Liquefaction Resistance of Clean and Nonplastic Silty SandsBased on Cone Penetration Resistance

J. A. H. Carraro, S.M.ASCE1; P. Bandini, S.M.ASCE2; and R. Salgado, M.ASCE3

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Abstract: Liquefaction of granular soil deposits is one of the major causes of loss resulting from earthquakes. The accuracyassessment of the likelihood of liquefaction at a site affects the safety and economy of the design. In this paper, curves of cyclic reratio ~CRR! versus cone penetration test~CPT! stress-normalized cone resistanceqc1 are developed from a combination of analysis anlaboratory testing. The approach consists of two steps:~1! determination of the CRR as a function of relative density from cyclic triaxitests performed on samples isotropically consolidated to 100 kPa; and~2! estimation of the stress-normalized cone resistanceqc1 for therelative densities at which the soil liquefaction tests were performed. A well-tested penetration resistance analysis based oexpansion analysis was used to calculateqc1 for the various soil densities. A set of 64 cyclic triaxial tests were performed on specimof Ottawa sand with nonplastic silt content in the range of 0–15% by weight, and relative densities from loose to dense for each grto establish the relationship of the CRR to the soil state and fines content. The resulting (CRR)7.5-qc1 relationship for clean sand isconsistent with widely accepted empirical relationships. The (CRR)7.5-qc1 relationships for the silty sands depend on the relative effectsilt content on the CRR andqc1 . It is shown that the cone resistance increases at a higher rate with increasing silt content thanliquefaction resistance, shifting the (CRR)7.5-qc1 curves to the right. The (CRR)7.5-qc1 curves proposed for both clean and silty sands aconsistent with field observations.

DOI: 10.1061/~ASCE!1090-0241~2003!129:11~965!

CE Database subject headings: Silty soils; Penetration resistance; Liquefaction; Triaxial tests; Cohesionless soils; Sand.

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Introduction

The loss of life and damage to facilities and infrastructure dueliquefaction have been very significant in past earthquakes. Moof the damage in the Marina district in San Francisco and in areof east San Francisco resulting from the 1989 Loma Prieta earquake in California, for example, was caused by liquefactio~Earthquake Engineering Research Institute 1990!. The impact ofrefinements in the accuracy of the methodology available for liquefaction analysis is greater in borderline cases. Increased acracy in liquefaction potential assessment may lead either to rduced construction costs or to the adoption of a safer desidecision with respect to the results of a less accurate method; brepresent beneficial outcomes. Greater accuracy in evaluatinguefaction potential should continue to be a goal of geotechnicengineering research and is the underlying motivation of thpresent study.

Liquefaction potential assessment requires the determinatiof two values:~1! the loading the deposit will be subjected to as

1PhD Candidate, School of Civil Engineering, Purdue Univ., WesLafayette, IN 47907. E-mail: joao@purdue.edu

2PhD Candidate, School of Civil Engineering, Purdue Univ., WesLafayette, IN 47907. E-mail: paola@ecn.purdue.edu

3Professor, School of Civil Engineering, Purdue Univ., West Lafayette, IN 47907. E-mail: rodrigo@ecn.purdue.edu

Note. Discussion open until April 1, 2004. Separate discussions mube submitted for individual papers. To extend the closing date by omonth, a written request must be filed with the ASCE Managing EditoThe manuscript for this paper was submitted for review and possibpublication on September 18, 2000; approved on February 12, 2003. Tpaper is part of theJournal of Geotechnical and GeoenvironmentalEngineering, Vol. 129, No. 11, November 1, 2003. ©ASCE, ISSN 10900241/2003/11-965–976/$18.00.

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a result of the earthquake; and~2! the resistance of the soil toliquefaction. In the widely used liquefaction assessment procdure initially outlined by Seed and Idriss~1971!, and later im-proved by Seed~1979!, Seed and Idriss~1982!, and Seed et al.~1983, 1985!, these two quantities are the cyclic stress ratio~CSR! and the cyclic resistance ratio~CRR!. The CSR is the ratioof the shear stress generated by the earthquake to the verteffective stresssv8 at the desired depth. The CRR is the ratio othe cyclic resistance to liquefaction tosv8 . Liquefaction at a givendepth is expected to occur when CSR.CRR at that depth.

Empirical correlations with the standard penetration test~SPT!stress-normalized blow countN1 or with the cone penetration test~CPT! stress-normalized cone resistanceqc1 are used to estimatethe CRR in most cases~Robertson and Campanella 1985; Seeand De Alba 1986; Stark and Olson 1995; Robertson and Wrid1998!. The stress-normalized cone resistanceqc1 for a given pointwithin a soil deposit is defined as the cone resistance that the swould have at the same relative density and coefficient of laterstress at rest,K0 , if the vertical stress were equal to 100 kPaMitchell and Tseng~1990! developed a CRR liquefaction resis-tance relationship from combining the results of laboratory tesand a cone resistance analysis. The present paper aims to deva CRR-qc1 relationship for both clean and silty sands from cyclictriaxial test results and an extensively tested cone penetrationsistance analysis~Salgado et al. 1997a,b, 1998; Salgado and Radolph 2001!.

Liquefaction Potential Assessment

Assessment of Liquefaction Potential of Clean Sands

The basic idea behind the development of the usual empiricSPT- and CPT-based liquefaction resistance curves is the follo

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ing: ~1! select sites for which SPT or CPT results obtained befo~or, much more commonly, after! the occurrence of a given earthquake are available,~2! compute the cyclic stress ratio for eacsite for the given earthquake, and~3! plot the SPT blow countNSPT or cone resistanceqc versus the cyclic stress ratio both fosites that have and for sites that have not liquefied. The end reis a liquefaction resistance curve that separates sites that are lito liquefy from those that are not, based on previous experienThere is an important source of uncertainty in this approach:assessment of whether a soil deposit has liquefied~and if it did,whether it liquefied completely or locally!. In general, the evi-dence of liquefaction consists of sand boils, tilted structures, aruptured pipelines. Identification of the zone within a soil deposwhere liquefaction initially occurred, which is necessary for corelating the occurrence of liquefaction with the appropriateqc ~orNSPT) value, is not a simple task based on this type of evidenc

