Responses of a circular tunnel in an elastic ground with an improvement of the subgrade modulus

Abstract

One of the key problems in the application of the beam on the Winkler model for tunnel responses is the assessment of the modulus for the Winkler spring. Contrary to the commonly used radial Winkler modulus, which is dependent on the tunnel radial deformation, the derivation of radial Winkler springs considering the relative tunnel-soil stiffness is introduced, which changes with angles. Furthermore, an explicit fitted expression in terms of relative tunnel-soil stiffness is presented for practical application. To consider the effects of shear forces at the soil-tunnel interface, a circumferential Winkler spring stiffness is derived based on elastic continuum theory. The error of using two independent radial and circumferential Winkler springs, which neglects coupling effects compared to the actual continuous soil behavior, is estimated, and a relative stiffness of larger than 0.005 is proposed for the estimation of tunnel response with Winkler models. Finally, case studies of a tunnel subjected to different soil stresses are illustrated. Comparisons show that for the conventional symmetrical loading conditions of geostress due to gravity, the use of only the radial Winkler modulus is acceptable. However, the combination of radial and circumferential Winkler moduli is necessary for asymmetrically distributed loads caused by construction activities nearby.