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<br />1 <br /> <br />1 <br />1 <br />1 <br />1 <br />1 <br /> <br /> <br />San Luis Mine Phase n, Raise 2 Design Report <br />percent increase in the factor of safety computed in two dimensional analyses (Ladd, 1991). As <br />shown on Figure 10, the lowest factor of safety for potential failures of the upstream slope under <br />a pseudostatic coefficient of O.15g is 1.89. <br />4.5.2 Deformation Analyses <br />4.6.2.1 Background <br />Although pseudostatic stability analyses similar to those presented in the Amendment demonstrate <br />adequate stability, dynamic deformation analyses, developed to more accurately predict the behavior <br />of an embankment during an earthquake, have also been conducted to confirm that the structure will <br />be stable. Newmark (1965) proposed a method of dynamic analysis of potential failure surfaces <br />within an embankment analogous to a block resting on an inclined plane. If am acceleration pulse <br />results in an inertia force which when coupled with static shear stresses is large enough to overcome <br />the resisting force, the block will slide down the plane until the acceleration reduces sufficiently for <br />the resisting forces to be larger than the combined inertia and static forces. For a series of <br />acceleration pulses, such as from an earthquake, the total displacement of the block down the plane <br />will be the sum of the displacements which occur during each pulse producing imertia forces greater <br />than the available resisting forces. <br />Newmark utilized four earthquake strong motion records to determine the effective number of pulses <br />' , in an actual earthquake. He then normalized these records to a peak ground alcceleration of O.Sg <br />and maximum ground velocity of 30 in/sec and determined the normalized displacements for various <br />' ratios of resistance to earthquake acceleration. Newmark presented his results iri a chart giving the <br />upper bound displacements calculated for each of the normalized strong motion records. <br />1 <br />1 <br /> <br /> <br /> <br />1 <br />The Corps of Engineers (Franklin and Chang, 1977) has extended the data base for Newmark's chart <br />by processing many additional strong motion records and revised his upper bound limits for <br />displacement. A total of 169 horizontal and 10 vertical records from 27 earthquakes and 10 <br />synthetic accelerograms were used with the sliding block analyses. All strong motion records were <br />scaled to a maximum acceleration of O.Sg and maximum ground velocity of 30 in/sec by adjusting <br />the acceleration and time scales. The results are presented in the form of a chart giving <br />standardized values of displacement which can then be utilized for any value of acceleration and/or <br />velocity through scaling factors. <br />Professor H. Bolton Seed and his colleagues at the University of California at Berkeley incorporated <br />the dynamic response of the embankment into the displacement concepts originally proposed by <br />Newmark. Makdisi and Seed (1977) utilized a finite element program to deterttline the time-history <br />of average accelerations in a variety of embankments and utilized the results of many other studies <br />u y q_7 rorect o. <br />1 <br />