376 Design of underground excavations
(c) Square shaft
induced around a square opening is not
available, because of the discontinuous --t
geometry at the comers. However, if
we use the streamline analogy, together
with knowledge of the relation between
induced stresses and radius of curvature
of the boundary of the opening, we can make an estimate of the stability
of the excavation.
The small radius of curvature at the corners indicates that the tangen-
tial stress induced at this location will be large and compressive. Along
each wall of the opening, the radius of curvature is effectively infinite,
and so we can expect low, and probably tensile, stresses to be induced at
these locations. This will be the case regardless of the orientation of the
square within the stress field, or the exact values of the stresses.
large compressive
A closed form solution for the stresses induced stress
large tensile
induced stressThus, the design strategy is to use an elliptical shaft oriented with its
major axis parallel to the major principal stress, and the axial ratio of the
opening equal to the stress ratio, i.e. 3.420.2 You have been asked for an initial decision on the orientation
of an underground structure. The structure comprises ten parallel
tunnels, each 5 km long, to be built in a rock mass containing
definite fracture sets. You have also been asked about the best
shape for the cross-section of the tunnels.
The dip direction and dip of the fracture sets are 270/45 and
90/45; the direction of the maximum principal stress is horizontal,
west-east, and its magnitude is twice the value of both the ver-
tical and the other horizontal stress component. The ratio of the
maximum principal stress component to the intact rock uniaxial
compressive strength is 0.5.
What would be your initial design based on this information
alone?A20.2 The initial design should be based on avoiding instability of rock
blocks and instability of the intact rock due to rock stress failure.
Given that there are only two main fracture sets, there may not
be any potential for block failure (the minimum number of faces a
rock block can have is four - a tetrahedral block - which requires
the excavation surface and three fractures). However, it is good rock
engineering policy to tunnel perpendicular to fractures where possible,
because this reduces the problems of block instability, which would
indicate a tunnel orientation of west-east.
The ratio of rock stress to rock strength is high: for example, a stress
concentration value of 2 will raise the induced stress to the value of
the rock strength. To reduce stress concentration problems, the tunnel
should be parallel to the maximum principal stress, i.e. in a west-east
direction. Since this is the same direction as indicated by avoidance of