Engineering Geology 105 (2009) 44–50

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Engineering Geology

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Drying response and effective stress in a double porosity aggregated soil

A.R. Bagherieh a, N. Khalili b,⁎, G. Habibagahi a, A. Ghahramani a

a Department of Civil Engineering, Shiraz University, Shiraz, Iranb School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia

⁎ Corresponding author. Tel.: +612 9385 5074; fax: +E-mail address: n.khalili@unsw.edu.au (N. Khalili).

0013-7952/$ – see front matter © 2008 Elsevier B.V. Adoi:10.1016/j.enggeo.2008.12.009

a b s t r a c t

a r t i c l e i n f o

Article history:

Shrinkage and water retenti Received 24 April 2008Received in revised form 9 December 2008Accepted 19 December 2008Available online 6 January 2009

Keywords:Double porosityAggregated soilsShrinkageEffective stressUnsaturated soils

on characteristics of a double porosity compacted soil are studied. Results from aseries of suction controlled oedometric drying tests at different net stresses are presented. Water retentioncurves exhibit a bimodal response which is a characteristic of the double porosity structure of the soil.Validity of the expression proposed by Khalili et al. [Khalili, N., Witt, R., Laloui, L., Vulliet, L., Koliji, A., 2005.Effective stress in double porous media with two immiscible fluids. Geophys. Res. Lett. 32 (15): Art. No.15309.] for the determination of the effective stress in double porosity media is investigated. It is shown thatquantitative predictions of volume change in unsaturated aggregated soils can be made using the effectivestress concept.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Natural and made geomaterials frequently exhibit two scales ofporosity, with micro pores surrounded by macro pores such as thoseencountered in fractured rock formations (e.g. see Burger andShackelford, 2001;Mandique et al., 2007). In soils, double porositinessmay arise due to root holes, worm holes and cracks (Jongmans et al.,2003), or the aggregated nature of the medium (Coppola, 2000).Fissuring and cracking are most commonly observed in heavilyoverconsolidated and desiccated clays (Garga, 1988), whereas aggre-gation occurs in agricultural soils and compacted soils, particularlywhen the soil is compacted on the dry side of the optimum moisturecontent (Romero et al., 1999). In addition to showing two scales ofporosity, the void space in natural soils is frequently filled with morethan one fluid implying the need for a multi-phase constitutivemodelling approach (Khalili, 2008).

A substantial amount of work has been undertaken in the field ofdouble porosity media over the past four decades. Some of the notablecontributions include: field and laboratory investigations of Evans(1966), Gringarten et al. (1975), Bawden et al. (1980), Garga (1988),Federico and Musso (1991), Mayo and Koontz (2000), Khalili (2003),Illman and Neuman (2003) and Mandique et al. (2007); theoreticaldevelopments of Barrenblatt et al. (1960), Warren and Root (1963)and Kazemi (1969) for fluid flow through rigid double porosity media;coupled flow and deformation models of Aifantis (1977), Khalili-Naghadeh and Valliappan (1991), Auriault and Boutin (1993), Bai et al.(1993), Khalili and Valliappan (1996), Tuncay and Corapcioglu (1996),Wang and Berryman (1996), and Loret and Rizzi (1999); and multi-

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ll rights reserved.

phase flow and deformation contributions of Lewis and Ghafouri(1997), Bai et al. (1998), Pao and Lewis (2002), Nair et al. (2004) andmore recently Khalili (2008).

Nevertheless, all the above contributions have been confined to thestudy of fluid flow through fissured/fractured porous media, in thecontext of reservoir engineering. Indeed, there have been very fewinvestigations of the mechanical behaviour of aggregated materials,irrespective of their prevalence in agricultural and geotechnical engi-neering. Only recently, Romero et al. (1999) and Coppola (2000)reported experimental data on the behaviour of aggregated doubleporosity soils. However, their investigationwas limited to the hydrau-lic and water retention characteristics of aggregated soils.

In this paper, experimental results are presented on the volumechange as well as water retention characteristics of a laboratory pre-pared aggregated soil. A series of one-dimensional consolidation anddrying tests are performed and analysed. The characteristic features ofthe hydraulic andmechanical response of the soil are investigated, andthe effect of net stress on thewater retention curve and volume changeis highlighted. The application of the effective stress principle (Khaliliet al., 2005) to unsaturated aggregated soils is examined, and it isshown that quantitative predictions of volume change in aggregatedmaterials can be made using the effective stress principle. To theauthors' knowledge, this is the first reported case of investigating theapplicability of the effective stress principle to aggregated soils. Byusing the effective stress principle, the effect of suction and net stresson the soil response is represented by a single stress variable, therebysimplifying the deformation analysis. Observations are also made as tothe existence of suction hardening in unsaturated aggregated soils.

