For tunnels exhibiting large degree of squeezing, experience shows that it is very difficult to provide support using conventional systems. Very heavy steel ribs or a thick concrete lining would be needed in order to provide the required support pressure, but it is practically impossible to install these safely in an advancing tunnel. One method that has been used successfully in such circumstances is the umbrella arch system.

The current example illustrates the use of umbrella arch of a horse-shoe shaped tunnel with an excavated span of 12 m and has been initially presented by Hoek (2001). The cover over the tunnel crown is 44 m and the poor-quality flysch in which it is to be excavated has a friction angle φ = 23°, a cohesive strength of c = 0.06 MPa and a deformation modulus of E = 318 MPa. The estimated global rock mass strength is σ_cm = 0.17 MPa and, for an in-situ stress of p₀ = 1.35 MPa, this gives a ratio of rock mass strength to in situ stress σ_cm / p₀ = 0.13 would suggest that very severe squeezing and face instability problems are likely unless appropriate support measures are implemented.

In this example the friction angle of φ = 23° which according to Hoek (2001) suggests that the rock mass has a low clay mineral content and that its behaviour is sufficiently frictional to justify the use of 6 m long 32 mm diameter fully grouted untensioned rockbolts for the tunnel arch and sidewalls and of 12 m long grouted fiberglass dowels for face support. Because of the anticipated face stability problems, a forepole umbrella consisting of 114 mm diameter pipes at 500 mm centre to centre spacing will be used over an arc of about 140°. These forepoles are 12 m long and successive umbrellas are installed at 8 m spacing, giving an overlap of 4 m between umbrellas.

Figure 1 summarizes one possible method for driving a tunnel through squeezing ground. To illustrate the numerical FEA work that would be considered for such a case, a set of modelling procedure is described in PLAXIS 3D, and comments are provided on the assumptions made and the reliability of each step. In the present situation, the invert struts (#5) and the invert lining (#8) will not be considered in the framework of the present analysis.

1	Forepole pipes
2	Shotcrete – Initial coat
3	Grouted fiberglass dowels
4	Steel sets
5	Invert struts
6	Shotcrete lining
7	Rockbolts
8	Invert lining

 

The detailed analysis of the grouted fiberglass dowels (#3) and their interaction with surrounding rock has not been explicitly accounted for. Instead, considering that their purpose is to stabilize the tunnel front face and that they are progressively removed as the tunnel front advances, an equivalent stabilizing front pressure as suggested by Peila (1994) has been used:

where:

• N is the number of bolts,
• A is the cross-sectional area of the bolt,
• σ_b is the yielding strength of the bolt material,
• S is the tunnel face surface,
• s_l is the lateral surface of the bolt,
• τ_a is the soil-bar limit skin friction.

The rockbolts (#7) will be modelled with using cable elements assuming they will remain fully bonded with the surrounding rock mass.

The steel sets (#4) and shotcrete lining (#6) will be modelled as a homogenised composite support system (plate element) the properties of which will be obtained by summing the rigidity of shotcrete layer and steel sets. Once calculated composite plate structural forces can be redistributed to obtain structural forces for shotcrete lining and steel sets independently.