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BRAY, RATHJE, AUGELLO AND MERRY D Seismic Design for Lined Solid-Waste Landfills <br />214 GEOSYNTHETICS INTERNATIONAL S 1998, VOL. 5, NOS. 1-2 <br />by Seed et al. (1991) for deep cohesionless and stiff cohesive soils, because the range <br />in dynamic stiffness of this site category is close to that of waste fill. Additionally, the <br />mean period,Tm , was used in lieu of the predominant period, because this parameter <br />better represents theoverall frequency content ofagroundmotion andcan beestimated <br />more reliably with empirical ground motion data (Rathje et al. 1998). <br />Incorporating these two improvements, a revised normalization was developed (Fig- <br />ure6),withdatafromover300analysesoflandfillsatrocksites(BrayandRathje 1998). <br />The results follow a well-defined trend, except near the resonance condition which oc- <br />cursat Ts /Tm <1,whichisduetodegradingwaste stiffnessathigherstrain levels. Results <br />for landfills located at soil sites indicate that site conditions play a less significant role <br />in the estimate of MHEA , with slightly lower MHEA values forsoil sites. Inan extreme <br />case,MHEA values at deep, soft clay sites were about two-thirds of the MHEA values <br />calculated at rock sites, but this apparent conservatism for soft sites is balanced by the <br />larger displacements calculated at these sites, and the implications ofthese compensat- <br />ingerrorswillbediscussedinSection2.7.1.Figure6maybeusedasaguideintheselec- <br />tion of an appropriate seismic coefficient for simplified pseudo-static and deformation <br />analyses, as this graph has been prepared with normalization parameters that may be <br />estimated for most projects. <br />The use of a 1-D model to represent the seismic response of an earth/waste fill has <br />been discussed in Vrymoed and Calzascia (1978), Elton et al. (1991), and Bray et al. <br />(1996), and it hasbeen foundthat dynamic shear stresses near the base of a two-dimen- <br />sional (2-D) earth/waste fill can be approximated reasonably well with a 1-D analysis. <br />This issue, as well as the reliability of capturing a landfill’s cover response with a 1-D <br />analysis, was investigated using the programs SHAKE91 and QUAD4M(Hudson et al <br />1994) to analyze five generic landfill configurations and five landfills shaken by the <br />Northridge earthquake (Rathje 1997). <br />Figure 6. Normalized maximum horizontal equivalent acceleration for base sliding <br />versusnormalizedfundamental periodofwastefill (adaptedfromBrayandRathje1998). <br />0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 <br />0.0 <br />0.2 <br />0.4 <br />0.6 <br />0.8 <br />1.0 <br />1.2 <br />1.4 <br />1.6 <br />1.8 <br />2.0 <br />0.1 1.35 <br />0.2 1.20 <br />0.3 1.09 <br />0.4 1.00 <br />0.5 0.92 <br />0.6 0.87 <br />0.7 0.82 <br />0.8 0.78 <br />Rock site median <br />MHARock (g)NRF <br />MHEABase/[(MHARock)(NRF)]Ts-WASTE /Tm-EQ <br />16th and 84 <br />th probability of exceedance lines