Questions 7 9.7-7 9.70: underground excavation instability mechanisms 479(a) compare the stress in the centre of the roof of the excavation with that
for an elliptical excavation with the same width/height ratio; and
(b) compare the stress in the side wall with that for a boundary of equal
radius of curvature.419.10 The axes of a long horizontal elliptical excavation are inclined
at f 45" to the horizontal, and their lengths are in the ratio 2.5 : 1. The
vertical and horizontal principal field stresses are 8.5 MPa and 25.5 MPa,
respectively.
(a) Calculate the maximum and minimum elastic stress values induced
on the boundary of the excavation.
(b) Investigate the possibility of failure of the rock on the excavation
boundary, on the basis that the strength of the rock in compression is
given by c = 30 MPa and 4 = 400, and in tension is zero.