deformation characteristics of two cemented calcareous soils

Deformation characteristics of two cementedcalcareous soils

Shambhu S. Sharma and Martin Fahey

Abstract: The effect of cementation on the deformation characteristics of two cemented calcareous soils was investi-gated through a series of undrained triaxial tests performed under both monotonic and cyclic loading conditions. In-creasing the level of cementation significantly increased the initial stiffness, resulting in the stiffness being moreindependent of the confining pressure. The curves of stiffness degradation with strain obtained from both cemented anduncemented calcareous soils compared with those of other noncalcareous soils revealed that calcareous soil attains afaster rate of modulus reduction with a higher strain threshold. It was also observed that the pattern of stiffness degra-dation is very similar in both cemented and uncemented samples. The stiffness degradation curves obtained from cyclictests were found to lie within the range defined by the corresponding monotonic tests. The effect of number of cycleson the stiffness during cyclic loading was also examined and is found to depend on whether the postyield behaviour iscontrolled by the cohesive or the frictional response. Examination of the variation of damping ratio with strain revealedthat the observed difference in the stiffness degradation curves between calcareous and noncalcareous soils was also re-flected in the damping ratio, with the damping ratio of calcareous soils being below the range defined fornoncalcareous soils.

Key words: calcareous soils, triaxial test, shear modulus, damping ratio, repeated loading.

Résumé : On a étudié l’effet de la cimentation sur les caractéristiques de déformation de deux sols calcaires cimentésau moyen d’une série d’essais triaxiaux non drainés réalisés dans des conditions de chargement tant cyclique quemonotonique. L’augmentation du niveau de cimentation a augmenté appréciablement la rigidité initiale, ce qui a résultéen une rigidité plus indépendante de la pression de confinement. Les courbes de dégradation de rigidité en fonction dela déformation obtenues sur les sols calcaires tant cimentés que non cimentés comparées avec celles d’autres sols noncalcaires révèlent que les sols calcaires atteignent plus rapidement le taux de réduction du module avec un seuil plusélevé de déformation. Il a été également observé que le schéma de dégradation de la rigidité est très similaire dans leséchantillons tant cimentés que non cimentés. On a trouvé que les courbes de dégradation de rigidité obtenues des es-sais cycliques se situent à l’intérieur de la plage définie par les essais monotoniques correspondants. L’effet du nombrede cycles sur la rigidité durant le chargement cyclique a aussi été examiné, et dépend du fait que le comportementpost-pic est contrôlé par la réponse soit de cohésion, soit de frottement. L’examen de la variation du rapport d’amortis-sement avec la déformation révèle que la différence observée entre les courbes de dégradation de la rigidité des solscalcaires et non calcaires se reflétait dans le rapport d’amortissement, le rapport d’amortissement des sols calcairesétant sous la plage définie pour les sols non calcaires.

Mots clés : sols calcaires, essai triaxial, module de cisaillement, rapport d’amortissement, chargement répété.

[Traduit par la Rédaction] Sharma and Fahey 1151

Introduction

The nonlinear stress–strain behaviour of different geo-materials has been investigated extensively in recent yearswith the use of different small-strain measuring devices.This has led to evaluation of the initial maximum stiffnessand stiffness degradation curves for different geomaterials,which provided guidelines for calculating ground movement

due to the application of different types of loads (Seed andIdriss 1970; Kokusho 1980; Saxena et al. 1988; Alarcon-Guzman et al. 1989; Yasuda and Matsumoto 1993; Lo Prestiet al. 1997).

Although the practical importance and the simplicity inanalysis of ground movement using stiffness degradationcurves have been recognised (e.g., Schnabel et al. 1972), abrief review of the literature reveals that, despite the largeamount of research on calcareous soils (Houston andHerrmann 1980; Jewell and Khorshid 1988; Jewell and An-drews 1988; Kaggwa 1988; Coop 1990; Airey and Fahey1991; Airey 1993; Carter and Airey 1994; Lagioia and Nova1995; Hyodo et al. 1998), no attempt has been made to gen-erate such curves for calcareous soils, especially with con-sideration of cyclic loading and the effect of cementation.Considering the fact that most calcareous soils, which areoften encountered beneath the foundations of many offshore

Can. Geotech. J. 41: 1139–1151 (2004) doi: 10.1139/T04-066 © 2004 NRC Canada

1139

Received 6 March 2003. Accepted 16 June 2004. Publishedon the NRC Research Press Web site at http://cgj.nrc.ca on7 December 2004.

S.S. Sharma and M. Fahey.1 Centre for Offshore FoundationSystems, School of Civil and Resource Engineering, TheUniversity of Western Australia, 35 Stirling Highway,Crawley, WA 6009, Australia.

1Corresponding author (e-mail: [email protected]).

structures, possess some degree of bonding between theirconstituents, research on the cyclic behaviour of cementedcalcareous soil is of immense practical importance.

