Intermittent swelling and shrinkage of a highly expansive soil treated with polyacrylamide

Amin Soltani ,An Deng ,Aas Taheri ,Brendan C.O’Kelly

aSchool of Engineering,Information Technology and Physical Sciences,Federation University,Churchill,VIC,3842,Australia

b School of Civil,Environmental and Mining Engineering,The University of Adelaide,Adelaide,SA,5005,Australia

c Department of Civil,Structural and Environmental Engineering,Trinity College Dublin,Dublin,D02 PN40,Ireland

Keywords:Expansive soil Polyacrylamide(PAM)Consistency limits Sediment volume Swell-shrink cycles Swelling and shrinkage strains Accumulated axial strain

ABSTRACT This laboratory study examines the potential use of an anionic polyacrylamide(PAM)-based material as an environmentally sustainable additive for the stabilization of an expansive soil from South Australia.The experimental program consisted of consistency limits,sediment volume,compaction and oedometer cyclic swell-shrink tests,performed using distilled water and four different PAM-to-water solutions of P D=0.1 g/L,0.2 g/L,0.4 g/L and 0.6 g/L as the mixing liquids.Overall,the relative swelling and shrinkage strains were found to decrease with increasing number of applied swell-shrink cycles,with an‘elastic equilibrium’condition achieved on the conclusion of four cycles.The propensity for swelling/shrinkage potential reduction(for any given cycle)was found to be in favor of increasing the PAM dosage up to P D=0.2 g/L,beyond which the excess PAMmolecules self-associate as aggregates,thereby functioning as a lubricant instead of a flocculant;this critical dosage was termed‘maximum flocculation dosage’(MFD).The MFD assertion was discussed and validated using the consistency limits and sediment volume properties,both exhibiting only marginal variations beyond the identi fied MFD of P D=0.2 g/L.The accumulated axial strain progressively transitioned from‘expansive’for the unamended soil to an ideal‘neutral’state at the MFD,while higher dosages demonstrated undesirable‘contractive’states.

1.Introduction

The design and implementation of linear infrastructure,such as pavements,are often negatively affected due to the presence of expansive clay formations(Soltani et al.,2020a).The term‘expansive’refers to the soils’vulnerability to seasonal moisture fluctuations,periodically expanding and contracting in volume,thereby adversely affecting the serviceability(and hence safety)of road infrastructure(Jones and Jefferson,2012).To maintain engineering requirements,pavement engineers are often faced with a choice between(i)completing the design process within the limitations in flicted by the expansive subgrade,which mainly involves over-designing the upper pavement layers,or(ii)attempting to moderate the swell-shrink potential through soil stabilization.The latter is often preferred,since the former is not always financially and/or logistically viable(Soltani et al.,2020b;Zhang et al.,2021).Unless successful,periodic maintenance may be required to preserve the end performance for either option.

Soil stabilization refers to the practice of altering a natural soil’s structure,by physical and/or chemical alteration techniques,such that it is able to meet speci fic engineering requirements.Stabilization of expansive soils has been traditionally accomplished using calcium-based binders,particularly Portland cement and hydrated lime.The introduction of these agents to the soil-water complex initiates a course of short-and long-term chemical reactions,which encourage clay particle flocculation or aggregation,thereby leading to major improvements in critical soil attributes,such as shear strength/stiffness,load-bearing capacity,compressibility and swelling/shrinkage potential(e.g.Kalkan,2011;Thyagaraj and Zodinsanga,2014;Garzón et al.,2015;Al-Taie et al.,2020;Consoli et al.,2021).While effective from a stabilization perspective,calcium-based binders are not environmentally sustainable,as their application is commonly associated with substantial carbon emission footprints;this drawback highlights the urgency to minimize reliance on these binders(Ikeagwuani and Nwonu,2019).A common solution in this context involves replacing calciumbased materials with low-cost and more environmentally friendly ones.Promising alternatives,in terms of both geotechnical performance and sustainability,include polymers,resins and sulfonated oils(e.g.Mirzababaei et al.,2009;Yazdandoust and Yasrobi,2010;Khatami and O’Kelly,2013;Onyejekwe and Ghataora,2015;James,2020;Soltani et al.,2021).

