(a) Determine the factor of safety for the slope conditions indicated in Problem by using the simplified Bishop method, but with soil whose properties are y = 16 kN/m3, c' = 10kN/nr, = 20. (b) Using the soil properties in part (a), solve Problem using the simplified Bishop method. Use a grid 3 m by 3 m. Problem: (a) Utilizing the basic method for a stability analysis, determine a slope's factor of safety against a rotational slide for the following conditions Slope height is 50 ft. Slope inclination is 40. Trial failure arc center of rotation is 40 ft above slope midpoint; radius of failure arc is 80 ft. Soil profile determined from top of slope shows clay soil from 0 to 100 ft (y= 102 pcf, c = 940 psf, $ = 0). A line loading of 3 kips per ft of length of slope acts along the top of the slope 20 ft from the edge. The failure mass involves 3,725 ft3 of soil per foot of slope, and the horizontal distance from the center of gravity of the failure mass to the center of rotation is 26 ft. (b) Find the most critical failure circle and the least factor of safety for the above conditions by systematically changing the point representing the center of rotation by 10 ft horizontally and 10 ft vertically. (A suggested class project in which each student checks one or two different trial failure circles.)