T. Collotta, SEPA Ingeneria Europea s.p.a., Milan, Italy
I would like to thank Professor Oreste for adding to the literature on this subject.
I would suggest, however, that the results of the proposed method, as well as other similar limit equilibrium methods (LEM), are very sensitive to
(a) the shape of the collapse surface above and below the tunnel roof
(b) the angle of shear resistance (peak, residual or intermediate?)
(c) the cohesion intercept (peak, residual or intermediate?)
(d) the limit shear stress along the failure surfaces
(e) the limit shear stress at the mortar–ground interface, outside and inside the unstable block
(f) the water table levels
(g) the position of the fibreglass dowels on the excavation face
(h) the drilling hole diameter
(i) the safety factor (Fs) passing from τlim to τadm.
It would be valuable if the paper could indicate the influence of the variation of these parameters on the values of the safety factor Fs.
My personal experience, in relation to the large number of parameters that affect the result, is that the proposed criterion, as well as others that follow the same approach, can be used during the implementation of the work only after an appropriate calibration with the convergences and displacements observed during the first excavation stages. Unfortunately, it is apparent that the best calibration can be obtained only after some ground movement.
Nonetheless, this method, like others based on the limit equilibrium, can be used during the design in an initial definition of the ground reinforcement at the excavation face: at this phase, however, the experience of the designer becomes a key factor, although assisted by the use of 3D numerical analyses.
Author's reply
The author is grateful to the discusser for his interest in the paper.
Some parameters quoted in the discussion (friction angle, cohesion, limit shear stress at mortar–ground interface, water table depth below ground surface) are fundamental for evaluation of the stability of the excavation face. They significantly influence the safety factor of the excavation face. The same parameters have an important role to play in many other geotechnical problems.
It is important to take their influence into account correctly when the stability of the excavation face is examined. The developed calculation method allows consideration of the influence of these fundamental parameters by adopting a simple collapse surface, without losing calculation accuracy.
The author agrees that it is useful to perform calculations by varying the fundamental parameters of the problem in order to analyse their influence on the safety factor of the face, and to obtain charts that are able to support the tunnel design. This will be the subject of a future paper.
The exact evaluation of the parameters is a crucial point for each geotechnical problem: in the face stability problem the calibration procedure can be of little help, because in general the measured displacements are negligible for shallow tunnels when support structures and ground reinforcing are used. However, the instability phenomenon generally exhibits brittle behaviour, and precursor movement cannot be identified. Only the experience of the designer, and a necessary cautiousness, can help in the definition of the calculation parameters. For these reasons it is better to assume soil residual strength conditions and precautionary values for the local safety factors.
The limit equilibrium method represents a powerful tool, which is able to quickly evaluate the stability of the excavation face. The only alternatives are the experience of the designer and/or three-dimensional numerical modelling. The first on its own can be unsafe; the second requires many other input parameters to perform calculations, it is time-consuming, and it does not provide a unique safety factor for the excavation face. Three-dimensional numerical modelling can be used with difficulty in the design stage, but can be adopted for a final verification of the defined face-reinforcing intervention.
