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Y
<br /> ti
<br /> h
<br /> 0.4 Shear allce
<br /> (range for all date) Figure 10.19 Depth of sliding surface.
<br /> r
<br /> and H are defined in Figure 10.19.Thus with known Um,,,Y. and H. the k,a„value
<br /> 0.8
<br /> can be determined. Alternatively, k,,,,,, the maximum average acceleration for a
<br /> potential sliding mass extending to a specified depth, y, can be estimated directly
<br /> from dynamic response analysis.
<br /> The value y is the maximum depth of the critical sliding surface, as shown in
<br /> 0.8-
<br /> Figure 10.19. For example, if the.critical slide surface is tangent to the base of the
<br /> Average of embankment,y1H= 1.0.The critical slide su
<br /> all data rface is the slide surface corresponding
<br /> to the yield acceleration of the section being analyzed.
<br /> It should be noted that due to the lack of information regarding the dynamic
<br /> 1.4-
<br /> material properties of refuse and limited case histories of seismic responses of land-
<br /> o,A o.e fill,many engineers simply equate asJO1 W with k,,,,,.The rationale behind this is the
<br /> 0
<br /> kmtx/Omax belief (as discussed earlier) that refuse tends to dampen seismic accelerations,
<br /> Equating a with k
<br /> Figure 10,18 Variation of c(fective peak acceleration with depth of base of potential slide iroan0 n,.�is therefore considered a conse
<br /> Reproduced rvative assumption.At this
<br /> time (1994), limited data indicate that landfills may accentuate smaller-magnitude
<br /> mass. (From Seed. 1979. Red by permission of the Institution of Civil Engineers.) earthquakes but higher magnitude earthquakes(M-7 or larger) may amplify(An.
<br /> derson, et al, 1992 and Hushmand Associates, 1994). Further data collection and
<br /> also requires shear wave velocities for the refuse.Some field measurements of shear evaluation is required before a definitive conclusion can be made regarding seismic
<br /> waves in refuse have been reported(Singh and Murphy, 1990;Sharma et al., 1990), response of landfills. The value of a..,,4 can be obtained either from a SHAKE
<br /> A recommended range for shear wave velocities for dynamic response analysis is analysis or from Figures 10.20 and 10.21. If Figures f0.20 and 10.21 are used,
<br /> Figure 10.22 is used to estimate a,,,�t,for a known magnitude of earthquake gamer.
<br /> from 500 to 800 ft/s. Further work is required in this area.
<br /> aced dr a fault a known horizontal distance from the site. If the landfill foundation
<br /> Singh and Murphy 0990) performed SHAKE analyses, using these values, for
<br /> a 400-foot-high landfill and reported attenuation of baserock motions as the trav- is bedrock, then
<br /> a„�k=ate, Alternatively, if soil overburden exists between the
<br /> y landfill base and bedrock, Figures 10.20 and 10.21 can be used to estimate a ,�
<br /> sled up through the refuse. Similar results arc reported by Sharma and Go al
<br /> (1991). In general, it is reported that there may be some amplification of base for the type of overburden(e.g.,soft soil,stiff soil,and cohesionless soils),
<br /> accelerations up to abirut SO foot high landfills, For landfills higher than SO feet,the Step 3, estimating permanent deformations caused by seismic events, can be
<br /> base accelerations attenuate. This may be one of the reasons that during the Loma (1977)
<br /> using Figure 10.23. Figure t0.23 was developed.by Makdisi and Seed
<br /> Tbe chart shows
<br /> Prieta earthquake of 1989, landfills experienced negligible distress (Buranek and (1977)and is commonly referred to as a modified Newmark chart,
<br /> that the deformations induced by an earthquake are a Function of the ratio of yield
<br /> Prasad, 1991). Anderson et al. (1992), used atwo-dimensional, equivalent-linear
<br /> finite element technique QUAD 4) to better 'understand landfill behavior under acceleration (ky calculated in step I) to maximum acceleration (k.,. calculated
<br /> in step 2) and the magnitude of the earthquake. It is important to note that the
<br /> seismic loading and concluded that energy from smaller-magnitude earthquakes
<br /> (e.g. MCS)will attentuate as it passes through the landfill: displacements represented on this chart are based on field observations and the
<br /> results of finite-element analyses performed on a limited number of soil embank.
<br /> SNAKE analysis results, as discussed above,will provide the maximum acceler-
<br /> ation (Um„)at the top (crest) of a landfill that has a narrow crest width. With the mart cases. Although Makdisi and Seed note that this chart should be modified as
<br /> known tJy, and H. the ratio k /lJ further information becomes available, the Newmark chart has been widely used
<br /> m„ „,,,can be obtained from Figure 10.18;y without modification to predict seismic displacements on earth slopes. Altana.
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