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BRAY, RATHJE, AUGELLO AND MERRY D Seismic Design for Lined Solid-Waste Landfills 218 GEOSYNTHETICS INTERNATIONAL S 1998, VOL. 5, NOS. 1-2 Figure 9. Yield acceleration coefficient for solid-waste landfills: (a) base sliding (after Shewbridge 1996); (b) cover sliding (infinite slope solution). (a) (b) S1 L H S2 1 1 H ¨ Some investigators have noted that occasionally the decoupling assumption was not conservative. This was reexamined by the authors of the current paper. A decoupled analysis generally provides an estimate of the coupled sliding displacement within a factor ofthree (Bray and Rathje 1998). Conservative decoupled displacements are cal- culated for lower yield acceleration coefficient values (i.e.ky /kmax < 0.6) when the fun- damental period of the sliding mass is less than twice the mean period of the input groundmotion (Figure 10). Forsystems withlarger valuesof ky /kmax orlargefundamen- tal periods, a decoupled analysis may predict smaller displacements than a fully coupledanalysis. However,inthesecases, thedisplacements calculated frombothanal- ysesare generally small (i.e. less than a few centimeters), because ofthe relatively low kmax andhigh ky /kmax valuesforthese cases. Asaseismic performance index, adecoupled analysis isjudged to be reasonable forcurrent design practice. Conversely, a rigid slid- ing block analysis (i.e. direct integration of the input acceleration-time history) can be significantly unconservative, and it should not be used (Figure 10). Seismically induced permanent displacements,U, for the base sliding case for 19 landfill configurations sited onrock undergoing 33input rock motions were calculated at ky /kmax ratiosof0.2,0.4,0.6,and0.8(i.e. 309valuesat each ky /kmax ratio) with thecon- ventional procedure discussed previously (Bray and Rathje 1998). As expected, there was considerable scatter both with respect to results from different input motions and results from different landfill configurations. For example, for a given input motion, significantly larger displacements are calculated for landfill configurations with stiffer response characteristics that more closely match the high frequency motionscontained in most rock records. At a specified ky /kmax ratio, the calculated displacement isroughly proportional to MHEA , indicating that those factors that have been shown to affect MHEA , also affect U. Considerably less inter- and intra-earthquake scatter was produced by normalizing the calculated displacement,U, bythe maximum seismic coefficient,kmax (=MHEA /g) and the significant duration,D5-95 , of the input motion (Figure 11). Hence, an estimate