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Deep tunnel fronts in cohesive soils under undrained conditions: a displacement-based approach for the design of fibreglass reinforcements

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Abstract

The fronts of tunnels excavated under particularly difficult ground conditions by employing conventional tunnelling methods are commonly supported: the stabilization is usually achieved either by improving the mechanical properties of the soil (injections, jet grouting, soil freezing, etc.) or by introducing linear inclusions. This last technique, consisting in the introduction of pipes (usually made of fibreglass reinforced polymers) in the front, is particularly popular since it is very simple to adapt the reinforcement geometry, length and number to the different conditions encountered during the excavation. The design of this reinforcement technique is nowadays based on very simplified approaches: on either empirical formula or the limit equilibrium method. In a previous paper, the authors numerically studied the mechanical response of unreinforced fronts in cohesive soils and defined a non-dimensional front characteristic curve. In this paper, the authors intend to take into consideration the role of reinforcements by following the same approach. A procedure allowing the definition of the reinforced non-dimensional front characteristic curve, once the reinforcement pattern is assigned, is introduced. The practical use of this curve is described.

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Abbreviations

a f :

Qf value defining the limit of the linear response of the reinforced characteristic curve

a fu :

Qf value defining the limit of the linear response of the unreinforced characteristic curve

D :

Tunnel diameter

d :

Reinforcement diameter

\( \overline{E} \) :

Relative reinforcement stiffness

E r :

Reinforcement Young modulus

E u :

Soil undrained Young modulus

H :

Tunnel cover

\( \overline{k} \) :

Initial (geostatic) stress anisotropy factor

L :

Reinforcement length

LSR:

Load sharing ratio [37]

N :

Reinforcement axial load

\( \overline{N} \) :

Reinforcement axial load associated with the complete soil–reinforcement interface yielding

N np :

Reinforcement axial load at the neutral point

N y :

Failure reinforcement axial load

n :

Reinforcement number

Q f :

Non-dimensional stress applied on the front [11] (Q*f = QfD/afL)

Q y :

Non-dimensional stress corresponding to the failure of the most loaded reinforcement (Q*y = QyD/afL)

q f :

Non-dimensional front displacement [11]

q f,r :

Residual (for σf = 0) non-dimensional front displacement

R 1 :

Function defining the influence on ΔR of the reinforcements length

R 2 :

Function defining the influence on ΔR of the reinforcements diameter and number

R 3 :

Function defining the influence on ΔR of the reinforcements relative stiffness

r1, r2, r3 :

Interpolating parameters

r :

Initial slope in the \( N_{\text{np}} /\overline{N} - Q_{\text{f}}^{*} \) plane

S u :

Undrained strength

u f :

Average front displacement

u f,adm :

Admissible front displacement

u fr,el :

Elastic residual (for σf = 0) front displacement [11]

x l :

Distance from the front (Fig. 3)

x r :

Distance from the front (Fig. 3)

γ sat :

Saturated soil unit weight

ΔQf :

Vertical distance between the reinforced and the unreinforced curves for large qf values

ΔR :

Increment in the initial stiffness with respect to the unreinforced case

η :

Reinforcement efficiency

ν u :

Undrained Poisson’s ratio

σ f :

Average stress applied on the front

σ f0 :

Initial geostatic value of σf

σ v :

Vertical stress applied to the lining

σ v0 :

Geostatic vertical stress applied to the lining

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Acknowledgements

This research was funded by Rocksoil S.P.A. and Maccaferri S.P.A. within the framework of an experimental/numerical program aimed at defining innovative design solutions for the front reinforcements by means of fibreglass tubes.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Claudio di Prisco, Luca Flessati & Davide Porta

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  1. Claudio di Prisco
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  2. Luca Flessati
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  3. Davide Porta
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Correspondence to Luca Flessati.

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di Prisco, C., Flessati, L. & Porta, D. Deep tunnel fronts in cohesive soils under undrained conditions: a displacement-based approach for the design of fibreglass reinforcements. Acta Geotech. 15, 1013–1030 (2020). https://doi.org/10.1007/s11440-019-00840-8

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