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Comparing CPT and VsLiquefaction Triggering Methods
P. K. Robertson, M.ASCE1
Abstract: Significant developments have taken place over the past 20 years to evaluate the liquefaction potential of soils using in situ tests.
The cone penetration test (CPT) is now commonly used to evaluate liquefaction potential in soils. There have also been significant develop-
ments to evaluate liquefaction potential based on in situ shear wave velocity (Vs) measurements. Liquefaction methods base on shear wave
velocity have the advantage that they are essentially independent of soil characteristics, such as fines content, but often lack the stratigraphic
detail obtained using the CPT. Liquefaction methods based on the CPT have the advantage of continuous, repeatable measurements but
require corrections based on soil characteristics that can be significant in soils with high fines content. Comparing the most recent Vs-based
method with a CPT-based method provides an independent evaluation of the associated corrections applied to the CPT-based method. This
paper compares the current Vs-based method with a specific CPT-based method from the literature to evaluate the associated CPT-based
corrections. The paper also examines the advantage of using both CPT and Vsmeasurements (e.g., using the seismic CPT) to evaluate
liquefaction potential. DOI: 10.1061/(ASCE)GT.1943-5606.0001338.© 2015 American Society of Civil Engineers.
Author keywords: Liquefaction; Cone penetration test; Shear wave velocity.
Introduction
Significant developments have taken place over the past 20 years to
evaluate the liquefaction potential of soils. The cone penetration
test (CPT) is now commonly used to evaluate liquefaction potential
in most liquefaction-prone geologic settings. Major developments
of CPT-based liquefaction methods have occurred since the early
1980’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 profile
of the soil. However, CPT-based liquefaction methods require cor-
rections based on soil characteristics that can be significant in sandy
soils with high fines content. There have also been significant
developments to evaluate liquefaction potential based on in situ
shear wave velocity (Vs) measurements (e.g., Robertson et al.
1992;Andrus and Stokoe 2000;Kayen et al. 2013). Liquefaction
methods based on shear wave velocity have the advantage that they
are essentially independent of soil characteristics, such as fines
content, but often lack the stratigraphic detail obtained using the
CPT. Current CPT and Vsmethods 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 no
bonding. Kayen (personal communication, 2014) suggested that by
comparing the most current Vs-based method with a CPT-based
method would provide an independent evaluation of the associated
‘fines’corrections of the CPT-based method.
This paper compares the Vs-based liquefaction triggering method
suggested by Kayen et al. (2013) with the CPT-based liquefaction
triggering method by Robertson and Wride (1998) to evaluate the
associated CPT-based corrections. The paper also examines the ad-
vantage of using both CPT and Vsmeasurements (e.g., using the
seismic 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 stress
exponent, n, defined as follows:
Qtn ¼½ðqt−σvoÞ=paðpa=σ0
voÞnð1Þ
where qt= measured cone resistance (qc) corrected for water
pressure ðqt−σvÞ=pa= dimensionless net cone resistance;
ðpa=σ0
voÞn= stress normalization factor (CN); n= stress exponent;
pa= atmospheric pressure in same units as qtand σvo ;σvo = in-situ
total vertical stress; and σ0
vo = in-situ effective vertical stress.
Robertson and Wride (1998) and Zhang et al. (2002) used the
term, qc1Nthat was subsequently updated by Robertson (2009)to
the more generalized term Qtn used here (where Qtn ¼qc1N).
Zhang et al. (2002) suggested that the stress exponent, n, could
be estimated using the normalized Soil Behavior Type (SBTn)
Index, Ic, used by Robertson and Wride (1998) and that Icshould
be defined using Qtn. Robertson (2009) suggested an updated
method to evaluate the stress exponent, n, based on the following:
n¼0.381ðIcÞþ0.05ðσ0
vo=paÞ−0.15 ð2Þ
where n≤1.0;Ic= Soil Behavior Type Index ¼½ð3.47 −
log QtnÞ2þðlog Frþ1.22Þ20.5;Fr¼½ðfs=ðqt−σvoÞ100%; and
fs= CPT sleeve resistance.
Robertson (2009) suggested that the normalization using
Eqs. (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, when
50 <Qtn;cs <160:
CRR¼93ðQtn;cs=1,000Þ3þ0.08 ð3Þ
1Professor Emeritus, Univ. of Alberta and Technical Advisor to Gregg
Drilling and Testing, Inc., 2726 Walnut Ave., Signal Hill, CA 90755.
