Question and answers: design of underground excavations 37520.2 Question and answers: design of underground
excavations420.1 A vertical shaft is to be sunk through a rock mass in which
the magnitudes of the two horizontal principal stresses have a ratio
of 3: 1. A clear space of 5 m x 5 m must be maintained within the
shaft for equipment installation. The three excavation cross-sections
shown in the sketch are under consideration for the shaft design.
Discuss the relative design merits of each cross-section in terms
of rock mechanics principles, and hence provide recommendations
for the optimal shape (and in the case of profile (b) and (c), optimal
orientation) for the excavation.
A20. I (a) Circular shaft
around the circular shaft using the
Kirsch solution shows that there
will be a variation in the stress
concentrations, from a
value of 8 to a value of 0. Suchto rock failure, and it is dif-
ficult to design the shaft with a single support or reinforcement solution.A CHILE analysis of the stresses high induced stress
(tangential stress = 80h)-6-
1 low induced stress
large variations in stresses may lead (tangential stress = 0)(b) Elliptical shaft
When the shaft is elliptical, if the ratio ofthe equal major to the axis stress to the ratio, minor and axis the is excava- made cz3
A+
Oh
tion is aligned with its long axis parallel
to the major principal stress, then the tan-
gential stresses at points A and B are givencase the axial ratio is made equal to 3, then
the stresses at points A and B are both equal to 4uh. In fact, this tangential
stress magnitude is constant around the periphery of the opening.
Providing that this stress is sufficiently less than the strength of the
rock, the elliptical geometry is preferred because the uniform, induced
stress field provides a zone of uniform tangential compression around
the opening. This stabilizes the rock, in contrast to the stresses induced
around the circular shaft.by ff~ = ff~ = (1 -k k)ffh. Thus, if in this t