Abstract
A circular tunnel lining is idealized as a perfectly elastic annulus either keyed to, or a sliding fit in a hole in an infinite elastic medium of different Young's modulus, the system being under stress at infinity. The solution to this problem is used to give a qualitative discussion of two situations:
The resistance of a tunnel lining is limited amongst other things by its inability to withstand tensile stress. It is shown that in the above idealization, the more flexible the lining the less likely are tensions to arise. Such flexibility might be achieved by allowing the lining freedom to slide relative to the surrounding rock rather than by keying it to the walls, by making it of laminated construction or by lowering its Young's modulus. Increasing the thickness may increase the liability to tension. As a means of estimating the load on a lining, gauges may be placed to measure circumferential strain, and from these measurements the load is deduced by assuming that the lining behaves like a bending beam. A difficulty in interpreting such measurements is pointed out in the case of a keyed lining, when the shearing stresses are very large.
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