Like calcium-based binders,the introduction of polymers to the soil-water medium can induce flocculation of the clay particles through relevant clay-polymer interaction mechanisms,i.e.charge neutralization,van der Waals or hydrogen bonding,and cationic bridging for cationic,neutral and anionic polymers,respectively(Theng,1982;Ben-Hur et al.,1992).Among the multitude of commercially manufactured and readily available polymeric stabilizers,polyacrylamide(PAM)seems to possess a variety of favorable soil stabilization attributes and hence demands further attention.PAMrefers to a group of synthetic polymers constructed from acrylamide(AMD)monomers(CH2=CHC(O)NH2);they are hydrophilic(and hence water-soluble)in nature and can be synthesized in anionic,neutral or cationic forms(Seybold,1994).PAMbased agents have been successfully employed within a variety of industries,including their application as a flocculant in sludge dewatering and water treatment processes,as well as their adoption in the agricultural sector to increase the soil-water retention capacity under drought conditions(e.g.Orts et al.,2007;Xiong et al.,2018;Chang et al.,2020).In the geotechnical context,reported applications for PAM include dewatering of mine tailings,increasing soil compaction ef ficiency,mitigating desiccationinduced cracking in clays,for shear strength enhancement and seepage/erosion control(e.g.Lei et al.,2018;Soltani et al.,2019a;Soltani-Jigheh et al.,2019;Zhang et al.,2019;Georgees and Hassan,2020;Kou et al.,2021).Though promising,the results reported by these studies,especially for expansive clays,are still limited(and somewhat inconsistent)to warrant PAM as anadhocsoilstabilization scheme.Moreover,to the authors’knowledge,the available data on PAM-treated soils have been mainly limited to certain routine geotechnical laboratory tests,which,though valuable,have not been suf ficient so far as to provide the con fidence needed to promote PAM-based materials for widespread usage in soil stabilization projects.In the expansive soil context,for instance,a full review of the existing literature shows that the swell-shrink volume change potential of PAM-treated expansive soils when subjected to intermittent wetting and drying,as would be the case for field conditions,has not yet been investigated,thus implying the need for further research to better understand PAM’s durability and hence its true stabilization potentials and/or limitations.

This laboratory study examines the potential use of an anionic PAM-based material as an environmentally sustainable material for the stabilization of an expansive soil from South Australia.The primary objectives are to investigate the effects of PAM treatment,at different PAM-to-water(mass-to-volume)dosages,on the soil’s consistency,sedimentation,compactability,and swell-shrink volume change behaviors.The principles of soil chemistry are then combined with the soil mechanics framework to identify and discuss the clay-PAM amending interactions in the context of cyclic swelling and shrinkage.

2.Test materials

2.1.Test soil

The soil selected for this experimental investigation was a reddish-brown clay material sourced from a site near Adelaide,South Australia.Table 1 summarizes the main physical and mechanical properties of the test soil.In terms of texture,the soil contained 20%sand(0.075-4.75 mm),36%silt(2-75μm)and 44%clay(＜2μm),as per ASTM D422-63(2007)e2(2007).The liquid limit(LL),obtained using a standard 80 g-30°fall-cone device for a cone penetration depth at theLLof 20 mm(AS 1289.3.9.1,2015),and the rolling-thread plastic limit(PL)(AS 1289.3.2.1,2009)were obtained asLL=78%andPL=22.4%;hence,producing a plasticity index(PI=LL-PL)value of 55.6%(see Table 1).Note that the described fall-cone de finition forLLand the testing method forPLare different from those speci fied in the Chinese testing standard JTG E40-07(2007),TestMethodsofSoilsforHighwayEngineering,whereby the fall-cone approach is employed forPLas well asLLdeterminations;with a discussion on these aspects and their implications presented in the paper by Vardanega et al.(2020).In view of its fines content(＜75μm)of 80%,along with its measuredLLandPIvalues,the test soil can be graded as clay with high plasticity(CH)based on the uni fied soil classi fication system(USCS)(ASTM D2487-17,2017).

Table 1Physical and mechanical properties of the test soil.

The maximum dry unit weight(MDUW)and optimum moisture content(OMC),determined for the standard Proctor(SP)compaction test(ASTMD698-12,2012),were measured as 15.9 kN/m3and 20.2%,respectively.The swelling potential(PSW)for the SPcompacted soil sample,de fined as the sample’s ultimate axial swelling strain measured using an oedometer set-up for an applied surcharge of 7 kPa(ASTM D4546-14,2014),was found to be 10.7%.According to thePSW-based classi fication framework(Seed et al.,1962),the test soil is classi fied as highly expansive.The free swell ratio(FSR)is de fined as the ratio of equilibrium sediment volume of 10 g oven-dried soil(＜425μm)in distilled water to that in kerosene(Prakash and Sridharan,2004).According to theFSR-based classification framework(Prakash and Sridharan,2004),linking theFSRvalue to the type of principal clay mineral present in fine-grained soils,it can be concluded that the clay fraction of the test soil was mainly dominated by montmorillonite.