The research on natural cemented calcareous soils is lim-ited mainly because of the difficulty and cost associated withobtaining consistently cemented natural soil from a site. Thisdifficulty has been overcome to some extent in recent yearsby testing artificially cemented samples (Allman and Poulos1988; Coop and Atkinson 1993; Ismail et al. 2002a, 2002b).Nevertheless, the extent to which artificially cemented sam-ples replicate the behaviour of natural soil is questionable, asthe type of cement has a significant influence on the behav-iour of the soil (Ismail et al. 2002a). The innovative calcitein situ precipitation systems (CIPS) technique, which wasfound to be very promising in capturing the natural patternof cementation, has opened a new frontier for testing ce-mented samples (Kucharski et al. 1996; Ismail et al. 2002a,2002b).

Results from CIPS-cemented calcareous soils are pre-sented in this paper. Although the main objective of thispaper is to contribute to the database on the deformationcharacteristics of cemented calcareous soils, it also providessome insight into the behaviour of calcite-cemented soils ingeneral. It is believed that information on the effect of someof the most influential parameters such as the level ofcementation, consolidation history, and confining pressureshould be of considerable importance even in the area wherecementation has been used for purposes other than replicat-ing natural material (e.g., stabilized soils).

It is worth mentioning here that, despite excellent data-bases on the deformation characteristics of uncementedmaterial, most of the available research is limited to investi-gation of the stiffness reduction after a particular number ofcycles (e.g., 10 cycles). This may be due to the common ob-servation that for small-strain cycling, there is little effect ofincreasing number of cycles on the stiffness after 10 cycles.More recently it has been reported that, although this propo-sition is true for clays, the number of cycles has a significanteffect on stiffness reduction in dry sand, especially at an ele-vated strain level, which becomes even more pronounced invirgin specimens (Lo Presti et al. 1997). Further, the consid-eration of only a small number of repeated cycles in most ofthe available research is because these studies were focusedon resolving the problems encountered during earthquakeloading. In contrast, to simulate loading due to waves, appli-cation of a large number of repeated cycles needs to be con-sidered for a wide range of stresses. Considering this, thecyclic tests performed in this study cover a wide range of cy-clic stresses, and tests were performed up to 30 000 cycles toinvestigate the influence of number of repeated cycles on thecyclic behaviour of cemented samples. Hopefully, the degra-dation of stiffness with strain presented herein for differentnumbers of cycles obtained from cyclic tests on cementedcalcareous soils will also provide some insight into the effectof number of cycles on the stiffness degradation characteris-tics of soils in general. It is worth mentioning that the focushere is more on the deformation characteristics of cementedcalcareous soils, and hence the features associated withstrength of cemented calcareous soils are not discussed. Dis-cussion on the strength aspects can be found in Sharma andFahey (2002a).

Material used and experimental procedure

Soil testedTwo types of reconstituted calcareous soils were used in

this study. The first is a fine-grained offshore calcareous soilrecovered from the seabed near the vicinity of the Goodwyn‘A’ gas platform on the North West Shelf of Australia. Thesecond is a coastal aeolian calcareous soil from Ledge Point,100 km north of Perth, Western Australia. The gradationcurves of these soils are shown in Fig. 1. The gradationcurves for the fraction finer than 0.075 mm were determinedusing a laser technique. These soils were selected becausethey represent the extremes of formation conditions, grada-tions, and void ratios as they exist naturally. Additional de-tails on the physical properties of the soils can be found inIsmail et al. (2002b).

Calcite cementA proprietary chemical cementation system called CIPS

(calcite in situ precipitation system), developed by the Com-monwealth Scientific and Industrial Research Organisation(CSIRO) Australia, was used in this study for artificialcementation. The CIPS is a water-based, nonparticulate,low-viscosity, neutral in pH, nontoxic solution (Ismail et al.2002b). In the CIPS technique, cementation is achieved byflushing a mixture of two proprietary chemical solutionsthrough the soil sample, resulting in precipitation of calciteon the surface and between the soil grains, and this impartscohesive strength due to bonding at particle contacts(Kucharski et al. 1996; Ismail et al. 2000).

Sample preparationThe sample preparation technique described by Ismail et

al. (2000) was used to prepare artificially cemented samplesfor triaxial testing in this study. This technique consisted ofpluviating the dry soil to a certain density into a formerlined with a rubber membrane. Carbon dioxide gas was thenflushed through the sample from bottom to top to displace

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1140 Can. Geotech. J. Vol. 41, 2004

Fig. 1. Particle-size distribution curves for the two calcareoussoils used in the study.

all the entrapped air from the sample to aid the subsequentsaturation of the sample. Water was then flushed through thesample, followed by the CIPS solution. The flushing pres-sure was maintained equal to 25 kPa in Ledge Point (LP)soil and 75 kPa in Goodwyn (GW) soil. The seating pressureapplied on the LP and GW soil samples was 50 and100 kPa, respectively. The flushing time was maintained at4 and 8 min for the LP and GW samples, respectively. Thelarger flushing pressure and more time required in flushingCIPS through the GW sample is due to the large amount offines present in this soil.

