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<br />• Where: ~ pc = Failure Surface <br /> ~ f = Slope Angle <br /> ¢ = Friction Angle <br />Although no wa ter pressure within the slope occurs, tension cracks filled with water <br />have been considered in this stability analysis. !T is assumed that o tension crack will <br />form and that due to the precipitation in this area, the tension crack and sliding <br />surface will fill with water and generate water pressure. The depth and position of a <br />criTical tension crack, if i t were to form, can be calculated us ing The following <br />equations: <br />Tension Crack Depth <br />Zc/H I - /cot ~f • tan yip <br />Tension Crack Position <br />be/H = /cot y f • cot ~p -cot ~f <br />Where: <br />• Zc =Tension Crack Depth <br />be Tension Crock Position <br />H =Height of Slope Face <br />The depth and position of the tension crack and the position of The failure surfoce <br />is shown on Table 3.5-8. Now that o theoretical failure surface and tension crack <br />have been defined, the factor of safety can be calculated using the following equation: <br />F cA = (VJ•cos ~ p-U-V•sin W p) tan ~ <br />V~~•sin tlrp = V•cos yp <br />Where: <br />c =Cohesion Factor <br />A = Area of the Sliding Surface <br />U = Water Pressure on Sliding Surface <br />V Water Pressure in the Tension Crack <br />W = Weight of The Sliding Mass <br />The location of the acting forces for U, V, and W are shown in the figures on Table <br />3.5-9 and can be calculated using The following equations: <br />• <br />3.5-10 <br />f~....foo.l 7/A7 <br />