Effectiveness of Cement on Hydraulic Conductivity Of

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Effectiveness of cement on hydraulic conductivity ofcompacted soil–cement mixturesI. BELLEZZA and E. FRATALOCCHIFIMET Department, Technical University of Marche, Ancona Italy

The paper presents the results of an experimental study on

the hydraulic conductivity of compacted soil–cement mix-tures. The effectiveness of 5% cement addition is evaluatedby the permeability value at 28 days’ curing and by theratio of the hydraulic conductivity of the untreated soil to

that of the mixture, both compacted wet of optimum witha Proctor Standard effort. Laboratory compaction and per-meability tests were performed on 15 soils of different

grain size (sandy to clayey soils) and mineralogy. For allthe investigated soil–cement mixtures hydraulic conduc-tivity values lower than 2 3 1027 cm/s have been achieved

after the cement addition. A statistical analysis was devel-oped in order to evaluate relationships between hydraulicconductivity and soil compositional and compaction vari-

ables. Prediction models for all soil types and for fine-grained soils are given. In particular, for fine-grained soilsa regression equation is proposed that can be used toreliably predict the hydraulic conductivity of compacted

soil–cement mixture as a function of clay fraction, finefraction and liquid limit. Practical applications of theproposed prediction models and the precautions for using

them are discussed.

Keywords: compacted soil; hydraulic barrier;hydraulic conductivity; soil–cement mixture

Cet expose presente les resultats d’une etude experimentale

sur la conductivite hydraulique de mixtures sol-cimentcompactees. L’efficacite de l’adjonction de ciment est eva-luee a 5% en utilisant la valeur de permeabilite apres 28jours de cuisson et en utilisant le rapport entre la permeabi-

lite du sol non traite et celle de la mixture, dans les deux cassous compactage mouille optimum avec un effort ProctorStandard. Le compactage en laboratoire et les essais de

permeabilite ont ete effectues sur 15 sols avec differentestailles de grains (sableux a argileux) et differentes miner-alogies. Pour toutes les mixtures sol-ciment etudiees, des

valeurs de conductivite hydraulique inferieures a 2 3 1027cm/s ont ete obtenues apres adjonction de ciment. Nousavons developpe une analyse statistique pour evaluer les

relations entre la conductivite hydraulique et les variantesquant a la composition du sol et au compactage. Nousdonnons des modeles de prediction pour tous les types desol et pour les sols a grains fins. Pour les sols a grains fins

en particulier, nous proposons une equation de regressionqui peut etre utilisee pour predire avec fiabilite la conducti-vite hydraulique de mixtures sol-ciment compactees comme

fonction de la fraction argileuse, de la fraction fine et de lalimite liquide. Nous discutons des applications pratiquesdes modeles de prediction proposes ainsi que des precau-

tions a prendre pour les utiliser.

Notation

A activityAF activity of fine fractionAk acceptability factor at 28 days’ curingB Skempton coefficientc cement content (by weight)D30 diameter corresponding to 30% passingD50 mean grain sizeEk28 efficiency factor at 28 days’ curingEk7 efficiency factor at 7 days’ curingGs specific gravityk hydraulic conductivityk0 hydraulic conductivity of soilka maximum acceptable hydraulic conductivity value at 28

days’ curingkc28 hydraulic conductivity of soil–cement mixture at 28 days’

curingkc7 hydraulic conductivity of soil–cement mixture at 7 days’

curingLOOR2 leave one out R2

nXs number of variables in regression modelP40 fraction passing No. 40 sieveR2 coefficient of determinationR2 adjusted coefficient of determinationR210 coefficient of determination of tenth best model

SEE standard error of estimateSi(0) initial degree of saturation of compacted soilSi(c) initial degree of saturation of compacted soil–cement

mixturew water contentw0 water content of soil before cement additionwc water content of soil after cement additionwopt optimum water content of compacted soilwopt(c) optimum water content of compacted soil–cement mixtureªd dry unit weight

Introduction

Cement is usually added to soil to amend undesirableproperties (e.g. plasticity) or increase the shear strength forconstruction purposes. The improvement in the mechanicalproperties of cement-treated soils is due to the soil–cement–water reactions, which produce primary and secondary

Ground Improvement (2006) 10, No. 2, 77–90 77

1365-781X # 2006 Thomas Telford Ltd

(GI 4221) Paper received 15 September 2004; last revised 2 December2005; accepted 19 December 2005


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cementitious materials (hydrated calcium silicates and alu-minates and hydrated lime) in the soil–cement matrix (e.g.Herzog and Mitchell, 1963; Bergado et al., 1996).Three different types of cement-stabilised soil systems are

distinguished in the literature (PCA, 1995): soil–cement,cement-modified soil, and plastic soil–cement. Whereasplastic soil–cement is a hardened mixture containing enoughwater to produce a consistency similar to a plasteringmortar, in the other two systems a relatively small propor-tion of cement is added, resulting in an unhardened materialthat can be still considered as a soil or aggregate(Winterkorn and Pamukcu, 1991).This paper focuses on soil–cement obtained by compact-

ing pulverised soil, cement and water, thoroughly mixed.Soil–cement mixtures are typically used in earth structuressuch as embankments (e.g. PCA, 1975), road foundations(Kezdi, 1979; Jonker, 1982), earth dam cores (Nussbaum andColley, 1971), bank and bridge abutment protection (Hansenand Schexnayder, 2000), and liners for water reservoirs(PCA, 1996). Furthermore, waste water treatment lagoons,sludge drying and settling ponds (PCA, 1982; Adaska, 1985),coal storage areas and municipal and hazardous wastelandfills have been lined with soil–cement (Brandl, 1992;Manassero et al., 1994).In all soil–cement applications the designer must know all

