SQUEEZING GROUND | ROCK TUNNELS
is slow and all viscoplastic deformations, due to creep, occur practically simultaneously with excavation progress. The problem was analysed in a simplified manner
using, sequentially, two models: (i) an axisymmetric model of the advancing tunnel heading; and, (ii), a plane-strain, twin-tunnel model of a cross section.
3.1 Consolidation Case The short-term shield–lining–ground interaction in Tunnel 1 was analysed using the axisymmetric model (Figure 1b) to establish rock pressure distribution along the shield and, so, the thrust force required to overcome shield skin friction. The model was used to calculate the required thrust force in Tunnel 2, with different initial conditions that reflect stress redistribution, pore pressure relief and ground consolidation induced by Tunnel 1. The alteration of the initial stress and pore pressure
fields were quantified using the plane-strain model (Figure 7). The comparison of the rock pressure in the two
tunnels reflects the very favourable effect of the drainage-induced consolidation in the vicinity of Tunnel 2. It is remarkable that the Tunnel 2 thrust force is about 65% less.
3.2 Creep Case The creep case essentially follows the same approach. Computations start with the axisymmetric analysis of Tunnel 1, which provides the longitudinal stress distributions on the shield and lining, as well as the equilibrium point of the rock. The analysis showed that construction of Tunnel
1 does not have a relevant effect on the Tunnel 2 thrust force for the considered spacing and this lack of relevant interaction can be observed also in the extreme squeezing and large overcut case. The difference to the consolidation case is remarkable—at a spacing of 2.5D or even greater, the interaction in the consolidation case leads to a reduction of the Tunnel 2 thrust force by 65%–90%.
CONCLUSIONS The investigations into the scale effect showed time development of the convergences of an unsupported opening gave the findings of: independence of the tunnel diameter (creep); and, being inversely proportional to the square of the diameter (consolidation), which means that convergences develop slower in larger tunnels. The latter is directly analogous to the well-known
quadratic dependency between consolidation time and length of the drainage path, but holds only if there is one significant geometric parameter: the tunnel diameter. In the more complex problem of shield jamming
risk, the investigations demonstrated that a larger diameter is more favourable than a smaller one in poor-quality ground with time-independent behaviour; the opposite is true for better-quality ground, creep or consolidation.
Funding: Open access funding provided by Swiss Federal Institute of Technology Zurich. No funding was received for conducting this study.
Declarations (Conflict of interest): The authors have no relevant financial or non-financial interests to disclose.
These papers were originally published online in Rock Mechanics and Rock Engineering (RMRE) Journal, from Springer, in 2024, as Parts A and B of ‘Creep Versus Consolidation in Tunnelling through Squeezing Ground,’ under a Creative Commons Attribution 4.0 International Licence,
http://creativecommons.org/licenses/by/4.0/. As permitted under the particular open access facility, this version of the original papers is combination of two full papers, abridged and edited for space, and images adapted to house-style. The original papers are available in full, online: Part A - Rock Mechanics and Rock Engineering (2024) 57:5537–5555;
https://doi.org/10.1007/ s00603-024-03968-6; and, Part B - Rock Mechanics and Rock Engineering (2024) 57:5519–5536; https://doi. org/10.1007/s00603-023-03720-6.
Left, figure 6:
Interaction problem: geotechnical situation during the advance of the second tunnel, long after construction of the first tunnel (plan view x–y)
Left, figure 7:
Interaction problem: plane-strain model (cross section A–A of Figure 6) in the computational stage that simulates the excavation of the first tunnel
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