Free of many of the disadvantages present in the SPT, the cpenetration test is now routinely used in site characterizatioRobertson and Campanella~1985! and Seed and De Alba~1986!proposed CPT-based liquefaction potential assessment relatships developed from the original SPT-based relationships uscorrelations between cone resistance and SPT blow count~Fig. 1!.Shibata and Teparaksa~1988! generated liquefaction assessmecharts from a large database of CPT field data~Fig. 2!. Morerecent CPT-based correlations have been proposed by StarkOlson ~1995! and Robertson and Wride~1998! ~Fig. 3!. Mitchelland Tseng~1990!, using calibration chamber test results for varous clean sands, calibrated a penetration resistance theoryused it to compute field cone resistance for soil states at whliquefaction occurred in laboratory liquefaction tests for 15 loaing cycles, obtaining the curves shown in Fig. 2. The relationshof Figs. 1–3 were developed for earthquakes with magnitude7.5. A magnitude scaling factor~MSF! must be used for differentearthquake magnitudes. The 1996 National Center for EarthquEngineering Research~NCEER! Workshop on liquefaction rec-ommended a range of MSF values for use in practice~Youd andIdriss 2001!. Participants in the NCEER Workshop endorsed thuse of the curve by Robertson and Campanella~1985!, slightlyadjusted for low CRR values by Robertson and Wride~1998! toaccount for recently available data. This relationship does n

Fig. 1. Semiempirical correlations between cyclic resistance ra(CRR)7.5 for 7.5-magnitude earthquake and normalized cone restanceqc1 for sands according to Robertson and Campanella~1985!and Seed and De Alba~1986!

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account for two factors that may be important in liquefactsusceptibility assessment: lateral stress effects~Salgado et al.1997a! and the amount and nature of fines. The present pfocuses on the effect of nonplastic fines on liquefaction resista

Assessment of Liquefaction Potential of Silty Sands

Several SPT- and CPT-based liquefaction potential assesscurves for sand containing fines have been proposed formagnitude earthquakes. Liquefaction resistance curves forcontaining fines have been commonly referred to the mean gsizeD50 and fines content~Figs. 1–3!. The liquefaction resistanccharts by Robertson and Campanella~1985!, Seed and De Alba~1986!, Shibata and Teparaksa~1988!, and Stark and Olson~1995! do not refer to the plasticity of the fines fraction of th

os- Fig. 2. Semiempirical correlations between cyclic resistance r

(CRR)7.5 for 7.5-magnitude earthquake and normalized cone retanceqc1 according to Shibata and Teparaksa~1988! and Mitchelland Tseng~1990!

Fig. 3. Semiempirical correlations between cyclic resistance r(CRR)7.5 for 7.5-magnitude earthquake and normalized cone retanceqc1 for sands according to Stark and Olson~1995! and Robert-son and Wride~1998!

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Table 1. Maximum and Minimum Void Ratios, Limit Void Ratio, Limit Relative Density, Critical-State Friction Angle, Regression ParameCg , eg , andng for Calculation ofG0 , and Dilatancy ParametersQ andR for Clean and Silty Ottawa Sand~Salgado et al. 2000!

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0 0.78 0.48 — — 29.5a 611 2.17 0.437 9.9a 0.86a

5 0.70 0.42 0.69 3 31.0a 453a 2.17 0.458a 9.1a 20.33a

10 0.65 0.36 0.60 17 32.0a 354a 2.17 0.584a 9.3a 20.30a

15 0.63 0.32 0.51 38 32.9a 235a 2.17 0.751a 11.8a 1.54a

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soils contained in the field database used to develop the charts.The approach proposed by Robertson and Wride~1998!, on theother hand, suggests that soils containing nonplastic silt~plasticityindex PI,5! for a given fines content have lower liquefactionresistance~in terms of CRR! than that of soils with plastic fines.

The plasticity index of the fines fraction has been recognizedas an important factor in the liquefaction susceptibility of siltysand~Ishihara and Koseki 1989; Ishihara 1993!. These authorsfound that sands containing fines with PI,10 do not exhibit asignificant increase of liquefaction resistance with respect to thatof clean sands, while sands with plastic fines~PI.10! show aconsiderable increase in liquefaction resistance with increasingPI. Ishihara~1993! attributes the greater resistance to liquefactionof sands containing plastic silt to the cohesion of the fines. Ac-cording to Ishihara~1985!, tailing silty sands can be as liquefiableas clean sands due to the origin and nonplastic nature of the fines.Troncoso and Verdugo~1985! found that the liquefaction resis-tance of tailing sands can even be reduced by the presence ofnonplastic silt and attribute this effect to a decrease in the particleinterlocking by the presence of fines between sand contacts.

Chang~1987! reported that data for earthquakes in China andJapan suggest that soils containing either plastic or nonplasticfines are not exempt from liquefaction. In the recent earthquakesin Kobe, Japan~1995!, and Adapazari, Turkey~1999!, numerouscases of liquefaction occurred in sands containing both plastic andnonplastic fines. These were made evident by widespread shallowfoundation failures, numerous cases of lateral spreading, andsome landslides~e.g., Ishihara 1997; Yoshida et al. 2001!. It ap-pears that in at least some of these cases sites that might havebeen considered safe according to current SPT-based liquefactionresistance correlations not only underwent liquefaction, but did soin a very significant way. This suggests that study of this topic istimely and may provide the basis for future revisions in currentlyaccepted correlations.

Liquefaction susceptibility is also influenced by other compo-sitional characteristics that influence volume change behavior,such as particle shape and gradation. According to Kramer~1996!, well-graded soils are generally less susceptible to lique-faction than poorly graded soils. The filling of voids betweenlarger particles by smaller particles in a well-graded soil results inlower volume change potential under drained conditions and, con-sequently, lower excess pore pressures under undrained condi-tions. Field evidence indicates that most liquefaction failures haveinvolved uniformly graded soils. One of the few cases of lique-faction failure of well-graded deposits is reported by Ishihara~1997!, who refers to the liquefaction of a silty, sandy gravelunder intense shaking during the Kobe earthquake.

