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66 Table 6-1. (Continued). Ratio of Seismic Coefficient Response Seismic Coefficient Response Input Motion vs. Input Motion PGV PGV PGV PGV I Model File Name Block (max) (max) Sa1 File Name (max) (max) Sa1 PGA PGV Sa1 g in/s g g in/s g g in/s g 59 80 ft wall w80-day-.Q4K 2 0.224 9.800 0.41 DAY-L.acc 0.936 11.684 0.39 0.24 0.84 1.05 60 80 ft wall w80-day-.Q4K 3 0.202 9.545 0.40 DAY-L.acc 0.936 11.684 0.39 0.22 0.82 1.03 61 80 ft wall w80-lan-.Q4K 1 0.257 14.593 0.38 LAN-L.acc 0.771 15.173 0.36 0.33 0.96 1.06 62 80 ft wall w80-lan-.Q4K 2 0.243 14.504 0.38 LAN-L.acc 0.771 15.173 0.36 0.32 0.96 1.06 63 80 ft wall w80-lan-.Q4K 3 0.221 13.858 0.37 LAN-L.acc 0.771 15.173 0.36 0.29 0.91 1.03 Average of Above 9 0.275 12.732 0.403 L.B. Spectrum 0.867 14.076 0.380 0.319 0.899 1.061 64 80 ft wall w80-imp-.Q4K 1 0.607 37.264 1.12 IMP-M.acc 0.812 37.054 1.12 0.75 1.01 1.00 65 80 ft wall w80-imp-.Q4K 2 0.599 37.154 1.13 IMP-M.acc 0.812 37.054 1.12 0.74 1.00 1.01 66 80 ft wall w80-imp-.Q4K 3 0.550 36.002 1.10 IMP-M.acc 0.812 37.054 1.12 0.68 0.97 0.98 67 80 ft wall w80-lom-.Q4K 1 0.672 41.988 1.22 LOM-M.acc 1.026 32.275 1.20 0.65 1.30 1.02 68 80 ft wall w80-lom-.Q4K 2 0.635 41.563 1.22 LOM-M.acc 1.026 32.275 1.20 0.62 1.29 1.02 69 80 ft wall w80-lom-.Q4K 3 0.569 39.643 1.19 LOM-M.acc 1.026 32.275 1.20 0.55 1.23 0.99 70 80 ft wall w80-san-.Q4K 1 0.762 45.732 1.24 SAN-M.acc 0.948 42.312 1.18 0.80 1.08 1.05 71 80 ft wall w80-san-.Q4K 2 0.732 44.796 1.23 SAN-M.acc 0.948 42.312 1.18 0.77 1.06 1.04 72 80 ft wall w80-san-.Q4K 3 0.669 42.321 1.18 SAN-M.acc 0.948 42.312 1.18 0.71 1.00 1.00 Average of Above 9 0.644 40.718 1.181 Mid Spectrum 0.929 37.214 1.167 0.697 1.104 1.012 73 80 ft wall w80-elc-.Q4K 1 0.895 42.781 1.76 ELC-U.acc 1.083 45.320 1.78 0.83 0.94 0.99 74 80 ft wall w80-elc-.Q4K 2 0.878 43.230 1.77 ELC-U.acc 1.083 45.320 1.78 0.81 0.95 0.99 75 80 ft wall w80-elc-.Q4K 3 0.828 42.279 1.73 ELC-U.acc 1.083 45.320 1.78 0.76 0.93 0.97 76 80 ft wall w80-erz-.Q4K 1 1.181 52.435 1.77 ERZ-U.acc 1.089 52.950 1.69 1.08 0.99 1.05 77 80 ft wall w80-erz-.Q4K 2 1.135 52.091 1.77 ERZ-U.acc 1.089 52.950 1.69 1.04 0.98 1.05 78 80 ft wall w80-erz-.Q4K 3 1.055 49.750 1.70 ERZ-U.acc 1.089 52.950 1.69 0.97 0.94 1.01 79 80 ft wall w80-tab-.Q4K 1 1.025 43.980 1.83 TAB-U.acc 1.060 46.922 1.76 0.97 0.94 1.04 80 80 ft wall w80-tab-.Q4K 2 1.011 42.697 1.83 TAB-U.acc 1.060 46.922 1.76 0.95 0.91 1.04 81 80 ft wall w80-tab-.Q4K 3 0.936 40.261 1.78 TAB-U.acc 1.060 46.922 1.76 0.88 0.86 1.01 Average of Above 9 0.994 45.500 1.771 U.B. Spectrum 1.077 48.397 1.743 0.922 0.939 1.016 82 120 ft wall w12-cap-.Q4K 1 0.221 12.815 0.47 CAP-L.acc 0.894 15.370 0.39 0.25 0.83 1.21 83 120 ft wall w12-cap-.Q4K 2 0.202 12.610 0.46 CAP-L.acc 0.894 15.370 0.39 0.23 0.82 1.18 84 120 ft wall w12-cap-.Q4K 3 0.199 12.263 0.43 CAP-L.acc 0.894 15.370 0.39 0.22 0.80 1.10 85 120 ft wall w12-day-.Q4K 1 0.195 10.675 0.45 DAY-L.acc 0.936 11.684 0.39 0.21 0.91 1.15 86 120 ft wall w12-day-.Q4K 2 0.176 10.497 0.44 DAY-L.acc 0.936 11.684 0.39 0.19 0.90 1.13 87 120 ft wall w12-day-.Q4K 3 0.189 10.159 0.42 DAY-L.acc 0.936 11.684 0.39 0.20 0.87 1.08 88 120 ft wall