Significant developments have taken place over the past 20 years toevaluate the liquefaction potential of soils. The cone penetrationtest (CPT) is now commonly used to evaluate liquefaction potentialin most liquefaction-prone geologic settings. Major developmentsof CPT-based liquefaction methods have occurred since the early1980’s (e.g., Seed and Idriss 1981; Shibata and Teparaksa 1988;Suzuki et al. 1995; Robertson and Wride 1998; Moss et al. 2006;Idriss and Boulanger 2008; Boulanger and Idriss 2014). Liquefac-tion methods based on the CPT have the advantage of near-continuous, repeatable measurements that provide a detailed profileof the soil. However, CPT-based liquefaction methods require cor-rections based on soil characteristics that can be significant in sandysoils with high fines content. There have also been significantdevelopments to evaluate liquefaction potential based on in situshear wave velocity (Vs) measurements (e.g., Robertson et al.1992; Andrus and Stokoe 2000; Kayen et al. 2013). Liquefactionmethods based on shear wave velocity have the advantage that theyare essentially independent of soil characteristics, such as finescontent, but often lack the stratigraphic detail obtained using theCPT. Current CPT and Vs methods to evaluate liquefaction poten-tial are based on a large number of liquefaction case histories(e.g., Boulanger and Idriss 2014; Kayen et al. 2013) that are com-prised of very young (Holocene-age) silica-based soils that have nobonding. Kayen (personal communication, 2014) suggested that bycomparing the most current Vs-based method with a CPT-basedmethod would provide an independent evaluation of the associated‘fines’ corrections of the CPT-based method.
This paper compares the Vs-based liquefaction triggering methodsuggested by Kayen et al. (2013) with the CPT-based liquefaction
triggering method by Robertson and Wride (1998) to evaluate theassociated CPT-based corrections. The paper also examines the ad-vantage of using both CPT and Vs measurements (e.g., using theseismic CPT) to evaluate liquefaction potential.
CPT-Based Triggering Method
Robertson and Wride (1998) and updated by Zhang et al. (2002)suggested a normalized cone parameter with a variable stressexponent, n, defined as follows:
Qtn ¼ ½ðqt − σvoÞ=pa�ðpa=σ 0voÞn ð1Þ
where qt = measured cone resistance (qc) corrected for waterpressure ðqt − σvÞ=pa = dimensionless net cone resistance;ðpa=σ 0
voÞn = stress normalization factor (CN); n = stress exponent;pa = atmospheric pressure in same units as qt and σvo; σvo = in-situtotal vertical stress; and σ 0
vo = in-situ effective vertical stress.Robertson and Wride (1998) and Zhang et al. (2002) used the
term, qc1N that was subsequently updated by Robertson (2009) tothe more generalized term Qtn used here (where Qtn ¼ qc1N).
Zhang et al. (2002) suggested that the stress exponent, n, couldbe estimated using the normalized Soil Behavior Type (SBTn)Index, Ic, used by Robertson and Wride (1998) and that Ic shouldbe defined using Qtn. Robertson (2009) suggested an updatedmethod to evaluate the stress exponent, n, based on the following:
n ¼ 0.381ðIcÞ þ 0.05ðσ 0vo=paÞ − 0.15 ð2Þ
where n ≤ 1.0; Ic = Soil Behavior Type Index ¼ ½ð3.47−logQtnÞ2 þ ðlogFr þ 1.22Þ2�0.5; Fr ¼ ½ðfs=ðqt − σvoÞ�100%; andfs = CPT sleeve resistance.
Robertson (2009) suggested that the normalization usingEqs. (1) and (2) was based on a constant state parameter. Robert-son and Wride (1998) proposed the following CPT-based lique-faction triggering relationship based on case histories, when50 < Qtn;cs < 160:
CRR� ¼ 93ðQtn;cs=1,000Þ3 þ 0.08 ð3Þ
1Professor Emeritus, Univ. of Alberta and Technical Advisor to GreggDrilling and Testing, Inc., 2726 Walnut Ave., Signal Hill, CA 90755.E-mail: [email protected]
The liquefaction case history database is composed of predomi-nately silica-based soils that are (1) very young (Holocene-age),(2) unbonded, (3) have similar geologic depositional environments,and (4) have limited stress history (i.e., essentially normally con-solidated with similar in situ stress ratios of Ko ∼ 0.5). Throughoutthis paper, the term “young unbonded soils” will be used to refer tosoils that are young (Holocene-age) with essentially no bonding(e.g., no cementation).
Robertson and Wride (1998) developed the correction factor(Kc) by plotting CPT case history data on the normalized soilbehavior type (SBTn) chart suggested by Robertson (1990). Theresulting contours of normalized clean sand equivalent cone resis-tance values, Qtn;cs, suggested by Robertson and Wride (1998) areshown in Fig. 1. The contours ofQtn;cs indicate that two soils on thesame Qtn;cs contour, but with different CPT measurements (i.e., Qtnand Fr), would have the same response to cyclic loading. Robert-son (2010a) showed that the contours of Qtn;cs are also essentiallycontours of the state parameter (ψ).
