Volume Loss Prediction for a Longitudinally Inclined Tunnel Face Advancement in Undrained Clay

This paper presents a novel analytical approach for predicting the volume loss of a tunnel face during advancement with different longitudinal slope angles. The proposed approach utilizes the continuous velocity field of a circular tunnel face in undrained clay and combines the upper-bound limit analysis with the mobilized strength design method to derive the relationship between the load factor and the volume loss. An analytical expression is proposed for the relationship between the face support pressure and surface deformation, accounting for the longitudinal slope angle. Parametric studies are conducted to explore the impact of the longitudinal slope angle on the ground surface settlement during tunnel face advancement. The results reveal that the ground surface settlement increases with the tunneling longitudinal gradient in a downward direction but decreases for tunneling in an upward direction when the supporting pressure remains unchanged and the ground surface is horizontal. As the tunneling direction is parallel to the inclined ground surface, the impact on the ground surface settlement becomes more significant and cannot be ignored in engineering practice.