2.2.PAM-based stabilizer

A proprietary anionic PAM-based material,similar to that examined by Soltani et al.(2018,2019a)and Zhang et al.(2021),was used as the soil-stabilizing agent.Referring to Fig.1a,the product was supplied in granular form and,as per the manufacturer’s instructions,was to be diluted with water for application.In terms of charge development,the anionic character(see Fig.1b)can be established through two common pathways(Barvenik,1994):(i)copolymerization of AMDand acrylic acid(CH2=CHCOOH)or a salt of acrylic acid,and(ii)hydrolysis of the neutral PAM with sodium hydroxide(NaOH)or a similarly strong base.As reported in the manufacturer’s literature,the PAM-based material possessed a neutral pH value of 6.9(at 25°C),a speci fic gravity of 0.8,a rather high molecular weight ranging between 12 Mg/mol and 15 Mg/mol(i.e.equivalent to approximately 1.5×105monomer units per PAM molecule),and a moderate density charge of approximately 18%.

3.Experimental work

3.1.Soil-PAM mix designs and preliminary tests

The primary objective of this experimental study is to examine the effects of PAM treatment on the soil’s consistency,sedimentation,compactability,and swell-shrink volume change behaviors.Accordingly,five soil-PAM mix designs(i.e.unamended soil and four PAM-treated blends)were examined.For the PAM-treated cases,PAM solutions with dosages(i.e.mass of granular PAM to volume of distilled water)ofPD=0.1 g/L,0.2 g/L,0.4 g/L and 0.6 g/L were prepared as the mixing liquids,which were used in wetting the dry soil to the required moisture contents for forming the various test samples.For ease of presentation,the unamended soil and the four PAM-treated blends(withPD=0.1 g/L,0.2 g/L,0.4 g/L and 0.6 g/L)are designated as P0,P1,P2,P4 and P6,respectively.

The preliminary tests included consistency limits(AS 1289.3.2.1,2009;AS 1289.3.9.1,2015),sediment volume(Prakash and Sridharan,2004)and SP compaction(ASTM D698-12,2012)tests,performed using distilled water(for P0)and different PAM solutions(for P1,P2,P4 and P6)as the mixing liquid.The primary testing stage investigated the oedometer cyclic swell-shrink behavior(see Section 3.2)of SP-compacted samples for each of the considered mixing liquids.In preparing these samples,the unamended and PAM-treated soils prepared at their respective OMCs were statically compacted in three equal-height layers into a series of con fining rings(height=20 mm and diameter=50 mm),such that each layer achieved its respective MDUW(values are presented and discussed in Section 4.3).To ensure even moisture distribution throughout the sample volume,a 24-h standing period,during which the compacted samples were hermetically sealed and stored at ambient laboratory temperature,occurred between static compaction and commencement of the oedometer test.

3.2.Oedometer cyclic swell-shrink tests

The SP-compacted unamended soil and various PAM-treated samples were exposed to intermittent swelling and shrinkage processes in a temperature-controlled oedometer apparatus,as employed previously in Soltani et al.(2019b,2021).The samples placed within the oedometer cell were inundated with distilled water and allowed to freely swell under an applied 7-kPa surcharge(ASTM D4546-14,2014),at ambient laboratory temperature,to a point at which the axial swelling strain achieved a stabilized state(i.e.completion of the primary swelling phase).The strain corresponding to this state is referred to as the‘swelling potential’.In performing the subsequent shrinkage stage,the inundation water was first drained away via a drainage valve fitted to the base of the oedometer cell.Next,the cell’s external heating component was set to a temperature of(40±2)°C,causing the samples to shrink(while still subjected to the same applied 7-kPa surcharge).Shrinkage was carried on to a point at which the ultimate axial shrinkage strain(i.e.completion of the normal/primary shrinkage phase),referred to as the‘shrinkage potential’,could be obtained.Intermittent wetting and drying of the samples were replicated in a similar fashion,with the combination of one swelling stage and the following shrinkage process being de fined as one swell-shrink cycle.The swelling and shrinkage potentials have been reported to equalize on the conclusion of several cycles(Subba Rao,2000;Tripathy et al.,2002).In the present investigation,the swell-shrink equilibrium condition was mainly attained on the conclusion of four cycles;as such,the test samples were exposed to a maximum of six cycles.The relative swelling and shrinkage potentials(for any given cycle)were calculated as follows(Soltani et al.,2019c):

Fig.1.(a)Anionic PAM in its granular form,and(b)Structural formula of anionic PAMs.

wherePSW(N),HSW(N)andΔHSW(N)are the swelling potential,sample height and increase in sample height,respectively,on conclusion of theNth swelling cycle;PSH(N)andΔHSH(N)are the shrinkage potential and decrease in sample height,respectively,on conclusion of theNth shrinkage cycle;andHSH(N-1)is the sample height on conclusion of the(N-1)th shrinkage cycle.