Once the flushing of CIPS was finished, both the inlet andoutlet valves were closed and the sample was then left tocure for 24 h. The same procedure was repeated for the nextflush of CIPS whenever multiple flushes were needed. Aninterval of 24 h was always maintained between each suc-cessive flush of CIPS. After the last flush, the sample wasleft to cure for another 24 h before testing.

A number of advantages of this sample preparation tech-nique were described in Ismail (2000). The key issues withthis procedure, however, were that it controlled both thedensity and cementation of the sample and eliminated anydisturbance of the sample during extrusion and during as-sembling the sample on the triaxial base. Nevertheless, duecare was taken while setting up the samples in the triaxialmachine to avoid any breakage of cementation. All the tri-axial tests were carried out under full saturation and withpore pressure parameter (B) values of at least 0.95.

Depending on the type of soil, initial void ratio, and num-ber of CIPS flushes, samples with different levels of strengthwere created. The unconfined compressive strengths (qucs)and tensile strengths (TS) obtained are as reported in Ta-ble 1. The values reported in Table 1 are the averages of atleast two samples. The variation of strength between sam-ples under each condition was less than 5%, which confirmsthe reproducibility of these samples. It is worth mentioningthat reproducibility of the CIPS-cemented samples was ex-tensively examined by Ismail (2000) and Sharma (2004) andwas found to be highly reproducible.

The behaviour of cemented samples depends on thestress–cementation histories. Two most common stress–cementation sequences in nature are loading before cementa-tion and cementation before loading (e.g., Fernandez andSantamarina 2001). It is worth mentioning that the cementedsamples prepared in this study were cemented and curedinside the mould before loading, and hence the results and

discussion presented in this paper are limited to this particu-lar type of stress–cementation history.

Laboratory equipmentThe experiments were performed using a computer-

controlled triaxial machine designed and fabricated at theUniversity of Western Australia (UWA). Axial load and dis-placement were measured using an internal load cell and anexternal potentiometer, respectively, both attached to theloading ram. Internal submersible linear variable differentialtransformers (LVDTs) were also used to measure the strainslocally. The LVDTs were fixed in the sample using four alu-minium footings implanted in the sample by gluing theminside the rubber membrane prior to sample preparation(Sharma and Fahey 2003). The arrangement used to fix theLVDTs is shown in Fig. 2. This arrangement avoids possibleerrors due to the relative slippage between the rubber mem-brane and sample surface (Tatsuoka and Kohata 1995). Thismeasuring system can resolve axial strain down to about 1 ×10–5 (or 10–3%).

Terminology usedThe stress state is described using “Cambridge” in-

variants: deviator stress q = σ1′ – σ3′ and mean effectivestress p′ = (σ1′ + 2σ3′ )/3, where σ1′ and σ3′ are the major andminor principal effective stresses, respectively. The shearstrain parameter used is the deviator strain εs = 2/3(ε1 – ε3),which is equal to ε1 for undrained tests, where ε1 and ε3 arethe principal strains. Tests were performed on both isotro-pically and anisotropically consolidated samples. Radialstress paths in q–p′ space with constant stress ratio (=q/p′)were followed during anisotropic consolidation. The stressratio at the end of anisotropic consolidation is termed theconsolidation stress ratio (CSR = qo/po′ ), where qo and po′are the deviator stress (which is zero for isotropically con-solidated samples) and mean effective stress at the end ofconsolidation, respectively.

The terminology illustrated in Fig. 3 has been adopted todescribe the cyclic loading tests. During cyclic loading tests,a cyclic shear stress amplitude qcyc is superimposed on themean shear stress qmean. Depending on the relative magni-tude of qcyc with respect to qmean, the cyclic test is classifiedas a “one-way” (qcyc ≤ qmean) or “two-way” (qcyc > qmean)test. The initial tangent stiffness Go is obtained from themonotonic tests. The secant shear modulus for the whole

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Sharma and Fahey 1141

Soil

No. ofCIPSflushes

γdi

(kN/m3)qucs

(kPa)TS(kPa)

Percentcalcite addedby weight

γdf

(kN/m3)

LP 1 12.70 524 51 4.61 13.4LP 1 13.20 590 70 3.70 13.7LP 1 13.90 655 91 3.52 14.4LP 2 12.70 1200 — 8.05 13.8GW 2 9.81 350 — 15.00 11.3GW 2 9.81 600 — 17.00 11.5GW 3 9.81 2500 — 23.00 12.1

Note: γdf, unit weight of sample after cementation; γdi, unit weight of uncemented sample.

Table 1. Unconfined compressive strength (qucs) and tensile strength (TS) results of CIPS-cemented samples.

loop (Gloop) and cyclic shear strain (εscyc) are calculated asshown in Fig. 3.