E-mail: probertson@greggdrilling.com
Note. This manuscript was submitted on June 25, 2014; approved on
March 20, 2015; published online on May 4, 2015. Discussion period open
until October 4, 2015; separate discussions must be submitted for indivi-
dual papers. This paper is part of the Journal of Geotechnical and Geoen-
vironmental Engineering, © ASCE, ISSN 1090-0241/04015037(10)/
$25.00.
© ASCE 04015037-1 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng.
Downloaded from ascelibrary.org by Peter Robertson on 06/25/15. Copyright ASCE. For personal use only; all rights reserved.
CRR= cyclic resistance ratio, adjusted to moment magnitude
Mw¼7.5and σ0
vo ¼100 kPa; and Qtn;cs = normalized clean sand
equivalent cone resistance, where
Qtn;cs ¼KcQtn ð4Þ
and
Kc¼5.581I3
c−0.403I4
c−21.63I2
cþ33.75Ic−17.88 ð5Þ
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). Throughout
this paper, the term “young unbonded soils”will be used to refer to
soils 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 soil
behavior type (SBTn) chart suggested by Robertson (1990). The
resulting contours of normalized clean sand equivalent cone resis-
tance values, Qtn;cs, suggested by Robertson and Wride (1998) are
shown in Fig. 1. The contours of Qtn;cs indicate that two soils on the
same Qtn;cs contour, but with different CPT measurements (i.e., Qtn
and Fr), would have the same response to cyclic loading. Robert-
son (2010a) showed that the contours of Qtn;cs are also essentially
contours of the state parameter (ψ).
The correction factor (Kc) to determine Qtn;cs can be significant
in soils with high fines content (FC). Robertson and Wride (1998)
and Robertson (2009) suggested that the CPT-based soil behavior
index, Icwas 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%;Ic¼2.60),
the correction factor Kcis almost 3.5. This represents a correction
of up to 250% on a measured normalized cone resistance (Qtn)of
20 in a loose sandy soil with high fines content. A correction of
similar magnitude is also applied using the more recent CPT-
based methods (e.g., Boulanger and Idriss 2014) when FC ¼35%
and Qtn ¼20. The primary cause of these large corrections is
the increased large strain compressibility of sandy soils with high
fines content, which can significantly reduce the measured cone
resistance.
Vs-Based Trigger Method
Kayen et al. (2013) presented an updated shear wave velocity (Vs)
liquefaction trigger relationship based on a global catalog of 422
case histories. The relationship is based on normalized shear wave
velocity, Vs1, which can be defined as
Vs1¼Vsðpa=σ0
voÞ0.25 m=sð6Þ
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 hence
are mostly young unbonded silica-based soil. Kayen et al. (2013)
also showed that the liquefaction trigger relationship based on Vs1
is insensitive to soil characteristics, such as fines content (FC).
They showed that the boundary shift associated with a fines content
adjustment from <5to 35% has a maximum value of only 5m=s.
This amounts to a maximum correction of 5% when Vs1¼
100 m=s. The reason for the insensitive nature of the Vs1lique-
faction relationship to fines content is due to the small strain
measurement. This adjustment is consistent with previous studies
(e.g., Andrus and Stokoe 2000). Kayen et al. (2013) correctly stated
that this adjustment is minor in comparison with other aspects of
the analysis. Most of the data from sites where liquefaction was
observed was for 100 <Vs1<200 m=s.
CPT–VsCorrelations
CPT cone resistance (qt) is a large strain response that, in sandy
soils, is controlled primarily by relative density, effective stress
state, stress history, mineralogy, age, and bonding (e.g., cementa-
tion). Shear wave (Vs), is a small strain response that, in sandy
soils, is controlled by the same factors as the cone resistance, but
is more sensitive to factors such as age and cementation. Although
there is no unique correlation between qtand Vs(e.g., Rix and
Stokoe 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 for
predominately Holocene-age, unbonded silica-based soils linking
Vs1to CPT normalized cone resistance, Qtn, given by
Vs1¼ðαvsQtn Þ0.5m=sð7Þ
where αvs ¼10ð0.55Icþ1.68Þ; and Vs1is in m=s.
The resulting contours of Vs1,(Robertson 2009), are shown
in Fig. 2. The previously mentioned correlation was based on a
database of silica-based soils that had similar characteristics
(e.g., depositional environment, age, unbonded, little or no stress
history) as the soils in the liquefaction case history database.
Fig. 3shows an example SCPT profile from a site in San
Francisco 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)
© ASCE 04015037-2 J. Geotech. Geoenviron. Eng.
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Vsvalues. The soils at the site are mostly of Holocene-age and un-
cemented, and show good agreement between measured and esti-
mated Vsvalues. Fig. 3also illustrates the different level of detail in
the profile where the cone resistance (qt) is measured at 5 cm
intervals compared to Vsat 1.5 m intervals.
