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Fig. 12.16. Criticalslope stabilityfailure surfaces fordifferent values
of pile restraining force
S r / σ vc ratios and SPT or CPT penetration resistances. The total shear force
(
V t )
and
bendingmoment
inthepilesattheslopestabilityfailuresurfacecanberepresented
by an equivalent force-couple, such as having the pile shear force act alone at a distance
equal to M t /
(
M t )
V t above the slope stability failure surface. Large point forces can produce
numerical errors in the limit equilibrium analyses, such that V t is often represented as a
distributedforceoranequivalentincreaseinsoilshearstrengthalongsomeportionofthe
failuresurface.Theslopestabilityanalysesareusedtodetermineyieldaccelerations
k y )
forarangeofpossiblerestrainingforces.Foreachrestrainingforce,theyieldacceleration
is the value of the horizontal seismic coefficient that produces a factor of safety of unity
against slope instability. These slope stability analyses must consider a range of possible
failuresurfacesbecausethemostcriticalfailuresurfacecanincreasesubstantiallyinsize
withincreasing restrainingforce (e.g., Figure 12.16).
(
Embankmentdisplacementsforeachofthepossiblerestrainingforcesarethencomputed
basedontheyieldaccelerationandthedesigngroundmotionparameters.Thisstepcould
beperformedbyeither:(1)performingNewmarkslidingblockcalculationsusingaspec-
ified set of acceleration time series or (2) using a regression model for Newmark sliding
block displacements, such as the one developed by Bray and Travasarou (2007). The
results of these analyses are a plot of embankment displacement versus restraining force
per unit thickness ofthe analyzed section.
Thetributary(transverse)widthfortheembankmentmassisusedtoestablishacommon
dimensionbetweentheforce-displacementrelationshipsfortheembankmentandforthe
pilefoundation/bridgesuperstructure.Considertheembankmenttransversecross-section
showninFigure12.17.Thepilesandbridgesuperstructurewillberestrainingmovement
of an embankment mass that includes the soil defined by the embankment crest width,
plus a portion of the side slope masses. This is accounted for by adopting an equivalent
tributary width whose mass includes a portion of the side slope masses, with one-half of
the sideslopemass recommended asa reasonable value for design.
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