Stiffness during monotonic loading

Initial stiffnessThe maximum initial tangential stiffnesses (Go) of both

cemented and uncemented soils were calculated using theinitial portion of the stress–strain curves obtained frommonotonic undrained triaxial tests. Samples with differentlevels of cementation were created and tested at differentconsolidation pressures under both isotropic and anisotropicconditions. The results are summarized in Fig. 4. Examina-tion of Fig. 4a clearly demonstrates that increasing the levelof cementation increases the initial stiffness and reduces the

effect of confining pressure on the initial stiffness. This isconsistent with results reported by other investigators (e.g.,Baig et al. l997; Fernandez and Santamarina 2001). On theother hand, results from samples subjected to anisotropicconsolidation shown in Fig. 4b reveal that the CSR hasa significant effect on the initial stiffness of the samples,where CSR is defined as the stress ratio (q/p′) correspondingto the radial stress path followed during anisotropic consoli-dation in q–p′ space. It can be observed that increasing theCSR significantly reduces the initial stiffness. Further, com-parison of the results from samples subjected to similar CSRat different cell pressures, shown in Fig. 4b, reveals that theinitial stiffness of anisotropically consolidated samples re-duces with increasing confining pressure. In other words, al-though all the isotropically consolidated cemented samples upto po′ of 1000 kPa have similar Go, it can be observed fromFig. 4b that samples consolidated at CSR of 0.75 at po′ of 200,

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Fig. 2. Schematic diagram of the setup of a sample in thetriaxial apparatus with internal LVDTs.

Fig. 3. Symbols and definitions for cyclic loading tests. Aloop,area of the hysteresis loop in an unloading–reloading cycle.

Fig. 4. Variation of initial stiffness of cemented GW samples:(a) isotropically consolidated samples; (b) anisotropically consol-idated samples.

600, and 1000 kPa show Go(ani)/Go(iso) of 0.83, 0.59, and 0.40,respectively, where Go(ani) is the Go value obtained from ananisotropically consolidated sample, and Go(iso) is the initialmaximum tangential stiffness obtained from isotropically con-solidated samples subjected to similar po′ .

These observations suggest that it is the level of cementa-tion that controls the initial stiffness of the samples ratherthan the mean effective stress, and the degradation of ce-mentation is more likely to occur with increasing deviatorstress than with increasing isotropic mean effective stress.

Degradation of stiffnessAs it has been observed that increasing the consolidation

deviator stress has a tremendous effect on the initial stiffnessof the samples, it is worth investigating the pattern of stiff-ness degradation with strain during monotonic shearing. Toexamine this, normalized curves of stiffness degradationwith strain are plotted for different monotonic tests inFigs. 5–10. The shear modulus considered in these figures isthe secant shear modulus normalized using the initial maxi-mum shear modulus values (Go) reported in Fig. 4.

Figure 5 shows the modulus reduction curve obtainedfrom uncemented GW samples consolidated to confiningpressures (po′ ) of 200 and 600 kPa. This figure clearly showsthat confining pressure has a significant effect on the posi-tion of the modulus reduction curve, which is similar towhat is often observed for other cohesionless soils. To exam-ine how the modulus reduction curves of uncemented GWsoil compare with those of other cohesionless soils, therange of modulus reduction curves obtained by Seed andIdriss (1970) is also shown in Fig. 5. Although the qualita-tive pattern of modulus reduction with strain is similar, cal-careous soil attains a faster rate of modulus reduction with ahigher strain threshold.

Figure 6 shows the modulus reduction curves obtainedfrom isotropically consolidated cemented GW samples withqucs of 0.6 MPa. There is not much difference in these threecurves, but there is nevertheless an indication that increasingthe confining pressure from 600 to 1000 kPa gives morerapid reduction in stiffness, although increasing the confin-ing pressure from 200 to 600 kPa gives a trend of decreasingrate of modulus reduction with increase in strain. This sug-gests that although confining pressure has a negligible effecton the initial stiffness of cemented samples, it can affect thepattern of stiffness reduction with strain. In particular, thefaster rate of stiffness degradation observed at the smallestconfining pressure (po′ = 200 kPa) may be due to the in-creasing brittleness in the stress–strain response resultingfrom the localized failure of the sample.

To facilitate comparison between uncemented and ce-mented samples, the range of modulus reduction curves ob-tained from Fig. 5 are replotted in Fig. 6. It can be observedfrom Fig. 6 that, within the range of confining pressuresused in this study, the stiffness degradation curves obtainedfrom cemented samples lie within the range of the un-cemented samples, although some difference can be ob-served if tests at similar confining pressures are compared.

