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29 SNAIL, and GOLDNAIL. Example problems in the Pockoski and Duncan report addressed design and analysis of MSE, soil nail and anchored (tieback) walls, and examined issues such as ease of use, accuracy, and efficiency. However, the Pockoski and Duncan study considered only static loading conditions. The programs MSEW (based on AASHTO Specifications for MSE walls) and ReSSA (a limit equilibrium program for re- inforced soil slopes), both developed by ADAMA Engineer- ing Inc. (ADAMA, 2005a and b) and licensed to the FHWA, also were considered in this review. An application of the latest version of ReSSA has been illustrated in a paper by Leshchinsky and Han (2004) and compared to FLAC analyses. Based on the review of the above report by Pockoski and Duncan, information from some of the software suppliers, and discussions with various researchers and practitioners, the programs SLIDE, MSEW, and ReSSA (2.0) appeared to be Figure 4-4. Effects of spatially varying ground the best suited for use in the analytical methodology develop- motions on seismic coefficient. ment of the Project. Checks with an alternate program were also performed to confirm the flexibility of the methodology being recommended for development. Application examples The acceleration time history response at different points are further discussed in Chapter 7. in the soil mass will be different from each other. Total force In the case of semi-gravity walls validation of the GLE acting when normalized by the soil mass within the failure approach with the closed-form M-O solutions is discussed plane gives rise to an equivalent seismic coefficient for wall in Chapter 7. Parametric studies and examples of design design. As the retaining wall height and the lateral dimension applications to representative walls including wall-height of the mass increase, an increasing degree of the high fre- effects and deformation analyses (discussed in Sections 4.2.2 quency content of the ground motion will be eliminated. and 4.2.3, respectively), along with comparative examples Hence, the seismic coefficient for earth pressure determina- using existing AASHTO design methods, also are discussed tion should be a function of wall height, as well as a function in Chapter 5 and 6. of the frequency content of the ground motion record. High frequency-rich ground motions tend to be more incoherent and result in a lower seismic coefficient. This observation also 4.2.2 Wall Height-Dependent means that the seismic coefficient should decrease for the low, Seismic Coefficient long-period content of CEUS motion records as compared to The next area of analytical methodology development WUS, or for rock motion records as opposed to soft soil site involved a sound technical procedure for selecting the seis- records. mic coefficient to be used in the limit equilibrium approach. This analytical development to quantify the effects of The current practice in selecting the seismic coefficient as- incoherency (also referred to as scattering or wave scattering sumes rigid body soil backfill response where the seismic in this Final Report) involved use of a library of spectrum- coefficient is defined by the peak ground acceleration oc- compatible time histories representing a range of conditions, curring at a point in the free field. For wall heights in excess including earthquake magnitudes, soil versus rock sites, and of approximately 30 feet, this rigid-body assumption can be CEUS versus WUS locations. This information was used questioned. to evaluate the dependence of the seismic coefficient on Figure 4-4 presents two schematic diagrams illustrating the wall height. Coherency (wave-scattering) analyses were con- issues pertaining to the seismic coefficient used for wall pres- ducted, and then the acceleration time histories for various sure determination compared to the free-field motion at a failure mechanisms were integrated to evaluate the relation of point on the ground surface. For simplicity, a massless re- seismic coefficient versus the original reference PGA and taining wall is used to eliminate the inertial response of the spectral acceleration at 1 second (S1). The wave scattering retaining wall, thereby resulting in a relatively simple prob- analyses were conducted for multiple wall heights (for exam- lem involving inertial response of the retained fill acting on ple, 30-foot, 60-foot, and 100-foot heights). The variation in the wall. For this problem the soil mass behind the retaining seismic coefficient was established as a function of time, wall is governed by incoherency in the ground motion at dif- thereby defining "seismic coefficient time histories" for dif- ferent points of the soil mass. ferent locations behind the retaining wall.