4.Results and discussion

4.1.Effect of PAM treatment on soil consistency behavior

Fig.2.Effect of PAM treatment on the test soil’s consistency limits:(a)Variations of the LL,PL and PI against PAMdosage P D;and(b)The tested mix designs plotted on the Casagrande-style PI-LL chart.

Fig.2a illustrates the variations of the soil consistency limits against PAM dosagePDfor the tested mix designs.The soil-PAM mixtures(P1,P2,P4 and P6)all had higherLL,PLandPIvalues compared to those measured for the unamended soil(P0).The greater the PAMdosage,the higher theLL,PLandPIparameters up toPD=0.2 g/L,beyond which only marginal variations occurred.From Fig.2a,the rates of increase in the consistency indices with respect toPD≤0.2 g/L,de fined as the slopes of linear trendlines fitted through theLL-PD,PL-PDandPI-PDdatasets,were calculated asR=47.9%L/g,12.2%L/g,and 35.7%L/g,respectively,whereRrepresents the rate of increase in the consistency parameters with respect toPD≤0.2 g/L.

Fig.2b illustrates the tested mix designs when represented on the Casagrande-style soil plasticity chart,with all mixtures plotting between the A-and U-lines,thereby indicating that the unamended soil and its various PAM-based blends categorize as clay materials.Despite the PAM addition causing a considerable rightward-upward translation in thePI-LLspace,the original CH classi fication of the unamended soil remained valid for all PAMtreated cases.ThePI-LLrelationship for these materials was found to be linear(somewhat parallel to the A-line),according to the expressionPI=0.68(LL+3.3)(withR2=0.978).

TheLLcan be considered as a guide towards perceiving soil fabric evolution in response to changes in pore-water chemistry(Sivapullaiah,2015;Muguda and Nagaraj,2019).During the fallconeLLtest,as clay particle flocculation begins to dominate the soil matrix,the resistance to penetration by the fall-cone(and hence shear strength)increases;as such,the cone penetration depth criteria forLLdetermination will be achieved at higher moisture contents(Kim and Palomino,2009;Soltani et al.,2019a).Accordingly,one can postulate that an increase in theLL,as achieved by PAM treatment,signi fies an increased tendency for clay particle flocculation.On this basis,the maximum flocculation tendency appears to be attained at 0.2 g/L PAM,since higher dosages did not produce notable further increases in theLL.Moreover,the hydrophilic character of PAM molecules may provide extra adsorption sites(in addition to the clay particles)for water molecules,thereby further contributing towards higher consistency limits for soil-PAM mixtures(Kim and Palomino,2009;Soltani-Jigheh et al.,2019).

4.2.Effect of PAM treatment on soil sedimentation behavior

Results of the sediment volume tests are shown in Fig.3.The soil-PAM suspensions(P1,P2,P4 and P6)all produced lower equilibrium sediment volumes compared to that of the soil-water suspension(P0).The equilibrium sediment volume was found to follow an exponentially-decreasing trend with increasing PAM dosage;only minor added bene fits/reductions were noted beyond 0.2 g/L PAM.The soil-water suspension resulted in a relatively high equilibrium sediment volume ofVSD=34 mL,while the PAMtreated suspensions withPD=0.1 g/L,0.2 g/L,0.4 g/L and 0.6 g/L had lower values ofVSP=28.5 mL,25 mL,24.5 mL,and 23 mL,respectively.With the soil-kerosene suspension having an equilibrium sediment volume ofVSK=15 mL,theFSRparameter,calculated asFSR=VSD/VSK(for P0)orVSP/VSK(for PAM-treated cases),can be calculated as 2.27,1.9,1.67,1.63,and 1.53 for P0,P1,P2,P4 and P6,respectively,whereVSD,VSPandVSKare the equilibrium sediment volumes of 10 g oven-dried soil(＜425μm)in distilled water(the‘polar’liquid),PAM solution and kerosene(the‘non-polar’liquid),respectively.

