A continuous upper bound limit analysis for the transverse stability of shallow shield tunnelling in undrained clays

Abstract

For a cross sectional ‘convergence-oval deformation-sagging/uplifting’ composite volume loss model of shallow shield tunnels in undrained clays, the ground displacement field is calculated using complex variables, and the most critical tunnel stability number as well as its supremum are determined by using continuous upper bound limit analysis. Illustrative calculations reveal: (1) the method can be verified via finite element modelling and comparisons with other limit analysis solutions and centrifuge model test results; (2) with the increase of the tunnel sagging coefficient or oval-deformation coefficient, the ground surface settlement increases mainly in magnitude but minor in trough width; (3) the influence of the tunnel uplifting coefficient on ground displacement is similar in pattern but opposite in direction to that of the tunnel sagging coefficient; (4) the effect of the tunnel oval-deformation coefficient on the supremum of the tunnel stability number is more significant than that the tunnel sagging/uplifting coefficient; (5) the uniform convergence volume loss model can reflect the most critical pattern of tunnel instability and the most critical tunnel stability number with sufficient accuracy. The proposed method and the relevant observations can serve as references for limit support pressure calculations concerning shallow shield tunnel excavations in undrained clays.