The Buoyancy of the Tunnel Segmental Lining in the Surrounding Filling Material and its Effects on the Concrete Stress State

Abstract

Segmental lining is subject to significant upward buoyancy forces when a grouting material (slurry), initially fluid, is adopted to fill the gap between its external profile and the wall of a tunnel excavated with a TBM machine. The analysis of the effects of these forces is important in order to correctly dimension the segmental lining and avoid damage to the lining and subsequent costly maintenance and restoration actions. Given the complexity of the behavior of a segmental lining consisting of segmental rings and circular joints that alternate in the longitudinal direction of the tunnel, a specific numerical model has been implemented, adopting the Finite Element Method (FEM). This model is able to obtain the development of the vertical displacements of the segmental lining starting from the TBM tail, together with the bending moments and the shear forces induced inside it. The developed model is able to assess the risks of breaking and damaging the concrete and steel bolts that are used to connect the segmental rings at the circular joints; therefore, it represents a useful design tool for being able to correctly dimension the segmental lining also in relation to the risks produced by the appearance of considerable buoyancy forces around it, due to the presence of the initially fluid filling material. The proposed numerical model was applied to a real case (Ningbo metro tunnel) and allowed to obtain satisfactory results from the comparison of the calculated displacements with in situ measurements. Some sensitivity analyzes developed on the studied case have made it possible to detect which are the influencing parameters that have the greatest impact on the behavior of segmental lining in the presence of the studied buoyancy forces.

The important role of stiffnesses values of circular joints on the stress state developed in the tunnel segmental lining

“…Simplified analytical methods are also widely applied for the fast evaluation of tunnel lining based on the geotechnical and geometrical information (Einstein and Schwartz 1979); it simplifies the tunnel lining as beams or beams connected by springs (Chen et al 2018;Cheng et al 2021;Geng et al 2019;Gil Lorenzo 2019;Huang et al 2015Huang et al , 2012Li et al 2019;Liang 2019;Liang et al 2021Liang et al , 2017Liu et al 2021;Wu et al 2015;Yu et al 2019).…”

“…2a). Huang et al (2012), Talmon and Bezuijen (2013), Huang et al (2015) and Gil Lorenzo (2019) (2023) 9:37 the longitudinal continuous model based on the Euler-Bernoulli beam and analysed the longitudinal deformation and the internal forces. However, the Euler-Bernoulli beam can't represent the shear deformation; the continuous Timoshenko beam was used to calculate the longitudinal deformation considering the bending stiffness and the shear stiffness (Cheng et al 2021;Shi et al 2022;Wu et al 2015Wu et al , 2018.…”

“…where K hole is the compression stiffness of the hole wall, K hole can be estimated by the following equation (Han et al 2022):…”

“…A FEM numerical model with the standard element which represent segmental rings and the joint element which represent circular joints, was adopted to simulate the longitudinal deformation based on the hyperstatic reaction method (Han et al 2022). 4 standard elements with a length of 20 cm and 1 joint element with a length of 40 cm are adopted to simulate a lining ring (Fig.…”