Comparing Figs. 1and 2shows that the contours of Qtn;cs have a
similar shape to the contours of Vs1. This similarity in shape of the
contours for Qtn;cs and Vs1suggests that the CPT corrections (Kc)
used to form the contours of Qtn;cs are generally consistent with the
Vs1liquefaction correlations suggested by Kayen et al. (2013). To
evaluate this in more detail, it is possible to link Vs1directly with
Qtn;cs by combining Eqs. (4) and (7) to get
Vs1¼ðQtn;csαvs =KcÞ0.5m=sð8aÞ
or Qtn;cs ¼ðKc=αvsÞðVs1Þ2ð8bÞ
Eqs. (8a) and (8b) are only valid for 50 <Qtn;cs <160, since
they are derived from the liquefaction case history database.
As soils become more compressible (e.g., increasing fines
content) and Icincreases, both Kcand αvs also increase and the
resulting ratio (αvs=Kc) remains almost constant, with an average
value of around 360 over the limited range of 50 <Qtn;cs <160.
Hence, the relationship between the CPT Qtn;cs and Vs1is almost
constant regardless of fines content. The ratio (αvs =Kc) represents
the small strain stiffness to strength ratio, similar to Go=qt. It can
be shown that
Go=qt¼ðρ=paÞ½ðVs1Þ2=Qtn;cs¼ðρ=paÞ½αvs =Kcð9Þ
where Go= small strain shear modulus = ρðVsÞ2;ρ= soil mass
density = γ=g;γ= soil unit weight; and g= acceleration due to
gravity.
The observed average value of ðαvs =KcÞ¼360 for young un-
bonded soils produces an average Go=qtof about 7 that is only
valid for 50 <Qtn;cs <160. This value of Go=qtis consistent with
observations made by others (e.g., Rix and Stokoe 1991;Eslaamizaad
and 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 Vsprofile
© ASCE 04015037-3 J. Geotech. Geoenviron. Eng.
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for young, silica-based soils that have no bonding when
50 <Qtn;cs <160.
Robertson (2010b), based on case histories of flow liquefaction,
showed that young unbonded soils can be strain softening when
Qtn;cs <70; it follows that the same soils can be contractive and
strain softening when Vs1<160 m=s. This is consistent with the
value of Vs1suggested 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-age
unbonded sands using
ðVs1Þcs ¼62.6ðQtn;csÞ0.231 m=sð10Þ
As discussed earlier, there is little difference observed between
Vs1and ðVs1Þcs, hence Eq. (10) can also be used to estimate Vs1.
The relationship suggested by Andrus et al. (2004) produces similar
values (within 10%) to that given by Eq. (8) in the range of
50 <Qtn;cs <160 m=s but differs outside this range.
Fig. 4presents a summary of SCPT data (Robertson 2009)
obtained in Holocene-age uncemented deposits from California
comparing Vs1with Qtn;cs. The SCPT data was screened using the
procedure suggested by Schneider and Moss (2011) to identify
Holocene-age, uncemented deposits (details provided later). Fig. 4
illustrates that there is some uncertainty in the correlation and con-
firms that it is preferred to measure Vsrather than estimate from the
CPT. 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 the
influence of the “fines”correction on the CPT-based liquefaction
triggering method.
Research (e.g., Andrus et al. 2007) has shown that any relation-
ship between small-strain shear wave velocity and large-strain cone
resistance is also a function of soil age and bonding. Since all the
liquefaction case histories that are the basis of both the Vs1and
CPT 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 expressed
by Eq. (8) has the same limitation. Youd et al. (2001) suggested
that the soils that comprise the liquefaction database are mostly
<3,000 years old, and Andrus et al. (2009) suggested an average
age of only 23 years.
Comparing CPT-Based and Vs-Based Methods
Combining the CPT-based trigger relationship suggested by
Robertson and Wride (1998), represented by Eq. (3), and the rela-
tionship between Qtn;cs and Vs1suggested by Robertson (2009),
represented by Eq. (8b), produces an equivalent CPT-based
CRR–Vs1relationship, as follows:
CRR¼93½ðKc=αvsÞðVs1Þ2=1,0003þ0.08 ð11Þ
Based on the suggested values by Robertson and Wride (1998)
and Robertson (2009), the following range of values for Kcand αvs
are obtained:
1. Clean sands (apparent fines content <5%), Ic¼1.60,αvs ¼
363.08 and Kc¼1.066; and
2. Silty sands (apparent fines content ∼35%), Ic¼2.60,αvs ¼
1,288.25 and Kc¼3.427.