From theFSR-based classi fication framework presented in Table 2(Prakash and Sridharan,2004),the unamended soil is classi fied as highly expansive,while all PAM-treated cases produced an improved classi fication of moderately expansive.Like theLL,theFSRcan be used to infer,and hence predict,the evolution of soil fabric(Sridharan and Prakash,1999;Soltani et al.,2018).Adecrease in theFSR,as achieved by suspending the soil in PAM solution,indicates an increased tendency for clay particle flocculation;this hinders the clay particles from expanding to their full potential,which would have otherwise occurred in distilled water(Kim and Palomino,2009;Soltani et al.,2019a).Like theLL-PDrelationship(see Section 4.1),the maximum tendency for flocculation,based on theFSRresults,appears to also be attained atPD=0.2 g/L,with higher PAM dosages not providing notable further improvements(or reductions)inVSPand hence by association theFSR.

4.3.Effect of PAM treatment on soil compactability behavior

Typical SP compaction curves for the mixtures P0,P2 and P6 are shown in Fig.4,with the complete test results presented in Table 3.The compaction curve experienced a considerable upward translation for the addition of(and dosage increase in)PAM,hence improving the soil’s compactability.While marked increases were noted for the MDUW(increasing from 15.9 kN/m3for the unamended soil to 16.1 kN/m3,16.3 kN/m3,16.4 kN/m3,and 16.7 kN/m3for the mixtures P1,P2,P4 and P6,respectively),the corresponding OMC values exhibited negligible changes(follow the arrowed line in Fig.4).

An increase in pore-water viscosity,which is the case when employing PAM solutions(in lieu of distilled water)as the compaction liquid,induces inter-particle lubrication.Consequently,the movement of the soil agglomerations(and clay flocs)relative to each other during compaction is confronted with much less friction(Onyejekwe and Ghataora,2015;Soltani et al.,2021).This mechanism allows a relatively denser packing of the soil particles to be obtained for the same compactive energy,which produces higher MDUWvalues for the soil-PAM mixtures.

The OMC and MDUW parameters are often estimated using rolling-of-threadsPLmeasurements.Two of the more common,yet simple,correlations in this context are given as follows(Gurtug and Sridharan,2002,2004):

The empirical coef ficientsβMandβDare functions of the compaction energy level.For typical fine-grained soils and the SP compaction energy,they can be taken asβM=0.92 andβD=0.98(Gurtug and Sridharan,2004).Comparing the experimental results and empirical predictions presented in Table 3,the routine practice of interpreting the compaction characteristics using rolling-ofthreadsPLmeasurements cannot be reliably extended to PAMtreated soils(i.e.R2=0.086 and 0.654 for the OMC and MDUW predictions,respectively).

4.4.Effect of PAM treatment on soil cyclic swell-shrink behavior

4.4.1.Relativeswellingandshrinkagepotentials

The evolution of the swelling potentialPSW(see Eq.(1))with respect to the number of imposed swell-shrink cyclesNis shown in Fig.5a.For the samples P0 and P1,thePSW-Nrelationship demonstrated a rise-fall trend,peaking atN=2 and then decreasing exponentially up to the fourth(or equilibrium)cycle,beyond which only marginal reductions occurred(follow the trend curves‘P0’and‘P1’in Fig.5a).Meanwhile,thePSW-Nrelationship for the samples P2,P4 and P6 exhibited an exponentiallydecreasing trend.Overall,for any given cycle,the greater the PAM dosage,the lower the developed swelling potential;compared to 0.2 g/L PAM,however,the relative reductions in the swelling potential forPD=0.4 g/L and 0.6 g/L were noticeably small(e.g.compare the trend curves‘P2’and‘P6’in Fig.5a).For instance,atN=3,the samples P0,P1,P2,P4 and P6 resulted inPSW=9.6%,7.7%,4.2%,3.5%and 3.3%,respectively.The degree of expansivity for the investigated mix designs was assessed using the threePSW-based classi fication frameworks summarized in Table 4(Holtz and Gibbs,1956;Seed et al.,1962;Sridharan and Prakash,2000).From the final results presented in Table 5,compared to the highly expansive classi fication of the test soil,the expansivity classi fications were either maintained(N=1)or substantially improved(N≥2)for all PAM dosages,especially forPD≥0.2 g/L.

Table 2Classi fication procedures for expansive soils based on the FSR parameter(Prakash and Sridharan,2004).

Table 3Summary of the SP compaction characteristics for the tested samples.

