evapotranspirationrdquoAgricultural Research Report Rep 659 1965

[43] J R Philip ldquoLinearized unsteady multidimensional in-filtrationrdquo Water Resources Research vol 22 no 12pp 1717ndash1727 1986

[44] D G Fredlund and A Xing ldquoEquations for the soilndashwatercharacteristic curverdquo Canadian Geotechnical Journal vol 31no 3 pp 521ndash532 1994

[45] S F Averjanov ldquoAbout permeability of subsurface soils incase of incomplete saturationrdquo English Collection vol 7 asquoted by P

[46] S T Yuster ldquoeoretical consideration of multiphase flow inidealized capillary systemsrdquo in Proceedings of the Eird WorldPetroleumCongress vol 2 p 437445 Hague Netherlands 1951

[47] S Irmay ldquoOn the hydraulic conductivity of unsaturated soilsrdquoTransactions American Geophysical Union vol 35 no 3p 463 1954

[48] A T Corey ldquoe interrelation between gas and oil relativepermeabilitiesrdquo Producerrsquos Monthly vol 19 pp 7ndash10 1954

[49] E C Childs and G N Collis-George ldquoe permeability ofporous materialsrdquo Proceedings of the Royal Society AMathematical Physical and Engineering Sciences vol 201no 1066 pp 392ndash405 1950

[50] N T Burdine ldquoRelative permeability calculation from poresize distribution datardquo Journal of Petroleum Technology vol 5no 3 pp 71ndash78 1953

[51] S Nazari Evaluation of Liquefaction Potential Analysis ofPartially Unsaturated Silty Sands PhD thesis University ofIsfahan (Khorasgan) Branch Islamic Azad University Isfa-han Iran 2017

[52] ASTM ldquoStandard Classification of Soils for EngineeringPurposes (Unified Soil Classification System)rdquo Annual Booksof ASTM Standard D2487ndash93 vol 4ndash8 pp 217ndash227 ASTMPhiladelphia PA USA Section 4 1997

12 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom