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Functional Catastrophe Analysis of Progressive Failures for Deep Tunnel Roof Considering Variable Dilatancy Angle and Detaching Velocity

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Abstract

The phenomena of progressive failures are very common and important in geotechnical engineering. In this paper, a reliable prediction model is proposed to interpret the progressive failure phenomenon of roof collapse in deep tunnels using the functional catastrophe theory. The progressive collapse mechanisms and collapsing block shapes of deep circular tunnels under conditions of plane strain are investigated. The analytical solutions for the shape curves of the collapsing blocks of circular tunnels are derived based on the nonlinear power-law failure criterion considering variable dilatancy angle and detaching velocity. Moreover, criterions with variable dilatancy angle on progressive failure occurrence for deep tunnels are obtained. Then, the analytical predictions obtained in this paper are compared with experimental testing results, which indicate that the impacts of variable detaching velocity on the shape curves of the several continuous collapsing blocks should be considered to obtain more consistent prediction results with the corresponding experimental testing results.

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Abbreviations

L 1 :

Half-width of the first collapsing block

h 1 :

Intercept in y axis of the first collapsing block

L 2 :

Half-width of the second collapsing block

h 2 :

Intercept in y axis of the second collapsing block

R :

Tunnel radius

w :

Thickness of the plastic detaching zone

g(x):

Function describing the shape of a circular tunnel

f(x):

Shape curves of the collapsing blocks

f 1(x):

Shape curves of the first collapsing blocks

f 2(x):

Shape curves of the second collapsing blocks

m :

Nonlinear coefficient

c 0 :

Initial cohesion of soil at zero stress

J :

Functional of f(x), total potential energy of the studied system

U i :

Strain energy of the internal forces on the detaching zone

W e :

Applied loads of the detaching surface

P :

Parameter describing the variable detaching velocity

Q :

Parameter describing the variable detaching velocity

P i :

Overall weight of each collapsing block

ρ :

Weight per unit volume of the rock mass

σ n :

Normal stress on the failure surface

τ n :

Shear stress on the failure surface

σ t :

Absolute value of tensile stress when τ = 0

ψ :

Dilatancy angle

η :

Dilative coefficient

K ψ :

Dilatancy factor

γ p :

Plastic shear strain

η′ :

Angle between u and the vertical direction

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Acknowledgements

The authors appreciate the support from the Fundamental Research Funds for the Central Universities of China (Grant no. 2015YJS128).

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Authors and Affiliations

  1. Underground Polis Academy of Shenzhen University, Shenzhen, 518060, China

    Kaihang Han

  2. Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, 90095, USA

    Kaihang Han & Jiann-Wen Woody Ju

  3. Beijing Municipal Construction Co., Ltd, Beijing, 100048, China

    Heng Kong

  4. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Mengshu Wang

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  1. Kaihang Han
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  2. Jiann-Wen Woody Ju
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  3. Heng Kong
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  4. Mengshu Wang
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Correspondence to Kaihang Han.

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Han, K., Ju, JW.W., Kong, H. et al. Functional Catastrophe Analysis of Progressive Failures for Deep Tunnel Roof Considering Variable Dilatancy Angle and Detaching Velocity. Rock Mech Rock Eng 52, 3987–3997 (2019). https://doi.org/10.1007/s00603-019-01808-6

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  • DOI: https://doi.org/10.1007/s00603-019-01808-6

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