Table 4Classi fication procedures for expansive soils based on the P SW parameter.

Table 5Degree of expansivity for the tested samples during various swelling cycles.

Fig.5b shows the variations of the shrinkage potentialPSH(see Eq.(2))against the number of applied cycles.For any given PAM dosage,the shrinkage potential followed an exponentially-decreasing trend for an increasing number of applied cycles,with negligible reductions occurring beyond the equilibrium cycle(N=4).Like the swelling potential,for any given cycle,the propensity for shrinkage potential reduction was in favor of increasing the PAM dosage up toPD=0.2 g/L,beyond which the observed reductions became marginal,with the trend curves for the samples P2,P4 and P6 observed to overlap with each other.For instance,atN=3,the samples P0,P1,P2,P4 and P6 resulted inPSH=7.8%,6.6%,4.5%,4.1%and 4.3%,respectively.

Fig.4.Typical SP compaction curves for the unamended soil(P0)and soil-PAM mixtures containing 0.2 g/L and 0.6 g/L PAM(P2 and P6).Note that ZAV denotes zero-air-voids(saturation degree S R=100%).

Clay particles carry an unbalanced negative charge,such that they would naturally repel the anionic PAMmolecules(owing to electrostatic repulsions).However,clay-PAMattractions can still be developed through the cationic bridging mechanism,explained as follows.Exchangeable cations present near the clay particle surfaces,particularly divalent cations such as Ca2+and Mg2+,function as‘attraction bridges’between the negatively charged clay and PAMcomponents(Seybold,1994;Laird,1997;Lu et al.,2002;Soltani et al.,2018;Georgees and Hassan,2020).This immobilizes the exchangeable cations near the clay surfaces,decreasing the soil’s overall cationexchange capacity and accordingly its volume change potential.Further,the formation and diffusion of these strong cationic bridges between adjacent clay surfaces(which bring and hold the clay particles together)induce flocculation of the clay particles,thus decreasing the soil’s swell-shrink tendency.The maximumtendency for flocculation,however,would be limited by the number of attraction sites(i.e.the soil clay content)and the amount of exchangeable divalent cations available for the PAM molecules(Lati fiet al.,2016;Soltani et al.,2021).In other words,for a given soil type,beyond a critical PAM dosage,for which the available attraction sites are exhausted,the flocculation process will cease.Increasing the PAM dosage beyond this so-called‘maximum flocculation dosage’(MFD)may cause the excess PAMmolecules to self-associate as aggregates,thereby functioning as a lubricant instead of a flocculant(Soltani et al.,2019a).Accordingly,an increase in PAMdosage beyond the soil’s MFD should not provide further notable improvements in the soil’s mechanical properties.This mechanismexplains the marginal variations observed in the consistency limits(see Fig.2),sediment volume features(see Fig.3),and swell-shrink volume changes(see Fig.5)forPD＞0.2 g/L,implying for the present investigation that MFD equals 0.2 g/L.

Fig.5.Variations of(a)swelling and(b)shrinkage potentials(i.e.P SWand P SH)against the number of applied swell-shrink cycles N for the tested samples.

Referring to Fig.5,overall,the swelling and shrinkage potentials decreased with increasing number of applied swell-shrink cycles.This behavior,as reported by previous researchers(e.g.Subba Rao,2000;Zhang et al.,2006;Estabragh et al.,2015;Soltani et al.,2019c;Estabragh et al.,2020),can be ascribed to the reconstruction of the soil/soil-PAMmicrostructures on completion of the second(for P0 and P1)or first(for P2,P4 and P6)drying cycle.As the moisture content decreases during drying,capillary stresses begin to rise due to an increased surface tension leading strong van der Waals bonds to form and propagate between adjacent soil particles(and clay flocs),causing them to aggregate.This change in soil fabric leads to an apparent reduction in the sample’s clay content,consequently decreasing its overall water adsorption-retention capacity and its volume change potential during subsequent cycles.

4.4.2.Cumulativeswell-shrinkpatterns

For any given cycle,the accumulated axial strain,given as the sum of the axial plastic strain(APS)values up to that cycle,can be calculated as follows(Zhao et al.,2019;Soltani et al.,2021):

whereεac(N)is the accumulated axial strain on conclusion of theNth swelling(for SW)or shrinkage(for SH)cycle(in%);PSW(N)is the relative swelling potential on conclusion of theNth swelling cycle(obtained by Eq.(1),as%);andPSH(N-1)andPSH(N)are the relative shrinkage potentials on conclusion of the(N-1)th andNth shrinkage cycles,respectively(obtained by Eq.(2),as%).

