The circular tunnel in elastic ground

Abstract

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, Rs. 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 Rc. 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 Rc. 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. Ni le terrain autour du tunnel, ni généralement le tunnel proprement dit, ne se comportent d'une manière élastique. Néanmoins, les caractéristiques linéaires d'une analyse élastique ou visco-élastique ont beaucoup de mérite, particulièrement quand, comme cela arrive fréquemment, les limitations des connaissances du comportement du sol ne justifient pas une plus grande précision. Cette communication tente d'établir le chargement sur un tunnel circulaire se déformant d'une manièrc elliptique en faisant certaines simplifications dans les hypothèses. Les forces de cisaillement entre le sol et le tunnel sont en première phase ignorées et ensuite introduites d'une manière explicite. Les moments fléchissants dans la voûte sont reliés à un coefficient de raideur Rs. Alors qu'un mode de déformation plus important d'une voûte de tunnel est seulement applicable aux problèmes de stabilité des tunnels minces, on considère néanmoins que cette condition conduit à un coefficient de réaction du sol &amda; évalué pour les conditions de déformation asymétrique. Le chargement direct radial d'un tunnel est relié à son facteur de compressibilité Ro. La composante de la charge radiale provoquée par la migration de l'eau vers le tunnel est aussi établie. Quelques aspects de l'application de la méthode sont discutés y compris les effets des joints dans un tunnel et le bénéfice résultant de la prise en compte des variations délibérées de Rc. La méthode a de sérieuses limitations, mais sert fréquemment comme première et très utile indication pour mettre en évidence l'importance relative des principaux facteurs avant une analyse plus raffinée. Un point important, fréquemment négligé, concerne les effets de variation du coefficient de Poisson du sol lors des modifications de charges, ce qui peut gravement affecter la distribution des contraintes dans le sol et en conséquence les charges sur lc tunnel.

Hydraulic Tunnels

“…Therefore, a rational analysis of concrete lining can provide great economic benefits by indicating its reasonable thickness and reinforcement (Deere et al 1970;Kuesel 1987;Muir Wood 1975;Pender 1980;Sulem et al 1987;Wang 1982).…”

Key parameters governing the performance of soft tunnel coating for seismic isolation

“…In this derivation, the presence of the thin exible coating is ignored. Though its rigorous solution is available in a number of papers [5], radial and tangential displacements u r; soil and u Â; soil are tentatively approximated by the static solutions for a cylindrical cavity inclusion in an unbounded medium under alternate shearing ( Figure 1) [6]; the approximation yielding the simple description of u r; soil and u Â; soil on the cavity wall as u r; soil ∼ =ûr;soil sin 2Â (3a)…”

Stress Analysis of Segmental Tunnel Lining Using Artificial Neural Network

“…Analytical methods have been developed from the start of the tunnel support design history up to now [6][7][8][9][10][11][12][13][14][15][16]. Some of these analytical methods are restricted either to only elastic behaviour of tunnel lining and soil material or only to shallow tunnel conditions.…”