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0.2
<br /> y
<br /> 0.4 once
<br /> (rangege tor all dale) Figure 10:19 Depth of sliding surface,
<br /> tot
<br /> r
<br /> a and H are defined in Figure 10.19.Thus with known y, and H, the km$A value
<br /> can be determined. Alternatively, kthe 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 /> Figure 10.19. For example, if the critical slide surface is tangent to the base of the
<br /> o.e Average of embankment,y/H= 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 /> '°0 0.2 0.4 o e o e 1 o fill,many engineers simply equate awith k .The rationale behind this is the
<br /> belief (as discussed earlier) that refuse tends to dampen seismic accelerations,
<br /> kmaa/ max Equating awith k,,,.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(Mm7 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 /> response of landfills. The value of a� can be obtained either from a SHAKE
<br /> waves in refuse have been reported(Singh and Murphy. 1990;Sharma et al., 1990).
<br /> A recommended range for shear wave velocities for dynamic response analysis is analysis or from Figures 10.20 and 10.21. If Figures 10.20 and 10.21 are used,
<br /> y Figure 10.22 is used to estimate a„,k for a known magnitude of earthquake gener
<br /> from 500 to 800 ft/s. Further work is required in this area.
<br /> -
<br /> 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,,.,=aa,g,,,w. Alternatively, if soil overburden exists between the
<br /> a 400-fool-high landfill and reported attenuation of baserock motions as they tray. landfill base arld bedrock,Figures 10.20 and 10.21 can be used to estimate a.,�
<br /> eled up through the refuse. Similar results are reported by Sharma and Go al
<br /> Y for the type of overburden(e.g.,soft soil,stiff soil,and cohcsionless soils).
<br /> (1991). In general, it is reported that there may be some amplification of base Ste 3 estirnatin
<br /> scccleratiuns up to abitut SO ftwt high landlills. For landfills higher than 50 feet the p B permanent deformations caused by seismic events, can be
<br /> 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
<br /> Pricta earthquake of 1989, landfills experienced negligible distress (Buranek and (1977)and is commonly referred to as a modified Newmark chart.The chart shows
<br /> Prasad, 1991). Anderson et al. (1992), used a two-dimensional, c uivalent-linear that the deformations induced by an earthquake ars a function of the ratio of yield
<br /> finite element technique (QUAD 4) to better Understand landfill behavior under acceleration (k., calculated in step t) to maximum acceleration (k,,,,, calculated
<br /> nitude earthquakes 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-ma
<br /> g q displacements represented on this chart are based on Field observations and the
<br /> (e.g. MCS)will altentuate as it passes through the landfill: 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- ment cases. Although Makdisi and Seed note that this chart should be modified as
<br /> anon ((/m„)at the top (crest) of a landfill that has a narrow crest width. With the
<br /> known tJ further information becomes available, the Newmark chart has been widely used
<br /> y, and H, the ratio k /(/m„can be obtained from Figure 10.18;y without modification to predict seismic displacements on earth slopes. Altema•
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