the possible effects of cement addition on the mechanical,chemical and hydraulic performance of the soil: for example,modifications in the stress–strain behaviour (Tatsuoka et al.,1997; Consoli et al., 1998); the effectiveness in terms ofresistance against chemical attack (Broderick and Daniel,1990; Rollings et al., 1999); and the reduction in compressi-bility and plasticity (Mitchell, 1981; Chew et al., 2004;Horpibulsuk et al., 2004). Some of these modifications aredesired, but some others could compromise the effectiveperformance of the structure.As far as the effect of cement on hydraulic conductivity is

concerned, the role of factors such as cement percentage,curing time and curing conditions (confining pressure andhumidity) has been investigated (e.g. Brandl, 1992; Bellezza,1996; Bellezza and Pasqualini, 1997), but the influence of soilcharacteristics has not yet been completely clarified. Inparticular, for sandy soils the addition of cement has generallybeen found to reduce the soil hydraulic conductivity, although

the soil characteristics governing the hydraulic performanceof sandy soil–cement mixtures have not been clearly identi-fied. On the other hand, controversial results have beenobtained for fine-grained soil–cementmixtures: both increasesand decreases with respect to soil permeability can occur(Adaska, 1985; Pasqualini et al., 2002). This behaviour needsparticular attention when the hydraulic performance is one ofthe main requirements of the design (e.g. in landfill liners). Atpresent a model suitable to predict the hydraulic performanceof soil–cement mixtures is not available. Only for clays theaddition of cement is expected to increase the short-termpermeability because of modifications of the surface chemistryof the clay particles by cation exchange and consequentflocculation (Mitchell, 1992; Chew et al., 2004).On the basis of the aforesaid results the main purpose of this

paper is to study the influence of soil characteristics on thehydraulic behaviour of compacted soil–cement mixtures.Similarly to previous studies on clay liners (e.g. Benson et al.,1994) a statistical analysis is presented herein in order toidentify the soil compositional variables that correlate with thehydraulic conductivity of compacted soil–cementmixtures.

Experimental programme

Materials and processing of soils

The study analyses 15 soils with different grain size andmineralogy (Table 1): five natural soils, a kaolin and nineblended soils.In particular, seven blended soils were prepared by

mixing Ticino sand, as coarse fraction, and a kaolin or abentonite or both, as fine fraction. Ticino sand is a wellknown uniformly graded sand, composed mainly of quartz(further details are given in Baldi et al., 1981). A commercialkaolin, a calcium bentonite and a combination of them wereselected as representative of a wide range of plasticity. Theirmain characteristics are shown in Table 2. The bentonite wasused up to a maximum percentage of 37.5% because of itshigh plasticity, which makes the soil unworkable.All these blended soils are labelled by a symbol indicating

the composition and quantity of the fine fraction. Inparticular, B, K and BK means that the fine fraction is

Table 1. Main characteristics of the soil investigated

Grain-size characteristics Consistency limits*

Soil

Sand, SF (4.75 mm–

75 �m): %

Clay, CF

(,2 �m): %

Fine fraction, FF

(,75 �m): %

Passing No. 40, P40

(,420 �m): %

D50:

�m

D30:

�m

Liquid limit,

LL: %*

Plasticity index,

PI: %*

Fine

activity, AF USC

K100 0 25 100 100 3 2.2 46 14 0.56 ML

K75 25 18.75 75 77 3 2.2 44 (45) 12 (14) 0.56 ML

K50 50 12.5 50 54 75 3.4 43 (43) 11 (13) 0.56 ML

K25 75 6.25 25 30 650 400 37 (38) 11 (12) 0.56 SM

B25 75 19.5 25 30 650 450 103 (101) 64 (62) 0.97 SC

BK75 25 38.6 75 77 3 1.3 80 (78) 48 (45) 0.90 CH

BK50 50 25.8 50 54 75 2.5 78 (75) 45 (43) 0.90 CH

BK25 75 12.9 25 30 650 400 67 (66) 42 (38) 0.90 SC

N1 15 35 85 94 5 1.5 44 20 0.57 CL

N2 0 45 100 100 2.5 0.9 55 30 0.67 CH

N3 13 28 87 97 7 2.5 48 21 0.75 CL

N4 44 17 56 95 65 9 31 7 0.41 ML

N5 12 32 88 97 11 1.5 42 18 0.56 CL

N1.25 79 8.8 21 27 650 400 37 (36) 19 (17) 0.57 SC

N2.25 75 11.3 25 30 650 400 47 (45) 26 (25) 0.67 SC

* Values in brackets calculated with equation (1).

78

Bellezza and Fratalocchi


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bentonite, kaolin, and half bentonite and half kaolin respec-tively; the number in the label represents the fine percent-age; the complement to 100% is the Ticino sand. Forexample, BK25 is a soil with 12.5% bentonite, 12.5% kaolinand 75% Ticino sand; K100 is the kaolin.In addition, five natural fine-grained soils (N1 to N5) were

analysed, including data for two soils considered in previousstudies (Bellezza et al., 1995; Bellezza, 1996). Finally, twofurther blended soils were investigated (N1.25 and N2.25),obtained by mixing 25% of a natural soil (N1 or N2) and75% of the Ticino sand.For all the blended soils the Atterberg limits were meas-

ured (Tables 1 and 2), and they were found to be consistentwith the values calculated by the following equation(Winterkorn and Pamucku, 1991).