The correction factor (Kc) to determine Qtn;cs can be significantin soils with high fines content (FC). Robertson and Wride (1998)and Robertson (2009) suggested that the CPT-based soil behaviorindex, Ic was a better indicator of in situ soil behavior than a physi-cal characteristic such as fines content measured on disturbed
samples. In soils with high fines content (FC > 35%; Ic ¼ 2.60),the correction factor Kc is almost 3.5. This represents a correctionof up to 250% on a measured normalized cone resistance (Qtn) of20 in a loose sandy soil with high fines content. A correction ofsimilar magnitude is also applied using the more recent CPT-based methods (e.g., Boulanger and Idriss 2014) when FC ¼ 35%and Qtn ¼ 20. The primary cause of these large corrections isthe increased large strain compressibility of sandy soils with highfines content, which can significantly reduce the measured coneresistance.
Vs-Based Trigger Method
Kayen et al. (2013) presented an updated shear wave velocity (Vs)liquefaction trigger relationship based on a global catalog of 422case histories. The relationship is based on normalized shear wavevelocity, Vs1, which can be defined as
Vs1 ¼ Vsðpa=σ 0voÞ0.25 m=s ð6Þ
where Vs = measured shear wave velocity in m=s.The Kayen et al. (2013) liquefaction case history database was
composed of many of the same soils as the CPT database and henceare mostly young unbonded silica-based soil. Kayen et al. (2013)also showed that the liquefaction trigger relationship based on Vs1is insensitive to soil characteristics, such as fines content (FC).They showed that the boundary shift associated with a fines contentadjustment from <5 to 35% has a maximum value of only 5 m=s.This amounts to a maximum correction of 5% when Vs1 ¼100 m=s. The reason for the insensitive nature of the Vs1 lique-faction relationship to fines content is due to the small strainmeasurement. This adjustment is consistent with previous studies(e.g., Andrus and Stokoe 2000). Kayen et al. (2013) correctly statedthat this adjustment is minor in comparison with other aspects ofthe analysis. Most of the data from sites where liquefaction wasobserved was for 100 < Vs1 < 200 m=s.
CPT–Vs Correlations
CPT cone resistance (qt) is a large strain response that, in sandysoils, is controlled primarily by relative density, effective stressstate, stress history, mineralogy, age, and bonding (e.g., cementa-tion). Shear wave (Vs), is a small strain response that, in sandysoils, is controlled by the same factors as the cone resistance, butis more sensitive to factors such as age and cementation. Althoughthere is no unique correlation between qt and Vs (e.g., Rix andStokoe 1991), it is possible to obtain a good correlation if the re-lationship and database is limited to soils of similar mineralogy,stress history, age, and cementation (e.g., Andrus et al. 2004).
Based on an extensive database obtained using the seismic CPT(SCPT), Robertson (2009) proposed a generalized relationship forpredominately Holocene-age, unbonded silica-based soils linkingVs1 to CPT normalized cone resistance, Qtn, given by
Vs1 ¼ ðαvsQtnÞ0.5 m=s ð7Þwhere αvs ¼ 10ð0.55Icþ1.68Þ; and Vs1 is in m=s.
The resulting contours of Vs1, (Robertson 2009), are shownin Fig. 2. The previously mentioned correlation was based on adatabase of silica-based soils that had similar characteristics(e.g., depositional environment, age, unbonded, little or no stresshistory) as the soils in the liquefaction case history database.
Fig. 3 shows an example SCPT profile from a site in SanFrancisco that compares measured to estimated [based on Eq. (7)]
Fig. 1. Contours of normalized clean sand equivalent cone resistance,Qtn;cs, based on liquefaction case histories using the method of Robert-son and Wride (1998)
Vs values. The soils at the site are mostly of Holocene-age and un-cemented, and show good agreement between measured and esti-mated Vs values. Fig. 3 also illustrates the different level of detail inthe profile where the cone resistance (qt) is measured at 5 cmintervals compared to Vs at 1.5 m intervals.
Comparing Figs. 1 and 2 shows that the contours ofQtn;cs have asimilar shape to the contours of Vs1. This similarity in shape of thecontours for Qtn;cs and Vs1 suggests that the CPT corrections (Kc)used to form the contours of Qtn;cs are generally consistent with theVs1 liquefaction correlations suggested by Kayen et al. (2013). Toevaluate this in more detail, it is possible to link Vs1 directly withQtn;cs by combining Eqs. (4) and (7) to get
Vs1 ¼ ðQtn;csαvs=KcÞ0.5 m=s ð8aÞ
or Qtn;cs ¼ ðKc=αvsÞðVs1Þ2 ð8bÞ
Eqs. (8a) and (8b) are only valid for 50 < Qtn;cs < 160, sincethey are derived from the liquefaction case history database.