Using these values in Eq. (11), the CRRvalues (based on the
CPT–Vs1correlation) can be compared to the Vs1−CRRcurves
proposed by Kayen et al. (2013). Ku et al. (2012), based on an
expanded database of liquefaction case histories, showed that the
Robertson and Wride (1998) deterministic CPT-based CRRrela-
tionship has a probability of liquefaction PLof about 30%. Fig. 5
compares the CRR–Vs1curves suggested by Kayen et al. (2013)
for a PL¼30% and the equivalent CPT-based curves derived from
Robertson and Wride (1998) using Eq. (11). There is generally
good agreement between the CPT-based curve for clean sand
(Ic¼1.6) and the Vs1-based clean sand curve (FC < 5%).
The CPT-based curve at high apparent fines content (Ic¼2.60)
produces CRRvalues that are slightly lower than the Kayen et al.
(2013) relationship, especially at high normalized shear wave
velocity. This would indicate that the original corrections suggested
by Robertson and Wride (1998), based on Ic, are somewhat
conservative compared to the Vstrigger 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 curves
the Kc–Icrelationship was modified slightly, as shown in Fig. 6
and the resulting improved agreement shown in Fig. 7. The
0
50
100
150
200
250
300
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 deposits
in terms of Qtn;cs and Vs1(data from Robertson 2009)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300
CRR*
Vs1 (m/s)
Fig. 5. Comparison between Vs1-based trigger curves by Kayen et al.
(2013) (KET13) and equivalent CPT-based trigger curves derived from
Robertson and Wride (1998) (RW98) using the CPT −Vs1correlation
proposed by Robertson (2009) (R09) for probability of liquefaction,
PL¼30%
© ASCE 04015037-4 J. Geotech. Geoenviron. Eng.
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“modified”Robertson and Wride (1998) correction (shown in
Fig. 6) was derived using trial and error to find an improved match
between the CPT-based trigger curves and the Vs1-based curves.
Fig. 7illustrates that a slight modification in the CPT-based
(Kc) correction can produce a very good match with the Vs1-based
trigger curves by Kayen et al. (2013). Figs. 5and 6also show that
using the original Robertson and Wride (1998) corrections produce
slightly conservative lower estimates of CRRin soils with
Ic>1.80.
The modified correction factor Kc–Icrelationship shown in
Fig. 6can be represented by
Kc¼1.7793I3
c−8.4301I2
cþ14.386Ic−7.7282 ð12Þ
That is valid between 1.60 <Ic<2.60 and Kc¼1.0when
Ic<1.60.
Any relationship between CPT tip resistance and Vshas some
uncertainty. This uncertainty is reduced when restricted to soils of
similar geologic origin and age (e.g., very young Holocene-age,
essentially normally consolidated, unbonded, silica-based soils),
as used to develop the CPT −Vs1relationship by Robertson
(2009) and the liquefaction trigger curves for the CPT and Vs
(Robertson and Wride 1998;Kayen et al. 2013). The relationship
to estimate Vs1suggested by Robertson (2009) has an average rel-
ative standard error of about 10% (Fig. 4). Fig. 8illustrates the level
of uncertainty in the CRR–Vs1curves for PL¼30% for clean
sand (FC ¼5% and Ic¼1.6) based on the relative standard error
of 10% from the CPT-based estimated Vs1.
Application of Combined CPT and Vs
Measurements to Evaluate Liquefaction Triggering
One of the advantages of the seismic CPT (SCPT) is that it provides
a profile of CPT tip and sleeve resistance, as well as Vsat the same
location in a very cost effective manner (Robertson et al. 1986). The
30-years experience with the SCPT has shown that the Vsmeasure-
ments are generally accurate, reliable, and more cost effective than
most invasive seismic methods (e.g., cross-hole testing). The added
cost of the Vsmeasurements is small if CPT is performed at the site.
Hence, the SCPT is becoming a popular in situ test (e.g., Mayne
2014) and the author recommends that SCPT be performed, where
possible, to measure Vsalong with the CPT measurements.
The above comparison between the Vs1-based method of Kayen
et al. (2013) and the CPT-based method of Robertson and Wride
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
Correction factor, 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 Kcas a function of Icbased on
Robertson and Wride (1998) (RW98) and suggested modification to
provide good agreement with Kayen et al. (2013)Vs1–liquefaction
correlation at PL¼30%
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300
CRR*
Vs1 (m/s)
Fig. 7. Comparison between Vs1-based trigger curves by Kayen et al.
(2013) (KET13) and the equivalent CPT-based trigger curves derived
from Robertson and Wride (1998) (RW98) using the CPT −Vs1
correlation proposed by Robertson (2009) (R09) using a modified
Kc−Icrelationship
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300
CRR*
Vs1 (m/s)
Fig. 8. Comparison between Vs1-based trigger curve by Kayen et al.