X ¼ X(1)P40(1)S(1) þ X(2)P40(2)S(2)

P40(1)S(1) þ P40(2)S(2)(1)

where S(1) and S(2) are the percentages of soils 1 and 2respectively; P40(1) and P40(2) are the percentages passingsieve No. 40 in soils 1 and 2 (for Ticino sand, P40 ¼ 7%); X(1)

and X(2) are the plasticity index PI (or liquid limit LL) ofsoils 1 and 2; and X is PI (or LL) for the blended soil.The final database of Table 1 contains a quite wide range

of soils. For example, the plasticity index ranges from 7% to57%, the fine percentage (, 75 �m) ranges from 21 to 100,and the clay content (, 2 �m) ranges from 6% to 45%.All the soils investigated, except B25, were selected or

prepared taking into account the recommendation by Daniel(1993) concerning the plasticity index of soils for compactedbarriers, in order to assure good workability (PI lower than50%). Soils with high clay contents were not examined inthis study because they have poor practical application, asthey are difficult to pulverise before cement addition andmay result in systems with excessive shrinkage properties,and a consequent increase in the overall permeability.A slag cement (type III/B ordinary Portland cement/

ground granulated blast-furnace slag; Table 3) was selected,mainly because of its better resistance against chemicalattack than that of ordinary Portland cement. For this reasonit is suitable to be used for earthworks in aggressiveenvironments, typically in compacted soil liners for wastelandfills (Manassero et al., 1994).

Sample preparation and testing procedures

The experimental programme included tests on com-pacted soils and soil–cement mixtures. Each soil was firstpulverised, carefully mixed (if blended), and then wetted toa predetermined moisture content and kept for at least 24 hin a sealed plastic bag for moisture equilibration. Themixtures were obtained by mixing a constant quantity ofcement, c, equal to 5% of the soil dry weight. The cementwas added to wetted soil (and not to the dry soil, asrecommended by ASTM (1997)) because this reflects the in

situ procedure when the soil has a proper natural watercontent and does not need to be wetted, as frequentlyoccurs. Considering that delayed compaction results in avariation in the dry unit weight (Arman and Saifan, 1967)and in a potential variation of hydraulic conductivity, allsamples were compacted with a Standard Proctor compac-tion effort immediately after mixing. To reduce the consoli-dation time before permeation, one single layer wascompacted (sample height ¼ 3.5 cm; diameter ¼ 10.16 cm).Only the data for soils N3 and N4 refer to samples ofstandard dimensions (height ¼ 11.65 cm).Permeability tests were set up immediately after compac-

tion in flexible wall permeameters (ASTM, 2003), withmaximum effective confining stress and back-pressure equalto 45 kPa and 400 kPa respectively; the hydraulic gradientranged from 15 to a maximum of 30.All the samples were first saturated and consolidated and

then permeated with tap water after 5 days from setting up,so that all the samples had the same curing conditions. Thisaspect is important, because the curing conditions have beenfound to strongly affect the hydraulic conductivity of soil–cement mixtures (Bellezza and Pasqualini, 1997). All themeasured k-values refer to saturated samples; control ofsaturation was effected by the Skempton B coefficient,according to Black and Lee (1973). It was observed that the Bvalues measured at the beginning of the saturation phase forthe compacted mixtures were very low, and systematicallylower than those from the corresponding untreated soil; forthis reason a high value of back-pressure was applied.

Water content

It is well known that the hydraulic conductivity ofcompacted fine-grained soils depends strongly on the moist-ure water content w, and that lower permeability values canbe obtained for water contents wet of optimum (Mitchell etal., 1965; Daniel and Benson, 1990). To compare the resultsfrom samples with and without cement, for each soilpermeability tests were performed on samples compacted atthe same water content wet of optimum (2–3%). This hasrequired construction of the compaction curves for all thesoils and soil–cement mixtures investigated. Consideringthe inevitable approximation to identify the optimum watercontent and to obtain exactly a predetermined water content,a range from 1% to 4% wet of optimum was accepted for thewater content of the samples to be tested. This range istypically required in the construction specifications for clayliners (e.g. Benson et al., 1999).

Table 2. Main data for fine fraction of blended soils

LL:

* %

PI:

* %

CF:

% A GS

Kaolin (Rotoclay-HB) 46 14 25 0.56 2.65

Bentonite (Bentosund AU/C) 122 75 77 0.97 2.77

50% Bentonite + 50% Kaolin 80 (84) 46 (45) 51 0.90 2.71

*Values in brackets calculated with equation (1).

Table 3. Physical-chemical properties of cement type used in this study

Property Value

Specific gravity, Gs 2.96

Blanie fineness: cm2/g 4110

Calcium oxide, CaO: % 48.83

Magnesium oxide, MgO: % 5.30

Ferric oxide, Fe2O3: % 1.39

Sulphur trioxide: SO3: % 1.5

Potassium oxide: K2O: % 0.50

Sodium oxide: Na2O: % 0.31

Silicon dioxide: SiO2: % 30.55

Aluminium oxide: Al2O3: % 9.63

Loss of ignition: % 1.02

Insoluble residue: % 1.5

79

Hydraulic conductivity of compacted soil–cement mixtures


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The addition of cement to a wetted soil results in areduction of its water content, owing to the increase of solidsand to the cement hydration process. Therefore the watercontent of the soil before mixing with cement (w0) mustnecessarily be higher than the target value (wc ¼ 2–3% wetof optimum). In this work, w was roughly assessed consider-ing a loss of 1% during the sample preparation (soilmoistening, mixing, compaction and cement hydration), asfollows:

w0 ¼ wc 100þ cð Þ þ 1 (2)

where c is the cement percentage by dry weight.

