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• Finite element method
<br /> 0 0.2 y ;7
<br /> h
<br /> 0.4 Shear slice Figure 10.19 Depth of sliding surface.
<br /> (range for all date)
<br /> and H are defined in Figure 10.19.Thus with known Uma.,y and H, the kmu value
<br /> can be determined. Alternatively, k,,,,,,, the maximum average acceleration for a
<br /> o.s 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 /> Figure 10.19. For example, if the critical slide surface is tangent to the base of the
<br /> 0.8 Average of embankment,y1H= 1.0. The critical slide surface is the slide surface corresponding
<br /> all data 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 /> material properties of refuse and limited case histories of seismic responses of land-
<br /> 1.0 0
<br /> and-
<br /> to0 0.2 0.4 o.s
<br /> fill,many engineers simply equate a,—,a,—,with k,,,,;.The rationale behind this is the
<br /> 0.s 1.0 belief (as discussed earlier) that refuse tends to dampen seismic accelerations.
<br /> kmax/Vmax Equating ag, .,,a with kmu is therefore considered a conservative assumption. At this
<br /> Figure 10.18 Variation of effective peak acceleration with depth of base of potential slide time (1994), limited data indicate that landfills may attentuate smaller-magnitude
<br /> mass. (From Seed, 1979. Reproduced 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 /> evaluation is required before a definitive conclusion can be made regarding seismic
<br /> also requires shear wave velocities for the refuse. Some field measurements of shear response of landfills. The value of ag,.,,,m can be obtained either from a SHAKE
<br /> waves in refuse have been reported(Singh and Murphy, 1990;Sharma et al., 1990). analysis or from Figures 10.20 and 10.21. If Figures 10.20 and 10.21 are used,
<br /> A recommended range for shear wave velocities for dynamic response analysis is Figure 10.22 is used to estimate arock for a known magnitude of earthquake gener-
<br /> from 500 to 800 ft/s. Further work is required in this area. ated by a fault at a known horizontal distance from the site. If the landfill foundation
<br /> Singh and Murphy (1990) performed SHAKE analyses, using these values, for is bedrock, then a,ak=ag,o,,m. Alternatively, if soil overburden exists between the
<br /> a 400-foot-high landfill and reported attenuation of baserock motions as they trav- landfill base and bedrock, Figures 10.20 and 10.21 can be used to estimate ag,a,,,d
<br /> eled up through the refuse. Similar results are reported by Sharma and Goyal for the type of overburden (e.g., soft soil, stiff soil, and cohesionless soils).
<br /> (1991). In general, it is reported that there may be some amplification of base Step 3, estimating permanent deformations caused by seismic events, can be
<br /> accelerations up to about 50 foot high landfills. For landfills highcr than 50 feet, the performed using Figure 10.23. Figure 10.23 was developed by Makdisi and Seed
<br /> base accelerations attenuate. This may be one of the reasons that during the Loma (1977)and is commonly referred to as a modified Newmark chart.The chart shows
<br /> Prieta earthquake of 1989, landfills experienced negligible distress (Buranek and that the deformations induced by an earthquake are a function of the ratio of yield
<br /> Prasad, 1991). Anderson et al. (1992), used a two-dimensional, equivalent-linear acceleration (ky calculated in step 1) to maximum acceleration (k,,,,,, calculated
<br /> finite element technique (QUAD 4) to better understand landfill behavior under 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 displacements represented on this chart are based on field observations and the
<br /> (e.g. MC5)will attentuate as it passes through the landfill.• results of finite-element analyses performed on a limited number of soil embank-
<br /> SHAKE analysis results,as discussed above,will provide the maximum acceler- ment cases. Although Makdisi and Seed note that this chart should be modified as
<br /> anon (Umar) at the top (crest) of a landfill that has a narrow crest width. With the further information becomes available, the Newmark chart has been widely used
<br /> known Uma„ y, and H, the ratio kma,/Uma. can be obtained from Figure 10.18; y without modification to predict seismic displacements on earth slopes. Altema-
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