Particle shape can also influence liquefaction susceptibility.According to Kramer~1996!, soils with rounded particle shapesare known to densify more easily than soils with angular particles.Particle rounding frequently occurs in fluvial and alluvial envi-

ronments where loosely deposited saturated soils are frequefound, and liquefaction susceptibility is often high in those area

Liquefaction Resistance of Silty Sands: PreviousLaboratory Studies

Research on liquefaction initiation of silty sands, particularly intiation due to cyclic loading, has been limited. Whether liquefation resistance goes up or down with fines content depends onbasis of comparison, of which there are three:~1! same overall~total or global! void ratio;~2! same relative density; and~3! samesand skeleton~or matrix! void ratio. Shen et al.~1977! testedmixtures of Ottawa C-109 and Ottawa C-190 with nonplastic sranging from 0 to 25%, all prepared by moist tamping at a costant dry unit weight of 16.7 kN/m3 and void ratio of approxi-mately 0.56. Their results show that liquefaction resistancecreases due to the presence of fines for the same sand skelvoid ratio. The skeleton void ratio of a silty sand is calculated bassuming that the volume occupied by silt particles is part of tvolume of voids~Kuerbis et al. 1988!. However, when overallvoid ratio is used as a basis of comparison, the same results sha significant reduction in the liquefaction resistance of silty sanwith increasing fines. Since Ottawa C-109 was also used in tpresent experimental program, the maximum and minimum voratios for this sand with various percentages of silt are availab~Table 1!. This allowed estimation of the relative densities of thsilty sand samples tested by Shen et al.~1977!. Comparison of theCRR of silty sand with the CRR of clean sand, provided by Sheet al.~1977! for various densities, shows that the addition of fineincreases the CRR of silty sand above that of clean sand for fixvalues of relative density.

Kuerbis et al.~1988! also used the skeleton void ratio as thbasis for comparison of liquefaction testing done on a silty saand observed the same increase in CRR with fines contentobserved by Shen et al.~1977!. They observed no fundamentadifference in behavior between clean and silty sands. In triaxcompression, an increase in fines content led to increased dtancy. In triaxial extension, an increase in fines content ledreduced contractiveness. Both observations are consistent wincreased liquefaction resistance. Kuerbis et al.~1988! also foundthat liquefaction resistance progressively decreases as silt conincreases up to 21%, for a given value of either void ratio orelative density. Kuerbis et al.~1988! used the slurry depositionmethod for preparation of their specimens. This method attemto simulate the natural sedimentation of these materials outsuspension in water, as is often observed in alluvial deposits ahydraulic fills. It differs from water sedimentation techniques ithat homogeneous specimens are obtained, as segregationnot happen.

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Lade and Yamamuro~1997! studied the static liquefaction oftwo sands~Nevada and Ottawa!, each with two different grada-tions, deposited with various percentages of nonplastic silt invery loose state. They found evidence of ‘‘unexpected’’ soil behavior. While clean sands are usually increasingly dilatant witincreasing relative density and decreasing effective confininstress, the silty sand specimens they tested showed increasdilatancy with increasing effective confining stress. It was alsobserved that increasing fines content led to lower peaks ofq5s182s38 (s18 ands38 are the major and minor effective principalstresses, respectively! in undrained triaxial compression testseven with slight increases in relative density. They explained thbehavior as resulting from the fabric obtained by dry depositioof the silty sand. Some of the silt particles are positioned betweesand particles, keeping them from developing an effective cotact, or even any contact at all. Indeed, Vaid~1994! noted that theskeleton void ratio of silty sand obtained through dry depositiotends to be high, and Mulilis et al.~1977! noted that, even atsimilar densities, specimens of clean sand prepared dry weweaker than specimens of clean sand prepared by moist tampiTherefore, the fabric of specimens formed by dry deposition appears to be less stable or strong than that of specimens formedother processes. A soil with the fabric postulated by Lade anYamamuro~1997! is very contractive while the silt particles havenot yet been displaced from between the sand particles. As eithconfining or shear stress is applied, these silt particles are dplaced into the voids between sand particles, the volume dcreases, and better contact develops between the sand particleis this better contact that leads to an increase in dilatancy~orreduction in contractiveness! with increasing effective confiningstress.

The proposed fabric generates skeleton void ratios higher ththe maximum void ratioemax of the sand matrix, as is indeedobserved for all specimens tested by Lade and Yamamuro~1997!.It is interesting to note that the specimens tested by Shen et~1977! had skeleton void ratios lower than theemax of Ottawasand for all but 17.5, 20, and 25% fines contents. The specimbehavior observed in their testing is normal, correspondingincreasing dilatancy~or decreasing contractiveness! with increas-ing relative density and decreasing effective confining stresShen et al.~1977! do note that the trends of the CRR with densitychange markedly as the silt content rises above 20%, an obsertion that is consistent with the postulated changin fabric at this value of fines content. The findings of Zlatovic´and Ishihara~1997! corroborate the conclusions of Lade andYamamuro~1997! regarding the effect of fabric. Yamamuro andCovert ~2001! performed drained and undrained monotonic anundrained cyclic triaxial tests at different effective confiningstresses on very loose Nevada sand with 40% silt content ppared by the dry deposition method. Their specimens resultedhighly contractive, even at large axial strains, because of the mocompressible structure of this material compared with that oclean sand or sand with low silt contents, such as those testedLade and Yamamuro~1997!.

Troncoso and Verdugo~1985! studied the liquefaction resis-tance of tailings sand with nonplastic silt in various percentageThey used the void ratio as the basis of comparison among tdifferent silt contents. They did find that the CRR decreases wiincreasing fines content at a given void ratio, but that the voiratio would correspond to radically different relative densities fodifferent fines contents.

From a series of cyclic triaxial tests on specimens preparedthe moist tamping method, Singh~1994! found that sand with 10,

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20, and 30% nonplastic silt~by weight! shows less resistance toliquefaction than clean sand, for either a given relative densitvoid ratio, or skeleton void ratio. Koester~1994! observed similarbehavior for numerous sand specimens with low plasticity finecontent up to 24–30%, for a given void ratio. Further increase ofines content resulted in specimen strengthening with respectliquefaction. Erten and Maher~1995! performed cyclic triaxialtests on specimens of Ottawa sand with various gradationsSil-Co-Sil ~a nonplastic silt!, prepared following the moist tamp-ing method. Using the void ratio as the base of comparison, theauthors found that the presence of nonplastic fines reduces tliquefaction resistance with respect to that of clean sand. Erteand Maher~1995! also noticed that this reduction is less pro-nounced for low-plasticity fines. Since the maximum and minimum void ratios of combinations of these materials were detemined by Salgado et al.~2000!, it is possible to compare theirresults with respect to relative density. It is observed that, forgiven relative density, the CRR corresponding to attainment o5% double-amplitude axial strain in 20 cycles increases consideably with the addition of 10% nonplastic silt~by weight! to cleanOttawa sand, while further increase of the silt content to 20%causes a reduction of the CRR to values below those of cleasand.