Results and analysis

Figure 1 shows the compaction curves of all soils listed inTable 1, with and without 5% cement. As expected, for theblended soils the higher the sand percentage is, the higher isthe dry density and the lower the optimum water content(compare, for example, soils K100, K75, K50 and K25 in Fig.1 and Table 4). For most soils, the compaction curves withand without cement are very similar (notwithstanding thegrain size and chemical modifications). In particular, theaddition of 5% cement does not significantly modifythe optimum water content: the differences are always lessthan 1% (Table 4). This result has an important practicalimplication in the design phase: as it is the wet-sidecompaction content that minimises the hydraulic conductiv-ity, the best hydraulic performance of a soil–5% cementmixture can be searched for with reference to the compac-tion curve of the untreated soil, without developing furthercurves.As far as hydraulic conductivity is concerned, the results

of the permeability tests performed on all the investigatedsoils, with 5% cement and without cement (untreated soils)are reported in Fig. 2 and Table 4, and are discussed in thefollowing.

Untreated soils

Various criteria based on soil properties have beenproposed in the literature in order to achieve low hydraulicconductivity values with soils compacted wet of optimum:in particular, Daniel (1993) recommends a minimum finepercentage ranging from 20% to 30% to achieve a hydraulicconductivity , 1 3 10�7 cm/s together with a plasticityindex greater than 7–10%. More restrictive criteria have beenproposed by Benson et al. (1994), including a minimum clayfraction ¼ 15%, liquid limit . 20% and activity > 0.3. Thenatural soils investigated in this study fully satisfy both theaforesaid criteria. As expected, the measured k-values arelower than 1 3 10�7 cm/s, as shown in Fig. 3. For theblended soils and the kaolin the criteria of Daniel (1993) andBenson et al. (1994) are not applicable. For soils with a finepercentage ranging from 20% to 30% variations in per-meability of two or three orders of magnitude can occur,depending on the soil plasticity (Fig. 3). In particular, soilscontaining bentonite have hydraulic conductivity valueslower than 1 310�7 cm/s, in accordance with the wellknown hydraulic behaviour of compacted sand–bentonitemixtures (e.g. Daniel, 1987; Chapius, 1990), whereas soilswith low plasticity are much more permeable. For the lattersoils the effect of the cement addition is particularlyimportant to evaluate.

Effectiveness of cement

The results in Fig. 2 and Table 4 show that the permeabil-ity of clayey soil can be increased by the addition of 5%cement: this is due mainly to the cement hydration process,which increases the Caþþ concentration of the pore waterwith consequent modification of the surface chemistry of theclay particles and flocculation (Mitchell, 1992).The addition of cement results not only in a structural

modification due to chemical interaction with water and soilparticles, but also in a variation of grain-size distribution.This aspect can affect the mixture’s hydraulic conductivity,especially for soils with a fine fraction in the range 20–30%,which may have high k values. In order to highlight thispossible effect, a special sample of the blended soil K25 wasprepared by replacing the 5% cement with the same quantityof kaolin, which is similar to the cement in terms of grainsize. The results of the permeability tests are compared inFig. 4, which clearly demonstrates that a small variation ofthe grain-size distribution can itself significantly contributeto the permeability reduction, when the fine fraction is about25%. In particular, a reduction of permeability of two ordersof magnitude is achieved by adding 5% of fine soil; theaddition of 5% cement instead of fine soil further reducesthe permeability with curing time (Fig. 3).The cement hydration process produces a reduction in the

hydraulic conductivity over time for all the mixtures, as isclearly shown in Fig. 2. This phenomenon, well known inthe literature (e.g. Brandl, 1992), is due to a reduction inboth the soil porosity and the size of the voids between soilparticles; the availability of water due to immediate permea-tion has surely favoured this process (Bellezza, 1996). Theresults in Fig. 2 show that the factors affecting the per-meability of soil–cement mixtures include the soil mineral-ogy and the initial hydraulic conductivity value. Furtherinvestigations are being performed, based mainly on ana-lyses of soil–cement chemical interactions; in this paper theeffectiveness of cement with reference to the untreated soilis focused on.The effectiveness of cement addition in modifying the k

value was quantified by two non-dimensional factors: theefficiency factor Ek and the acceptability factor Ak, definedas follows:

Ek ¼ k0kc

(3)

Ak ¼ kakc

(4)

where k0 is the hydraulic conductivity of the untreatedcompacted soil, kc is the hydraulic conductivity of thecompacted soil with 5% cement, and ka is the maximumacceptable hydraulic conductivity. The efficiency factor ex-presses the relative variation of the hydraulic performancedue to the addition of cement (Ek .1 means a reduction inhydraulic conductivity in comparison with the untreatedsoil; Ek , 1 means an increase), whereas Ak expresses theabsolute value of k normalised to the reference k value for aspecific design. Therefore Ak allows us to verify whether theaddition of cement matches the design requirements. In thisstudy the acceptable value of ka is assumed to be 1 3

10�7 cm/s (usually required for hydraulic barriers).Because of the reduction of kc with time, both Ek and Ak

tend to increase as the curing time increases. Therefore tworepresentative values of curing time were considered for Ek,7 days and 28 days (termed Ek7 and Ek28 respectively),whereas Ak was evaluated at 28 days’ curing, as the target

80



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Fig. 1. Compaction curves of soils (c ¼ 0%) and soil–cement mixtures (c ¼ 5%) (solid symbols indicate permeated samples): (a) N1; (b) N2; (c) N3; (d) N4;(e) N5; (f) K100; (g) K75; (h) K50; (i) BK75; (j) BK50; (k) K25; (l) BK25; (m) B25; (n) N1.25; (o) N2.25

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hydraulic conductivity value is commonly referred to thiscuring time.

