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28 Along with the difference in the PGA between WUS and high seismic coefficients. With a few exceptions, these problems CEUS sites, these figures show the drastic difference in the preclude practical modification of the M-O equations for shaking hazard as measured by the peak spectral acceleration general use. The problem for seismic active earth pressures at 1 second (S1) or PGV between a WUS and a CEUS site. Such can be overcome by the use of commercially available, limit- changes between the WUS and CEUS are also reflected in equilibrium computer programs--the same as used for the AASHTO 1,000-year maps. analysis of seismic slope stability. Current versions of many In view of the differences in ground motion characteris- of these programs have the versatility to analyze conventional tics, hence response spectra, between CEUS and WUS, as semi-gravity walls, as well as MSE, soil nail, or anchored walls. well as the NCHRP 20-07 Project recommendation to use These analyses can be performed for complex wall profiles, the spectral acceleration at a 1-second period as the parame- soil stratigraphy, surcharge loading, and pseudo-static lateral ter for defining the level and requirements for bridge design, earthquake loading. a focused ground motion study was conducted during the In the case of semi-gravity walls, values of earthquake- NCHRP 12-70 Project to establish a consistent approach for induced wall loads (PAE) induced by retained soils can be both projects. The NCHRP 12-70 ground motion study in- computed from a limit equilibrium stability analysis by cal- volved development of an analytical methodology that relates culating the maximum equivalent external load on a wall face PGV and spectral acceleration at 1-second period (S1) and (Figure 4-3) corresponding to a safety factor of 1.0. This con- between PGV and PGA for CEUS and WUS. Effects of local cept, referred to as the generalized limit equilibrium (GLE) soil conditions on the relationship between these ground method, can be calibrated back to an idealized M-O solution motion parameters were avoided by developing the rela- for uniform cohesionless backfill, and has been used in prac- tionships for NEHRP Site Class B conditions (that is, rock tice to replace M-O solutions for complex wall designs. The with a shear wave velocity between 2,500 and 5,000 feet per line of action of the external load can reasonably be assumed second), and then applying site coefficients to correct for at the mid-height of the wall acting at an appropriate friction soil conditions. This development was accomplished using angle. In the case of MSE or soil nail walls, internal and exter- an available ground motion database, including spectrum- nal stability evaluations may be undertaken using limit equi- compatible time history development reflecting differences in librium computer programs without the empiricism presently WUS and CEUS conditions. associated with AASHTO Specifications. Such an approach has been described by Ling et al. (1997). Potential computer programs for evaluating the GLE 4.2 Developments for methodology were reviewed. One of the most valuable docu- Retaining Walls ments for this review was a study by Pockoski and Duncan The next major area of development involved improved (2000) comparing 10 available computer programs for limit methods for estimating the forces on and the displacement equilibrium analysis. Programs included in the study were response of retaining walls. The approach for evaluating the UTEXAS4, SLOPE/W, SLIDE, XSTABLE, WINSTABL, RSS, seismic displacement response of retaining walls consisted of using a limit equilibrium stability analysis in combination with the results of the seismic demand (ground motion) stud- ies described above. Analytical developments were required in three areas, as discussed in the following subsections. The focus of these developments was on rational methods for es- timating forces on and deformation of retaining walls located in CEUS and WUS. 4.2.1 Generalized Limit Equilibrium Analyses The problems and knowledge gaps associated with existing AASHTO Specifications for seismic earth pressure determi- nation have been summarized in the Chapter 3 discussion. Many problems are associated with the M-O equations used to compute seismic active and passive earth pressures for wall design. These problems include the inability of the M-O equa- Figure 4-3. Limit equilibrium method for estimating tions to handle complex wall profiles, soil stratigraphies, and seismic active earth pressures.