Since the influence of consolidation history on the initialstiffness is significant, it is useful to examine how the CSRaffects the pattern of modulus reduction. Cemented sampleswith qucs of 0.6 MPa were tested at different CSRs and con-

fining pressures and the results are presented in Figs. 7 and8. To facilitate the comparison between isotropic and aniso-tropic consolidation, the modulus reduction curve obtainedfrom an isotropically consolidated sample is also superim-posed on Fig. 7. It can be observed that, although the CSRhas a significant effect on the initial stiffness, its influenceon the modulus reduction curve is rather insignificant, espe-cially at smaller confining pressures. On the other hand, ifthe samples subjected to a similar consolidation stress ratio(qo/po′ ) are compared (e.g., samples with qo/po′ = 0.75) asshown in Fig. 8, it can be observed that increasing the con-fining pressure decreases the rate of modulus reductionslightly.

Since the level of cementation is one of the most impor-tant parameters in controlling the stiffness of the sample,examination of the effect of level of cementation on modulusreduction is essential. Samples with qucs of 0.35 and

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Fig. 5. Degradation of stiffness obtained from isotropically con-solidated uncemented GW samples.

Fig. 6. Degradation of stiffness obtained from isotropically con-solidated cemented GW samples (qucs = 0.6 MPa).

2.5 MPa were tested and their corresponding modulus reduc-tion curves are shown in Figs. 9 and 10, respectively. Super-imposed on these figures is the range of modulus reductioncurves obtained from uncemented samples presented inFig. 5. Although there is some scatter, it can be observedthat, within the range of po′ examined in this study, themodulus reduction curves obtained from cemented sampleswith different levels of cementation, and even with higherpo′ , lie within the range of curves for uncemented samples.This is because, unlike the case for uncemented samples, ce-mented samples showed faster rates of modulus reductiondue to the rapid breakage of cementation, even at higher po′ .

To further examine curves of stiffness degradation withstrain obtained from different conditions, all the curves ofstiffness degradation with strain presented for different con-ditions in Figs. 6–10 are replotted together, and the range

defined by these plots is shown in Fig. 11. The range ofcurves for cemented samples obtained from monotonic testslie within the band represented by solid lines in Fig. 11. Therange of curves for uncemented samples and from Seed andIdriss (1970) are superimposed on the same figure. Fig-ure 11 clearly demonstrates that, within the range of po′ usedin this study, the modulus reduction curves for cemented anduncemented calcareous soil lie within a narrow range, but aclear difference can be observed between calcareous andnoncalcareous soils.

The pattern of degradation of stiffness with strain ob-tained from cemented LP samples is shown in Fig. 12. Onlyone level of cementation was used for this soil, giving qucs ofabout 0.5 MPa, and all the samples were consolidated underisotropic conditions. The maximum initial shear modulusobtained from these samples was about 600 MPa. Superim-posed on Fig. 12 is the range of modulus reduction curves

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Fig. 7. Degradation of stiffness obtained from anisotropicallyconsolidated cemented GW samples (po′ = 200 kPa, qucs =0.6 MPa).

Fig. 8. Degradation of stiffness obtained from anisotropicallyconsolidated cemented GW samples (qucs = 0.6 MPa).



obtained from cemented GW samples shown in Fig. 11.Although significant differences can be observed for thestress–strain behaviour of cemented LP and GW soils, withpeak monotonic strength being controlled by the cohesivecomponent in GW soil and by the frictional component inLP soil (Sharma and Fahey 2002a), the modulus reductioncurves for the two soils lie within a narrow band.

Loading rate is often found to control the rate of degrada-tion of stiffness. The monotonic tests on the GW and LPsoils were at an axial strain rate of 0.067 and 0.13%/min, re-spectively. To examine the effect of loading rate, monotonictests on cemented LP samples with qucs of 0.5 MPa werealso performed at strain rates of 1.33 and 13%/min; the re-sults are presented in Fig. 13 together with the results ob-tained from a sample tested at a loading rate of 0.13%/min.

It can be observed that, although the initial stiffness is inde-pendent of loading rate, increasing the loading rate results ina slight reduction in the rate of stiffness degradation.

Stiffness during cyclic loading

A large number of stress-controlled cyclic triaxial testswere performed on cemented GW and LP samples at a cy-clic frequency of 0.1 Hz. Different combinations of cyclicdeviator stress (qcyc) and mean deviator stress (qmean) wereimposed on samples with different consolidation historiessubjected to different cell pressures and levels of cementa-tion. The loop shear modulus (Gloop) is calculated as shownin Fig. 3, and the degradation of stiffness with respect to thenumber of cycles (N) and cyclic shear strain (εscyc) is investi-gated in detail.

An examination of degradation of stiffness with N ob-tained from cemented GW samples was presented in detailby Sharma and Fahey (2002b), who showed that the stiffnessof cemented GW samples reduces linearly with increasingN. Typical results obtained from one-way cyclic tests per-formed on isotropically consolidated cemented GW samplesat po′ = 200 kPa are shown in Fig. 14, with the correspond-ing monotonic stress–strain curve shown in the inset. All thecemented GW samples tested in this series showed similarresults, and further details can be found in Sharma andFahey. In Fig. 14 and subsequent figures, the cyclic loadingrange is indicated by quoting the maximum and minimumdeviator stress (qmax:qmin) in the cycles.