(2013) (KET13) for PL ¼30% and FC ¼5% and the equivalent
CPT-based trigger curves derived from Robertson and Wride (1998)
(RW98) for Ic¼1.6showing 1standard deviation (SD)
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(1998) has shown that both methods will produce very similar
results in terms of liquefaction triggering for most loose young,
unbonded silica-based sands.
The data base of liquefaction case histories are comprised of
soils that are essentially normally consolidated with in situ stress
ratio (Ko) likely in the range 0.4<Ko<0.7. Hence, although both
CPT measurements and Vsare influenced by horizontal effective
stresses, the application of vertical effective stress in the normali-
zation of both qtand Vscan be effective when Kois similar to the
case history database (i.e., 0.4<Ko<0.7). However, application
of the methods for soils where Kois significantly larger than around
0.5 can introduce uncertainty, unless a correction for Kois applied
(e.g., Maki et al. 2014). This can be an issue when applying these
liquefaction assessment methods at sites where ground improve-
ment may have increased Ko.
An interesting problem occurs when the CPT-based method
predicts triggering of liquefaction, for a given design earthquake
loading, but the Vs1-based method does not predict triggering of
liquefaction in the same soil for the same design earthquake. Which
method should be assumed correct?
Kayen et al. (2013) correctly cautioned that the “Vs1–liquefaction
correlations requires the cautionary understanding that some
soils with unusual soil-specific void ratio–relative density charac-
teristics or bonding may exhibit liquefaction behavior that differs
from the generalized proposed relationships.”Essentially Kayen
et al. (2013) cautioned that the Vs1–liquefaction correlations may
not apply to soils that have “unusual”characteristics. The term
microstructure is often used to describe soils that have “unusual”
characteristics (Leroueil and Hight 2003) compared to “ideal”soils
that have no microstructure. There are several causes for the devel-
opment of microstructure in soils, such as: aging, cementation, cold
welding, etc. Most of these factors give soil a strength and stiffness
that cannot be accounted for by void ratio and stress history alone.
Microstructure tends to reinforce the links between particles, and so
increase the small strain modulus and hence Vs(e.g., Hatanaka and
Uchida 1995;Goto et al. 1992). Leroueil and Hight (2003) showed
that, in soils with bonding, Godoes not depend only on confining
stresses but also on the strength of the bonds. Cuccovillo and Coop
(1997) showed that peak strength is controlled by the strength of
the bonds, while at large strains most of these bonds are broken.
Because the CPT tip resistance (qt) is predominately a large-strain
measure of soil strength, it tends to be less influenced by the
strength of the bonds than Go(and Vs), especially in lightly bonded
soils. In heavily cemented sands, where the strength of the bonds
can be very high, the CPT may reach refusal due to limits in avail-
able push force to break the bonds. Schmertmann (1991) showed
that relatively short-term aging (e.g., days) increases the stiffness of
some sands, whereas long-term aging (≫10,000 years) can alter
particle arranges and shapes so that there is also a significant in-
crease in large strain strength (e.g., Dusseault and Morgenstern
1979). 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 SCPT
can be helpful in identifying soils with “unusual”characteristics
(i.e., soils with microstructure) based on a link between Go=qtand
Qtn, since both aging and bonding tend to increase the small-strain
stiffness (Go) significantly more than they increase the large-strain
strength of a soil (reflected in Qtn). Hence, for a given soil, both age
and bonding tend to increase the small-strain shear wave velocity
more than the larger-strain cone resistance, all other factors (in situ
stress state, etc.) being constant.
Schneider and Moss (2011) extended the link between CPT
and Vsto establish a method to evaluate the threshold to trigger
liquefaction in sandy soils with microstructure. Schneider and
Moss (2011) suggested using an empirical parameter, KG(after Rix
and Stokoe 1991) defined by
KG¼ðGo=qtÞðQtnÞ0.75 ð13Þ
where Gois in same units as qtand Qtn is dimensionless.
Eq. (13) is modified slightly from Schneider and Moss (2011),
since they used qcinstead of qtand qc1Ninstead of Qtn .Inmost
sandy soils, the error in using qcinstead of qtis very small
(e.g., Robertson 2009). As described earlier, Qtn is the more general
term used here instead of the older term qc1N.KGis essentially a
normalized rigidity index.
