SQUEEZING GROUND | ROCK TUNNELS
extended area, in turn affecting other existing or planned underground structures. Interaction effects may be more or less pronounced by the method of construction, moreso with conventional tunnelling with yielding support, and less so where ground deformations are limited by stiff support close to the face. Shield tunnelling is closer to the second case. A special situation arises in the case of saturated,
water-bearing ground, as excavation-induced drainage results in pore pressure relief over an extended area. In the case of a twin tunnel, the pore pressure relief due to construction of the first tube results in higher effective stresses and helps the second tube, such as experienced at Simplon rail tunnel and the Gotthard road tunnel in Switzerland. It is expected that time-dependent interaction effects
will be more pronounced in the case of consolidation than in the case of creep.
2 SCALE EFFECT Starting with a simple plane-strain problem, the study looked at the time-development of tunnel convergences in a cross section far behind the face, and then the scale effect with respect to the risk of shield jamming.
2.1 Time-Dependent Contraction of a Deep Tunnel
2.1.1 Homogeneous Ground The problem is analysed based on the classic, rotationally symmetric, plane-strain model of a cylindrical and uniformly supported tunnel located deep below the ground surface and the water table. The rock is assumed to obey a linear elastic and
perfectly plastic constitutive model with a Mohr– Coulomb yield condition and a non-associated plastic flow rule. The rheological ground behaviour due to creep is modelled as purely viscoplastic. Seepage flow in water-bearing ground is modelled according to Darcy’s law. It is inferred that the time required to attain a given
percentage of displacement during consolidation is proportional to R2 or where given ground parameters, initial stress and pore pressure. Such a dependency does not exist in the case of creep. Practically, this means that given displacements would develop slower in the case of consolidation. The quadratic dependency holds as long as the tunnel lies deep under the water table.
2.1.2 Confined Aquitard In the case of an aquitard (low permeability layer confined between permeable layers), the in-situ pore pressure practically acts at the layer interfaces. The hydraulic head difference between the aquifer and tunnel is dissipated only within the aquitard, along a drainage path whose length corresponds to half the aquitard thickness (d/2 in Figure 5). This constraint may give rise to a secondary, non-
trivial scale effect, which becomes relevant when the ratio of the aquitard thickness to the tunnel diameter (d/D) is small, and generates two competing effects:
the drainage path becomes shorter, accelerating consolidation, but the hydraulic gradients and seepage forces are higher, which induces more extensive ground plastification and thereby decelerates consolidation. The key takeaway is that in confined aquitards the
consolidation rate may deviate dramatically from the quadratic rule of consolidation theory—even moreso for lower aquitard thickness and weaker ground, indicating that deformations may continue for a long time after excavation. This may prove critical in respect of serviceability requirements or structural safety of the final lining.
2.2 Risk of Shield Jamming The effect of the tunnel diameter on the risk of shield jamming was investigated only for homogeneous ground. Due to technical limitations, the TBM parameters
(over-cut, shield length, and shield and lining stiffnesses) in practice vary within a specific range, independently of the tunnel diameter, while the advance rate decreases with increasing diameter. Consequently, the nondimensional parameters in general cannot take the same values for different tunnel diameter, which gives rise to a scale effect with respect to the risk of shield jamming (Ramoni and Anagnostou 2011). The strength and stiffness of the ground may also
tentatively decrease with increasing representative volume, and thus tunnel diameter. Assessing the scale effect qualitatively is cumbersome.
Therefore, numerical simulations were necessary to scale effect.
2.2.1 Simplified Theoretical Analysis The start of the analysis considered conditions during TBM restart after a standstill. As rock pressure may already have developed, its value depends not only on the standstill duration but also on the advance rate. To eliminate the influence of the latter, rapid excavation was assumed. Conditions during the advance phase were examined.
In the case of creep, for a given average advance rate, the advance would be slower in a larger-diameter tunnel (equivalent effect to lower viscosity), and hence a higher rock pressure will develop; alternatively, to achieve a given rock pressure the advance rate must be higher in the larger-diameter tunnel. In the case of consolidation, the effect is opposite. To compare rock pressure in different diameter
tunnels the average rate alone is not the most suitable measure of the rate of advance. At any given tunnel cross section, a shield remains exposed to pressure locally while it passes. Shield pressure, ultimately, depends on the time for the TBM to advance by one shield length, which becomes a function of v/R only, as L/R, the normalised shield length, is considered fixed. For a given v/R: in the case of creep, the normalised
advance rate [(v/R) (η/Ε)] being constant means the pressure develops at the same rate regardless of R; in the case of consolidation, its normalised advance rate
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