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WORKSHEET 3 <br /> ---------------------------------------------------------------------- <br /> Worksheet #3 -- Slope Stability Analysis, Factor of Safety <br /> ---------------------------------------------------------------------- <br /> ;Limit equilibrium analysis method, see attached sheets for derivation <br /> ;and equations. <br /> i i <br /> ;reference: Stability Analysis of Earth Slopes, Y.H. Huang, Van <br /> Nostrand Reinhold Publ. , 71-78, 1983, ISBN 0-442-23689-1. <br /> ---------------------------------------------------------------------- <br /> ***** INPUT BLOCK ***** <br /> ** SECTION ANALYZED: XS-4 (largest sectional area) <br /> ;Geometric Variables Soil Properties <br /> --------------------- ------------------ <br /> L1 = 93 ft effective cohesion, c = 0.2 tsf <br /> L2 = 85 ft effect. frict. angle, f = 32 deg <br /> alpha, a = 27 deg unit weight of waste,Gs = 86 lb/ft3 <br /> area,Al = 1162 sq-ft pore press. ratio, ru = 0.25 <br /> area,A2 = 774 sq-ft W1, W2 - weight of each block <br /> ---------------------------------------------------------------------- <br /> ***** COMPUTE QUADRATIC COEFFICIENTS ***** <br /> W1 = 99932 al = 30219.4 = 30219.4 <br /> W2 = 66564 a2 = 33145.4 69524.1 34000.0 = 136669.5 <br /> a3 = 10553.1 13285.9 = 23839.0 <br /> ----------------------------------------------------------------------� <br /> Quadratic eq. for factor of safety, F: al*F^2 + a2*F + a3 =0 <br /> ---------------------------------------------------------------------- <br /> ***** TRIAL AND ERROR SOLUTION TO QUADRATIC ***** <br /> F RHS F RHS <br /> -------------------- ------------------ <br /> 4 -87006 4.65 -5933 <br /> 4.2 -64780 4.66 -4486 <br /> 4.4 -40137 4.67 -3033 <br /> 4.6 -13076 4.68 -1574 <br /> 4.8 16403 4.69 -110 <br /> 5 48299 <--- 4.7 1361 <---- Solution <br /> 5.2 82613 4.71 2838 <br /> ----------------------------------------------------------------------� <br /> FACTOR OF SAFETY = 4.7 <br /> ----------------------------------------------------------------------� <br />