Schneider and Moss (2011) showed that for soils with little or
no microstructure (i.e., young Holocene-age, sandy soils with no
bonding), 110 <KG<330, with an average of 215. Hence, using
SCPT data, where both qtand Vsmeasurements are available in
the same soil, it is possible to determine if a sandy soil falls within
the range of 110 <KG<330, for young unbonded soil. If a soil has
KG>330 it can be considered to have “unusual”characteristics
(i.e., microstructure) in terms of the application of the liquefaction
triggering correlations.
Schneider and Moss (2011) showed that the lower limits of
liquefaction resistance can be defined where induced cyclic strains
are 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 of
about 1×10−4. The cyclic stress ratio at the threshold strain
(CSRth) can be given by
CSRth ¼ðGo=σ0
voÞγth ð14Þ
Combining Eqs. (13) and (14), Schneider and Moss (2011)
showed that
CSRth ¼½KGqtγth=½σ0
voðQtn Þ0.75ð15Þ
It is possible to define a normalized small strain shear modules,
Go1, where
Go1¼ðρ=paÞðVs1Þ2ð16Þ
Then it can be shown that
Go=qt¼Go1=Qtn ð17Þ
Eq. (17) is correct when the stress exponent (n) to determine Qtn
is 0.5, which is approximately valid for most sandy soils when
σ0
vo <1.5atmosphere, as is the case for the majority of the lique-
faction cases histories. Then KGbecomes slightly simpler:
KG¼Go1ðQtnÞ−0.25 ð18Þ
Hence, the cyclic stress ratio at the threshold strain (CSRth) can
be given by
CSRth ¼KGγthðQtn Þ0.25ðpa=σ0
voÞ0.5ð19Þ
For σ0
vo ¼100 kPa, this simplifies to
CSR
th ¼KGγthðQtn Þ0.25 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 pore
pressures will not develop. Schneider and Moss (2011) suggested
that at low values of Qtn, small-strain stiffness controls liquefaction
resistance and at higher values of Qtn the consequences of
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liquefaction are limited by soil dilation, where correlations based
on 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 at
larger values of Qtn;cs, triggering liquefaction will produce a slower
build-up of strains. Robertson and Wride (1998) showed that that
when 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 when
Qtn;cs >70.WhenQtn;cs is less than about 70, the threshold strain
has a more significant role. When Qtn;cs <70 and the threshold
strain 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 play
an increasing role.
Andrus et al. (2009) and Hayati and Andrus (2009) suggested
a method to account for soil aging on the resistance to cyclic load-
ing based on CPT and Vsresults using a measured to estimated
velocity ratio (MEVR), where
MEVR ¼Vs1;M=Vs1;Eð21Þ
where Vs1;M¼Vs1measured in situ; and Vs1;E¼Vs1estimated for
a 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 ¼1.08MEVR −0.08 ð22Þ
The age corrected cyclic resistance ratio, CRR
Kis then given by
CRR
K¼KDRCRR
CPT ð23Þ
where CRR
CPT is the CPT-based CRR.
Eq. (23) indicates a uniform increase in CRRregardless of in
situ density (i.e., Qtn).
Hayati and Andrus (2009) showed that the MEVR approach is
based on a reference age (where KDR ¼MEVR ¼1.0) of about
23 years for Vs1;Eand stated that this reference age “seems a rea-
sonable average for the CRRcurves because many liquefaction
cases are associated with deposits that were 1–100 years old prior
to the earthquake shaking.”Hayati and Andrus (2009) essentially
identified that there is a “behavioral age”that could be less than the
geologic age, where “behavioral age”is defined as the time since
the last critical disturbance and that the measured Vs1was a mea-
sure of the “behavioral age”.
A similar approach can be applied to the Schneider and Moss
(2011) empirical parameter KGusing a similar measured to esti-
mated KGratio defined by
MEKG¼KG;M=KG;Eð24Þ
where KG;M¼KGbased on measured values of Vsand qt; and
KG;E¼KGestimated for very young, unbonded soil.
Based on the definition of KG[Eq. (13)], the MEKGratio is
insensitive to changes in CPT qtand Qtn;cs due to aging. Since
qthas been shown to be relatively insensitive to aging and/or light
bonding, it is reasonable to assume that
MEKG¼ðMEVRÞ2ð25Þ
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 KG¼215 sug-
gested by Schneider and Moss (2011) for Holocene-age, siliceous
unbonded sandy soils. Hence, a similar approach can be applied
using MEKGinstead of MEVR and apply Eqs. (22) and (23)to
estimate CRR
K.