The paper is organised into five sections. Section 2 is devoted to thebasic concepts: the effective stress principle and the suction hardeningin unsaturated soils. Details of the experimental program including the

Fig. 1. Particle size distribution of kaolin.

Table 1Index and physio-chemical properties of kaolin.

Liquid limit, LL (%) 49Plastic limit, PL (%) 29Plasticity index, PI (%) 20N2 μm (%) 33b2 μm (%) 67Quartz (%) 8.5Kalonite (%) 79.5Illite (%) 12Surface area (m2/g) 21.1Specific gravity of solids, Gs 2.63USCS classification ML

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index properties of the test soil, sample preparation technique and thetesting procedure are presented in Section 3. The interpretation of theresults and volume change analysis are presented in Section 4. Thefindings of the investigation are summarised in Section 5.

2. Basic concepts

2.1. Effective stress

The effective stress principle is one of the key axioms of soilmechanics. Expressed as, “that function of the externally applied stressesand the internal fluid pressures which controls themechanical effects ofa change in stress, the effective stress converts a multi-phase, multi-porous media to a mechanically equivalent, single-phase, single-stressstate continuum” (Khalili et al., 2004, 2005; Nuth and Laloui, 2008). Itenters the elastic as well as elasto-plastic constitutive equations of thesolid phase, linking a change in stress to straining or any other relevantquantity of the soil skeleton (Khalili et al., 2004).

For saturated soils, the effective stress is expressed as (Skempton,1961; Nur and Byerlee, 1971),

σV= σ − 1− csc

� �uwI ð1Þ

inwhichσ′ is the effective stress tensor,σ is the total stress tensor, uwis the water pressure, cs is the compressibility of the solid grains, c isthe drained compressibility of the soil, and I is the second orderidentity tensor.

For unsaturated soils, the effective stress is defined as (Bishop,1959),

σV= σ − χuwI − 1− χð ÞuaI ð2aÞor

σV= σnet + χsI ð2bÞin which ua is the pore air pressure and χ is the effective stressparameter, realising a value of 1 for saturated soils and zero for dry soils.σnet≡(σ−uaI) is the net stress, and s≡(ua−uw) is the matric suction.

For aggregated soils, saturated with air and water, the effectivestress is defined as (Khalili et al., 2005),

σV= σ − αm χmumw + 1− χmð Þuma½ �I− αM χMuMw + 1− χMð ÞuMa½ �I ð3aÞ

or

σV= σ − αmumaI − αMuMaIð Þ + αmχmsmI + αMχMsMI ð3bÞ

in which umw, uma, uMw and uMa are the micro pore-water, micropore-air, macro pore-water and macro pore-air pressures, respec-

tively. χm and χM are the unsaturated effective stress parameters ofthe micro pores and macro pores, respectively. sm≡uma−umw is thematric suction of the micro pores and sM≡uMa−uMw is the matricsuction of the micro pores. αm and αM are the conventional effectivestress parameters of saturated double porous media (Khalili andValliappan, 1996),

αm =cgc; αM = 1−

cgc

ð4Þ

in which c is the drained compressibility of the aggregated soil, and cgis the drained compressibility of the material forming the aggregates.

The physical interpretation of χm, χM, αm and αM is that χm and χM

scale/average air andwater pressure in themicropores andmacroporesto equivalentpressures ofmicro pore-fluid andmacro pore-fluid.αm andαM quantify the contribution of these equivalent pressures to theeffective stress of the double porosity medium (Khalili et al., 2005).

Khalili and Khabbaz (1998) showed that for single porosity mediaχm may be estimated as,

χm =sm eð Þsm

� �X

for sm zsm eð Þ

1 for sm Vsm eð Þ

8<: ð5Þ

where exponent Ω is a material parameter, with a best fit value of0.55. sm(e) is the suction value separating saturated from unsaturatedconditions in the micro pores. It is equal to the air entry value, sm(ae),for the main drying path, and the air expulsion value, sm(ex), for themain wetting path (Khalili et al., 2004). For suction values betweenthe main drying and the mainwetting paths an interpolation functionsimilar to that in Khalili et al. (2008) may be used.

Extending the observation of Khalili and Khabbaz (1998) for singleporosity media to macro pores, we then write,

χM =sM eð ÞsM

� �X

for sM zsM eð Þ

1 for sM VsM eð Þ

8<: ð6Þ

inwhich sM(e) represents thematric suction separating saturated fromunsaturated conditions in the macro pores.