Statistical analysis

Several studies indicate that the factors influencing thehydraulic conductivity of compacted clay liners include soilcomposition and structure, water content relative to opti-mum, compaction effort, effective stress, and permeant char-acteristics (e.g. Lambe, 1958; Mitchell et al., 1965; Garcia-Bengochea et al., 1979; Acar and Olivieri, 1989; Daniel andBenson, 1990; Shackelford, 1994). Taking into account theparticular conditions followed in this study for specimenpreparation and testing, a statistical analysis was conductedusing the variables related to Atterberg limits (liquid limitLL, plastic limit PL, plasticity index PI) and grain sizedistribution: clay fraction (CF), fine fraction (FF), sandfraction (SF), fraction passing the ASTM No. 40 sieve (P40),and particle diameters corresponding to 50% and 30% finer(D50 and D30) on the cumulative particle size distributioncurve (Masch and Denny, 1966). The effective grain size D10

(Hazen, 1911) and the related coefficients (e.g. the uniformitycoefficient Cu ¼ D60/D10), were not considered because theD10 value was not available for all the soils investigated (asoften occurs with fine-grained soils), and an arbitrarymethod of extrapolation would have been necessary.The activity A, as defined by Skempton (1953), was

included in the regression analysis, even though it is poorlyreliable in blended soils. For example, all the blended soilswith kaolin as fine fraction would have a very differentactivity as they have similar plasticity indices (PI ¼ 11–12%)but a very different fine fraction (25–75%); moreover, thevalue of activity calculated for soil K25 (A ¼ PI/CF ¼ 11/6.25 ¼ 1.76) should indicate Ca-montmorillonite as claymineral, whereas the actual clay mineral is kaolinite. There-fore a further parameter related to the soil mineralogy wasincluded in the analyses, defined as the activity of the finefraction (AF) of the blended soils (A and AF coincide fornatural soils).As far as compaction variables are concerned, the percent-

age compaction was not included in the analysis, on thebasis of the results of previous studies (Benson et al., 1999),which showed that no trend is evident between hydraulicconductivity and percentage compaction. The initial degreeof saturation Si was considered as a parameter reflectingboth dry unit weight (i.e. void ratio) and water content atcompaction, because it was found to be unequivocallyrelated to the hydraulic conductivity of soil compacted atdifferent compaction efforts (Fratalocchi et al., 1993; Bensonet al., 1994). For treated soil the weighted average of specificgravity was considered to calculate Si(c). The optimum watercontent, wopt, and the water content wet of optimum (w �wopt) were also considered as variables.Some of the aforesaid variables were considered with

functional forms (logarithmic, cubic, inverse); they weredifferently combined (e.g. CF/FF, PL/LL, etc.), also on thebasis of results from the literature: PI + CF (Tavenas et al.,1983); log(D50) 3 PL (Wang and Huang, 1984); SF � CF(Basma and Tuncer, 1992). In all, 40 variables (somecorrelated) were considered; they are listed in the Appendix.The base-10 logarithms of Ek and Ak were used in the

regression analysis, because it is commonly accepted thatpermeability is log-normally distributed (Wang and Huang,1984; Boutwell and Hedges, 1989; Benson et al., 1999; Boadu,2000).The statistical analyses were performed by the commercial

program CoStat (Jones, 1998–2003), which provides a list ofTable4.Maindata

forsamples

forperm

eabilitytests

Cem

ent¼

0%

Cem

ent¼

5%

Soil

wopt(

0):

%w

:%

ªd:kN

/m3

Gs

S i(0

):%

k 0:cm

/sw

opt(

c):%

wc:%

ªd:kN

/m3

Gs

S i(c

):%

k c7:cm

/sk c

28:cm

/s

K100

29. 0

31. 6

13. 6

2. 6

591. 9

4. 03

10�

728. 5

32. 2

13. 5

2. 6

65

91. 6

7. 33

10�

87. 53

10�

9

K75

17. 5

21. 0

15. 7

2. 6

53

84. 7

3. 13

10�

718. 5

21. 6

15. 6

2. 6

67

85. 1

1. 23

10�

77. 03

10�

9

K50

13. 0

15. 9

17. 6

2. 6

55

88. 0

2. 23

10�

713. 3

16. 0

17. 7

2. 6

70

89. 1

3. 73

10�

83. 03

10�

9

K25

11. 0

12. 3

18. 8

2. 6

58

84. 5

4. 03

10�

511. 0

12. 1

19. 1

2. 6

72

86. 8

1. 23

10�

74. 23

10�

8

B25

18. 0

19. 7

16. 4

2. 6

88

87. 1

9. 03

10�

917. 5

20. 1

16. 9

2. 7

00

95. 6

1. 83

10�

86. 33

10�

9

BK

75

28. 8

31. 6

13. 5

2. 6

98

88. 8

2. 43

10�

829. 0

31. 5

13. 7

2. 7

10

90. 8

2. 93

10�

71. 93

10�

7

BK

50

19. 5

20. 8

15. 9

2. 6

85

85. 1

2. 43

10�

818. 8

19. 9

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models containing a specified number of independent vari-ables (nXs). Taking into account the limited number ofexperimental data (15), only models containing a maximumof three variables were considered. This allowed us toinvestigate all combinations of the selected variables avoid-ing heuristic methods (e.g. stepwise regression).The best model was selected on the basis of the coefficient