Typical results showing the variation of stiffness with Nobtained from cemented LP sand are shown in Fig. 15. Thedegradation is expressed as the value of Gloop in cycle N(Gloop-N) compared with Gloop in cycle 1 (Gloop-1). The insetto Fig. 15 is the corresponding monotonic stress–straincurve. Degradation curves are shown for tests with four dif-ferent cyclic stress ranges (qmax:qmin), viz. 600:10, 600:–100,800:10, and 1200:10 kPa. Three of these show modulus re-

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Fig. 11. Range of curves of stiffness degradation with strain ob-tained from cemented GW samples compared with the range ofcurves for uncemented GW samples and other sands.

Fig. 12. Degradation of stiffness obtained from isotropically con-solidated cemented LP samples (qucs = 0.5 MPa) compared withrange of curves for cemented GW samples.

Fig. 13. Effect of loading rate on the degradation of stiffness ob-tained from isotropically consolidated cemented LP samples(qucs = 0.5 MPa).

duction with increasing N, but one (1200:10 kPa) shows amodulus increase (“hardening”) with increasing N.

Comparison of these results with those obtained from ce-mented GW sand in Fig. 14 reveals that there are differencesin the pattern of degradation of stiffness between the twotypes of soils. In fact, such differences in degradation ofstiffness between these two types of soils can be expected ifthe postyield shearing behaviour of these samples is takeninto consideration. It can be observed from Fig. 15 that thepatterns of degradation of stiffness with N in cemented LPsand depend on the magnitude of the cyclic stresses, i.e.,qmax:qmin. The inset to Fig. 15 shows that in monotonicshearing, there is an initial yield (qyield) at about 900 kPa,followed by a softening phase, and then a gradual hardeningphase to a peak strength of about 1400 kPa. When subjectedto qmax smaller than qyield during cyclic loading, the ce-mented LP samples showed linear degradation of stiffness atsmall strain in a fashion similar to that for the cemented GWsamples. This reflects the degradation of cementation duringcyclic loading. On the other hand, when subjected to qmaxgreater than qyield during cyclic loading, a significant degra-dation of cementation (and hence stiffness) occurred duringfirst loading, and during subsequent loading the stiffnessshowed a tendency to increase. This is because at this stage,with the breakdown in cementation in the first cycle, thevariation of stiffness is controlled by the variation in themean effective stress in a pattern similar to that of the un-cemented soils where the response is frictional.

This means that for the samples in which a dilatant re-sponse dominates (samples subjected to very large qmaxcompared with qyield, e.g., test subjected to qmax:qmin of1200:10 kPa) an increase in stiffness could be observed withan increase in N. On the other hand, for samples subjected toqmax < qyield, following the breakdown of cementation, stiff-ness may remain nearly constant (e.g., test subjected toqmax:qmin of 600:10 kPa) or show a slight tendency to in-crease (e.g., test subjected to qmax:qmin of 800:10 kPa) withan increasing number of cycles, depending on the values of

p′ associated with that particular stage. It should be noted,however, that in both samples (samples with qmax:qmin of600:10 and 800:10 kPa) the initial reduction in stiffness withincreasing N is associated with the degradation of cementa-tion. In contrast, in samples subjected to two-way cyclicstress, a drastic decrease in stiffness is always observedtowards failure (e.g., test subjected to qmax:qmin of 600:–100 kPa).

The experimentally determined G/Go values for cementedGW soil are plotted against the deviator strain in Figs. 16–21, with deviator strain being εscyc for cyclic tests and εs formonotonic tests. The term G refers to Gloop in cyclic testsand Gsec in monotonic tests. Further, the term εscyc refersto cyclic deviator strain, which is the difference in strainbetween the maximum and minimum points of a loop asshown in Fig. 3. The results shown in Fig. 16 were obtainedfrom different tests with different isotropic consolidation

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Fig. 14. Degradation of loop stiffness with number of cycles ob-tained from isotropically consolidated cemented GW sampleswith qucs = 0.6 MPa and po′ = 200 kPa (after Sharma and Fahey2002b).

Fig. 15. Degradation of loop stiffness with number of cycles ob-tained from isotropically consolidated cemented LP samples(qucs = 0.5 MPa, po′ = 600 kPa): (a) qmax:qmin of 600:10 and600:–100 kPa; (b) qmax:qmin of 800:10 and 1200:10 kPa.

pressures and different combinations of one-way cyclicstresses. The stiffnesses obtained from cycle numbers 10,20, and 50 are shown in Fig. 16a; those from cycle numbers100, 200, and 500 in Fig. 16b; and those from cycle num-bers 1000, 2500, 5000, and 10 000 in Fig. 16c. Superim-posed on these plots is the range of modulus reductioncurves obtained from monotonic tests performed onisotropically consolidated cemented samples with po′ be-tween 50 and 1000 kPa.