As soils become more compressible (e.g., increasing finescontent) and Ic increases, both Kc and αvs also increase and theresulting ratio (αvs=Kc) remains almost constant, with an averagevalue of around 360 over the limited range of 50 < Qtn;cs < 160.Hence, the relationship between the CPT Qtn;cs and Vs1 is almostconstant regardless of fines content. The ratio (αvs=Kc) representsthe small strain stiffness to strength ratio, similar to Go=qt. It canbe shown that
where Go = small strain shear modulus = ρ ðVsÞ2; ρ = soil massdensity = γ=g; γ = soil unit weight; and g = acceleration due togravity.
The observed average value of ðαvs=KcÞ ¼ 360 for young un-bonded soils produces an average Go=qt of about 7 that is onlyvalid for 50 < Qtn;cs < 160. This value of Go=qt is consistent withobservations made by others (e.g., Rix and Stokoe 1991; Eslaamizaadand Robertson 1996; Schnaid et al. 2004; Schneider and Moss 2011)
Fig. 2. Contours of normalized shear wave velocity, Vs1, for predomi-nately Holocene-age, unbounded soils (adapted from P. K. Robertson,“Interpretation of cone penetration tests—A unified approach”,Canadian Geotechnical Journal, Vol. 46, No. 11, pp. 151–158)
Fig. 3. Example SCPT profile in Holocene-age deposits (San Francisco, CA) comparing measured and CPT estimated Vs profile
for young, silica-based soils that have no bonding when50 < Qtn;cs < 160.
Robertson (2010b), based on case histories of flow liquefaction,showed that young unbonded soils can be strain softening whenQtn;cs < 70; it follows that the same soils can be contractive andstrain softening when Vs1 < 160 m=s. This is consistent with thevalue of Vs1 suggested by Robertson et al. (1995) based on labo-ratory testing of clean fresh (i.e., very young) silica-based sands.
Andrus et al. (2004), suggested an alternate relationship be-tween an equivalent clean sand ðVs1Þcs and Qtn;cs for Holocene-ageunbonded sands using
ðVs1Þcs ¼ 62.6ðQtn;csÞ0.231 m=s ð10Þ
As discussed earlier, there is little difference observed betweenVs1 and ðVs1Þcs, hence Eq. (10) can also be used to estimate Vs1.The relationship suggested by Andrus et al. (2004) produces similarvalues (within 10%) to that given by Eq. (8) in the range of50 < Qtn;cs < 160 m=s but differs outside this range.
Fig. 4 presents a summary of SCPT data (Robertson 2009)obtained in Holocene-age uncemented deposits from Californiacomparing Vs1 with Qtn;cs. The SCPT data was screened using theprocedure suggested by Schneider and Moss (2011) to identifyHolocene-age, uncemented deposits (details provided later). Fig. 4illustrates that there is some uncertainty in the correlation and con-firms that it is preferred to measure Vs rather than estimate from theCPT. The author is not advocating using the average relationship,represented by Eq. (8), in performing liquefaction triggering evalu-ation, but rather using the correlation to explain and evaluate theinfluence of the “fines” correction on the CPT-based liquefactiontriggering method.
Research (e.g., Andrus et al. 2007) has shown that any relation-ship between small-strain shear wave velocity and large-strain coneresistance is also a function of soil age and bonding. Since all theliquefaction case histories that are the basis of both the Vs1 andCPT trigger relationships are young, essentially normally consoli-dated, unbonded silica-based soils (e.g., Youd et al. 2001;Boulanger and Idriss 2014), the simplified relationship expressedby Eq. (8) has the same limitation. Youd et al. (2001) suggestedthat the soils that comprise the liquefaction database are mostly<3,000 years old, and Andrus et al. (2009) suggested an averageage of only 23 years.
Comparing CPT-Based and Vs-Based Methods
Combining the CPT-based trigger relationship suggested byRobertson and Wride (1998), represented by Eq. (3), and the rela-tionship between Qtn;cs and Vs1 suggested by Robertson (2009),represented by Eq. (8b), produces an equivalent CPT-basedCRR�–Vs1 relationship, as follows:
CRR� ¼ 93½ðKc=αvsÞðVs1Þ2=1,000�3 þ 0.08 ð11Þ
Based on the suggested values by Robertson and Wride (1998)and Robertson (2009), the following range of values for Kc and αvsare obtained:1. Clean sands (apparent fines content <5%), Ic ¼ 1.60, αvs ¼
363.08 and Kc ¼ 1.066; and2. Silty sands (apparent fines content ∼35%), Ic ¼ 2.60, αvs ¼
1,288.25 and Kc ¼ 3.427.Using these values in Eq. (11), the CRR� values (based on the
CPT–Vs1 correlation) can be compared to the Vs1 − CRR� curvesproposed by Kayen et al. (2013). Ku et al. (2012), based on anexpanded database of liquefaction case histories, showed that theRobertson and Wride (1998) deterministic CPT-based CRR� rela-tionship has a probability of liquefaction PL of about 30%. Fig. 5compares the CRR�–Vs1 curves suggested by Kayen et al. (2013)for a PL ¼ 30% and the equivalent CPT-based curves derived fromRobertson and Wride (1998) using Eq. (11). There is generallygood agreement between the CPT-based curve for clean sand(Ic ¼ 1.6) and the Vs1-based clean sand curve (FC < 5%).