Fig.6 illustrates theεac-Nrelationship(see Eq.(5)),referred to as the swell-shrink rhythm/pattern,for the tested mix designs.As per common practice,for each of the tested samples,the accumulated axial strain was interpreted(in terms of character and extent)using the slope of a single-coef ficient trendline fitted to the sample’s respective swell-shrink rhythm(Soltani et al.,2019b):

whereλis the trendline slope(in%).Based on the sign and magnitude ofλ,the following three cases can be postulated:

(1)Expansive:Positive values ofλindicate that the net extent of the developedPSWstrains is greater than that of thePSHstrains(i.e.∑PSW＞∑PSH).As such,theεacparameter bears an undesirable expansive character,with higher values ofλ indicative of more extreme free-surface ground heave.

(2)Neutral:For those cases whereλis equal(or fairly close)to zero,one can postulate that∑PSW≈∑PSH.In other words,the εacparameter is neutral in character,with this case considered ideal in terms of minimizing free-surface ground movements.

(3)Contractive:Negative values ofλindicate that∑PSW＜∑PSH;thus,theεacparameter is contractive in character.Like the expansive case,this case is also undesirable,with higher absolute values ofλproducing more extreme free-surface ground settlements.

Referring to Fig.6,relative to the expansive deformational state of the unamended soil(P0 withλ=1.1%),theεac-Nrelationship for the treated soil underwent a progressive downward translation with increasing PAM dosage.The samples P1 and P2 produced lowerλvalues of 0.62%and-0.04%,respectively,signifying a progressive transition towards the ideal neutral case atPD=0.2 g/L.Higher PAM dosages of 0.4 g/L and 0.6 g/L produced highly pronounced negativeλvalues of-0.44%and-0.99%,respectively,both indicative of an undesirable contractive condition.In view of these findings,as well as the relativePSWandPSHstrain responses presented in Fig.5,the 0.2 g/L PAM dosage(which also happens to represent the soil’s MFD)can be deemed as the optimum dosage to minimize swell-shrink induced heave and settlements.

The incurred APS,described as the algebraic difference of the relativePSWandPSHstrains for a given cycle(e.g.see the double arrowed line‘APS’for P0 atN=2 in Fig.6a),decreased with increasing number of applied cycles and substantially diminished on the conclusion of four cycles.In other words,the relativePSWandPSHstrains became elastic in character forN≥4.Thus,on achieving swell-shrink equilibrium,thePSWandPSHstrains for each tested sample develop into their unique and interchangeable value,commonly referred to as the equilibrium bandwidth(EB)(Subba Rao,2000;Tripathy et al.,2002;Yazdandoust and Yasrobi,2010).As shown in Fig.6,the greater the PAM dosage,the lower the EB value;however,compared with that forPD=0.2 g/L(i.e.the MFD),the relative reductions in the EB for 0.4 g/L and 0.6 g/L PAM were marginal.The unamended soil(P0)produced an EB value of 7.7%,while the samples P1,P2,P4 and P6 resulted in lower values of 5.6%,3.8%,3.4%and 3.5%,respectively.

As discussed earlier,beyond the soil’s MFD of 0.2 g/L,the PAM material’s lubricant features may begin to dominate its flocculant properties.Consequently,where swell-shrink equilibrium has not yet been achieved(forN＜4),the movement of the soil agglomerations(and clay flocs)relative to each other,under the applied 7-kPa surcharge in these tests,would be confronted with less friction(particularly forPD＞MFD).This allows a denser packing of the soil particles to be obtained during drying,thereby potentially increasing the sample’s shrinkage-to-swelling(PSH/PSW)ratio and hence decreasing itsεac-Ntrendline slopeλ.To examine this hypothesis,a scatter plot showing the variations ofPSH/PSWagainst the number of imposed swell-shrink cycles is presented in Fig.7.Overall,the greater the PAM dosage,the higher thePSH/PSWratio,particularly evident forN=2-4,which elucidates the relatively larger contractive character of the samples P4 and P6 compared to those containingPD≤MFD.Accordingly,it can be concluded that,while PAM dosages greater than the MFD produce similar improvement effects to those achieved at the MFD,they may exhibit higherPSH/PSWratios during early cycles.As such,in addition to higher costs,PAM dosages greater than the MFD may be associated with potentially major settlement concerns.One can postulate that such concerns would tend to intensify as the applied surcharge(overburden stress)increases,which is a critical aspect that demands further examination.

