The circular tunnel in elastic ground

Neither the ground around a tunnel nor, usually, the tunnel lining, behaves in an elastic manner. Nevertheless, the linear characteristic of an elastic or visco-elastic analysis has great merit, particularly when, as frequently occurs, limitations of knowledge of the behaviour of the ground do not justify greater elaboration.

This Paper sets out to establish the loading on a circular tunnel in the ‘elliptical’ mode of deformation, making certain simplifying assumptions. The effects of shear forces between ground and lining are first ignored and subsequently introduced in an explicit manner. Bending moments in a lining are related to a stiffness factor, R_s.

While a higher mode of deformation of a tunnel lining is only applicable to problems of stability for thin linings, nevertheless, consideration of this condition allows the coefficient of ground reaction &amda; to be evaluated for conditions of asymmetrical deformation.

Direct radial loading of a tunnel lining is related to its compressibility factor R_c. The component of radial loading caused by migration of water towards the tunnel is also established.

Some aspects of application of the method are discussed including the effects of joints in a lining and the benefits established on account of the deliberate variation of R_c. The method has serious limitations but frequently serves as a first, and very useful, indication of the relative importance of the principal factors, prior to a more refined analysis. An important point, frequently overlooked, concerns the effect of variation of Poisson's ratio of the ground as loads change, which may greatly affect the stress distribution in the ground and, in consequence, the loads on the lining.