A direct shear test is conducted on a large specimen of dry sand (square cross section with following dimensions: 7.5 cm x 7.5 cm x 3.0 cm [height], Mass = 271.0 g) with a normal stress of 200 kPa. Failure occurred at a shear stress of 175 kPa. For the same sand, tests were also conducted to determine the specific gravity and the maximum and minimum void ratios. These tests yielded the following results: G s= 2.65, e max =0.80, e min = 0.45. a) Calculate the relative density of the sand specimen b) Determine the friction angle of the soil. c) Another test is performed on the same sand at the same relative density under a normal stress of 150 kPa. Assuming a linear failure envelope, what shear force would be required to reach failure? d) In this second test would you expected the soil to dilate more or less than in the original one