Abstract:  The doubleOtube(DOT) shield tunnel may undergo longitudinal uneven displacement due to adjacent constructions. The longitudinal equivalent bending stiffness(LEBS) stands as a pivotal mechanical parameter, delineating the longitudinal bending performance of the tunnel and forecasting its deformation in response to external loads. To ensure the safety of the DOT shield tunnel structure and predict its longitudinal stress and deformation, the analytical solution for the LEBS is deduced based on the longitudinal equivalent continuous model. This model considers the pretightening force of the bolts and the influential range of the circumferential seam. In addition, expressions for boundary bending moments are provided under conditions where the neutral axis is located at the upper edge, upper double arch, waist, and lower double arch. A case study on the first DOT shield tunnel in China is conducted to analyze the effects of the bending moment, pretightening force of bolts, and influential range of the circumferential seam on longitudinal bending performance. Key findings include: (1) Under the pretightening force of bolts, the LEBS decreases in a "reverse S" shape with increasing external bending moment, ultimately approaching that without pretightening force. (2) The neutral axis position varies and gradually moves downward with increasing bending moment. When the external bending moment is smaller than the activating bending moment of the circumferential seam, the LEBS aligns with that of a homogeneous tunnel. (3) The neutral axis position remains unchanged for an influential coefficient of the circumferential seam length less than 1. Still, the efficiency of the LEBS rapidly decreases with an increasing coefficient of the circumferential seam action zone. When the influential coefficient is greater than 1, the neutral axis moves upward, and the compression range of the segmental ring increases. However, the efficiency of the LEBS slowly decreases and tends toward a certain value with an increasing coefficient of the circumferential seam action zone. (4) Increasing the pretightening force of bolts raises the activating bending moment of the circumferential seam, leading to a slower decay in the LEBS of the tunnel. Simultaneously, the neutral axis position continuously moves upward, and the compression range of the segmental ring further expands.

Key words: doubleOtube shield tunnel, longitudinal equivalent bending stiffness, circumferential seam influential range, analytical solution, pretightening force of bolts; efficiency of longitudinal equivalent bending stiffness