2.2. Suction hardening

Suction hardening occurs in unsaturated soils as the combined effectof the pore air and porewater pressures affects the soil behaviour in twodifferentways. Firstly, it increases the effective stress of the soil skeletonthrough the equivalent pore fluid pressures, in the same way that thepore water pressure affects the mechanical behaviour of an equivalentsaturated soil. Secondly, it results in the formation of capillarymenisci atthe particle contact points, which generate inter-particle contact forcesnormal to the plane of contact. These forces tend to stabilize the contactsand inhibit grain slippage, altering the way the soil experiences plastic(non-reversal) deformation subjected to loading (Loret and Khalili,

Fig. 2. Test sample exhibiting double porosity structure with soil aggregates separatedby fine inter-aggregate macro pore.

46 A.R. Bagherieh et al. / Engineering Geology 105 (2009) 44–50

2002; Masin and Khalili, 2008). This effect is manifested by the widelyreported stiffened response of the soil skeleton with increasing suction(see, e.g. Alonso et al.,1990;Wheeler and Sivakumar,1995). This secondeffect, also known as the suction hardening, is conceptually similar to

Fig. 3. Schematics of the fixed ring pre

the chemical bonding in cementedmaterials. It enables the unsaturatedsoil, under a given effective stress, to exist at a higher void ratio than thesame material at the same effective stress when saturated (Masin andKhalili, 2008).

A direct consequence of the suction hardening is that it shifts thepreconsolidationpressure and the soil response enters the elastic regionwhen the increase in the effective stress is less than the increase inpreconsolidation pressure. Accordingly, elastic soil properties are oftenused in the prediction of volume change in unsaturated soils subjectedto increasing values of suction (i.e. a drying test). Another consequenceof the suction hardening is the collapse phenomenon in unsaturatedsoils upon wetting (Alonso et al., 1990; Wheeler and Sivakumar, 1995).

Early experimental data on the behaviour of unsaturated soilsappeared to suggest that suction hardening is a ubiquitous feature ofunsaturated soils. However, themore recentdata show that thismaynotbe the case, and certain soils experience little or no suction hardening(e.g. see Uchaipichat, 2005; Russell and Khalili, 2006; Thu et al., 2007).

3. Experimental program

The experimental program consisted of four drying tests and threesaturated one-dimensional consolidation tests. The soil used in theexperiments was a commercially available kaolin. The grain size dis-tributionof the soil is given in Fig.1. Indexandphysio-chemical propertiesare given in Table 1.

To make reproducible aggregated specimens, a sample preparationtechnique similar to that of Wheeler and Sivakumar (1995) wasadopted. Air dried powdered kaolin was carefully wetted with a spraygun to the target water content of 25% and placed in a sealed plastic bagand allowed to cure for 24 h formoisture equalisation. Themixwas thenbroken by hand and passed through a 2.36 mm sieve to obtain kaolingranules. A prescribed mass of the granules was placed in a 150 mmdiameter stainless steel mould and statically compressed to a targetheight of 19 mm and a very low dry unit weight of 12.0 kN/m3. Thesamples prepared showed a distinct double porosity structure withkaolin aggregates separated by fine inter-aggregate pore spaces (macropores), as shown in Fig. 2.

The drying tests were performed using a modified oedometer,capable of independent measurement and control of pore-airpressure, pore-water pressure, net vertical stress, vertical deformation

ssure chamber and sample setup.

Fig. 4. Results of one-dimensional consolidation tests in e~log σv′ plane on saturatedsamples. Fig. 6. Water retention curve for a net stress of 220 kPa.

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of the sample, and water volume change within the sample (Fig. 3).The pore-air pressure was controlled through a perforated loadingplaten and a porous disc placed at the top of the sample, whereas thewater pressure was controlled through a 15 bar saturated porousstone placed at the bottom of the sample. Suction within the samplewas established using the axis translation technique (Hilf, 1956).

