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December 27, 2023 Page 4-3 <br />Agapito Associates, Inc. <br />Furthermore, the proportion of the abutment load (R) that is applied to neighboring pillars and/or <br />barriers for a single front-abutment loading scenario is calculated using the equation presented by <br />Mark (1990): <br /> RR = 1-ቂD-൫wp +wr൯ <br />D ቃ <br />3 <br /> (Eqn. 4-5) <br />The remnant portion of the abutment load (i.e., 1 – R) is applied along the remaining length of the <br />abutment load distribution. A schematic of the abutment load distribution model used in this <br />assessment is shown in Figure 4-3. <br />4.5 Condition of Existing Pillars in Sunset Mains South <br />The condition of the existing pillars in the Sunset Mains South has been assessed utilizing the <br />above empirical methodologies. The pillar extraction areas have been divided up into seven <br />separate zones as shown in Figure 4-4. These zones will be used to assess pillar loading conditions <br />during simulated pillar extraction. The range of input parameters used for the assessment in each <br />zone are summarized in Table 4-1.