of multiple determination R2, which indicates how much ofthe variation in the dependent variable can be explained bythe independent variables. For each model, further statisticalindicators were evaluated (Tables 5 and 6): the standarderror of estimate SEE, and the adjusted coefficient ofdetermination R2, which adjusts for the number of indepen-dent variables in the model, so that R2 for models ofdifferent sizes can be directly compared. The reliability ofthe best model was assessed by the so called ‘leave one outR2’ (LOO R2), where each predicted value of the dependentvariable is calculated doing a regression without that row ofdata.Tables 5 and 6 also include R2

10, which is the value of R2

related to the tenth best model: a high value of R210 means

that at least 10 different models were found that give a goodprediction.

Regression models on Ak

Regression models on Ak were investigated both for theentire database and for fine-grained soils.The first regression analysis was conducted on the entire

database. The results for models with one or two indepen-dent variables are completely unsatisfactory (see Table 5).With three parameters the equation of best fit is

logAk ¼ �0:517þ 0:736 wc � wopt(c)ð Þ � 0:0903wopt(c)

þ 0:498LL

PL:AF(5)

where wc and wopt(c) are expressed as percentages. Fig. 5shows a plot of the measured Ak values against thecomputed values using the regression equation (5). Thestraight line in the figure represents the line of perfectequality, where the values being compared are exactly equal;the dashed lines indicate the 90% confidence interval.Similarly to natural compacted soils, equation (5) indicatesthat the permeability of compacted soil–cement mixturestends to decrease as the water content wet of optimum

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Fig. 3. Hydraulic conductivity of untreated soils against fine percentage and plasticity index

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Fig. 4. Influence of addition of 5% cement on hydraulic conductivity of blended soil with fine percentage ¼ 25%

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increases, notwithstanding the narrow range investigated(1.1–3.7%; Table 5).The accuracy of the model assessed by the LOO R2 value

(¼ 0.366) makes equation (5) poorly reliable, in spite of thequite satisfactory values of R2 (¼ 0.649) and SEE (¼ 0.361).This suggests that, with only three variables, it is impossibleto find a good model for Ak that is valid for all soil types.Moreover, equation (5) includes the determination of theoptimum water content, which requires the soil to becompacted, and the fine activity, whose definition inblended soils is questionable, as previously discussed.Therefore the multiple analysis regression was repeated

considering only the data referred to fine-grained soils(defined according to the Unified Soil Classification System:ASTM, 2000). Because only 10 sets of data are available(Table 1), one- and two-variables models were investigated.A significant improvement in all the statistical indicatorswas obtained (Table 5). In particular, the following best-fitequations were obtained by models with one and twoparameters respectively.

logAk ¼ 1:445� 11:7CF

FF

� �3

(6)

Table 5. Results of regression analyses for prediction of Ak

Dependent variable Database nXs Variables in the best model R2 R2 LOO R2 SEE R210

log Ak Entire 1 LL.CF/PL 0.220 0.160 0.023 0.538 0.049

log Ak Entire 2 wopt(c) 0.575 0.504 0.354 0.397 0.308

wc-wopt(c)

log Ak Entire 3 wopt(c) 0.649 0.553 0.366 0.361 0.595

wc-wopt(c)

LL/(PL.AF)

log Ak Fine-grained soils 1 (CF/FF)3 0.851 0.832 0.792 0.235 0.581

log Ak Fine-grained soils 2 (CF/FF)2 0.873 0.837 0.773 0.217 0.862

Si(c)

Table 6. Results of regression analyses for prediction of Ek

Dependent variable Database nXs Variables in the best model R2 R2 LOO R2 SEE R210

log Ek7 Entire 1 CF 0.660 0.634 0.562 0.703 0.327

log Ek7 Entire 2 CF/FF

D30

0.887 0.868 0.827 0.405 0.837


D30

Si(0)/Si(c)

0.897 0.869 0.787 0.386 0.891

log Ek28 Entire 1 LL.CF/PL 0.625 0.596 0.511 0.836 0.263


D30

0.805 0.772 0.688 0.603 0.741

log Ek28 Entire 3 D30

PI

1/LL

0.865 0.828 0.772 0.502 0.833

log Ek7 Fine-grained soils 1 CF/FF 0.902 0.889 0.861 0.249 0.560

log Ek7 Fine-grained soils 2 CF/(FF.AF)

1/LL

0.978 0.972 0.957 0.117 0.936

log Ek7 Fine-grained soils 2 (CF/FF)2

PI*

0.946 0.931 0.887 0.184 –

log Ek28 Fine-grained soils 1 CF/FF 0.923 0.914 0.890 0.285 0.600

log Ek28 Fine-grained soils 2 CF/FF

1/LL

0.986 0.982 0.976 0.121 0.975

* Neglecting variables containing AF.

