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magnitude as a proxy for duration in combination with the estimated
PGA
at the crest of
theembankment;Yegianetal.(1991b)usepredominantperiodandequivalentnumberof
cycles of loading in combination with
PGA
; and Bray et al. (1998) use the mean period
and significant duration of thedesign rock motion incombination with its
PGA
.
Spectral acceleration has been commonly employed in earthquake engineering to char-
acterizeanequivalentseismicloadingonastructurefromtheearthquakegroundmotion.
Similarly,Travasarou andBray(2003a)foundthatthe5%dampedelasticspectralaccel-
eration at the degraded fundamental period of the potential sliding mass was the optimal
groundmotionintensitymeasureintermsofefficiencyandsufficiency(i.e.,itminimizes
thevariabilityinitscorrelationwithseismicdisplacement,anditrenderstherelationship
independent of other variables, respectively, Cornell and Luco, 2001). The efficiency
and sufficiency of estimating seismic displacement given a ground motion intensity
measure were investigated for dozens of intensity measures. Other promising ground
motion parameters included
PGA
, spectral acceleration
(
S
a
)
, root mean square acceler-
ation
, effective peak velocity
(
EPV
), Housner's response spectrum intensity (
SI
), and Ang's characteristic intensity
(
(
a
rms
)
, peak ground velocity (
PGV
), Arias intensity
(
I
a
)
. For period-independent parameters (i.e., no knowledge of the fundamental period
of the potential sliding mass is required), Arias intensity was found to be the most effi-
cientintensitymeasureforastiff,weakslope,andresponsespectrumintensitywasfound
to be themost efficient for aflexible slope.
I
c
)
No one period-independent ground motion parameter, however, was found to be ade-
quately efficient for slopes of all dynamic stiffnesses and strengths. Spectral accelera-
tion at a degraded period equal to 1.5 times the initial fundamental period of the slope
(i.e.,
S
a
(
)wasfoundtobethemostefficientgroundmotionparameterforallslopes
(TravasarouandBray,2003a).Anestimateoftheinitialfundamentalperiodofthepoten-
tialslidingmass
1
.
5
T
s
)
isrequiredwhenusingspectralacceleration,butanestimateof
T
s
is
useful in characterizing the dynamic response aspects of the sliding mass (e.g., Bray and
Rathje, 1998). Spectral acceleration does directly capture the important ground motion
characteristics of intensity and frequency content in relation to the degraded natural
period of the potential sliding mass, and it indirectly partially captures the influence of
durationinthatittendstoincreaseasearthquakemagnitude(i.e.,duration)increases.An
additionalbenefitofselectingspectralaccelerationtorepresentthegroundmotionisthat
spectral acceleration can be computed relatively easily due to the existence of several
attenuation relationships and it is available at various return periods in ground motion
hazard maps (e.g.,http://earthquake.usgs.gov/research/hazmaps/).
(
T
s
)
3.3. DYNAMIC RESISTANCE
The earth/waste structure's yield coefficient
represents its overall dynamic resis-
tance,whichdependsprimarilyonthedynamicstrengthofthematerialalongthecritical
sliding surface and the structure's geometry and weight. The yield coefficient parameter
hasalwaysbeenusedinsimplifiedslidingblockproceduresduetoitsimportanteffecton
seismicdisplacement.
(
k
y
)