In the modified oedometer, the aggregated sample was subjectedto a seating net stress of 12 kPa, and soaked by water percolationthrough the base of the sample. Upon completion of soaking, the netstress was increased to its target value and the sample was brought toequilibrium under pore-air and pore-water pressures of 700 kPa. Thetarget net stresses used in the experiments were 110, 220, 440, and750 kPa. The suction in the sample was then increased, in severalstages, by decreasing the water pressure at the base of the sample andholding the air pressure constant at 700 kPa. This method ofapplication of suction was preferred to the commonly adoptedapproach of increasing the air pressure at the sample boundary,while keeping the pore water pressure constant. This was to avoid theundesirable instantaneous volumetric change of the sample due to theapplication of the air pressure — i.e. before the air pressure applied atthe sample boundary reaching equilibrium with the air pressurewithin the pore space (Khalili et al., 2004). The volume of waterexpelled at each stage was carefully measured using a thin wallburette and a GDS pressure system simultaneously. Once the volume

Fig. 5. Water retention curve for a net stress of 110 kPa.

of water expelled from the sample stabilised, the equalization processwas considered to be complete and the next increment of suction wasapplied. The equalisation for each suction took approximately three tofour days to complete. The vertical displacement of sample wasmeasured continuously during the tests.

A parallel set of saturated one-dimensional consolidation tests wereconducted using a conventional oedometer. Three tests were per-formed: two on the aggregated samples, and one on a non-aggregatedkaolin, for comparison as well as determination of the compressibilitycoefficients, c and cg. The non-aggregated samplewas prepared atwatercontent close to the liquid limit to ensure that the specimen containedno structure. The vertical loads used in the consolidation tests were:12.5, 25, 50, 100, 200, 300, 25, 400, 750, and 25 kPa for the aggregatedsamples, and 25, 50, 100, 200, 25, 400, 600 and 100 for the non-aggregated sample.

4. Experimental results

4.1. One-dimensional consolidation tests

The results of the one-dimensional consolidation tests are shownin Fig. 4. Identical responses are obtained for the two aggregated soils,demonstrating the appropriateness of the sample preparation tech-nique adopted. The non-aggregated sample exhibited a normally

Fig. 7. Water retention curve for a net stress of 440 kPa.

Fig. 8. Water retention curve for a net stress of 750 kPa. Fig. 10. Void ratio versus suction for drying test at net stress of 220 kPa.

48 A.R. Bagherieh et al. / Engineering Geology 105 (2009) 44–50

consolidated, straight line response in the e~ log σv′ plane (in whiche is the void ratio and σv′ is the mean vertical stress), whereasthe response of the aggregated soils was curved with a slightconcavity, typical of structured soils with a metastable pore space(Koliji et al., 2008). At a given value of the applied stress, theaggregated soils exhibited a greater void ratio in comparison withthe non-aggregated soil. As the macro pores closed, with theincreasing applied stress, the response of the aggregated soilapproached that of the non-aggregated soil. The two responsesmerged at around a vertical effective stress of around 650 kPa. Asexpected, the aggregated soils, due to the presence of macro pores,exhibited greater compressibility than the non-aggregated soil inboth the normal compression and unloading–reloading zones. Thegreatest contrast was at lower vertical stresses and they becameindistinguishable at higher stresses.

4.2. Drying tests

The drying tests were performed at net stresses 110, 220, 440 and750 kPa. Two sets of results were obtained from each test: 1) waterretention curve and 2) volume change data. The water retentioncurves, in terms of degree of saturation versus suction, are presentedin Figs. 5–8. The volume change data are shown in Figs. 9–12.

Fig. 9. Void ratio versus suction for drying test at net stress of 110 kPa.

4.2.1. Water retention curvesFor the net stresses 110, 220 and 440 kPa (Figs. 5–7) the water

retention curves show a bimodal response, reflective of the doubleporosity structure of the soils. Two distinct zones may be identified:one characterized by a rapid desaturation of inter-aggregate (macro)pores while the intra-aggregate (micro) pores remain saturated, andthe other by desaturation of micro pores after the macro pores havebeen virtually emptied. For the water retention curve at the net stressof 110 kPa (Fig. 5), desaturation of macro pores occurs at arounds=30 kPa, and continues until a suction value of 75 kPa. Beyond thispoint, the degree of saturation remains constant (equal to around90%) until s=300 kPa, at which point the micro pores startdesaturating, marked by a rapid reduction in the degree of saturationof the soil. The first break point in the water retention curvecorresponds to the air entry value of the macro pores, sM(ae), andthe second one to that of the micro pores, sM(ae).

Similar responses are also observed in the water retention curvesfor the net stresses of 220 and 440 kPa. However, the bimodalresponse is absent from the water retention curve for the net stress of750 kPa (Fig. 8). In this case, the macro pores would have been closedat a net stress of around 650 kPa, as evidenced from the consolidationdata presented in Fig. 4, and thus the response of the systemapproaches that of the non-aggregated single porosity soil. Notice that

Fig. 11. Void ratio versus suction for drying test at net stress of 440 kPa.

