BTS | HARDING PRIZE COMPETITION 2023
10 20 30 40 50 60 70
0 0
Bolted 0
0 0
0 0 0 0 00 0.01 0020.02 Joint rotation θ (rad) Above, figure 8: Bending moment (kNm) with joint rotation (rad) of the 11ft 81/4 0.0300 003 00. 4 Without bolts
10 20 30 40 50 60 70 80
0 0 0 0 0 0 0 0 0
0
Bolted Without bolts
0010.0
0020.02 Joint rotation θ (rad) in (3.562m) tunnel joint geometry without bolts for a tunnel depth of 48m – adapted from Ruiz López et al. (2023a) Left: (a) Positive bending Right: (b) Negative bending
0.030.0 003
004
The loading sequence comprised three steps: the
bolt preload; the confinement load; and, the bending load. The magnitude of the bolt preload was taken as 25% of the bolt load at yield; the influence of varying this magnitude was also investigated, as explained in the next Section (Influence of removing bolts and bolt preload on joint response). The confinement load consisted of a uniform normal stress acting all around the extrados of the ring and subjected the joint to a compressive axial force. Stress magnitudes corresponding to the full overburden acting at tunnel depths of 6m, 12m, 24m, and 48m, respectively, were considered in different analyses and kept constant throughout each of them. Lastly, the bending moment/ rotation at the joint was imposed via a vertical load, acting downwards for positive bending and upwards for negative bending, applied across the width of the segment at a certain distance from the joint. Figure 6 presents the bending moment-rotation (M- θ) curves for positive and negative bending, rotation
θ being defined as the relative rotation between two tunnel segments, as shown in Figure 3. Firstly, the rotational stiffness, i.e., slope of the M-θ
curve, of the joint gradually degrades with rotation from the onset of opening up until the curves reach a plateau which can be considered the end of the joint capacity. The rotational behaviour of the joint exhibits an obvious dependency on the compression level, the bending moment causing opening and ultimate bending moments both increasing with tunnel depth. Due to the asymmetry of the cross-section around the centroid, the joint behaves very differently under positive and negative bending. Consistent with the observations made in the latter
part (Derivation of bending stiffness reduction factors) of the previous Section, the bending moments causing opening are larger under negative bending for all tunnel depths. In relation to the ultimate bending moments, they are larger under positive bending for tunnel depths of 6m and 12m whereas the opposite is found for the
40 0 30 0 20 0 10 0 0 0 0010.0 0020.02 0.03 003 0.0 Joint rotation θ (rad) Above, figure 9: Bending moment (kNm) with joint rotation (rad) of the 11ft 81/4 004 0.050.0 005 006
12.5% 25% 50%
40 0 30 0 20 0 10 0 0 0 0010.0 0020.02 0.03 003 0.0 Joint rotation θ (rad) in (3.562m) tunnel joint geometry with different bolt preloads (expressed as percentage of the tensile load at yield) – Ruiz López et al. (2023a) Left: (a) Positive bending Right: (b) Negative bending 36 | July 2023 004 0.050.0 005 006
12.5% 25% 50%
Bending moment (kNm)
Bending moment (kNm)
Bending moment (kNm)
Bending moment (kNm)
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