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logAk ¼ �1:83� 6:99CF

FF

� �2

þ 0:0398Si(c) (7)

where Si(c) is a percentage .The Ak values predicted by equations (6) and (7) are

plotted against the measured values in Fig. 6. Both equations(6) and (7) indicate that it is not the fine percentage itselfthat governs the hydraulic behaviour of the soil–cementcompacted mixtures, but the clay content relative to finefraction; in particular, the higher this ratio is the lower arethe Ak values (i.e. the higher the mixture hydraulic con-ductivity). Equation (7) includes a term related to compac-tion procedure (Si(c)), the significance of which wasevaluated using the partial F-statistic (Draper and Smith,1981), giving F ¼ 46.6 and F ¼ 1.7 for (CF/FF)2 and Si(c)

respectively. As the latter variable results in a statisticallyinsignificant variable (Benson et al., 1999), equation (6)should be preferred to equation (7) to estimate the accept-ability factor Ak.The hydraulic conductivity values can be safely estimated

by equation (6) also for curing times longer than 28 days,considering that the hydraulic conductivity of soil–cementmixtures tends to reduce with time.

Regression models on Ek

The same procedure as followed to analyse Ak values wasrepeated for the data on the efficiency factor at 7 days’

curing (Ek7) and at 28 days (Ek28). Table 6 summarises theresults of the statistical analyses.

All soilsConsidering the entire database (fine-grained and sandy

soils) the SEE is quite high, and the accuracy of predictiondecreases with curing time; in particular, the followingprediction equations could be used for a rough estimation ofthe efficiency factor at 7 days’ curing.

log Ek7 ¼ 2:27� 6:68CF

FFþ 5:77D30 (8)

log Ek7 ¼ �3:62� 6:03CF

FFþ 5:81D30 þ 5:69

Si(0)

Si(c)(9)

where D30 is expressed in millimetres. Fig. 7 shows acomparison between the measured values of Ek7 and thosepredicted with equations (8) and (9).Both equations (8) and (9) suggest that:

(a) the efficiency factor is higher the greater is D30 (withinthe range investigated, D30 ¼ 9 3 10�4 to 4.5 3

10�1 mm); this means that the coarser the soil is, thehigher is the reduction of the hydraulic conductivity bya 5% cement, other factors being equal

(b) the greater the clay content of the fine fraction is, thelower is the efficiency of the cement addition (for clayto fine fraction ratios ranging from 0.25 to 0.78).

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The R2 and R2 values of equation (8) are slightly lower thanthose of equation (9) (see Table 6), but equation (8) is muchsimpler for practical application because it does not includecompaction variables; moreover, Si(0)/Si(c) was found to bestatistically insignificant (F ¼ 1.1).For prediction of Ek values at 28 days’ curing (Ek28), only

three variables-models were found to be satisfactory (Table6); in particular, the best model for all soil types is describedby the following equation.

log Ek28 ¼ 8:21þ 6:46D30 � 0:141PI� 217:31

LL(10)

As shown in Fig. 8, the predicted values approach theobserved ones quite well.

Fine-grained soilsThe statistical analyses were then limited to fine-grained

soils, considering that for these soils the effectiveness ofcement addition is doubtful. The best-fit equations given bymodels with one and two variables are as follows.

log Ek28 ¼ 3:88� 9:39CF

FF(11)

log Ek28 ¼ 6:17� 11:9CF

FF� 65:1

1

LL(12)

The statistical parameters in Table 6 show that the modeldescribed by equation (12) is highly reliable for predictingEk28 values (R2 ¼ 0:982). The values of the partial F-statistic(466.5 and 31.7) prove the high significance of the indepen-dent variables of equation (12).

In Fig. 9 the computed values of Ek28 using equation (12)are compared with the measured values.As far as Ek7 is concerned, the following prediction

equations were obtained considering only the fine-grainedsoils.

log Ek7 ¼ 2:46� 7:16CF

FF(13)

log Ek7 ¼ 0:496� 5:24CF

FF:AFþ 111:3

1

LL(14)

It can be observed that, when the curing time is varied (7and 28 days), the best models of Ek include the same soilparameters; in particular, the ratio of clay fraction to finefraction seems to be a good indicator of Ek (and of Ak, too,as shown by equations (6) and (7), although in differentfunctional forms).Equation (14) should be used with caution, because it

contains the activity of the fine fraction. Therefore the bestmodel neglecting the parameters containing AF wassearched for. As shown in Table 6, the prediction can beconsidered satisfactory (R2 ¼ 0.946 and SEE ¼ 0.184), withthe following equation.

log Ek7 ¼ 1:22� 16:5CF

FF

� �2

þ 0:0434PI (15)

Figure 10 shows a comparison of the predicted and meas-ured values of Ek7 with equations (14) and (15).

Sandy soilsStatistical analyses on mixtures of sandy soil and cement

were not performed because of the lack of a sufficient

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Fig. 10. Measured Ek7 values against computed values using regressionmodel of: (a) equation (14); (b) equation (15)

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number of experimental data and the absence of naturalsandy soils. In the absence of specific equations, theefficiency factors of sandy soil–cement mixtures can beroughly evaluated by the equations found for the entiredatabase (sandy and fine-grained soils): equation (8) andequation (10) for Ek7 and Ek28 respectively:It is important to point out that, for all the sandy soils

tested, a quantity of 5% cement is sufficient to achieve ahydraulic conductivity lower than 1 3 10�7 cm/s (the meas-ured Ak are always greater than 1, as shown in Fig. 5) and areduction of permeability after 28 days’ curing was alwaysfound in comparison with the untreated soil (Figs 2 and 8).