Polito and Martin~2001! performed cyclic undrained triaxialtests on Yatesville and Monterey sands with nonplastic silt prepared by moist tamping. They found that the liquefaction resistance increases with increasing silt content for a given value othe skeleton void ratio for Yatesville sand; however, this trendwas not observed for Monterey sand. Their specimens, preparat constant void ratio, exhibited a decrease in liquefaction resitance with increasing silt content up to 35–50%, after which thspecimens get stronger. Despite the scatter of the results for cycresistance versus relative density presented by Polito and Mar~2001!, it can be seen that specimens with low silt content~up to12%! have liquefaction resistance similar to or slightly higherthan clean sands. For higher silt content~up to 50%!, a trend isnot evident.

Dezfulian ~1984! presented results of cyclic triaxial tests onspecimens of alluvial sands and silty sands. Even though Defulian ~1984! reported a general trend of increasing liquefactionresistance with fines content, this author also recognized that tactual effect of silt content on the results was difficult to quantifybecause of the evident specimen disturbance and presence of cwithin the fine fraction. Specimens hadD50 varying from 0.002 to0.2 mm, approximately. Dezfulian~1984! concluded from his datathat there is no apparent relationship betweenD50 and liquefac-tion resistance. Amini and Sama~1999! and Amini and Qi~2000!performed undrained triaxial tests on uniform and layered specmens of sand-silt-gravel and sand-silt mixtures in various propotions. These researchers found no significant difference betwethe liquefaction resistance of stratified and uniform specimens fothe relative density and effective confining stress levels considered. Amini and Sama~1999! prepared specimens consolidated a100 kPa effective stress with a target relative density of 50% anvoid ratio of 0.64. They found that specimens with 25 and 50%low-plasticity silt ~PI513! had higher liquefaction resistance thanthose without silt. Specimens tested by Amini and Qi~2000! wereprepared at a target relative density of 40% and void ratio of 0.7and consolidated to effective stresses of 50, 100, and 250 kPThe results of Amini and Qi~2000! show that specimens with 10,30, and 50% silt content have higher liquefaction resistance thaclean sand, and that this effect is more pronounced as the scontent increases. They also found that the CRR decreases wh

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the effective confining stress is increased for a given relative dsity and silt content.

In summary, interpretation of the majority of the availablstudies suggests that the addition of nonplastic fines increasesCRR if the relative density is used as the basis for comparison.the same void ratio, addition of nonplastic fines leads to lowCRR values.

Experimental Program and Procedures

Material Tested and Specimen Preparation

All cyclic triaxial tests in this study were performed on reconsttuted specimens of Ottawa sand with 0, 5, 10, and 15% silt cotent by weight. Ottawa sand is a standard, clean quartz sadesignated as ASTM C 778~also known as ASTM C 109!. Ot-tawa sand particles are round to subround, with diameters rangfrom 0.1 to 0.6 mm. This sand is classified as SP according toUnified Soil Classification System, has a coefficient of uniformiCu of 1.43~poorly graded sand!, mean grain sizeD50 of 0.38 mm,and specific gravityGs of 2.65. The maximum and minimum voidratios emax and emin are 0.78 and 0.48, respectively, determineaccording to ASTM D 4254-91 and ASTM D 4253-93. The minmum density was obtained by pouring sand through a thin-wcylindrical tube~method B! into a standard compaction mold witha volume of 2,830 cm3; the loosest state was achieved by liftinthe tube while releasing the sand into the mold. Maximum denswas reached by densifying dry sand in an identical mold usingelectromagnetic, vertically vibrating table with a frequency of 6Hz ~calibrated according to Kaufman et al. 1979 as recommendby ASTM D 4253-93!. A value of the double amplitude of verticalvibration of 0.379 mm was found to be optimum for all gradations. The nonplastic fines are #106 Sil-Co-Sil ground silica froU.S. Silica Co., Ottawa, Ill. This nonplastic silt passes the #2sieve and is composed of SiO2 (99.8%), with Al2O3 (0.05%) andFe2O3 (0.035%) as secondary components. The specific gravof this silt is 2.65. The grain size distribution of both Ottawa sanand Sil-Co-Sil can be found in Salgado et al.~2000!.

One of the objectives of the present research was to stuspecimens prepared with a method that reproduces the natdeposition of silty sand in water, as observed in natural alluvdeposits and hydraulic fills. A modified version of the slurry depsition method~Kuerbis and Vaid 1988! was used in the presentstudy to prepare specimens of clean and silty sands.

First, the weights of sand and silt needed for the desired fincontent were estimated and dry mixed. The dry mixture wtransferred to a cylindrical plexiglass tube, partially filled witdeaired water, and then thoroughly mixed by shaking the tubeapproximately 20 min to achieve mixture uniformity and slurrconsistency. After that, the rubber cap was removed, a very smamount of deaired water was added to raise the water level bto the tube top, and the tube was topped with a filter paper aporous stone. The tube containing the slurry was immediatinverted, while holding the porous stone in place, and positioninside the triaxial split mold, where a stretched, thin membrafilled with deaired water was already in place. The contents of ttube were released into the membrane by slowly raising the tuDensification of the specimen was accomplished by carefully asymmetrically tapping the sides and base of the specimen mafter slurry deposition. Because the mass of sand and silt usespecimen preparation could be accurately estimated, it was psible to obtain a relative density that was reasonably close ttarget value by measuring the change in height of the specimen

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it densified. In this study, specimens had heights and diametersthe order of 165 and 70 mm, respectively. More details of thespecimen preparation and testing procedures will be found in J. AH. Carraro~PhD dissertation, Purdue University, West LafayetteInd., in preparation!.

Liquefaction Testing Procedure

The testing program for the assessment of the liquefaction resitance of silty sands consisted of a series of 64 cyclic, undrainetriaxial tests on clean and silty sands to establish the dependenof cyclic resistance ratio on soil state and silt content. The apparatus used to perform the cyclic triaxial tests in this study is aCKC automatic triaxial testing system~Soil Testing EquipmentCo., San Francisco, Calif.! ~Chan 1981!. The volume change, theeffective pressure, and the cell pressure during the test are mesured using sensitive differential pressure transducers.

