The state of stress on a small element is sv=28 kPa, sh=14 kPa, and the shear stress on the horizontal plane is +4 kPa. (30 points) (a) Find the magnitude and directions of the major and minor...

The state of stress on a small element is sv=28 kPa, sh=14 kPa, and the shear stress on the horizontal plane is +4 kPa. (30 points)

(a) Find the magnitude and directions of the major and minor principal stresses.

(b) If the material is a loose sand, can you say whether the element is in a state of failure? If it isn’t, how close is it? Why? State your assumptions clearly. (Assume f=30 ° for the loose sand.)

(c) Find the maximum values of shear stress on the horizontal and vertical planes to cause failure in a medium dense sand. Assume the angle of internal friction for the sand is 36 °.