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deeper tunnels. This trend is explained by the greater contribution of the bolts to the ultimate bending moment under positive bending prevailing in the lower range of tunnel depths, whereas the larger contribution from the axial compressive force under negative bending becomes dominant for the deeper tunnels. The M-θ curves converge to the plateau more


rapidly under negative bending due to the three bolts becoming active concurrently under this bending mode, while under positive bending the middle bolt develops tension only after yielding of the two outer bolts. The latter feature was also observed in the laboratory tests conducted by Afshan et al. (2017). The horizontal lines included in the two plots of


Figure 6 refer to the maximum capacity of the joint, for each tunnel depth, assuming that the three bolts reach their ultimate tensile load and that failure in compression, due to the contact force between segments, does not occur. It can be observed that the ultimate bending moments are generally close, particularly for negative bending, to the magnitude predicted by the maximum capacity. The slight drop of bending moments observed in the


M-θ curves for positive bending (see Figure 6a) as they approach their plateau is related to the propagation of tensile failure of GCI across the circumferential flange and skin, adjacent to the longitudinal flange. The darker coloured areas in Figure 7 indicate plastic tensile strains larger than the plastic strain at peak strength (0.55%) and therefore undergoing softening. Even though extensive areas of the longitudinal joint experience softening, as shown in the contour plots of Figure 7, complete breakage of the flanges did not occur and the bolts did not fully soften. Lastly, failure of GCI in compression did not generally occur in either of the two bending modes. The characterisation of the joint rotational response


informed the development of a new joint model to be adopted in geotechnical numerical analysis (Ruiz López et al., 2023b). Details of the formulation of the joint model are not provided here but it is worth mentioning that the new model incorporates the dependency, shown in Figure 6, of the joint response on the axial force and the gradual stiffness decay from opening to ultimate conditions. The new development enables the nonlinear behaviour of segmental GCI tunnel linings to be incorporated in geotechnical analysis.


INFLUENCE OF REMOVING BOLTS AND BOLT PRELOAD ON JOINT RESPONSE Undoing or tightening the bolts of GCI tunnel joints are commonly adopted measures (Kimmance et al., 1996; Moss & Bowers, 2005) to protect existing tunnels from developing excessive internal forces or deformations when subjected to new solicitations. While the adoption of such measures is based on several decades of experience in constructing close to LU infrastructure, their effectiveness is yet to be clearly demonstrated. A series of analyses, following the same set-up


discussed in the previous Section (Rotational behaviour of longitudinal GCI tunnel joints), were conducted with an aim of gaining further insights into the effect of removing the bolts and applying different bolt preloads on the joint rotational response. First, analyses for a tunnel depth of 48m under each


bending mode were carried out having removed the bolts from the 11ft 81/4


in tunnel joint geometry. Figure 8


shows the M-θ curves obtained in those analyses along those derived from the analyses with bolts for the same tunnel depth (already shown in Figure 6). It can be observed that the early part of the M-θ curves is very similar regardless of whether the joint has bolts or not, which can be explained by the bolts being mobilised only after certain joint rotation. The effect of removing the bolts becomes evident thereafter. The magnitude of the ultimate bending moments is


significantly reduced when the bolts are removed; the differences are most significant under positive bending as the action of the bolts is more relevant in this mode. It is also evident that the joint reaches its ultimate bending moment more rapidly when the bolts are removed. In relation to the potential for tensile failure of GCI,


analysis gives the distribution of the maximum principal plastic strain at the end of the analysis under positive bending. The extent of the region where plastic strains occur (coloured area) and the magnitude of these are considerably less than those observed in the analogous analysis with bolts (see Figure 7). The magnitude of the tensile plastic strains (<0.083%) is far from that required to cause failure of the material (0.55% as defined in the numerical model). These results suggest that the possibility of tensile failure around the longitudinal flange can be safely neglected when the bolts are removed and so that this can be an effective measure to protect the structural integrity of the tunnel. As explained above, tightening the bolts of GCI tunnel


joints is a common practice to minimise the potential tunnel deformations resulting from new construction adjacent to the tunnel. It is therefore instructive to consider the effect of bolt preload magnitudes different than that considered so far (25% of the load at yield). The rotational response of the joint is assessed below for a tunnel depth of 12m with bolt preloads of 12.5%, 25%, and 50%, respectively, of the tensile load at yield. Figure 9 presents the M-θ curves given by the


analyses with different bolt preloads. First, it can be observed that the effect of the bolt preload is apparent only after certain joint rotation has taken place, which is similar to the observations made above in relation to the effect of removing the bolts. The bending moment causing opening is therefore not affected by the bolt preload which is consistent with the experimental findings of Yu et al. (2017). Once the bolts are mobilised, the M-θ curves exhibit a stiffer response with larger bolt preloads. While modest differences are found between the


three analyses under positive bending they are more prominent under negative bending. The primary


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