5.Conclusions

This laboratory study examined the potential use of an anionic PAM-based material,employed at four PAM-to-water(mass-tovolume)dosage ratios ofPD=0.1 g/L,0.2 g/L,0.4 g/L,and 0.6 g/L,forthe stabilization of an expansive soil from South Australia.In view of the test results and their interpretation,conclusions can be drawn as follows:

(1)All soil-PAM mixtures exhibited higherLL,PLandPIvalues compared to those obtained for the unamended soil.The greater the PAM dosage,the higher theLL,PLandPIparameters up toPD=0.2 g/L,beyond which only marginal variations occurred.On this basis,and particularly considering that higher dosages did not lead to notable further increases in theLL,it was speculated that the maximum tendency for clay particle flocculation occurs at 0.2 g/L PAM.

(2)All soil-PAM suspensions produced lower equilibrium sediment volumes(and hence lowerFSRvalues)compared to that of the soil-water suspension.TheFSRfollowed an exponentially-decreasing trend with increasing PAMdosage,although only minor added reductions were achieved beyond 0.2 g/L PAM,further con firming that this dosage produced the maximum tendency for flocculation.

(3)Because of their relatively higher viscosity compared to water,the use of PAM solutions as the compaction liquid induced inter-particle lubrication,thereby permitting a denser packing of the soil particles(and hence a higher MDUW)to be obtained.It was noted that the corresponding OMC values exhibited negligible changes in relation to the compacted unamended soil.

Fig.6.Cumulative swell-shrink patterns for the tested samples:(a)P0,P1 and P2;and(b)P0,P4 and P6.

Fig.7.Variations of the shrinkage-to-swelling potential ratio(i.e.P SH/P SW)against the number of applied swell-shrink cycles N for the tested samples.

(4)Overall,the relative swelling and shrinkage strains decreased with increasing number of applied swell-shrink cycles,with an‘elastic equilibrium’condition achieved on the conclusion of four cycles.The tendency for swelling/shrinkage potential reduction was found to be in favor of increasing the PAM dosage up toPD=0.2 g/L,beyond which the observed reductions became marginal.It was postulated that increasing the PAM dosage beyond 0.2 g/L can cause the excess PAM molecules to function as a lubricant instead of a flocculant;thence,this critical dosage was termed MFD.

(5)With PAM addition,the accumulated axial strain progressively transitioned from expansive for the unamended soil to neutral atPD=0.2 g/L,while higher PAM dosages of 0.4 g/L and 0.6 g/L both demonstrated undesirable contractive states.Based on these results,0.2 g/L PAM,which also happens to represent the soil’s MFD,was deemed as the optimum dosage in terms of minimizing swell-shrink-induced heave and settlements.

Unlike traditional calcium-based binders,which can be optimized in terms of dosage(or mix design)by simple standardized laboratory tests(e.g.pH measurements for soil-lime mixtures)based on an extensive body of knowledge built up over the years,no such framework has been developed(nor suggested)for PAMbased materials.From this experimental study,it can be hypothesized that basic geotechnical laboratory tests,such as consistency limits and sediment volume tests,can be used to predict the MFD for PAM-treated expansive clayey soils(i.e.without the need for conducting more advanced oedometer tests).Additional tests,employing different types of clayey soils with varying mineralogical and plasticity characteristics,should be performed with the aims of(i)further exploring potential correlations between the MFD and fundamental clay properties,and(ii)establishing a universal test framework capable of quantifying the MFD in a practical manner.

Declarationofcompetinginterest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to in fluence the work reported in this paper.

Acknowledgments

The work presented in this paper has been funded by the Australian Research Council(ARC),Project No.DP140103004.The first author also acknowledges The University of Adelaide for making this research study possible through the provision of an Australian Government Research Training Program Scholarship.

Abbreviations

AMD Acrylamide

APS Axial plastic strain

AS Australian Standard

ASTM American Society for Testing and Materials

CH High-plasticity clay

EB Equilibrium bandwidth

FSRFree swell ratio

LLLiquid limit

MDUW Maximum dry unit weight

MFD Maximum flocculation dosage(for PAM)

OMC Optimum moisture content

P0 Unamended soil

P1 Soil stabilized with 0.1 g/L PAM

P2 Soil stabilized with 0.2 g/L PAM

P4 Soil stabilized with 0.4 g/L PAM

P6 Soil stabilized with 0.6 g/L PAM

PAM Polyacrylamide

PIPlasticity index

PLPlastic limit

SH Shrinkage

SP Standard Proctor

SW Swelling