The CPT-based curve at high apparent fines content (Ic ¼ 2.60)produces CRR� values that are slightly lower than the Kayen et al.(2013) relationship, especially at high normalized shear wavevelocity. This would indicate that the original corrections suggestedby Robertson and Wride (1998), based on Ic, are somewhatconservative compared to the Vs trigger method of Kayen et al.(2013) and could be adjusted slightly to obtain better agreement.To provide a better fit with the Kayen et al. (2013), trigger curvesthe Kc–Ic relationship was modified slightly, as shown in Fig. 6and the resulting improved agreement shown in Fig. 7. The
0
50
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0 20 40 60 80 100 120 140 160
Vs1
(m
/s)
Qtn,cs
Robertson 2009
Ic = 1.6
Ic = 2.6
Fig. 4. Summary of SCPT data for Holocene-age, uncemented depositsin terms of Qtn;cs and Vs1 (data from Robertson 2009)
0
0.1
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0 100 200 300
CR
R*
Vs1 (m/s)
Fig. 5. Comparison between Vs1-based trigger curves by Kayen et al.(2013) (KET13) and equivalent CPT-based trigger curves derived fromRobertson and Wride (1998) (RW98) using the CPT − Vs1 correlationproposed by Robertson (2009) (R09) for probability of liquefaction,PL ¼ 30%
“modified” Robertson and Wride (1998) correction (shown inFig. 6) was derived using trial and error to find an improved matchbetween the CPT-based trigger curves and the Vs1-based curves.Fig. 7 illustrates that a slight modification in the CPT-based(Kc) correction can produce a very good match with the Vs1-basedtrigger curves by Kayen et al. (2013). Figs. 5 and 6 also show thatusing the original Robertson and Wride (1998) corrections produceslightly conservative lower estimates of CRR� in soils withIc > 1.80.
The modified correction factor Kc–Ic relationship shown inFig. 6 can be represented by
That is valid between 1.60 < Ic < 2.60 and Kc ¼ 1.0 whenIc < 1.60.
Any relationship between CPT tip resistance and Vs has someuncertainty. This uncertainty is reduced when restricted to soils ofsimilar geologic origin and age (e.g., very young Holocene-age,essentially normally consolidated, unbonded, silica-based soils),as used to develop the CPT − Vs1 relationship by Robertson(2009) and the liquefaction trigger curves for the CPT and Vs(Robertson and Wride 1998; Kayen et al. 2013). The relationshipto estimate Vs1 suggested by Robertson (2009) has an average rel-ative standard error of about 10% (Fig. 4). Fig. 8 illustrates the levelof uncertainty in the CRR�–Vs1 curves for PL ¼ 30% for cleansand (FC ¼ 5% and Ic ¼ 1.6) based on the relative standard errorof �10% from the CPT-based estimated Vs1.
Application of Combined CPT and VsMeasurements to Evaluate Liquefaction Triggering
One of the advantages of the seismic CPT (SCPT) is that it providesa profile of CPT tip and sleeve resistance, as well as Vs at the samelocation in a very cost effective manner (Robertson et al. 1986). The30-years experience with the SCPT has shown that the Vs measure-ments are generally accurate, reliable, and more cost effective thanmost invasive seismic methods (e.g., cross-hole testing). The addedcost of the Vs measurements is small if CPT is performed at the site.Hence, the SCPT is becoming a popular in situ test (e.g., Mayne2014) and the author recommends that SCPT be performed, wherepossible, to measure Vs along with the CPT measurements.
The above comparison between the Vs1-based method of Kayenet al. (2013) and the CPT-based method of Robertson and Wride
1.0
1.5
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Cor
rect
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fac
tor,
Kc
SBT Ic
RW98 Modified
RW98
Qtn,cs = Kc Qtn (RW98)
Modified to fit Kayen et al (2013) Vs1 curves PL=30%
RW98
Fig. 6. CPT-based correction factor Kc as a function of Ic based onRobertson and Wride (1998) (RW98) and suggested modification toprovide good agreement with Kayen et al. (2013) Vs1–liquefactioncorrelation at PL ¼ 30%
0
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0.5
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0 100 200 300
CR
R*
Vs1 (m/s)
Fig. 7. Comparison between Vs1-based trigger curves by Kayen et al.(2013) (KET13) and the equivalent CPT-based trigger curves derivedfrom Robertson and Wride (1998) (RW98) using the CPT − Vs1
correlation proposed by Robertson (2009) (R09) using a modifiedKc − Ic relationship
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300
CR
R*
Vs1 (m/s)
Fig. 8. Comparison between Vs1-based trigger curve by Kayen et al.(2013) (KET13) for PL ¼ 30% and FC ¼ 5% and the equivalentCPT-based trigger curves derived from Robertson and Wride (1998)(RW98) for Ic ¼ 1.6 showing �1 standard deviation (SD)
(1998) has shown that both methods will produce very similarresults in terms of liquefaction triggering for most loose young,unbonded silica-based sands.