To illustrate how these approaches compare, example CPT and
Vsvalues from published case histories are shown in Table 1. The
examples in Table 1were selected to illustrate possible differences
between Holocene-age, uncemented sands; Pleistocene-age and
Tertiary-age, uncemented sands; and aged, cemented sands. The
soils at the Moss Landing State Beach (Moss landing, CA) site
are Holocene-age, uncemented, silica-based sands and are typical
of many sites in the current liquefaction database. The State Beach
site was described in detail by Boulanger et al. (1997) and was in-
cluded as an example in Boulanger and Idriss (2014). Liquefaction
was observed along the access road to the Moss Landing State
Beach 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 Entrance
Kiosk where significant liquefaction and large deformations were
observed. UC 16 was located nearby on the Beach Path where
minor liquefaction was observed and deformations were smaller
than at UC 15. UC 18 was located closer to the beach where
the sand was denser and no liquefaction was observed. Table 1
shows that the CRRvalues determined using the CPT-based
method of Robertson and Wride (1998) are very similar to the val-
ues determined using the Vs-based method of Kayen et al. (2013).
The KGvalues at the State Beach site are consistent with the values
suggested by Schneider and Moss (2011) for Holocene-age, unce-
mented sands (i.e., KG<330) and the MEVR values are close to
1.0, as suggested by Andrus et al (2009). The Moss Landing ex-
amples shown in Table 1illustrate that the CPT-based and Vs-based
liquefaction triggering methods generally provide similar results in
most Holocene-age, uncemented, silica-based sands.
Andrus et al (2009) presented case history data from sand sites
in South Carolina that had experienced the 1886 magnitude 7.3,
Charleston earthquake, where the estimated average cyclic stress
ratio (CSR) at the sites was about 0.25. The sites were of either
Pleistocene age or Tertiary age and were estimated to be unce-
mented. The sand at the James Island site was estimated to have a
geologic 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 a
behavioral age of only 110 years at the time of the SCPT (since
it had liquefied in 1886). The Aiken SRS-5 site did not experience
liquefaction and was estimated to have a geologic age of about
35 million years. Table 1shows that the KGvalues for the aged
sands in South Carolina that did not experience liquefaction exceed
330 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 method
by Andrus et al. (2009) correctly predict that these sands would
not liquefy during the 1886 earthquake, whereas the CPT-based
method underestimated the CRR. The estimated CSR at the
threshold strain (CSR
th) is less than 0.15, which suggests that the
1886 earthquake was of sufficient size to exceed the threshold
strain at these sites. The CPT and Vsvalues at the TEN-08 site that
had experienced liquefaction in 1886 were measured about
110 years after the liquefaction and may not reflected the state of
the soil prior to the earthquake.
Tab l e 1also includes SCPT data from several sites in Western
Australia that are lightly cemented and of late Pleistocene age.
These sites have not experienced any major earthquake events
and therefore provide no direct liquefaction resistance evidence.
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The KGvalues are significantly greater than 330 and would sug-
gest some microstructure. Although the sands are of late Pleisto-
cene age, the KGvalues are higher than those for the older
Tertiary sands from Savannah River, which would support the
possibility of cementation. The estimated CRRvalues derived
from either Vsor 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 threshold
strain (CSR
th) is greater than the estimated CRRfrom the
CPT (e.g., Shenton Park and Perth sands). An uncertainty that
exists for sandy soils with light cementation is that if the cyclic
loading exceeds the threshold strain (i.e., CSR>CSR
th)thereis
a risk that the bonding (cementation) could be either damaged or
destroyed and the soil may behave more like an uncemented soil
at larger strains.
These examples illustrate the importance to identify soils that
have microstructure (such as aging and/or cementation) and may
exhibit “unusual”characteristics that may make traditional
cyclic liquefaction trigger methods (either SPT, CPT, or Vs) un-
reliable. Knowledge of either geologic age or the time since past
liquefaction events (i.e., behavioral age) can assist in the lique-
faction analysis. A combination of CPT (qt)andVsmeasure-
ments in the same soil (e.g., SCPT) provides an opportunity
to 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 or
cementation. If the soils are aged and uncemented, the existing
Vs-based liquefaction methods suggested by either Andrus et al.
(2009)andKayenetal.(2013) appear to provide better estimates
than penetration (either SPT or CPT) liquefaction methods. If
the soils have light cementation, the approach suggested by
Schneider and Moss (2011) can assist in estimating if the design
earthquake loading (CSR*) would exceed the CSR to reach the
threshold strain (CSR
th). If the design earthquake could exceed
the threshold strain, there is a risk that the benefits of cementa-
tion may be lost and the larger strain CPT-based CRRmaybe
more appropriate.
It would appear that until further research on threshold strain for
lightly bonded soils is available, it may be prudent to assume that
any 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 the
influence of possible microstructure. Shear wave velocity measure-
ments can be made both in situ and on samples in the laboratory to
evaluate sample disturbance.