w12-lan-.Q4K 1 0.241 14.801 0.44 LAN-L.acc 0.771 15.173 0.36 0.31 0.98 1.22 89 120 ft wall w12-lan-.Q4K 2 0.224 14.223 0.43 LAN-L.acc 0.771 15.173 0.36 0.29 0.94 1.19 90 120 ft wall w12-lan-.Q4K 3 0.203 13.376 0.41 LAN-L.acc 0.771 15.173 0.36 0.26 0.88 1.14 Average of Above 9 0.206 12.380 0.439 L.B. Spectrum 0.867 14.076 0.380 0.240 0.881 1.156 91 120 ft wall w12-imp-.Q4K 1 0.625 40.256 1.24 IMP-M.acc 0.812 37.054 1.12 0.77 1.09 1.11 92 120 ft wall w12-imp-.Q4K 2 0.574 39.312 1.21 IMP-M.acc 0.812 37.054 1.12 0.71 1.06 1.08 93 120 ft wall w12-imp-.Q4K 3 0.516 37.327 1.16 IMP-M.acc 0.812 37.054 1.12 0.64 1.01 1.04 94 120 ft wall w12-lom-.Q4K 1 0.486 39.153 1.33 LOM-M.acc 1.026 32.275 1.20 0.47 1.21 1.11 95 120 ft wall w12-lom-.Q4K 2 0.435 38.141 1.30 LOM-M.acc 1.026 32.275 1.20 0.42 1.18 1.08 96 120 ft wall w12-lom-.Q4K 3 0.450 36.063 1.26 LOM-M.acc 1.026 32.275 1.20 0.44 1.12 1.05 97 120 ft wall w12-san-.Q4K 1 0.521 40.379 1.45 SAN-M.acc 0.948 42.312 1.18 0.55 0.95 1.23 98 120 ft wall w12-san-.Q4K 2 0.504 38.840 1.41 SAN-M.acc 0.948 42.312 1.18 0.53 0.92 1.19 99 120 ft wall w12-san-.Q4K 3 0.449 37.336 1.33 SAN-M.acc 0.948 42.312 1.18 0.47 0.88 1.13 Average of Above 9 0.507 38.534 1.299 Mid Spectrum 0.929 37.214 1.167 0.556 1.047 1.113 100 120 ft wall w12-elc-.Q4K 1 0.863 55.709 1.93 ELC-U.acc 1.083 45.320 1.78 0.80 1.23 1.08 101 120 ft wall w12-elc-.Q4K 2 0.843 53.682 1.90 ELC-U.acc 1.083 45.320 1.78 0.78 1.18 1.07 102 120 ft wall w12-elc-.Q4K 3 0.774 50.337 1.83 ELC-U.acc 1.083 45.320 1.78 0.71 1.11 1.03 103 120 ft wall w12-erz-.Q4K 1 0.921 55.895 1.81 ERZ-U.acc 1.089 52.950 1.69 0.85 1.06 1.07 104 120 ft wall w12-erz-.Q4K 2 0.860 54.019 1.77 ERZ-U.acc 1.089 52.950 1.69 0.79 1.02 1.05 105 120 ft wall w12-erz-.Q4K 3 0.820 50.339 1.68 ERZ-U.acc 1.089 52.950 1.69 0.75 0.95 0.99 106 120 ft wall w12-tab-.Q4K 1 0.874 43.529 2.09 TAB-U.acc 1.060 46.922 1.76 0.82 0.93 1.19 107 120 ft wall w12-tab-.Q4K 2 0.825 41.913 2.03 TAB-U.acc 1.060 46.922 1.76 0.78 0.89 1.15 108 120 ft wall w12-tab-.Q4K 3 0.738 40.690 1.93 TAB-U.acc 1.060 46.922 1.76 0.70 0.87 1.10 Average of Above 9 0.835 49.568 1.886 U.B. Spectrum 1.077 48.397 1.743 0.775 1.027 1.081 this ratio systematically decreased for increasing wall height duction being introduced in this discussion is for wave scat- and lowering of the spectral shape at long periods. Therefore, tering. Any further reduction for the duration of earthquake averaging the ratios (shown in the right-most column) from loading should be determined by the structural designer. the three failure mechanisms evaluated in this study would seem to be reasonable. Cursory review of the data supports to 6.2 Conclusions some degree, the presumptive historical practice of adopting about 1/2 to 2/3 of PGA for pseudo-static design analysis. How- Figure 6-13 provides a basis for determining a reduction ever, as noted above, rather than the prevalent view that the factor (that is, the factor) to be applied to the peak ground reduction is to account for the time variation in PGA, the re- acceleration used when determining the pseudo-static force

