Design against structurally-controlled instability 365The principle of the voussoir arch is open to some discussion, but a block
will not fall from the arch providing the vertically acting resisting forces
are greater than the sum of the weight of the block and any superimposed
forces. These resisting forces are, in turn, generated by the frictional and
dilational properties of the discontinuities between the blocks, which result
from horizontal or sub-horizontal forces induced in the arch by the weight
of the blocks themselves. Viewing the arch in Fig. 20.5, one can imagine
how the weight of the central block of the arch is transmitted via the inter-
block frictional shear forces to the abutments of the arch.
It is possible, as shown in the top of Fig. 20.6, to have an arch where the
radius of curvature is large, with the result that the arch becomes essentially
flat. A voussoir arch will have compressive stresses between all the blocks
and between the abutments. Although the arch is stable, and examples such
as that in Fig. 20.5 have survived for hundreds of years, the whole arch is
vulnerable to any block perturbation, which will affect the total arch
integrity: the voussoir arch is like a chain-all the elements have to be
present in order for it to function. Thus, although the voussoir arch
principle is elegant, the arch is not a robust design for underground
excavation roofs. We can use the principle, but the inherent vulnerability
of the arch needs to be overcome.
To do this, it is necessary to have an understanding of the precise
mechanics of the voussoir arch and its potential modes of instability which
can involve either insufficient or excessive inter-block compressive stress.
Underground, the voussoir arch is not built from masonry blocks: the arch
comes into existence once the empty space beneath it has been created by
excavation, with the result that there are thus two stability aspects to
consider-is the arch stable in the first place, and will it remain so?
In the event that the geometry of the arch is such that sufficient inter-
block compressive stress is not generated to mobilize sufficient frictional
shear forces, a block will become unstable, leading to complete collapse of
the arch. Such circumstances can arise from lateral movement of the
abutments, highly compliant elements in the arch (for example, low
modulus of elasticity of the intact rock and low stiffness discontinuities) or
simply an inappropriate rock block geometry. Conversely, if the geometry
7 Rock assumed blocks to within act as roof voussoirs stratum
CFigure 20.6 The voussoir arch in underground excavations.