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Stability Analysis of Surrounding Rock in Tunnel Crossing Water-Rich Fault Based on Catastrophe Theory

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Abstract

The failure of surrounding rock in tunnel crossing water-rich fault is a sudden damage phenomenon with obvious nonlinear and abrupt characteristics, which is characterized by the uncertainty of deformation, the nonlinearity of constitutive relation and the mutation of failure process. Based on the mechanical model of tunnel-fault system, the cusp catastrophe model of the failure of surrounding rock in tunnel crossing water-rich fault is established. Combining with the field monitoring data, the model is employed to judge the stability of surrounding rock. Results show that the deformation curve of tunnel vault has a good correlation to the cusp catastrophe model, and the results for stability analysis is consistent with the actual situation. The influences that the strength of rock mass, groundwater and fault width have on the failure of tunnel are further discussed, which provides scientific guidelines to the construction of tunnel.

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Abbreviations

x, y :

State variables

a, b, c :

Control variables

V(x):

Potential function

H :

Height of tunnel

Α :

Fault dip

h :

Width of fault

u :

Fault displacement

R e :

Radius of elastic zone

R p :

Radius of plastic zone

Mg :

Gravity of fractured rock mass

f(ω):

Weakening parameter

ω :

Water content

k R :

Saturation softening coefficient

G e :

Initial shear modulus

u 0 :

Average strain

m :

Brittleness index

G p :

Shear modulus

τ m :

Residual shear strength

l e :

Slip zone length in the elastic zone of fault

l p :

Slip zone length in the plastic zone of fault

ξ :

Geometrical–mechanical parameters

k :

Stiffness ratio of fault

f :

Water weakening parameter ratio

t :

Cumulative time

c i and d i :

Calculating parameters

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 41672260) and Hunan University of Science and Technology Doctoral Research Start-up Foundation (Grant No. E51884).

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Authors and Affiliations

  1. Hunan Provincial Key Laboratory of Geotechnical Engineering for Stability Control and Health Monitoring, Hunan University of Science and Technology, Xiangtan, China

    Yaxiong Peng

  2. College of Engineering, China University of Geoscieneces, Wuhan, China

    Li Wu & Chunhui Chen

  3. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, China

    Jian Yue

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  1. Yaxiong Peng
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  2. Li Wu
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  3. Chunhui Chen
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  4. Jian Yue
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Correspondence to Yaxiong Peng.

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Peng, Y., Wu, L., Chen, C. et al. Stability Analysis of Surrounding Rock in Tunnel Crossing Water-Rich Fault Based on Catastrophe Theory. Geotech Geol Eng 38, 415–423 (2020). https://doi.org/10.1007/s10706-019-01032-7

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