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Compression Factor of Safety

The iterative procedure used in a Voussoir analysis is considered to have converged when a stable minimum value of the induced lateral compressive stress can be determined. This is the stress which holds the arch in place. It arises from considering the moment equilibrium of the driving and resisting force couples acting on the arch.

Triangular stress distributions are assumed to act at the arch abutments and at the arch midspan, keeping the arch in place. The most stable configuration for the Voussoir arch is that which minimizes the maximum stresses of these assumed triangular distributions.

If this stress exceeds the uniaxial compressive strength of the rock, localized crushing failure is considered to have occurred, and arch snap-thru may follow, even though the primary snap-thru analysis may indicate a stable arch.

Crushing Factor of Safety = Crushing Factor of Safety Equation

The Crushing Factor of Safety will usually be quite high. It will only become a failure mode issue in its own right under certain conditions, when the uniaxial compressive strength is very low. Depending on the scale of the rock volume involved, and the presence of planes of weakness inclined at some angle from the lateral stress direction, the effective uniaxial compressive strength for the roof may be significantly lower than the value for the intact rock specimens. Thus the potential for compressive failure should be based on the minimum value of uniaxial compressive strength to be expected for the transversely isotropic lithological unit (Beer et al., 1982).

For rocks with low compressive strength, the critical displacement at midspan may be less than 10% of the beam thickness (Hutchinson et al., 1996).

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