It is clear from Fig. 16 that the higher stiffness is associ-ated with smaller strain, and a significant reduction in stiff-ness can be observed with increasing strain in cyclic tests, aresponse similar to that in monotonic tests. Further, signifi-cant degradation of stiffness occurred with an increasingnumber of cycles due to the larger strain mobilized at a

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Fig. 16. Degradation of loop stiffness with strain obtained fromisotropically consolidated cemented GW samples (qucs = 0.6 MPa):(a) cycle numbers 10, 20, and 50; (b) cycle numbers 100, 200,and 500; (c) cycle numbers 1000, 2500, 5000, and 10 000.

Fig. 17. Degradation of loop stiffness with strain obtained fromanisotropically consolidated cemented GW samples (qucs =0.6 MPa, CSR = 0.5).

Fig. 18. Degradation of loop stiffness with strain obtained fromanisotropically consolidated cemented GW samples (qucs =0.6 MPa, CSR = 2.25 and 2.50).

larger number of cycles. The comparison of the results fromN = 10 to 10 000 plotted in Fig. 16 clearly shows that thevariation of stiffness with strain lies within a very narrowband, suggesting that the number of cycles has very little in-fluence on the pattern of stiffness degradation with strain incemented samples. It can also be observed that the confiningpressure does not significantly influence the pattern of stiff-ness degradation of the cemented samples, even duringcyclic loading. This observation is in contrast with resultsobtained from uncemented materials, where a moderate ef-fect of confining pressure on stiffness during cyclic loadingwas reported (Lo Presti et al. 1997).

The type of loading, monotonic or cyclic, has a very neg-ligible effect on the variation of stiffness with strain on ce-mented samples. It is often reported that samples subjectedto cyclic loading showed a stiffer response and slower rate

of stiffness degradation compared with those subjected tomonotonic loading performed under similar conditions (LoPresti et al. 1997). This is because the mean effective stress,which has a significant influence on the stiffness, changescontinuously with increasing number of cycles duringundrained cyclic loading. The results presented in Fig. 16clearly show, however, that the pattern of degradation ofstiffness during monotonic and cyclic loading is very simi-lar.

Cyclic tests were also performed on anisotropically con-solidated samples with CSR varying from 0 to 2.5. Typicalresults obtained from these tests are shown in Figs. 17 and18. Superimposed on these figures is the range of curves ofstiffness degradation with strain obtained from monotonictests. It can be observed that CSR influences the pattern ofdegradation of stiffness. Thus, for samples subjected to CSRof 0.5 the pattern of degradation of stiffness with strain issimilar to that for isotropic samples (Fig. 17). A similar re-sponse was observed for samples subjected to CSR of 1.5.Once the CSR increases above 1.5, a clearer difference inthe pattern of degradation of stiffness with strain is observed(Fig. 18). In general, samples subjected to larger CSR showa relatively slower rate of degradation stiffness with increas-ing εs compared with samples subjected to smaller CSR.This is believed to be due to the significant degradation ofcementation occurring during consolidation of the samplesto larger CSR, i.e., Go is also affected by CSR, with highCSR resulting in lower Go, and therefore the pattern of re-duction in the absolute value of G is not much affected.

To examine the influence of the level of cementation onthe pattern of stiffness degradation, results obtained fromsamples with qucs of 2.5 MPa are shown in Fig. 19. If the re-sults shown in Fig. 19 are compared with weaker samplestested under similar conditions (Fig. 16), it can be observedthat a faster rate of degradation of stiffness occurs in sam-ples with a higher level of cementation due to the increasingbrittleness in the stress–strain response with increasing levelof cementation. Further, Fig. 19 shows that the confiningpressure and number of cycles have a very negligible effect

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Fig. 19. Degradation of loop stiffness with strain obtained fromisotropically consolidated cemented GW samples (qucs =2.50 MPa).

Fig. 20. Degradation of loop stiffness with strain obtained fromall tests performed on cemented GW samples.

Fig. 21. Degradation of loop stiffness with strain obtained fromall tests performed on cemented LP samples.

on the rate of degradation of stiffness on strongly cementedsamples. This suggests that the only difference observed inmodulus reduction between samples with different levels ofcementation is the rate of degradation of modulus, and theinfluence of other parameters, e.g., confining pressure andnumber of cycles, is qualitatively similar in samples withdifferent levels of cementation.

The variation of stiffness with strain obtained from a largenumber of tests performed on cemented GW samples is pre-sented in previous sections and the cyclic tests results werecompared with the range defined by monotonic tests. To fur-ther investigate the pattern of stiffness degradation withstrain obtained from cyclic and monotonic tests, all the cy-clic test results obtained from cemented GW samples areplotted in Fig. 20. In this figure, the range of stiffness degra-dation obtained from monotonic tests presented in Fig. 11 isalso replotted. It can be observed that all the cyclic test re-sults lie within the boundary defined by the monotonic tests.