The data base of liquefaction case histories are comprised ofsoils that are essentially normally consolidated with in situ stressratio (Ko) likely in the range 0.4 < Ko < 0.7. Hence, although bothCPT measurements and Vs are influenced by horizontal effectivestresses, the application of vertical effective stress in the normali-zation of both qt and Vs can be effective when Ko is similar to thecase history database (i.e., 0.4 < Ko < 0.7). However, applicationof the methods for soils whereKo is significantly larger than around0.5 can introduce uncertainty, unless a correction for Ko is applied(e.g., Maki et al. 2014). This can be an issue when applying theseliquefaction assessment methods at sites where ground improve-ment may have increased Ko.
An interesting problem occurs when the CPT-based methodpredicts triggering of liquefaction, for a given design earthquakeloading, but the Vs1-based method does not predict triggering ofliquefaction in the same soil for the same design earthquake. Whichmethod should be assumed correct?
Kayen et al. (2013) correctly cautioned that the “Vs1–liquefactioncorrelations requires the cautionary understanding that somesoils with unusual soil-specific void ratio–relative density charac-teristics or bonding may exhibit liquefaction behavior that differsfrom the generalized proposed relationships.” Essentially Kayenet al. (2013) cautioned that the Vs1–liquefaction correlations maynot apply to soils that have “unusual” characteristics. The termmicrostructure is often used to describe soils that have “unusual”characteristics (Leroueil and Hight 2003) compared to “ideal” soilsthat have no microstructure. There are several causes for the devel-opment of microstructure in soils, such as: aging, cementation, coldwelding, etc. Most of these factors give soil a strength and stiffnessthat cannot be accounted for by void ratio and stress history alone.Microstructure tends to reinforce the links between particles, and soincrease the small strain modulus and hence Vs (e.g., Hatanaka andUchida 1995; Goto et al. 1992). Leroueil and Hight (2003) showedthat, in soils with bonding, Go does not depend only on confiningstresses but also on the strength of the bonds. Cuccovillo and Coop(1997) showed that peak strength is controlled by the strength ofthe bonds, while at large strains most of these bonds are broken.Because the CPT tip resistance (qt) is predominately a large-strainmeasure of soil strength, it tends to be less influenced by thestrength of the bonds thanGo (and Vs), especially in lightly bondedsoils. In heavily cemented sands, where the strength of the bondscan be very high, the CPT may reach refusal due to limits in avail-able push force to break the bonds. Schmertmann (1991) showedthat relatively short-term aging (e.g., days) increases the stiffness ofsome sands, whereas long-term aging (≫10,000 years) can alterparticle arranges and shapes so that there is also a significant in-crease in large strain strength (e.g., Dusseault and Morgenstern1979). Essentially the current database for liquefaction case histor-ies are composed of mainly “ideal” soils with little or no micro-structure since they are dominated by very young, unbounded soils.
Eslaamizaad and Robertson (1996) suggested that the SCPTcan be helpful in identifying soils with “unusual” characteristics(i.e., soils with microstructure) based on a link between Go=qt andQtn, since both aging and bonding tend to increase the small-strainstiffness (Go) significantly more than they increase the large-strainstrength of a soil (reflected inQtn). Hence, for a given soil, both ageand bonding tend to increase the small-strain shear wave velocitymore than the larger-strain cone resistance, all other factors (in situstress state, etc.) being constant.
Schneider and Moss (2011) extended the link between CPTand Vs to establish a method to evaluate the threshold to trigger
liquefaction in sandy soils with microstructure. Schneider andMoss (2011) suggested using an empirical parameter,KG (after Rixand Stokoe 1991) defined by
KG ¼ ðGo=qtÞðQtnÞ0.75 ð13Þwhere Go is in same units as qt and Qtn is dimensionless.
Eq. (13) is modified slightly from Schneider and Moss (2011),since they used qc instead of qt and qc1N instead of Qtn. In mostsandy soils, the error in using qc instead of qt is very small(e.g., Robertson 2009). As described earlier,Qtn is the more generalterm used here instead of the older term qc1N . KG is essentially anormalized rigidity index.