Practical applications

The aforesaid prediction models can be used effectively toassess the hydraulic performance of compacted soil–cementmixtures on the basis of simple hydraulic conductivityrelated to the grain size distribution and consistency limitsof the soil. In particular, for fine-grained soils the hydraulicconductivity value at 28 days’ curing can be easily estimatedin the design phase by equation (6). Permeability tests onmixtures of soil and 5% cement with a predicted Ak , 1 canbe avoided, and mixtures with cement percentages greaterthan 5% can be directly investigated.If hydraulic conductivity values of the compacted un-

treated soil are available, for sandy soils the effectiveness ofthe addition of 5% cement can be roughly assessed byequation (10). For fine-grained soils a more accurate predic-tion arises from equation (12); for these soils a rapidestimation of the efficiency factor can be made by a newvariable called the fine index (FI), and defined as

FI ¼ CF

FFþ 5:47

LL(16)

so that equation (12) becomes:

log Ek28 ¼ 6:17� 11:9FI (17)

The values of Ek28 are plotted against the FI values in Fig.11; the dashed lines indicate the 90% confidence interval.The intercepts of these lines with the line Ek28 ¼ 1 demarcatea critical range of FI: in particular, when FI is lower than0.50 the addition of 5% cement results in a decrease inhydraulic conductivity, whereas for FI greater than 0.54 anincrease in the k-value with respect to untreated soil isexpected (Ek28 , 1).However, Ek28 itself is not sufficient for the soil screening.

A soil with Ek28 . 1 does not mean that the mixture achievesan acceptable hydraulic conductivity; on the other hand,soils with Ek28 , 1 could give acceptable k-values. To thispurpose, Fig. 11 allows us also to estimate the range of thehydraulic conductivity value for a given soil–cement mix-ture, once the hydraulic conductivity of the untreated soil isknown.

Conclusions

Laboratory compaction and permeability tests were per-formed on 15 soils with different grain size distributions andmineralogy. The effectiveness of the addition of 5% blastfurnace slag cement was evaluated by comparing thehydraulic conductivity values measured on samples oftreated and untreated soils, both compacted 1–4% wet ofoptimum with a Proctor standard effort. The followingconclusions can be drawn.

(a) For soils (natural or blended) with a fine fraction . 20%and plasticity index . 7%, the measured hydraulicconductivity values of soil–5% cement mixtures at 28days were always lower than 23 10�7 cm/s. Thismeans that an addition of 5% cement can be sufficientto ensure a good hydraulic performance, provided thatthe in situ mixing procedure is performed carefully andthe compaction and curing conditions are similar tothose in the laboratory (compaction effort, availability ofwater, and protection against desiccation).

(b) Based on regression analyses, empirical correlationsbetween the hydraulic conductivity of soil–5% cementmixtures and soil composition parameters have beenproposed that fit the experimental data very well,especially for fine-grained soils.

(c) The most significant parameter affecting the hydraulicperformance of fine-grained soils was found to be theratio of the clay fraction to the fine fraction (bothefficiency factor Ek and acceptability factor Ak alwaysresulted inversely proportional to this ratio).

(d) The proposed prediction models can be considered auseful tool for designing compacted soil–cement liners,provided that the soil has geotechnical properties lyingin the range investigated. The proposed equations areuseful in the design phase to predict whether or not agiven soil is suitable for the cement addition when alow hydraulic conductivity value is requested. Expen-sive and time-consuming tests can be avoided forunsuitable soils, and higher cement contents can bedirectly investigated. However, permeability tests arerecommended for confirming the predicted value,whenever acceptable.

Appendix: Variables of the statisticalanalyses

1. Clay fraction, CF2. Fine fraction, FF3. Sand fraction, SF4. Fraction passing No. 40 sieve, P40

5. Diameter corresponding to 50% passing, D50

6. Diameter corresponding to 30% passing, D30

7. Liquid limit, LL8. Plastic limit, PL9. Plasticity index, PI10. Activity, A

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Fig. 11. Design chart to assess the efficiency factor Ek28 of fine-grainedsoils

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11. Fine activity, AF

12. Optimum water content of soil–5% cement mixture,wopt(c)

13. Water content wet of optimum of soil–5% cementmixture, wc-wopt(c)

14. Initial degree of saturation of compacted soil–5% ce-ment mixture, Si(c)

15. Initial degree of saturation of compacted untreated soil,Si(0) (for regression analyses on Ek only)

16. S3i(c)

17. A�1F

18. LL�1

19. PL�1

20. log(LL)21. log(PL)22. LL/PL23. PL/LL24. PI/(LL � 20)25. LL/AF

26. CF/FF27. (CF/FF)2

28. (CF/FF)3

29. CF/LL30. SF � CF31. PI + CF32. D50/D30

33. P40/FF34. log(D50)35. PL.log(D50)36. Si(0)/Si(c) (for regression analyses on Ek only)37. CF/(FF.AF)38. CF.AF/FF39. LL/(PL.AF)40. CF.LL/PL

Acknowledgements

The authors are grateful to Professor Erio Pasqualini forhis valuable suggestions and discussion during preparationof this paper. M. Mercuri, R. Fentini and R. Mavelli areacknowledged for their help in laboratory tests.

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Discussion contributions on this paper should reach theeditor by 2 October 2006

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