The degradation of stiffness with strain obtained from cy-clic tests on cemented LP sand was also examined and thecyclic test results are presented in Fig. 21 together with therange defined by the monotonic tests. In general, cementedLP samples showed a pattern of degradation of stiffness sim-ilar to that observed in cemented GW samples. It can also beobserved that all the cyclic test results lie within a narrowband defined by the monotonic tests, as in the case of GWsamples.

Damping ratio

The hysteresis loops obtained at different numbers of cy-cles, from which the shear moduli of cemented GW soilswere determined in previous sections, were also used to cal-culate the damping ratio. The results obtained from all thetests are plotted in Fig. 22. Superimposed on the same figureis the range of damping ratios proposed by Seed and Idriss(1970) for silica sands. It can be observed that the differ-ences previously noted in stiffness degradation curves arealso reflected in the damping ratio, with the damping ratiobeing smaller at a particular strain level in cemented calcare-ous soils compared with that in uncemented noncalcareoussoils.

Summary and conclusions

Detailed experimental results on the deformation charac-teristics of two cemented calcareous soils obtained fromundrained monotonic and cyclic tests are presented in thispaper. The following conclusions are drawn from the analy-sis of the experimental results:(1) Increasing the level of cementation resulted in a signifi-

cant increase in the initial stiffnesses, with the latter be-ing less and less dependent on the confining pressure.Comparison of the pattern of stiffness degradationobtained from calcareous soils with that from other non-calcareous soils showed that calcareous soils attainedfaster rates of stiffness degradation with a higher strainthreshold.

(2) Examination of the effect of loading rate on the stiffnessshowed that, although the effect of loading rate on ini-tial stiffness is negligible, a slight difference in the pat-

tern of degradation of stiffness with strain is observed,with samples subjected to faster strain rates attaining aslightly slower rate of stiffness degradation, and viceversa.

(3) Examination of the influence of number of loading cy-cles on the stiffness revealed that the modulus reductionwith increasing number of cycles is found to depend onwhether the postyield behaviour is controlled by the co-hesive component or the frictional component. In theGW soil, where the sample showed a brittle postyieldresponse, the modulus reduction with increasing numberof cycles is found to be linear. In the LP samples, how-ever, where the postyield response is controlled by fric-tional behaviour, the pattern of modulus reduction isfound to depend on the magnitude of cyclic stress andthe strain mobilized during the cyclic test.

(4) Examination of the degradation of stiffness with cyclicstrain showed that samples subjected to different pre-cyclic and cyclic loading conditions, with the number ofcycles varying from 1 to 10 000, fall within a rangebounded by the monotonic tests.

(5) The damping ratio of the cemented calcareous soils wasalso examined and was found to lie below the range de-fined for other noncalcareous soils.

The results and discussion presented in this paper areobtained from samples cemented before consolidation, andapplication to other cementation sequences needs further in-vestigations.

Acknowledgements

The work presented in this paper forms part of theresearch activities of the Centre for Offshore FoundationSystems (COFS), established and supported under the Aus-tralian Research Council Research Centres Program. Thefirst author was supported by an International PostgraduateResearch Scholarship (IPRS) and a Geomechanics GroupStudentship. This support is gratefully acknowledged. Thecollaboration of Dr. Edward Kucharski and Mr. Bob Middle-

© 2004 NRC Canada


Fig. 22. Damping ratio with cyclic strain obtained from all testsperformed on cemented GW samples.

ton from Lithic Technology (who provided the CIPS solu-tion) is also appreciated.

References

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List of symbols

Aloop area of the hysteresis loop in an unloading–reloadingcycle

B pore pressure parameterD damping ratioG secant shear modulus for monotonic tests and loop shear

modulus for cyclic testsGloop secant shear modulus for the whole loop

Gloop-1 secant shear modulus for the whole loop correspondingto the first cycle

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Gloop-N secant shear modulus for the whole loop correspondingto the Nth cycle

Go initial tangent shear modulusGo(ani) Go value obtained from an anisotropically consolidated

sampleGo(iso) Go value obtained from an isotropically consolidated

sampleGsec secant shear modulus from monotonic tests

N cycle numberp′ mean effective stress (= (σ1′ + 2σ3′ )/3)po′ initial consolidation pressureq deviator stress (= σ1′ – σ3′ )

qcyc cyclic deviator stressqmax maximum deviator stress

qmean mean deviator stressqmin minimum deviator stress

qo deviator stress at end of consolidationqpeak peak strengthqucs unconfined compressive strength

qyield yield deviator stressTS tensile strength

ε1, ε3 principal strainsεs deviator strain (= 2/3(ε1 – ε3))

εscyc cyclic deviator strainγdf unit weight of sample after cementationγdi unit weight of uncemented sample

σ1′, σ3′ major and minor principal effective stresses

© 2004 NRC Canada


deformation characteristics of two cemented calcareous soils

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