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Ground Response to Tunnel Re-profiling Under Heavily Squeezing Conditions

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Abstract

This paper presents a finite strain theoretical analysis of the ground response around highly deformed circular tunnel cross sections that are subjected to (repeated) re-profiling in order to re-establish the desired clearance. Plane strain axially symmetric conditions are considered, with linearly elastic, perfectly or brittle plastic rock behaviour according to the non-associated Mohr–Coulomb model. On the basis of this theoretical analysis, some practical questions are addressed with respect to the ground response curve, the maximum rock pressure (as carried by a practically rigid new temporary support) and the maximum wall convergence (as expected in the presence of a light new support) after re-profiling. Finally, the paper revisits the question of the effectiveness of a pilot tunnel with respect to the ground response during enlargement of the tunnel cross section.

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Abbreviations

a 0, a :

Initial and current tunnel radius

c, c p, c r :

Cohesion and corresponding peak and residual values

E :

Elastic (Young’s) modulus

G :

Shear modulus

i :

Auxiliary variable

m :

Function of friction angle

r 0, r :

Initial and current radius of a material point

u :

Radial displacement of a material point

u * :

Radial displacement of the point lying on the elasto-plastic boundary

u a :

Radial displacement at the tunnel wall

u ρ :

Radial displacement at the elasto-plastic boundary

u I :

Initial excavation-induced tunnel convergence

u R :

Re-profiling-induced tunnel convergence

ε 1, ε 3 :

Major and minor principal strain

ε r, ε t :

Radial and tangential strain

κ :

Function of dilation angle

v :

Poisson’s ratio

ρ 0, ρ :

Initial and current radius of the plastic zone

σ, \(\bar{\sigma }\) :

Normal stress and transformed normal stress

σ 0 :

Isotropic in situ stress

σ 1, σ 3 :

Major and minor principal Cauchy stress

σ a :

Support pressure

σ D , σ D,p, σ D,r :

Uniaxial compressive strength and corresponding peak and residual values

σ R :

Rock pressure exerted upon a rigid new support after re-profiling

σ s :

Initial support pressure upon unloading

σ r, σ t :

Radial and tangential Cauchy stress

σ ρ :

Radial stress at the elasto-plastic boundary

φ :

Friction angle

ψ :

Dilation angle

el:

Elastic strain component

pl:

Plastic strain component

(n):

nth Excavation stage value

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Acknowledgments

This paper evolved within the framework of the research project ‘Analysis of large deformation problems in tunnelling considering geometric nonlinearities’, which is being performed at the ETH Zurich with the financing of the Swiss National Science Foundation (SNF) under Project No. 200021_153433.

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  1. ETH Zurich, Stefano-Franscini-Platz 5, 8093, Zurich, Switzerland

    Apostolos Vrakas & Georgios Anagnostou

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  1. Apostolos Vrakas
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  2. Georgios Anagnostou
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Correspondence to Apostolos Vrakas.

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Vrakas, A., Anagnostou, G. Ground Response to Tunnel Re-profiling Under Heavily Squeezing Conditions. Rock Mech Rock Eng 49, 2753–2762 (2016). https://doi.org/10.1007/s00603-016-0931-2

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  • DOI: https://doi.org/10.1007/s00603-016-0931-2

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