All specimens were consolidated and tested at an effectivisotropic confining stresss38 of 100 kPa. Consolidation was com-pleted in periods of time ranging, approximately, from 30 min forclean sand specimens to 240 min for silty sand specimens, resuing in full dissipation of the excess pore pressure. Because spemen saturation is essential in such tests, back pressures up to 5kPa were applied to ensure thatB values in excess of 0.96 wereobtained for all specimens~mostB values were higher than 0.98!.Tests were performed on various sets of specimens, varying threlative density and silt content to determine the effect of bothfactors on the liquefaction resistance. A deformation of 5%double-amplitude axial strain was the criterion used in this studto define liquefaction of specimens of clean sands and sands cotaining fines ~Ishihara 1993!; however, most specimens wereloaded until 15% double-amplitude axial strain was reached. Foeach set of specimens, the cyclic deviator stress was varied sinsoidally so that 5% of the axial strain could be reached in anumber of cycles ranging from 5 to 60 in most cases. Cycles werset to start in compression loading for all tests.

The values of relative densities and void ratios presented ithis paper are the values after consolidation. Liquefaction resistance was determined for specimens with relative densities varing from loose to dense for each gradation~the study was notfocused on a single value of relative density!. For practical pur-poses, target relative densities were not set identical for all gradations, but this did not prevent the comparison of results becauof the amount of available data. For mixtures with target siltcontents of 5, 10, and 15%, the averages of the actual silt contenwere 5.2, 10.5, and 14.7%, respectively, with a maximum coefficient of variation of 0.08. No particle segregation was observed aany stage of the testing.

Liquefaction Test Results

Undrained cyclic triaxial tests were performed on Ottawa sanwith 0, 5, 10, and 15% nonplastic fines over a wide range orelative densities for each gradation. For loose specimens, a staof zero effective stress was observed to coincide with the initiation of liquefaction marked by a large axial deformation of thespecimen. Dense specimens, on the other hand, reach 5% doubamplitude axial strain before the effective stress drops to zer~which, in fact, may never happen for a given test!. This showsthat the influence of the liquefaction criterion adopted for tesresult interpretation is more significant for medium-dense andense specimens, while it is unimportant for loose specimens.clear tendency of the specimens to initiate liquefaction in eitheextension or compression was not observed.

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Fig. 4. Cyclic resistance ratio CRR versus number of cyclesN required for liquefaction for~a! clean Ottawa sand;~b! Ottawa sand15%nonplastic silt;~c! Ottawa sand110% nonplastic silt;~d! Ottawa sand115% nonplastic silt

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Semilogarithmic plots of the CRR versus the number of cyclesN required for liquefaction were prepared for each gradation~Fig.4!. The criterion used in this study for defining initiation of liq-uefaction for both clean and silty sands is the number of cyclesrequired to develop 5% double-amplitude~peak-to-peak! axialstrain. N values were determined directly from the records ofaxial strain versus time~in seconds! because all tests were carriedout at the frequency of one cycle per second. Results from speci-mens with similar relative densities, within a range of63% inmost cases, were grouped together and are presented in Fig. 4. InFig. 4~b!, a single data point forDR566% was included with theonly purpose of giving a qualitative idea of the likely trend and tofurther support the rest of the data. Fig. 4 shows the averagerelative density and the corresponding void ratio of each set ofspecimens. The number of cycles required to produce liquefactiondecreases with increasing CRR for the same relative density,mean effective stress, and fines content, as expected.

Different criteria defining the cyclic resistance of soils basedon laboratory testing may be found in the literature. According toRobertson and Wride~1998!, the CRR is typically taken at about15 cycles of uniform loading to represent an equivalent earth-quake loading of magnitude 7.5, i.e., (CRR)7.5. Following Ishi-hara~1993!, the cyclic stress ratio (CRR)7.5 required to produce5% double-amplitude axial strain~peak to peak! at 20 uniformcycles was used as the criterion to define liquefaction of clean andsilty sands and generate the curves in Fig. 5. This is generallyconsidered to correspond approximately to a 7.5-magnitude earth-

quake. For a given value of relative density, the cyclic resistanof sand increases slightly with the addition of very low percenages of nonplastic silt. Between 0 and 5% fines content, the cyresistance rises slightly for relative densities ranging from 4070%. Increasing the silt content from 5 to 10% decreasescyclic resistance slightly for specimens with relative densitiranging from 40 to 70%. The cyclic resistance of mixtures with5, and 10% silt and relative densities around 80% is appromately the same. Further addition of nonplastic fines to 15causes the cyclic resistance to drop to values considerably lothan those obtained for specimens with 5 and 10% fines aslightly lower than those observed for clean sand with simirelative density. This reversal in the trend for 15% fines contemay continue for higher silt content and is likely due to thgradual change in the soil fabric with increasing silt content~Sal-gado et al. 2000!, as discussed in detail in a subsequent sectiThis reversal was also observed in previous studies, as discupreviously.

In Figs. 5~b–c!, the cyclic test results are compared with respect to global and skeleton void ratios after consolidation. Tcyclic resistance of sand progressively decreases when thecontent is increased for a given void ratio. When the skeleton vratio is used as the basis of comparison, the liquefaction retance of the silty sand mixtures is virtually independent of scontent and slightly higher than the liquefaction resistanceclean sand.

970 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / NOVEMBER 2003

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Hydraulic Conductivity Tests

Hydraulic conductivity tests using the flexible wall techniquwere also performed on the silty sand according to the standASTM D 5084-90 ~reapproved in 1997! as part of the testingprogram. The purpose of these tests was to determine the hydlic conductivity K, the coefficient of volume compressibilitymv ,and the coefficient of consolidationCv . Knowledge of the valuesof these quantities allows determination of whether cone penetion in silty sands takes place under drained or partially drainconditions, as discussed later. Specimens with 15% silt conwere prepared following the same procedure and tested inidentical cell as the triaxial test specimens. As an examplesaturated sand specimen with 15% nonplastic silt~by weight! andinitial global void ratio ~prior to consolidation! of 0.533 (DR

531.2%) has an averageK55.831027 m/s and mv57.9831025 kPa21, resulting in Cv54.4431024– 1.1531023 m2/s,depending on the effective confining stress. Values ofK, mv , and

Fig. 5. Cyclic resistance ratio (CRR)7.5 versus~a! relative densityDR ; ~b! global void ratioe; and ~c! skeleton void ratioesk for cleanand silty sands~after consolidation!

