With reference to Problem 8.5, the caved ground has a specific weight of 105 pcf (16.6kN/m3); the angle of friction between muck and rock is 23◦, while the angle of internal friction of the muck is 33◦. The ratio of horizontal to vertical stress in the caved ground is estimated to be 0.32.

(a) Find the average vertical stress σv at the bottom of the cave as a function of the cave height z measured from the bottom of the undercut.

(b) With the origin in the upper left hand corner, plot vertical stress horizontally as a function of cave depth (height) positive down.

(c) What values of vertical, horizontal, and shear stresses are realized at the undercut level when the cave height reaches 300 ft (90 m) 600 ft (180 m)?