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An improved closed-form solution is developed for calculating tunnel support thrusts, moments, and displacements. The solution directly models the interaction of an elastic, circular support with an elastic, isotropic, infinite ground mass. The major improvements in this solution over other solutions in the literature are: (1)A revised formulation of the compressibility ratio; and (2)the incorporation of the correct excavation unloading conditions for mined tunnels. The sensitivity of the tunnel support loads to variations in the relative support stiffness, support cross section, Poisson's ratio, and initial lateral stress ratio is demonstrated using the revised solution; these results are also compared to those from two other solutions in the literature. Discrepancies of up to 100% are found in the support forces calculated from the different solutions.
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Einstein et al. (1979) studied this question.
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