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Cv for this specimen are shown in Table 2. Thevanayagam et~2001! published values ofK, mv , andCv for various mixtures offoundry sand and #40 Sil-Co-Sil as nonplastic silt~the presentresearch used #106 Sil-Co-Sil! that are of the same order of mag-nitude as those obtained in this research. For 15% silt conteThevanayagam et al.~2001! reported the following values:K5931027 m/s, andCv5531024– 1.231023 m2/s.

Rowe ~1959! found that the difference in stress conditions ispartially responsible for the difference in the values ofCv ob-tained from the oedometer and triaxial tests. While the total laeral stresss3 is kept constant in isotropic consolidation,s3 de-creases during consolidation in the oedometer test, resultingfaster dissipation of pore pressure and higherCv . According toRowe ~1959!, the ratio ofCv obtained from oedometer and tri-axial tests is

Cv,oed

Cv,tx5

1

12@B~12A!~12K0!#(1)

in which A and B5Skempton’s pore pressure parameters; anCv,tx and Cv,oed5coefficients of consolidation determined in tri-axial and oedometer tests, respectively. The value ofA in Eq. ~1!is that atK0 conditions. For a normally consolidated sand, theparameterA may vary approximately from 0 to 0.5. For the caseof a silty sand specimen withB50.95 andK050.4, Rowe’s cor-rection factor ranges from 2.33 to 1.40. The corresponding ajustedCv,oed values are shown in Table 2.

CPT-Based Liquefaction Resistancefrom Penetration Resistance Analysisand Laboratory Testing

Determination of Cone Resistance

Most available correlations for liquefaction potential assessmeare based on field observations and SPT or CPT data for liquefiand nonliquefied sites. Liquefaction occurrence may not be easdetected on the ground surface, and penetration resistance dare usually obtained from sites that have already undergone cosiderable shaking. Prior cyclic loading can increase the liquefation resistance of soils~Finn et al. 1971; Ishihara and Okada1978; Seed et al. 1977, 1988! and thus affect the relationshipbetween penetration resistance and cyclic resistance. Seed e~1988! found, from cone penetration tests on large-scale triaxiaspecimens, that prior cyclic history also increases the cone-sleefriction, even though no significant effect on the tip resistancwas observed in these tests.

We developed our CPT-based liquefaction resistance relatioships following an approach targeted at avoiding the subjectiviinherent in the observation of liquefaction in the field and theffects of prior shaking. Cone resistance is determined from aanalysis based on the cavity expansion theory developed by Sgado et al.~1997b! and Salgado and Randolph~2001!. The analy-sis has been shown to predict successfully the cone resistancecarefully controlled calibration chamber tests on uncementeclean silica sands~Salgado et al. 1997b!. The analysis is imple-mented in the computer programCONPOINT ~Salgado 1993;Salgado et al. 1997b!. The input parameters for the analysis in-clude the relative densityDR , the vertical and lateral effectivestressessv8 andsh8 , the intrinsic variablesCg , eg , andng of thesand appearing in the equation for the small-strain shear modu~Hardin and Black 1968!, the critical-state friction anglefc , andthe intrinsic variablesQ andR of the sand appearing in the Boltonequation for peak friction angle~Bolton 1986!.

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Table 2. Hydraulic Conductivity, Coefficient of Volume Compressibility, Coefficient of Consolidation from Triaxial and Oedometer Tests, aNormalized Penetration Velocity for Sand Specimen with 15% Silt Content

s38~kPa!

K~m/s!

mv~kPa21!

Cv,tx

~m2/s!

A50 A50.5

Cv,oed

~m2/s! vdc /Cv

Cv,oed

~m2/s! vdc /Cv

60 7.03 1027 6.173 1025 1.153 1023 2.683 1023 0.27 1.613 1023 0.44100 4.03 1027 6.923 1025 5.953 1024 1.393 1023 0.51 8.333 1024 0.86180 4.43 1027 1.003 1024 4.443 1024 1.033 1023 0.69 6.213 1024 1.15260 6.53 1027 7.603 1025 8.713 1024 2.033 1023 0.35 1.223 1023 0.59350 6.93 1027 9.193 1025 7.623 1024 1.773 1023 0.40 1.073 1023 0.67

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The small-strain shear modulus is related to the stress staterelative density by the following expression~Hardin and Black1968!:

G05Cg

~eg2e!2

11esm

8ngpA12ng (2)

where e5void ratio after consolidation;sm8 5mean effectivestress;pA5reference stress~5100 kPa50.1 MPa'1 kgf/cm2'1tsf!; andCg , eg , andng5intrinsic soil variables.

The expression for the peak friction angle proposed by Bolto~1986! is

fp5fc10.8cp (3)

wherefc5critical-state friction angle; andcp5plane-strain peakdilatancy angle given by

cp5I DS Q2 ln100pp8

pAD 2R (4)

in which I D5relative density expressed as a number betweenand 1;pp85mean effective stress at peak strength in the same unas the reference stresspA ; Q andR5fitting parameters; andcp islimited to 25° for plane-strain conditions.

Salgado et al.~2000! obtained the values ofCg , eg , ng , R,and Q for clean and silty Ottawa sand. Additional monotonistatic triaxial tests were performed to increase the range of retive densities used in the determination offc , Q, and R. Therevised values of the intrinsic variables are given in Table 1. Tvalues used in all calculations made in the present study corspond to relative densities above the limit relative densityDR, lim

for each gradation, as defined by Salgado et al.~2000!. One of themain findings of Salgado et al.~2000! is that the small-strainstiffness of the sand at a given relative density and confinistress level decreases markedly with the addition of nonplasfines. This change in shear stiffness is correlated with increascompressibility. However, for nonfloating fabric (DR.DR, lim),the compressibility of silty sand is much smaller than that observed for silty sands with floating fabric.

The cone resistance analysis used for producing the propoliquefaction resistance charts is a drained analysis. For it toapplicable to cone penetration in silty sands at the standard petration rate of 2 cm/s, this penetration must take place unddrained conditions. Our calculations show that such is the casesilty sands with up to 15% fines. These calculations are basedtwo sets of data: hydraulic conductivity tests done at Purdue Uversity on silty sand specimens and centrifuge tests done atUniversity of Western Australia on soils with various granulometries and variousCv values. Table 2 shows normalized penetration rate, defined asvdc /Cv , wherev5penetration rate~2 cm/s isthe standard!; and dc5cone diameter~3.57 cm is the standard!.According to the centrifuge data~M. F. Randolph, personal com-

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munication, 2001!, the normalized cone penetration resistanqc /sv8 is independent ofvdc /Cv below a limiting value, and thendrops as the normalized penetration ratevdc /Cv increases be-yond this limiting value and excess pore pressures develop.transition from fully drained to partially drained penetration isa normalized velocity of approximately 1.5. The normalized peetration rates shown in Table 2 are lower than 1.5, indicating tcone penetration in sands with silt content up to 15% is fudrained for a standard cone diameter of 3.57 cm and a penetrarate of 2 cm/s.

