The strength of underground cavities of spherical and spheroidal geometry
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Expressions for the static-stress distribution over the surface of a degenerate prolate spheroidal cavity which is subjected to a given internal pressure and a given lithostatic loading at infinity. The hoop stress is evaluated at the apex of the spheroidal cavity and is compared with the hoop stress at the corresponding point of a spherical cavity, which is subjected to the same loading. Both cavities are presumed to fail when the hoop stress ceases to be compressive. It is shown that the maximum internal pressure which may be sustained by each of the cavities depends on the Poisson ratio. For certain values of the Poisson ratio, the spherical cavity can actually contain larger internal pressures than the spheroidal cavity, in spite of the fact that when the cavities are "empty," the spheroidal cavity has a hoop stress at its apex which is more compressive that that of the spherical cavity. Expressions for the static-stress distribution over the surface of a degenerate prolate spheroidal cavity that is subjected to a given internal pressure and a given lithostatic loading at infinity. The hoop stress is evaluated at the apex of the spheroidal cavity and is compared with the hoop stress at the corresponding point of a spherical cavity, which is subjected to the same loading. Both cavities are presumed to fail when the hoop stress ceases to be compressive. It is shown that the maximum internal pressure that may be sustained by each of the cavities depends on the Poisson ratio. For certain values of the Poisson ratio, the spherical cavity can actually contain larger internal pressures than the spheroidal cavity, in spite of the fact that when the cavities are "empty," the spheroidal cavity has a hoop stress at its apex that is more compressive than that of the spherical cavity. 34 pp
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