ROCK TUNNELS | SQUEEZING GROUND
[(v/R) (γw R2)/(kE)] is proportional to R2
, and the pressure develops at a rate inversely proportional to R2
and thus slower in a larger-diameter tunnel. The effect of the tunnel diameter, therefore,
becomes the same here as in the case of the standstill examined previously. Both during advance and restart, in the case of creep there will be no scale effect for tunnels excavated at the same rate, v/R; in the case of consolidation, though, the dependency on the square of the characteristic length—here R—holds.
2.2.2 Theoretical Analysis Under Realistic Assumptions The assumption adopted in the preceding section that v/R can be the same for the two tunnels is theoretical, for as is known, in practice, the larger the boring diameter the slower the TBM advance. In fact, v can be assumed to be inversely proportional to R, which then makes v/R inversely proportional to R2
.
Then: in the case of creep, its normalised advance rate becomes inversely proportional to R2
, which means
that the pressure develops faster in a larger tunnel (effect equivalent to lower viscosity); in the case of consolidation, its normalised advance rate becomes independent of R, and hence the shield pressure develops at the same rate in both tunnels. The assumption concerning the advance rate does not
influence the conditions during a standstill preceded by a rapid advance.
2.2.3 Time-Independent Ground Behaviour The theoretical analysis of the previous sections assumed that the dimensionless parameters do not depend on the tunnel radius, when in fact the dimensionless TBM parameters in general cannot take the same values for a large and a small tunnel. This generates a scale effect, even without time-dependent ground behaviour. The scale effect related to the TBM parameters was
assessed by comparing two tunnels with diameters of 12m and 4m, respectively, excavated under identical ground conditions, disregarding creep and consolidation. With respect to the risk of shield jamming, it is
not sufficient to consider only the shield loading or the required thrust force, Fr, but also the installed or installable thrust force, Fi
, the latter increasing with
tunnel diameter, which also introduces a scale effect. The comparison between the two tunnels is based on ratio Fr
/Fi , known as the Thrust Utilisation Factor (TUF).
The installed TBM thrust force is assumed to increase proportionally to the cross-sectional area, and thus to R2 The intuitive perception that the smaller-diameter
tunnel is less vulnerable than the larger-diameter one is unconditionally true for other potential hazards (e.g., an instability of the tunnel face) but not for the risk of shield jamming, where it is true only in better-quality ground. The opposite holds in weaker ground. Interestingly, this has been shown to be generally true
for any two tunnels with different radii, by means of a more extensive parametric study considering a wide
18 | December 2025 . ,
range of practically relevant in-situ stresses, boring radii, ground, and TBM parameters. For the parameters adopted herein, the TUF in the
larger-diameter tunnel is less sensitive to variations of rock quality than in the smaller-diameter tunnel, indicating that its excavation is feasible irrespective of the ground conditions. The small tunnel excavation, on the other hand, is only feasible in better-quality ground.
2.2.4 Time-Independent Ground Behaviour: TBM Advance The scale effect during TBM advance in the case of creep and consolidation was examined under the same assumptions, setting fc
= 3.2MPa to eliminate
the influence of the TBM parameters, and allowing advance rates of 90m/day and 30m/day for the 4m- and 12m-diameter tunnels, respectively. A scale effect clearly exists with respect to the risk
of shield jamming (expressed by the TUF) both in creep and consolidation. This is consistent with the results of the last section: time dependency delays squeezing, the rock thus responds to tunnel excavation as if it were of a higher quality, and an increase in rock quality renders a smaller diameter more favourable. The vertical distance between the two lines reflects
the scale effect.
Standstill The same conclusions can essentially be drawn for the thrust force needed for restart after a standstill. There are the same parameters as well as a high viscosity and low permeability, which ensure that the behaviour during advance is elastic (creep) or undrained (consolidation), and hence relevant shield loading develops only during the standstill. In graphing, the distances between lines indicate the
existence of a scale effect. The widths of those bands reflects the effect of tunnel radius.
3 INTERACTION The hypothesis that interaction is significant for consolidation but negligible for creep was tested, considering the problem of shield jamming in a twin tunnel (Figure 6). Tunnel 2 is assumed to have been built long after Tunnel 1, such that steady state conditions have been re-established. The limit cases examined were minimum interaction in consolidation versus maximum interaction in creep. Consolidation: the effect on Tunnel 2 is, first, due to
stress redistribution, and, second, pore pressure relief and the increase in undrained shear strength. This effect is minimum when the excavation-induced deformations are as small as possible, which is the case when the ground permeability is very low and its response to excavation practically undrained. Creep: the effect on Tunnel 2 is due to stress
redistribution. This effect is maximum if the deformations ahead of the face and around the shield of Tunnel 1 are as large as possible, as when the advance
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