Table 2Summary of material parameters used in volume change analysis of drying tests atdifferent net stresses.

Net stress(kPa)

cc cr sM(ae)

(kPa)sm(ae)

(kPa)c (Mpa−1) cg (MPa−1) αm = cg

c αM=1−αm

110 0.30 0.09 30 300 0.362 0.305 0.84 0.16220 0.28 0.09 30 300 0.231 0.206 0.89 0.11440 0.26 0.08 30 300 0.133 0.128 0.96 0.04750 0.25 0.08 – 400 0.077 0.077 1.00 0.00

cc, cr, c, and cg were obtained for the stress range of interest for each test.cc=compression index.cr=loading–reloading compression index.c=drained compressibility of the aggregated soil.cg=drained compressibility of the material forming the aggregates.

49A.R. Bagherieh et al. / Engineering Geology 105 (2009) 44–50

the air entry of the micro pores, in this case, is greater than the airentry of the micro pores at the net stresses of 110, 220, and 440 kPa.This is due to a reduction in the void ratio of the micro pores followingthe closure of the macro pores.

4.2.2. Volume change data and analysisThe volume change data alongwith the predicted drying responses

(represented by the solid lines) are shown in Figs. 9–12. The shrinkageevidenced by the void ratio reduction, at various net stresses, isrepresented by a curved line to the point of micro pore air entry, sm(ae),followed by a slight stiffening of the soil response.

The predicted drying responses are obtained using the effectivestress concept and the relationship,

Δe = ccΔ logσ Vv ð7Þ

inwhich e is the void ratio, cc is the slope of the normal compression linefor the aggregated soil in e~log σv′ plane, and σv′ is the vertical effectivestress. The effective stress was calculated using Eq. (3a), withparameters, αm, αM, χm and χM determined using Eqs. (4)–(6). Foreach test, cc, cg and c were obtained from the one dimensionalcompression tests data shown in Fig. 4 for the stress range of interest.The air entry values, sM(ae) and sm(ae), were obtained from the waterretention curves shown in Figs. 5–7. A summary of the numerical valueassigned to each of the material parameters used in the volume changepredictions is given in Table 2.

As can be observed, a very good correlation exists between theexperimental and predicted results (Figs. 9–12), demonstrating theappropriateness of the effective stress equation presented by Khaliliet al. (2005) for volume change analysis of unsaturated doubleporosity media. A further implication of this is that the constitutivemodelling of aggregated unsaturated soils can be made using aframework similar to that for saturated and unsaturated soils (Loretand Khalili, 2000, 2002) except that attention needs to be given to thedestruction of the soil structure with loading much in line with thework of Gens and Nova (1993) for cemented materials.

A notable feature of this investigation is that the predictions shownin Figs. 9–12 were obtained using the slope of the normal compressionline for the aggregated soils. This implies that suction hardeningwas nota factor in the present test results. Had suction hardening been present,the soil responsewould have entered the elastic zoneuponunsaturation(Khalili et al., 2004),markedbya dramatic increase in the stiffness of thesoil. In this case, the unloading–reloading compression index, cr, ratherthan normal compression index, cc, should have been used in thevolume change analysis. As shown in Figs. 9–12, the use of cr leads topredictions (shown by the dotted lines) in significant error compared to

Fig. 12. Void ratio versus suction for drying test at net stress of 750 kPa.

the measured experimental data. The lack of suction hardeningobserved in this investigation accords with similar observations madeby Uchaipichat (2005), Russell and Khalili (2006) and Thu et al. (2007)using other soils.

5. Conclusions

The response of a statically compacted kaolinwith double porositystructure is studied. Drying and one-dimensional consolidation testsare performed on initially saturated samples of the soil at different netstresses. Changes to the degree of saturation and volume change ofsamples are measured and reported. At low to intermediate netstresses, 110 to 440 kPa, the water retention curves exhibit a bimodalresponse due to the double porosity structure of the soil. At high netstresses (N650 kPa), the macro pores close and the water retentionresponse approach that of the single porosity non-aggregated soils.Application of the effective stress principle to volume change analysisof aggregated soils is investigated. It is shown that the method pro-posed by Khalili et al. (2005) for the evaluation of effective stress leadsto accurate predictions of the volume change in aggregated soils.Furthermore, it is shown that suction hardeningmay not be present inall unsaturated soils.

Acknowledgments

This research was performed during a visit of the first author to theUniversity of New South Wales. The authors wish to express theirappreciation toMr. P. Gwynne for his assistance in the laboratory workand toMrs. S. Beheshti for her invaluable support during this research.

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