Schneider and Moss (2011) showed that for soils with little orno microstructure (i.e., young Holocene-age, sandy soils with nobonding), 110 < KG < 330, with an average of 215. Hence, usingSCPT data, where both qt and Vs measurements are available inthe same soil, it is possible to determine if a sandy soil falls withinthe range of 110 < KG < 330, for young unbonded soil. If a soil hasKG > 330 it can be considered to have “unusual” characteristics(i.e., microstructure) in terms of the application of the liquefactiontriggering correlations.
Schneider and Moss (2011) showed that the lower limits ofliquefaction resistance can be defined where induced cyclic strainsare less than the elastic threshold shear strain, γth. Dobry et al.(1982) showed that the threshold strain is independent of the num-ber of cycles of typical earthquakes (<30 cycles) and has a value ofabout 1 × 10−4. The cyclic stress ratio at the threshold strain(CSRth) can be given by
CSRth ¼ ðGo=σ 0voÞγth ð14Þ
Combining Eqs. (13) and (14), Schneider and Moss (2011)showed that
CSRth ¼ ½KGqtγth�=½σ 0voðQtnÞ0.75� ð15Þ
It is possible to define a normalized small strain shear modules,Go1, where
Go1 ¼ ðρ=paÞðVs1Þ2 ð16ÞThen it can be shown that
Go=qt ¼ Go1=Qtn ð17ÞEq. (17) is correct when the stress exponent (n) to determineQtn
is 0.5, which is approximately valid for most sandy soils whenσ 0vo < 1.5 atmosphere, as is the case for the majority of the lique-
faction cases histories. Then KG becomes slightly simpler:
KG ¼ Go1ðQtnÞ−0.25 ð18ÞHence, the cyclic stress ratio at the threshold strain (CSRth) can
be given by
CSRth ¼ KGγthðQtnÞ0.25ðpa=σ 0voÞ0.5 ð19Þ
For σ 0vo ¼ 100 kPa, this simplifies to
CSR�th ¼ KGγthðQtnÞ0.25 ð20Þ
CSR�th is essentially independent of earthquake magnitude, since
any cyclic stress ratio less that CSR�th will not exceed the elastic
threshold strain and liquefaction will not result, since excess porepressures will not develop. Schneider and Moss (2011) suggestedthat at low values of Qtn, small-strain stiffness controls liquefactionresistance and at higher values of Qtn the consequences of
liquefaction are limited by soil dilation, where correlations basedon CPT Qtn may be more applicable.
Methods to estimate the maximum or limiting shear strain dur-ing cyclic loading have shown that at low values of Qtn;cs, trigger-ing liquefaction can quickly produce very large strains, whereas atlarger values of Qtn;cs, triggering liquefaction will produce a slowerbuild-up of strains. Robertson and Wride (1998) showed that thatwhen Qtn;cs < 70, shear strains quickly become very large (>20%)when liquefaction is triggered. This is consistent with the sugges-tion by Robertson (2010b) that soils are generally dilative whenQtn;cs > 70. When Qtn;cs is less than about 70, the threshold strainhas a more significant role. When Qtn;cs < 70 and the thresholdstrain is exceeded, strains can accumulate rapidly leading to lique-faction. When Qtn;cs > 70 and the threshold strain is exceeded,strains tend to accumulate more slowly and dilation tends to playan increasing role.
Andrus et al. (2009) and Hayati and Andrus (2009) suggesteda method to account for soil aging on the resistance to cyclic load-ing based on CPT and Vs results using a measured to estimatedvelocity ratio (MEVR), where
MEVR ¼ Vs1;M=Vs1;E ð21Þ
where Vs1;M ¼ Vs1 measured in situ; and Vs1;E ¼ Vs1 estimated fora very young unbonded soil.
Andrus et al. (2009) suggested using Eq. (10) to calculate Vs1;E,based on CPT measurements.
Hayati and Andrus (2009), based on laboratory and field cases,proposed a deposit resistance factor (KDR) to correct for age using
KDR ¼ 1.08MEVR − 0.08 ð22Þ
The age corrected cyclic resistance ratio, CRR�K is then given by
CRR�K ¼ KDRCRR�
CPT ð23Þ
where CRR�CPT is the CPT-based CRR�.
Eq. (23) indicates a uniform increase in CRR� regardless of insitu density (i.e., Qtn).
Hayati and Andrus (2009) showed that the MEVR approach isbased on a reference age (where KDR ¼ MEVR ¼ 1.0) of about23 years for Vs1;E and stated that this reference age “seems a rea-sonable average for the CRR� curves because many liquefactioncases are associated with deposits that were 1–100 years old priorto the earthquake shaking.” Hayati and Andrus (2009) essentiallyidentified that there is a “behavioral age” that could be less than thegeologic age, where “behavioral age” is defined as the time sincethe last critical disturbance and that the measured Vs1 was a mea-sure of the “behavioral age”.
A similar approach can be applied to the Schneider and Moss(2011) empirical parameter KG using a similar measured to esti-mated KG ratio defined by
MEKG ¼ KG;M=KG;E ð24Þ
where KG;M ¼ KG based on measured values of Vs and qt; andKG;E ¼ KG estimated for very young, unbonded soil.