Determination of Cyclic Resistance Ratio

The cyclic resistance ratio (CRR!field of a soil element in the fieldat a given depth is defined as the ratio of the cyclic shear sttcyc to sv8 , while the cyclic resistance ratio in the triaxial te(CRR!tx is given by the ratio of the maximum cyclic shear stretmax @or half the cyclic deviator stress5(s182s38)/2] to sv8 . Arelationship between these two quantities was proposed by Ca~1975!. It is given next with the reduction factor of 0.9 introduceby Seed et al.~1978!

(CRR!field50.92~112K0!

3A3~CRR!tx (5)

whereK05coefficient of lateral earth pressure at rest. Other retionships for (CRR!field versus (CRR!tx were proposed earlier byFinn et al.~1971! and Seed and Peacock~1971!. The reductionfactor of 0.9 is due to the evidence reported by Seed et al.~1978!and Seed~1979! of a greater buildup of pore water pressure undmultidirectional conditions in the field than under unidirectioncyclic loading. All the results in this paper apply to normalconsolidated conditions, soK050.4 was used in Eq.~5! to com-pute CRR values for field conditions.

Proposed (Cyclic Resistance Ratio …7.5– q c1Correlations for Clean and Nonplastic Silty Sands

A (CRR)7.5-qc1 correlation is obtained by combining the resulfrom the penetration resistance analysis of Salgado et al.~1997b!usingCONPOINTand a considerably large set of laboratory teresults for Ottawa sand with nonplastic silt; namely, results frothe cyclic triaxial tests of this paper and results from static triaxand bender element tests~Salgado et al. 2000!. For each finescontent, the theoretical cone resistance values were calculatethe same relative densities for which the CRR values forcycles were determined in the laboratory testing program. Cresistance was calculated forsv85100 kPa andK050.40. Fig. 6shows the correlations between the cyclic resistance and themalized cone resistance obtained usingCONPOINT for sand

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containing 0, 5, 10, and 15% nonplastic silt for 5% doubleamplitude axial strain reached in 20 cycles. The well-known corelation curves for clean sand proposed by Seed and De Al~1986! and Robertson and Campanella~1985!, adjusted by Rob-ertson and Wride~1998! to account for more recent data, havebeen included in Fig. 6 for comparison. Fig. 7 contains the curveobtained for 5% double-amplitude axial strain in 15 and 2cycles. These two sets of curves are nearly the same for very lorelative densities but separate as the relative density of the sincreases. From the curves in Fig. 7, it is observed that the seletion of the liquefaction criterion does not have much influence othe cyclic resistance of clean sand, but the curves for sand cotaining fines shift up as the liquefaction criterion changes from5% double-amplitude axial strain at 20 cycles to 5% doubleamplitude axial strain at 15 cycles.

The (CRR)7.5-qc1 correlation obtained for clean sand~Fig. 6!is located very close to and slightly to the right of Robertson anCampanella’s semiempirical curve, but they are in general agrement. The compositional characteristics of the sand used in tpresent study, such as its low coefficient of uniformity and higdegree of particle roundness, are consistent with the fact that tlocus of the boundary curve lies to the right of the semiempiricacurve. It was found in the present study that, for a given relativdensity, sand with nonplastic silt up to 10% has slightly highecyclic resistance than clean sand~Fig. 5!. However, cone resis-tance increases at a faster rate with fines content than cyclicsistance, and the proposed liquefaction resistance curves for 5,and 15% silt contents are located to the right of the clean sacurve.

Fig. 6. Proposed correlations between cyclic resistance rat(CRR)7.5 and normalized cone resistanceqc1 for sand with 0, 5, 10,and 15% nonplastic silt, usingCONPOINT

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As seen in Fig. 6, the curves for 5, 10, and 15% silt contenare very close in the lower range of cone resistanceqc1 ~corre-sponding to relative densities up to about 45% for these grations!, but separate for higherqc1 values.

As the fines content increases to 15%, the (CRR)7.5-qc1 curveshifts to the right. This behavior can be attributed to the fundmental changes of the fabric of the material when the silt conteis gradually increased, as discussed extensively by Salgado e~2000!. A significant increase in liquefaction resistance due to tpresence of fines~Ishihara 1993! is not observed for the materialsused in the present study because of the nonplastic nature offines added to the sand mixtures~e.g., Ishihara 1985; Troncosoand Verdugo 1985!.

The gradual shift to the right of the CRR-qc1 curves as thefines content is increased from 0 to 15% may be explainedobservations made by Salgado et al.~2000!. These authors found,for the same materials used in the present study, that sandslow silt content and a fabric in which the sand particles are mosor completely in contact are more dilative than clean sand. Fogiven relative density, dilative silty sands subjected to cyclic loaing show higher resistance to liquefaction than clean sand~Fig.5!. When the fines content is increased further, the fines eitreduce or prevent the contact between particles, reducing inlocking and dilatancy, and thus liquefaction resistance, whichsand with 15% nonplastic silt content is lower than that of clesand~Fig. 5!. Cone resistance, on the other hand, is increasedonly by dilatancy, but also by the critical-state friction anglewhich consistently increases with the addition of fines. It followthat cone resistance does not drop as much as CRR when thecontent is increased from 10 to 15%.

Fig. 7. Proposed (CRR)7.5-qc1 correlation for sand with 0, 5, 10, and15% nonplastic silt obtained usingCONPOINTfor 15 and 20 cyclesand 5% double-amplitude~DA! axial strain

ENVIRONMENTAL ENGINEERING © ASCE / NOVEMBER 2003 / 973

Fig. 8. Comparison of field data with proposed (CRR)7.5-qc1 correlation for sand with~a! 5% nonplastic silt and~b! 10% nonplastic silt~fielddata froma Shibata and Teparaksa 1988b Suzuki et al. 1995;c Mitchell and Tseng 1990;d Boulanger et al. 1997!

