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0.2
<br />0.4
<br />r
<br />0.8
<br />0.8
<br />1.0
<br />kmax/Vmax
<br />Figure 10.18 Variation of effective peak acceleration with depth of base of potential Slide
<br />mass. (From Seed, 1979. Reproduced by permission of the Institution of Civil Engineers.)
<br />also requires shear wave velocities for the refuse. Some field measurements of shear
<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
<br />from 500 to 800 fits. Further work is required in this area.
<br />Singh and Murphy (1990) performed SHAKE analyses, using these values, for
<br />:ledlandfill and reported attenuation of baserock motions as they trav-
<br />eled up through the refuse. Similar results are reported by Sharma and Goyal
<br />(1991). In general, it is reported that there may be some amplification of base
<br />accelerations up to about 50 ftwt high landfills. For landfills higher than 50 feet, the
<br />base accelerations attenuate. This may be one of the reasons that during the Loma
<br />Prieta earthquake of 1989, landfills experienced negligible distress (Buranek and
<br />Prasad, 1991). Anderson et al. (1992), used a two-dimensional, equivalent -linear
<br />finite element technique (QUAD 4) to better 'understand landfill behavior under
<br />seismic loading and concluded that energy from smaller -magnitude earthquakes
<br />(e.g. MC5) will attentuate as it passes through the landfill. -
<br />SHAKE 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
<br />known Um,,, y, and H. the ratio km„/(Jm„ can be obtained from Figure 10.18; y
<br />Y
<br />h
<br />Figure 10.19 Depth of sliding surface.
<br />and H are defined in Figure 10.19. Thus with known (J,,,,, Y. and H. the km„ value
<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 />Figure 10.19. For example, if the critical slide surface is tangent to the base of the
<br />embankment, y1H = I.O. The critical slide surface 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 />material properties of refuse and limited case histories of seismic responses of land-
<br />fill, many engineers simply equate a..,,,m with k,,.. The rationale behind this is the
<br />belief (as discussed earlier) that refuse tends to dampen seismic accelerations.
<br />Equating a`,,,a with k,,,u is therefore considered a conservative assumption. At this
<br />time (1994), limited data indicate that landfills may attentuatc smaller -magnitude
<br />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 />response of landfills. The value of aa,,,,d can be obtained either from a SHAKE
<br />analysis or from Figures 10.20 and 10.21. if Figures 10.20 and 10.21 are used,
<br />Figure 10.22 is used to estimate a,,,,k for a known magnitude of earthquake gener-
<br />ated by a fault at a known horizontal distance from the site. If the landfill foundation
<br />is bedrock, then a„ck=a6,,,,,w. Alternatively, if soil overburden exists between the
<br />landfill base and bedrock, Figures 10.20 and 10.21 can be used to estimate a
<br />for the type of overburden (e.g., soft soil, stiff soil, and cohesionless soils). a,,,nd
<br />Step 3, estimating permanent deformations caused by seismic events, can be
<br />performed using Figure 10.23. Figure 10.23 was developed. by Makdisi and Seed
<br />(1977) and is commonly referred to as a modified Newmark chart. The chart shows
<br />that the deformations induced by an earthquake are a function of the ratio of yield
<br />acceleration (ky calculated in step 1) to maximum acceleration (k,,,,, calculated
<br />in step 2) and the magnitude of the earthquake. It is important to note that the
<br />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 />ment cases. Although Makdisi and Seed note that this chart should be modified a$
<br />further information becomes available, the Newmark chart has been widely used
<br />without modification to predict seismic displacements on earth slopes. Alterna•
<br />1
<br />1
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