HARDING PRIZE COMPETITION 2023 | BTS
10 20 30 40 50 60 70 80
0 0 0 0 0 0 0 0 0
0 0010.0
Max capacity
6m depth 24m depth
0020.02 0.03 003 0.0 004 Joint rotation θ (rad) Above, figure 6: Bending moment (kNm) with joint rotation (rad) of the 11ft 81/4 0.0 005
12m depth 48m depth
0.0 006 0.0 007
10 20 30 40 50 60 70 80
0 0 0 0 0 0 0 0 0
0
Max capacity
6m depth 24m depth
0010.0 0020.02 0.03 003 0.0 004 Joint rotation θ (rad) in (3.562m) tunnel joint geometry – adapted from Ruiz López et al. (2023a) Left: (a) Positive bending Right: (b) Negative bending
ring was obtained from the expressions of the elastic continuum model provided by Duddeck and Erdmann (1985) for the radial displacement due to non-isotropic loading. The reduction factors depicted in Figure 5 can
be applied in preliminary assessments of potential damage of GCI tunnel linings to consider the influence of the joints on the structural response. In such assessments, the reduction factors ηc
and ηs can be
applied to determine the tunnel’s present-day bending moments, corresponding to an assumed or measured tunnel squat, at the crown/invert and springline sections, respectively. Likewise, these two factors can be used along with the elastic continuum model in assessing the changes of bending moments of an existing tunnel corresponding to given ground movements caused by nearby construction. The global reduction factor can be applied to the bending stiffness of the tunnel lining in numerical analyses focused on assessing the movements of an existing tunnel subjected to new solicitations.
ROTATIONAL BEHAVIOUR OF LONGITUDINAL GCI TUNNEL JOINTS Even though the advanced 3D numerical model shown in Figure 2b can reproduce the behaviour of segmental GCI rings as observed experimentally (Ruiz López et al., 2022), it is impractical for geotechnical
numerical analysis where the tunnel lining is usually simulated as a beam or shell and where 2D plane-strain conditions are often applicable. The need to consider the segmental nature of GCI tunnel linings in geotechnical numerical analysis prompted the development of a new model able to represent the nonlinear rotational stiffness of the joint using 2D beam elements. In order to develop the new joint model, detailed
knowledge of the rotational behaviour of GCI tunnel joints was required. While some insights into the rotational joint behaviour had been previously obtained from experimental (Thomas,1977; Tsiampousi et al., 2017) and numerical investigations (Li et al., 2014; Tsiampousi et al., 2017), these studies only examined the behaviour of the joint under zero compressive axial force and hence did not provide the required information for developing the model. Ruiz López et al. (2023a), however, conducted a
comprehensive characterisation of the behaviour of two joint geometries, those corresponding to the prototype 11ft 81/4
in (3.562m) running and the 21ft 21/2 in (6.464m)
station tunnels, considering the effect of different compression levels, under positive and negative bending. Only the results from the 11ft 81/4
in running tunnel are
discussed in the following. The adopted 3D numerical model was similar to
that illustrated in Figure 2b in most respects apart from including only the joint at the crown section.
0.0 005
12m depth 48m depth
0.0 006 0.0 007
Softened areas
Above, figure 7: Maximum principal plastic strain (%) at a joint rotation of 0.058 rad for a tunnel depth of 12m under positive bending – adapted from Ruiz López et al. (2023a)
July 2023 | 35
Bending moment (kNm)
(%) 0
0.55
Bending moment (kNm) 20
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