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The mean grain sizeD50 has been used in liquefaction resis-tance correlations for describing the soil gradation. Shibata andTeparaksa~1988! identified a relationship between the normalizedcone resistanceqc1 and D50 according to which the maximumvalues ofqc1 for liquefiable soils increase with mean grain size upto D5050.25 mm, after whichD50 shows no influence on coneresistance for their data set. However, both fines content and thenature of the fines have been recognized as two important factorsthat strongly affect the liquefaction resistance and the cone pen-etration resistance of sands. Unfortunately, for most of the sitescontained in the field database for liquefaction and nonliquefac-tion case histories available in the literature, both the plasticityand percentage of fines are unknown. The mean grain size givesonly an indication of the soil gradation. For some silty sands,large differences in fines content in the order of 10–20% repre-sent very small variations inD50. For this reason, the correlationspresented here are based on specific values of fines content.

Figs. 8~a–b! compare the proposed curves for 5 and 10% siltcontent with field CPT data from various sites that have beensubjected to earthquake loading. Only field data for which thefines content was reported were considered. The ranges of finescontent for each reference are reported in the figure. The datafrom Suzuki et al.~1995! presented in Fig. 8 correspond to cyclictriaxial tests~5% double-amplitude axial strain and 15 cycles! onundisturbed frozen specimens from sites with CPT data available.Their results, originally corrected for multidirectional shear, wererecalculated forK050.4. Data from Mitchell and Tseng~1990! inFig. 8 correspond to the results of cyclic triaxial and direct sheartests on undisturbed specimens retrieved from sites for whichCPT field data were also available. Field data from Boulangeret al. ~1997!, obtained after the Loma Prieta earthquake, were

based on a peak ground acceleration of 0.25g. Due to uncertain-ties in the evaluation of this peak ground acceleration~Boulangeret al. 1997!, data points in the range60.05g were also plotted inthis figure. The proposed correlations show good agreement wthe available field observations in support of the findings of thresearch, although it is apparent that more data are neededboth 5 and 10% silt content to further validate the proposcurves. The sources of the field data are identified in each figu

Summary and Conclusions

We proposed CPT-based liquefaction resistance relationshipssilty sands based on the results of numerous cyclic triaxial testsdetermine (CRR)7.5 and a penetration resistance analysis to detmine corresponding values of normalized cone resistanceqc1 .Cyclic triaxial tests were performed on reconstituted specimensOttawa sand with nonplastic silt content ranging from 0 to 15by weight at various relative densities. A penetration resistananalysis was used to calculateqc1 values from the results of statictriaxial tests and bender element tests published by Salgado e~2000! complemented by additional tests reported in the prespaper. Use of the analysis is possible because we have showncone penetration in sand with up to 15% silt content is a fuldrained process for a standard cone diameter of 3.57 cm anpenetration rate of 2 cm/s.

The results of the cyclic triaxial tests show that, for a giverelative density, the cyclic resistance of sand increases slighwhen small amounts of nonplastic silt are added. The cyclicsistance of sand with 5% silt content increases approximat25% with respect to the resistance of clean sand. The cyclic

974 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / NOVEMBER 2003

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sistances of sand with 5 and 10% silt content are not notadifferent. However, specimens containing 10% silt had (CRR)7.5

values below the corresponding value for sand with 5% silt. Thbehavior is believed to be caused by the progressive change ofsoil fabric with increasing silt content. At 15% silt content, thfines start controlling the soil response, fine particles tend tocreasingly separate the sand particles, and, as a result, parinterlocking is progressively reduced. In addition, shear stresapplied through the silt particles between sand particles resulhigher shear strains and faster pore pressure generation thanresulting from application of shear stresses through the sagrains. These two factors determine the observed behaviorexplain the small increase in liquefaction resistance for very losilt contents and the liquefaction resistance drop for 15% silt cotent.

The proposed (CRR)7.5-qc1 curve for clean sand is in generaagreement with widely used semiempirical correlations basedfield data. Even though it has been shown that soils with scontent up to 10% have greater liquefaction resistance (CRR7.5

than clean sand, the cone resistance increases at a higher raterespect to increases in nonplastic fines content than (CRR)7.5.Consequently, the (CRR)7.5-qc1 curves for nonplastic silty sandare located to the right of the clean sand curve. Field data suppthe proposed curves for 5 and 10% silt content. In the empiriccorrelations currently used to evaluate liquefaction susceptibilthe curves corresponding to sand containing fines are locatedthe left of the curve for clean sand. It is important to note that,the development of these correlations, the nature and plasticitythe fines present in the soil were not taken into consideration iconsistent manner.

The liquefaction criterion used in this paper@cyclic resistanceratio (CRR)7.5 required to produce 5% double-amplitude axiastrain~peak to peak! at 20 uniform cycles# to generate the bound-ary curves presented in Figs. 6, 7, and 8 follows the recommdations made by Ishihara~1993!. According to Robertson andWride ~1998!, the CRR is typically taken ‘‘at about 15 cycles’’ ofuniform loading to represent an equivalent earthquake loadingmagnitude 7.5, i.e., (CRR)7.5. We have shown that, particularlyfor higher relative densities, the liquefaction curves we proposethis paper~Figs. 6, 7, and 8! would shift to the left had the 15-cycle criterion been adopted.

The CPT-based liquefaction resistance relationships propoin this study are applicable to the sand and silt gradations usethe testing program. The results are applicable to fresh soilposits, where the effects of aging have not set in. Cautionrecommended when using the proposed correlations for soils wcharacteristics substantially different from those tested in thissearch.

Further study is needed to assess the effects of different gdations as well as silt plasticity on the liquefaction resistancesilty sands. Instead of using general liquefaction resistance cur~such as the ones presented in this paper!, in large-budget projectsit may be cost effective to develop site-specific liquefaction restance curves using the procedure we outlined in this paper.

Acknowledgments

This material is based upon work supported by the National Sence Foundation, Washington, D.C., Earthquake Hazards Mitition Program, under Grant No. CMS-9410361. However, aopinions, findings, and conclusions or recommendations epressed in this material are those of the writers and do not nec

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sarily reflect the views of the National Science Foundation. Wappreciate the assistance of Bryan Scott, Tejas Murthy, and Bumjoo Kim with some of the tests. Financial support to the firswriter by CNPq is also appreciated.

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