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BRAY, RATHJE, AUGELLO AND MERRY D Seismic Design for Lined Solid-Waste Landfills 217GEOSYNTHETICS INTERNATIONAL S 1998, VOL. 5, NOS. 1-2 disiandSeed(1978),areavailable toevaluate displacements thatmayoccurduetoslid- ing along a distinct, rigid-perfectly plastic slip surface. Hence, Newmark (1965)-type deformation analysesconstitute thebasisfordesignofmostMSWLFunits.Theassump- tionsinvolvedinthisapproachareactuallymorereasonableforslippagealongageosyn- thetic interface within a Subtitle D base/cover liner system than for the homogeneous earth embankment for which it was originally developed (Bray et al. 1995). Hence, its use isjudged to be reasonable forgeosynthetically lined landfills. Although this proce- dure is also often used to evaluate sliding within the waste fill, sliding is not likely to occur along a distinct shear plane forthiscase, thusits userequires acalibration forthis application. TheresultsfromaNewmark-type seismically inducedpermanentdeforma- tionanalysisactuallyprovidesonlyanindexoflikelyperformanceduringanearthquake. Seismically induced permanent displacements can be calculated using a procedure developed byFranklin andChang(1977)requiring twoinputs:(i)horizontal equivalent acceleration-time history based onthe horizontal shear stress-time history computed at thedepthofsliding fromadynamicresponseanalysis; and(ii)yield acceleration coeffi- cient,ky ,calculated astheseismic coefficient required toobtain afactor ofsafety ofone inapseudo-static slopestability analysis. Theyieldacceleration coefficient atthecover (infinite slopeanalysis, Equation 1)andbase(adaptation fromShewbridge 1996,Equa- tion 2) can be estimated for typical landfills (Figure 9) using the following formulas: (1) (2) (3) k y tan(¬¨)c H cos2 ¨(1 tan ¬tan ¨) k y (FS static 1) cos »1 sin »1 S 1 H2 H(S 1 S2)2 L FS static tan ¬(S 1 H2cos2 »1 L S 2 H2) cos »1 sin 1 S1 H2 »1 tan 1 (1S 1)(4) where:¨= slope angle ofthe cover measured from the horizontal;= total unit weight of the cover soil;c = soil cohesion;¬= internal friction angle;FSstatic = static factor of safety;»1 = back-slope geometry parameter;S1 = back-slope run to height ratio;S2 = front-slope run to height ratio; and L = length of the midsection of the landfill. Use of the equivalent acceleration allows for the seismic response of the deform- able potential sliding mass to be represented in the Newmark rigid sliding block pro- cedure (Makdisi and Seed 1978). However, a potentially important limitation of this procedure is that the seismic response of the potential sliding mass is decoupled from the subsequent double integration of the computed equivalent acceleration-time histo- ry. A number of investigators have examined the limitations of this assumption (e.g. Lin and Whitman 1983; Chopra and Zhang 1991; Gazetas and Uddin 1994; Kramer and Smith 1997), and for the most part, have arrived at similar conclusions. For exam- ple, Lin and Whitman (1983) concluded that “the errors arising from the decoupled assumption are insignificant compared to other uncertainties involved in the use of the sliding block analogy.”.