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noted that the case history based approach to estimating S
r
may implicitly account for
void redistribution effects, and is therefore preferred for practice over lab testing of field
samples.
A number of definitions have been used in the literature for the shear strength of lique-
fied soils. The ultimate shear resistance, or critical state strength, that is measured in
undrainedlaboratoryelementtestsmaybedenotedasS
CS
,whereasthequasi-steadystate
shear resistance, which corresponds to a local minimum in the stress-strain curve from
an undrained laboratory element test, may be denoted as S
QSS
. Residual shear strength,
as used in this paper, refers to the shear resistance that a liquefied soil mobilizes in the
field, which can be complicated by void redistribution and other field mechanisms that
are not replicated in laboratory element tests. These three “strengths” are fundamentally
different froma mechanics standpoint, and thus maintaining a distinction is essential.
This paper presents recommended SPT- and CPT-based relationships for estimating the
ratio of residual shear strength to initial vertical effective stress, S
r
/
σ
vo
, for liquefied
nonplastic soils in the field. Case history analyses by a number of investigators over the
past 20 years are reviewed and utilized. The available case history data only constrain
designrelationshipsatlowpenetrationresistances;therefore,theestimationofS
r
/
σ
vo
at
higherpenetrationresistancesrequiresextrapolationbeyondthecasehistorydata.Conse-
quently,developmentoftherecommendeddesignrelationshipswasguidedbylaboratory
testing studies and recent findings regarding void redistribution mechanisms. Develop-
ment of the SPT-based relationship is presented first, followed by development of the
CPT-based relationship. Limitations in the state of knowledge, including the uncertain-
ties in the empirical data and the challenge of quantifying void redistribution processes,
are considered.
2. Case history studies
Theback-analysisofacasehistoryinvolvesperformingapost-earthquakestaticstability
analysisoftheearthstructurewitheachzoneofnonliquefiedsoilassignedabestestimate
of itsshear strength,whilethezone considered tohave liquefied isassigned an unknown
shear strength of S
r
(with
0). This procedure is illustrated in Figure 1.3 for the
LowerSanFernandoDam(Seed,1987).AnupperboundestimateforS
r
isthevaluethat
gives a factor of safety against sliding equal to 1.0 for the undeformed geometry of the
slope. Another estimate for S
r
is similarly obtained for the final deformed geometry of
theslope,ifthatdeformedgeometryisreasonablydocumentedandifthefinalsoillayer-
ing has not been seriously modified in the deformation process. Various procedures have
thenbeenusedtointerpolatebetweenthesetwoestimatesofS
r
byattemptingtoaccount
for the role of sliding inertia, evolving geometry, strength losses due to intermixing with
adjacentwaterbodies,andotherfactors.Forexample,OlsonandStark(2002)calculated,
for the Lower San Fernando dam, S
r
values of about 36 and 5kPa for these two geome-
tries, respectively, and an interpolated best estimate of about 19kPa. This illustrates how
the interpolation of strengths between deformed and undeformed geometries is a very
φ
u
=