Based on the definition of KG [Eq. (13)], the MEKG ratio isinsensitive to changes in CPT qt and Qtn;cs due to aging. Sinceqt has been shown to be relatively insensitive to aging and/or lightbonding, it is reasonable to assume that
MEKG ¼ ðMEVRÞ2 ð25Þ
An equivalent average estimated KGE ∼ 200 for a very young(age ∼23 years), unbonded soil can be derived from case histories
(Table 1) that is slightly lower than the mean of KG ¼ 215 sug-gested by Schneider and Moss (2011) for Holocene-age, siliceousunbonded sandy soils. Hence, a similar approach can be appliedusing MEKG instead of MEVR and apply Eqs. (22) and (23) toestimate CRR�
K .To illustrate how these approaches compare, example CPT and
Vs values from published case histories are shown in Table 1. Theexamples in Table 1 were selected to illustrate possible differencesbetween Holocene-age, uncemented sands; Pleistocene-age andTertiary-age, uncemented sands; and aged, cemented sands. Thesoils at the Moss Landing State Beach (Moss landing, CA) siteare Holocene-age, uncemented, silica-based sands and are typicalof many sites in the current liquefaction database. The State Beachsite was described in detail by Boulanger et al. (1997) and was in-cluded as an example in Boulanger and Idriss (2014). Liquefactionwas observed along the access road to the Moss Landing StateBeach during the 1989 magnitude 6.9, Loma Prieta earthquake(Boulanger et al. 1997) where the estimated peak ground acceler-ation at the site was 0.28 g. UC 15 was located at the EntranceKiosk where significant liquefaction and large deformations wereobserved. UC 16 was located nearby on the Beach Path whereminor liquefaction was observed and deformations were smallerthan at UC 15. UC 18 was located closer to the beach wherethe sand was denser and no liquefaction was observed. Table 1shows that the CRR� values determined using the CPT-basedmethod of Robertson and Wride (1998) are very similar to the val-ues determined using the Vs-based method of Kayen et al. (2013).The KG values at the State Beach site are consistent with the valuessuggested by Schneider and Moss (2011) for Holocene-age, unce-mented sands (i.e., KG < 330) and the MEVR values are close to1.0, as suggested by Andrus et al (2009). The Moss Landing ex-amples shown in Table 1 illustrate that the CPT-based and Vs-basedliquefaction triggering methods generally provide similar results inmost Holocene-age, uncemented, silica-based sands.
Andrus et al (2009) presented case history data from sand sitesin South Carolina that had experienced the 1886 magnitude 7.3,Charleston earthquake, where the estimated average cyclic stressratio (CSR) at the sites was about 0.25. The sites were of eitherPleistocene age or Tertiary age and were estimated to be unce-mented. The sand at the James Island site was estimated to have ageologic age of about 100,000 years and did not experience lique-faction in the 1886 earthquake. The TEN-08 site experienced lique-faction during the 1886 earthquake and was estimated to have abehavioral age of only 110 years at the time of the SCPT (sinceit had liquefied in 1886). The Aiken SRS-5 site did not experienceliquefaction and was estimated to have a geologic age of about35 million years. Table 1 shows that the KG values for the agedsands in South Carolina that did not experience liquefaction exceed330 consistent with the suggestion by Schneider and Moss (2011).For the aged sands at James Island and Aiken, the Vs-based meth-ods by Kayen et al (2013) and the age adjusted CPT-based methodby Andrus et al. (2009) correctly predict that these sands wouldnot liquefy during the 1886 earthquake, whereas the CPT-basedmethod underestimated the CRR�. The estimated CSR at thethreshold strain (CSR�
th) is less than 0.15, which suggests that the1886 earthquake was of sufficient size to exceed the thresholdstrain at these sites. The CPT and Vs values at the TEN-08 site thathad experienced liquefaction in 1886 were measured about110 years after the liquefaction and may not reflected the state ofthe soil prior to the earthquake.
Table 1 also includes SCPT data from several sites in WesternAustralia that are lightly cemented and of late Pleistocene age.These sites have not experienced any major earthquake eventsand therefore provide no direct liquefaction resistance evidence.
The KG values are significantly greater than 330 and would sug-gest some microstructure. Although the sands are of late Pleisto-cene age, the KG values are higher than those for the olderTertiary sands from Savannah River, which would support thepossibility of cementation. The estimated CRR� values derivedfrom either Vs or MEVR suggest that these soils would not ex-perience cyclic liquefaction (CRR� > 0.7). However, the CRR�
values derived from the CPT suggest much lower cyclic resis-tance. In some cases, the estimated CSR to reach the thresholdstrain (CSR�
th) is greater than the estimated CRR� from theCPT (e.g., Shenton Park and Perth sands). An uncertainty thatexists for sandy soils with light cementation is that if the cyclicloading exceeds the threshold strain (i.e., CSR� > CSR�
th) there isa risk that the bonding (cementation) could be either damaged ordestroyed and the soil may behave more like an uncemented soilat larger strains.
