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BRAY, RATHJE, AUGELLO AND MERRY D Seismic Design for Lined Solid-Waste Landfills 213GEOSYNTHETICS INTERNATIONAL S 1998, VOL. 5, NOS. 1-2 The engineer must still decide if peak or residual (large displacement) interface strengths are appropriate. A sacrificial “slip layer” interface should be designed using residual strength, as some (and maybe significant) slippage is assumed to occur along this interface. Installation procedures, post-installation environmental changes, se- quencing oflayerswithin thebase, coverandsideslopeliner systems,andthestress-de- formation response of layered systems to placement of the waste all may contribute to relative displacement withinspecific interfaces. Thesecontributing factors,andthefact that peak strengths are mobilized at small displacements, suggest that the use of large displacement (residual) strength values for seismic stability analyses is appropriate. 2.6 Nonlinear Dynamic Response Analysis Parametric seismic response studies (Bray et al. 1995; Bray and Rathje 1998) have foundthatreasonablevariationsinwastefill dynamicproperties,fillheights,foundation conditions, and input bedrock motions produce significant variations in the landfill re- sponse. Moreover, developing goodcharacterizations ofwaste fill properties (dynamic strength,stiffness,anddamping)remainsatoppriority,astheresponseofaMSWLFunit foragivensuite ofmotionsislargelya function ofitsdynamic responsecharacteristics. The seismic loading for a potential sliding mass within the waste fill can be repre- sented bythe horizontal equivalent acceleration as HEA =(ºh /¹v )g (where ºh = horizon- tal shear stress and ¹v = total vertical stress at the depth of the sliding surface) which wasoriginally conceived bySeed and Martin (1966)and defined fora 1-Dsystem. The maximum seismic loading isdesignated MHEA. Using the 1-D equivalent-linear wave propagation program SHAKE91 (Idriss and Sun 1992), Bray et al. (1995) found that MHEA forthe important base sliding case dependsprimarily onthe dynamic properties and height of the waste fill (i.e. its fundamental period,Ts , asdescribed by Ts =4H/Vs , where H = height ofwaste fill, and Vs = average initial shear wave velocity ofthe waste fill) and the MHA and Tp of the input earthquake rock motion. Forcases where Ts-FILL >Tp-EQ , the normalized maximum horizontal equivalent accel- eration,MHEA /MHARock , was shown to be inversely proportional to the normalized fundamental period ofthe waste fill,Ts-FILL /Tp-EQ . This finding reemphasizes the impor- tance of characterizing the dynamic stiffness of waste fill, which is in sharp contrast to the design practices of the early 1990s described in Seed and Bonaparte (1992) where a site response analysis at a project site without the waste fill in place was often used to estimate the seismic loading. Usingthefullynonlinear 1-Dsite responseprogram D-MOD(Matasovic andVucetic 1995), which isbased onthe established DESRA-2 program(Lee andFinn 1978),Bray and Rathje (1998) reexamined this normalization at higher levels of acceleration (up to 0.8g) withupdated waste fill propertycharacterizations. D-MODand otherDESRA- based codes have been shown to calculate seismic responses similar to the established SHAKE91programatlowacceleration levels, butcalculate lowerresponsesathighac- celerations (Kavazanjian and Matasovic 1995), which is consistent with prevailing views(e.g.Seedetal.1991;UBC,International Conference ofBuildingOfficials1997). To achieve a useful normalization, the nonlinear response factor (NRF =MHASite / MHARock ) was developed to account for the nonlinear site response of materials, such as solid-waste, that exhibit strain-dependent shear modulus and damping characteris- tics. The nonlinear response factor for solid-waste is based on the site factor proposed