Geoscience Reference
In-Depth Information
3.4. DYNAMIC RESPONSE
Research by investigators (e.g., Bray and Rathje, 1998) has found that seismic displace-
ment also depends on the dynamic response characteristics of the potential sliding mass.
Withallotherfactorsheldconstant,seismicdisplacementsincreasewhentheslidingmass
is near resonance compared to that calculated for very stiff or very flexible slopes (e.g.,
Kramer and Smith, 1997; Rathje and Bray, 2000; Wartman et al., 2003). Many of the
available simplified slope displacement procedures employ the original Newmark rigid
sliding block assumption (e.g., Lin and Whitman, 1986; Ambraseys and Menu, 1988;
Yegian et al., 1991b), which does not capture the dynamic response of the deformable
earth/waste potential sliding mass during earthquake shaking.
As opposed to the original Newmark (1965) rigid sliding block model, which ignores
thedynamicresponseofadeformableslidingmass,MakdisiandSeed(1978)introduced
the concept of an equivalent acceleration to represent the seismic loading of a potential
sliding mass (Figure 14.2) based on the work of Seed and Martin (1966). The horizontal
equivalentacceleration(
HEA
)-timehistorywhenappliedtoarigidpotentialslidingmass
produces the same dynamic shear stresses along the potential sliding surface that is pro-
duced when a dynamic analysis of the deformable earth/waste structure is performed.
The decoupled approximation results from the separate dynamic analysis that is per-
formed assuming that no relative displacement occurs along the failure plane and the
rigid sliding block calculation that is performed using the equivalent acceleration-time
history fromthedynamic response analysis to calculate seismicdisplacement.
Although the decoupled approximation of Makdisi and Seed (1978) inconsistently
assumes no relative displacement in the seismic response analysis and then calculates
a seismically induced permanent displacement, it has been judged by many engineers
to provide a reasonable estimate of seismic displacement for many cases (e.g., Lin and
Whitman, 1983; Rathje and Bray, 2000). However, it is not always reasonable, and it
can lead to significant overestimation near resonance and some level of underestimation
for cases where the structure has a large fundamental period or the ground motion is
an intense near-fault motion. A nonlinear coupled stick-slip deformable sliding block
model offers a more realistic representation of the dynamic response of an earth/waste
structure by accounting for the deformability of the sliding mass and by considering the
simultaneousoccurrenceofitsnonlineardynamicresponseandperiodicslidingepisodes
Fig. 14.2. Equivalent acceleration concept fordeformable slidingmass
(Seed and Martin, 1966)
