Engineering Rock Mechanics

366 Underground excavation instability mechanisms

140 -

120 -

100 -

z- 80 ~

.E 60 ~

' I 40-

P

m 20 ~

a

V

• 0,

0-

-20 ~

-40

side walls

Solid lines: numerical analysis results

Crosses: approximate solution results

Roof, k= 1

X X

0 1 2 3 4 5 96

X A A A X

X X

Roof, k= 0

approximate solution

numerical analysis solution

Q19.10 The axes of a long horizontal elliptical excavation are in-

clined at f45O to the horizontal, and their lengths are in the ra-

tio 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 exca-

vation boundary, on the basis that the strength of the rock in com-

pression is given by c = 30 MPa and t$ = 40°, and in tension is zero.

A19.10 The equation for the circumferential stress induced in the ma-

terial at the boundary of an elliptical excavation is

where p is the vertical stress magnitude, k is the ratio of horizontal to

vertical stresses, q is the ratio of the two axes of the ellipse, p is the