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30 The resultant seismic coefficient time histories were used for A valuable source of reference material on this topic has conducting Newmark sliding block analyses for wall deforma- been documented in a University of Washington Master tion studies. More meaningful seismic coefficients for pseudo- of Science thesis by Paulsen (2002), where an equivalent static earth pressure design were established by relating the Newmark sliding block analysis was developed to accom- acceleration ratio in the Newmark analysis to a limiting perma- modate the additional deformations arising from rein- nent displacement value (say at 6 inches) from the conducted forcing strip deformation and slip. However, parameter analyses. The resultant product of this effort was charts of seis- selection for the model was empirical and based on cali- mic coefficient versus PGA for different wall heights. Charts brations from centrifuge and shake table tests. Whereas of wall height-dependent seismic coefficient versus 5 percent the model was promising, it was insufficiently mature for damped spectral acceleration at 1 second (S1) also were devel- practical application at this time. FLAC analyses also have oped. The latter charts might have better technical merit as been performed to evaluate deformation behavior under discussed earlier regarding fundamental differences between seismic loading, and may be applicable for analysis of spe- PGA versus S1. cial cases. However, with respect to AASHTO Specifica- tions, the analytical methodology attempted to relate the proposed pseudo-static limit equilibrium analyses to de- 4.2.3 Deformation Analyses formation performance criteria in an empirical way, based As part of this effort, an updated analytical methodology was on existing case histories and model tests, and the ap- developed for estimating wall deformations during seismic proach described by Ling et. al. (1997). loading as a function of yield acceleration. This approach was allowed within the then current (2006) AASHTO Specifica- 4.3 Developments for Slopes tions; however, the equation used for estimating displacements and Embankments was based on a limited database. The following approach was taken from the updated ana- The next major area of development involved methods for lytical methodology: evaluating the seismic performance of cut slopes and fill em- bankments. Relative to the development needs for retaining 1. Semi-gravity walls: Using the computed time histories as- walls, these needs were not as significant. In most cases suit- sociated with the wall height seismic coefficient studies, able analytical methodologies already existed for evaluating Newmark sliding block charts showing displacements ver- the seismic response of slopes and embankments, but these sus the ratio of yield acceleration to the peak ground ac- methods were not documented in the AASHTO LRFD Bridge celeration (ky /kmax) were determined. (Note that ky is the Design Specifications, suggesting that much of the work re- acceleration that results in a factor of safety of 1.0; kmax is lated to slopes and embankments involved adapting current the PGA adjusted for local site effects. The kmax term is methodologies into an LRFD specification and commentary. equivalent to As in the current AASHTO LRFD Bridge Although development needs for slopes and embankments Design Specifications. The seismic coefficient for retaining were less than for the other two areas, three developments wall design is commonly defined in terms of k rather than were required, as summarized below: PGA to indicate a dimensionless seismic coefficient. The use of k to define seismic coefficient during wall design is · Develop a robust set of Newmark displacement charts for followed in this Project.) These charts are a function of S1, slope displacement evaluations, reflecting both differences which relates strongly to PGV. The charts in turn were between WUS and CEUS and the influence of slope height. used to reassess the suitability of the 50 percent reduction In this respect, the analysis approach was similar to that factor in peak acceleration included within AASHTO for previously described for walls. However, additional param- pseudo-static wall design. As noted previously, the 50 per- eters were needed in examining the coherence of inertial cent reduction is based on acceptable horizontal displace- loads over potential sliding masses, including slope angle ment criteria, where walls are free to slide. For walls sup- and shear wave velocities of slope material, and strength ported by piles, displacement limits need to be integrated parameters ranging from those for cut slopes to fills. The with pile performance criteria associated with pile capac- analysis program used for wave scattering analyses involved ity. In such cases, questions related to pile pinning forces QUAD-4M (1994). and their influence on yield accelerations of the wall-pile · Develop a screening method for determining areas requir- system also need to be considered. ing no seismic analysis. The screening method depended on 2. MSE walls: Deformation analyses to assess performance a combination of the level and duration of ground shaking, criteria for MSE walls are clearly more complex than for the geometry of the slope, and the reserve capacity that the semi-gravity walls due to the flexibility of the wall system. slope has under static loading. A critical consideration in