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67 Figure 6-13. Resultant wave scattering coefficients for retaining wall design. in the design of retaining walls and slopes. Further discussion difficulties for the designer. The selection of the appropri- of the use of the factor is provided in Chapter 7. ate spectra shape should focus on the 1-second ordinate. Results of these height-dependent seismic coefficient studies Starting from the design response spectrum, the designer are general enough that they can be applied to either the seis- would normalize the response spectrum by the peak ground mic design of retaining walls, embankments and slopes, or acceleration to develop the normalized spectral shape for the buried structures. The design process involves first determin- specific project site. This spectrum is then overlaid on the ing the response spectra for the site. This determination is spectral shape shown on Figure 5-4 to determine the most made using either guidance in the 2008 AASHTO LRFD Bridge appropriate spectral curve shape for the design condition. Design Specifications or from site-specific seismic hazard After selecting the appropriate spectral shape (that is, in studies. Note that spectra in the 2007 AASHTO LRFD Bridge terms of UB, Mid, and LB spectral shapes), Figure 6-13 is Design Specifications do not distinguish between CEUS and used to select the appropriate reduction factor (the factor). WUS shapes and are not consistent with this recommended approach; however, the newly adopted AASHTO ground The approach described above was further simplified for motion maps will account for this difference. The only use in the proposed Specifications by relating the factor assumption made is that the ground motion design criteria to height, PGA, and S1 in a simple equation, as discussed in should be defined by a 5 percent damped design response spec- Chapter 7. Either the approach discussed in this chapter or the trum for the referenced free-field ground surface condition at equation given in Chapter 7 is an acceptable method of the project site. determining the factor. Once the design ground motion is established for a site, the As discussed earlier, wave scattering theory represents one of analyses could proceed following the methodology outlined the several justifications for selecting a pseudo-static seismic co- in this chapter. This methodology involves defining the seis- efficient lower than the peak ground acceleration. In addition mic coefficient for the evaluation of retaining walls, slopes to the wave scattering factor, additional reduction factors may and embankments, or buried structures, as follows: be applied as appropriate, including that some permanent movement is allowed in the design, as discussed in Chapter 7. The design ground motion demand is characterized by a Consideration also can be given to the use of a time-averaged design response spectrum that takes into account the seis- seismic coefficient based on the average level of ground shak- mic hazard and site response issues for the site. This re- ing, rather than the peak, as long as the structural designer con- quirement is rather standard, and should not present undue firms that the average inertial force is permissible for design.