These examples illustrate the importance to identify soils thathave microstructure (such as aging and/or cementation) and mayexhibit “unusual” characteristics that may make traditionalcyclic liquefaction trigger methods (either SPT, CPT, or Vs) un-reliable. Knowledge of either geologic age or the time since pastliquefaction events (i.e., behavioral age) can assist in the lique-faction analysis. A combination of CPT (qt) and Vs measure-ments in the same soil (e.g., SCPT) provides an opportunityto directly evaluate the potential for microstructure. When com-bined with knowledge of either geologic age or behavioral age,the SCPT can assist in separating the affects of either age orcementation. If the soils are aged and uncemented, the existingVs-based liquefaction methods suggested by either Andrus et al.(2009) and Kayen et al. (2013) appear to provide better estimatesthan penetration (either SPT or CPT) liquefaction methods. Ifthe soils have light cementation, the approach suggested bySchneider and Moss (2011) can assist in estimating if the designearthquake loading (CSR*) would exceed the CSR to reach thethreshold strain (CSR�
th). If the design earthquake could exceedthe threshold strain, there is a risk that the benefits of cementa-tion may be lost and the larger strain CPT-based CRR� maybemore appropriate.
It would appear that until further research on threshold strain forlightly bonded soils is available, it may be prudent to assume thatany benefits from bonding could be destroyed when CSR� >CSR�
th. For high-risk projects, careful undisturbed sampling com-bined with laboratory testing may be appropriate to evaluate theinfluence of possible microstructure. Shear wave velocity measure-ments can be made both in situ and on samples in the laboratory toevaluate sample disturbance.
It is likely that the benefits from aging could be different thanthe benefits from bonding (e.g., cementation). Aging and bondingwill tend to increase the small strain stiffness but aging may havelittle influence on the threshold strain, whereas bonding may alsoincrease the threshold strain depending on the nature and degree ofbonding. Light bonding may increase the small strain stiffness buthave little influence on the larger strain behavior. Clearly there is aneed for further research in this area.
The examples shown in Table 1 also confirm the cautionary noteprovided by Kayen et al. (2013) regarding application of the Vs1relationships for soils with “unusual” characteristics. A similar cau-tionary note should also be applied to existing penetration-based(i.e., CPT and SPT) liquefaction triggering methods. The examplesin Table 1 also illustrate how the SCPT can be very helpful inidentifying soils with “unusual” characteristics (i.e., microstruc-ture). The SCPT has the advantage that the Vs measurements areobtained at the same location as the CPT measurements in a costeffective way.T
A comparison has been made between the CPT-based liquefactiontriggering method by Robertson and Wride (1998) and the Vs1-based method by Kayen et al. (2013) to evaluate the associatedCPT-based corrections. Although the comparison requires an aver-age relationship between CPTand Vs1, which has some uncertainty,the comparison has shown that the Robertson and Wride (1998)’sCPT-based corrections, based on a generalized Ic relationship, pro-vided generally good agreement between the two independentapproaches. A slight modification to the CPT-based “fines” correc-tion is suggested to provide better agreement between the twomethods in soils with high fines content. The comparison indicatesthat the current Robertson andWride (1998) corrections are slightlyconservative compared to the Vs-based trigger relationship ofKayen et al. (2013) in soils with high fines content where Ic > 1.8.
The comparison also highlights the importance of recognizingthe limits in the existing liquefaction case history database. Theexisting CPT-based and Vs-based methods to evaluate liquefactiontriggering apply to “ideal” soils that are young (Holocene-age) andhave no significant microstructure, such as bonding and are essen-tially normally consolidated (i.e., Ko ∼ 0.5). Kayen et al. (2013)correctly cautioned applying the Vs-based method to soils that have“unusual” characteristics. Although an average relationship be-tween CPT and Vs has been shown, it is recommended that Vsbe measured (e.g., SCPT) to aid in the identification of soils with“unusual” characteristics, such as aging and/or bonding. The meth-ods suggested by Schneider and Moss (2011) based on the param-eter KG, and Hayati and Andrus (2009) based on the MEVR, showpromise as simple methods to detect “unusual” characteristics. Theapproach suggested by Schneider and Moss (2011) has the advan-tage that a generalized value for KGE (∼200) can be assumed thatdoes not require selection of a specific relationship between CPTand Vs with the associated uncertainty. Further research is neededto clarify the role of threshold strain on the response of soils withmicrostructure (e.g., aging and/or bonding) and if the effects of ageare different than cementation on the liquefaction resistance of soil.
Acknowledgments
This research could not have been carried out without the support,encouragement and input from John Gregg, Kelly Cabal and otherstaff at Gregg Drilling and Testing Inc. The author would also liketo thank the anonymous reviewers that provide valuable commentsand advice.
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