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99 less than about 6 inches, a screening value suggested as a po- The Hynes and Franklin "upper bound" curve presented in Fig- tential criteria to determine if a Newmark displacement ure 8-2 suggests that deformations will be less than 12 inches analysis is necessary. (30 cm) for yield accelerations greater than or equal to one- half the peak acceleration. In utilizing such curves, it must be recognized that slope- 8.2.2 Displacement-Based Approach height effects should be taken into account to determine a In contrast to the limit equilibrium approach, the height-dependent, average maximum acceleration for use as displacement-based approach involves the explicit calculation the kmax value (as was the case for retaining walls discussed in of cumulative seismic deformation. The potential failure mass Chapter 7). This was recognized by the studies published by is treated as either a rigid body or deformable body, depending Makdisi and Seed (1978), who developed slope displacement on whether a simplified Newmark sliding block approach or design charts for the seismic design of earth dams. more advanced numerical modeling is used. Results from the Makdisi and Seed (1978) analyses are shown in Figure 8-3. Analyses were conducted for a limited number of dam heights (for example, 75 to 135 feet) and 8.2.2.1 Newmark Sliding Block Approach earthquake records. The lower left figure illustrates the nor- The Newmark sliding block approach treats the potential malized reduction in average maximum seismic coefficient failure mass as a rigid body on a yielding base. The accelera- with slide depth (equivalent to an factor using the termi- tion time history of the rigid body is assumed to correspond nology from Chapters 6 and 7), and equals an average of 0.35 to the average acceleration time history of the failure mass. for a full height slide (average height studied equals approxi- Deformation accumulates when the rigid body acceleration mately 100 feet) which is compatible with values noted in exceeds the yield acceleration of the failure mass (ky) where ky Chapters 6 and 7. A range of displacements as a function of is defined as the horizontal acceleration that results in a factor ky/kmax is noted on the lower right figure and shows earth- of safety of 1.0 in a pseudo-static limit equilibrium analysis. quake magnitude variation. This approach may be used to calibrate an appropriate The Newmark displacement equations discussed in Chap- pseudo-static seismic coefficient reflecting acceptable dis- ter 5 show insensitivity to earthquake magnitude, which is be- placement performance, as discussed in Chapter 7 for retain- lieved to be better reflected in PGV. Makdisi and Seed note ing wall analysis. Similar discussions for slopes are presented in that variability is reduced by normalizing data by kmax and the the FHWA publication Geotechnical Earthquake Engineering natural period of embankments. The height parameter used (FHWA, 1998a). For example, Figure 8-2 shows results of in the analyses conducted for this Project reflects changes in Newmark seismic deformation analyses performed by Hynes natural period, and kmax is included in the Newmark equation. and Franklin (1984) using 348 strong motion records (all soil/ In 2000 an updated approach for estimating the displace- rock conditions; 4.5 < Mw < 7.4) and six synthetic records. ment of slopes during a seismic event was developed through the SCEC. The displacement analysis procedures documented in the SCEC (2002) Guidelines are relatively complex and would require simplification for use in a nationwide specifi- cation document. Recommended procedures described in the SCEC Guidelines are illustrated by Figures 8-4 and 8-5. Figure 8-4 shows the ratio of the maximum average seis- mic coefficient (averaged over the slide mass) to the maxi- mum bedrock acceleration multiplied by a nonlinear re- sponse factor (NRF) (equals 1.00 for 0.4g) plotted against the natural period (Ts) of the slide mass (4H/Vs, where H is the average height of slide and Vs is the shear wave velocity) di- vided by the dominant period Tm of the earthquake. In effect, this plot is analogous to the plot of versus the wall height (assuming the height of the slide equals the wall height) dis- cussed in Chapter 6. For example, if Tm = 0.3 sec, H = 20 feet, NRF = 1, Vs = 800 ft/sec, then Ts /Tm = 0.1/0.3 = 0.33, and hence = 1 as would be expected. However, if H = 100 feet with the same parameters, Ts /Tm = 0.5/0.3 = 1.66 and hence Figure 8-2. Permanent seismic deformation chart = 0.3, which is reasonably compatible with the curves (Hynes and Franklin, 1984). presented in Chapter 6.