It is likely that the benefits from aging could be different than
the benefits from bonding (e.g., cementation). Aging and bonding
will tend to increase the small strain stiffness but aging may have
little influence on the threshold strain, whereas bonding may also
increase the threshold strain depending on the nature and degree of
bonding. Light bonding may increase the small strain stiffness but
have little influence on the larger strain behavior. Clearly there is a
need for further research in this area.
The examples shown in Table 1also confirm the cautionary note
provided by Kayen et al. (2013) regarding application of the Vs1
relationships 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 examples
in Table 1also illustrate how the SCPT can be very helpful in
identifying soils with “unusual”characteristics (i.e., microstruc-
ture). The SCPT has the advantage that the Vsmeasurements are
obtained at the same location as the CPT measurements in a cost
effective way.
Table 1. Example Sites with CPT and Vs
Site and
characteristics Location
σ0
vo
(kPa)
qt
(MPa)
Vs
(m=s) Qtn;cs Vs1Go=qtGo1KGMEVR
CRRCPT CRRVsCRR
KCPT-aged CSR
thγth ¼10−4
ReferencesRW98 KET13 AET09 SM11
Moss Landing,
USA, Holocene,
uncemented
UC15 (liq) 47 5 128 74 155 5.9 432 147 0.92 0.12 0.12 0.09 0.04 Boulanger and
Idriss (2014)
UC16 (liq) 50 8.6 126 123 189 3.3 643 193 0.99 0.25 0.24 0.23 0.06 Boulanger and
Idriss (2014)
UC18 (no liq) 63 15.2 214 192 240 5.4 1037 279 1.14 0.7 0.7 >0.70.10 Boulanger and
Idriss (2014)
Charleston, SC,
aged, uncemented
TEN-08 (liq) 50 4.4 156 86 186 10 619 281 1.06 0.14 0.20 0.22 0.09 Andrus et al. (2009)
James Island
(no liq)
36 3.4 180 64 232 17.4 972 393 1.42 0.10 0.60 >0.70.11 Andrus et al. (2009)
Aiken SRS-5
(no liq)
300 18 345 107 262 11.9 1237 396 1.42 0.19 >0.7>0.70.13 Andrus et al. (2009)
Perth, Australia,
aged, cemented
Shenton Park 39 3.7 217 59 275 22.9 1357 489 1.71 0.10 >0.7>0.70.14 Schneider et al. (2004)
Ledge Point 100 16.3 324 163 324 11.6 1890 529 1.60 0.48 >0.7>0.70.19 Schneider and
Lehane (2010)
Perth Center 206 11.1 390 77 326 24.7 1908 643 1.90 0.12 >0.7>0.70.19 Fahey et al. (2003)
Note: liq = liquefaction; no liq = no liquefaction; RW98 = Robertson and Wride (1998); KET13 = Kayen et al. (2013); AET09 = Andrus et al. (2009); SM11 = Schneider and Moss (2011).
© ASCE 04015037-8 J. Geotech. Geoenviron. Eng.
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Summary
A comparison has been made between the CPT-based liquefaction
triggering method by Robertson and Wride (1998) and the Vs1-
based method by Kayen et al. (2013) to evaluate the associated
CPT-based corrections. Although the comparison requires an aver-
age relati onship between CPT and Vs1, which has some uncertainty,
the comparison has shown that the Robertson and Wride (1998)’s
CPT-based corrections, based on a generalized Icrelationship, pro-
vided generally good agreement between the two independent
approaches. A slight modification to the CPT-based “fines”correc-
tion is suggested to provide better agreement between the two
methods in soils with high fines content. The comparison indicates
that the current Robertson and Wride (1998) corrections are slightly
conservative compared to the Vs-based trigger relationship of
Kayen et al. (2013) in soils with high fines content where Ic>1.8.
The comparison also highlights the importance of recognizing
the limits in the existing liquefaction case history database. The
existing CPT-based and Vs-based methods to evaluate liquefaction
triggering apply to “ideal”soils that are young (Holocene-age) and
have 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 Vshas been shown, it is recommended that Vs
be 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, show
promise as simple methods to detect “unusual”characteristics. The
approach suggested by Schneider and Moss (2011) has the advan-
tage that a generalized value for KGE (∼200) can be assumed that
does not require selection of a specific relationship between CPT
and Vswith the associated uncertainty. Further research is needed
to clarify the role of threshold strain on the response of soils with
microstructure (e.g., aging and/or bonding) and if the effects of age
are 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 other
staff at Gregg Drilling and Testing Inc. The author would also like
to thank the anonymous reviewers that provide valuable comments
and advice.
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