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Effect of Spatial Variability on Disc Cutters Failure During TBM Tunneling in Hard Rock

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Abstract

This study examines the effect of variations of the rock property and TBM parameters on the cutter failure. A new disc cutter wear model is developed by coupling Archard’s model and TBM cutter kinematics. The rock property and the TBM parameters are modelled as anisotropic cross-correlated log-normal random fields. The proposed model with a discretized algorithm allows a quantitative evaluation of the possible cutter failure during the TBM tunneling. The failure of the cutter head system is characterized by a random failure pattern and its failure can be evaluated using a probability method. With this technique, it can be a useful tool in providing an indication for the cutters replacement. Both the cutter and its mechanical system life are determined based on their allowed working distance of the TBM at the targeted safety level. The obtained results indicate that the life of the cutters and its cutter head system decreases with the presence of rock spatial heterogeneity. Finally, the obtained attenuation factors incorporating different randomness levels is practically useful for the evaluation of the cutter life.

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Abbreviations

V :

Volume of wear debris

L :

Relative sliding distance

F N :

Total normal load applied to the material

H :

Vickers hardness of the material

K :

Dimensionless wear coefficient

k C :

Comprehensive wear coefficient

\(\sigma_{c}\) :

Uniaxial compressive strength(UCS) of the rock

\(\sigma_{t}\) :

Tensile strength (TS) of the rock

C :

Dimensionless constant for the cutter-rock interaction

\(\varphi\) :

Angle of the arc of contact between the cutter and rock

S :

Spacing between two adjacent cutters

R pm :

Rotation speed of the cutter head

r :

Radius of the cutter

T :

Tip width of the cutter

v 1 :

Advance rate of the TBM

d s :

Diameter of wear flat in the Cerchar test

c:

Unit correction factor in the Cerchar test

F c :

Normal force used in the Cerchar test

s c :

Test distance in the Cerchar test

v 2 :

Rotation speed around the cutter’s axis

v 3 :

Rotation speed around the tunnel axis

\(t_{p}\) :

Duration of the interaction for each revolution of the cutter

R :

Installed radius of the cutter at the cutter head

\(\theta\) :

Angle between the calculation point and bottom point of the cutter

w 0 :

Angular velocity of the cutter around its axis

\(l_{p}\) :

Relative sliding distance for one revolution of the cutter

L s :

Length of the element in the model

\(l\) :

Relative sliding distance in the element length Ls

\(\delta V\) :

Cutter wear in the element length Ls

ICA :

Cerchar abrasivity index

u :

Mean value of the input parameters

\(\sigma\) :

Standard deviation of the input parameters

\(\theta_{h}\) :

Scale of fluctuation (SOF) of the input parameters

x :

Spatial centre coordinates of two elements

\(\xi_{i}\) :

Independent standard normal distribution variables

M:

Truncation term of the expansion

\(\lambda_{i}\) :

Eigenvalues of the autocorrelation function

\(\psi_{i} (x)\) :

Eigenfunctions of the autocorrelation function

\(\rho\) :

Cross-correlation coefficients of the input parameters

\(\rho_{cr}\) :

Cross-correlations matrix of the input parameters

\(u^{\ln }\) :

Logarithmic mean value of the input parameters

\(\sigma^{\ln }\) :

Logarithmic standard deviation of the input parameters

\(G(x)\) :

Standard normally distributed random field

\(G(x)^{\prime}\) :

Cross-correlated standard normal random field

\(L_{u}\) :

Lower triangular matrix obtained from the cross-correlations matrix

\(L_{u}^{T}\) :

Transposed matrix of \(L_{u}\)

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Acknowledgements

The authors gratefully acknowledge financial support from the National Basic Research Program of China (973 program) under Grant No. 2015CB057800 and the National Natural Science Foundation of China under Grant No. C19A1500010.

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Authors and Affiliations

  1. School of Civil Engineering, Beijing Jiaotong University, Beijing, China

    Jin Dalong, Shen Zhichao & Yuan Dajun

  2. Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore

    Jin Dalong & Shen Zhichao

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  1. Jin Dalong
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Correspondence to Shen Zhichao.

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Dalong, J., Zhichao, S. & Dajun, Y. Effect of Spatial Variability on Disc Cutters Failure During TBM Tunneling in Hard Rock. Rock Mech Rock Eng 53, 4609–4621 (2020). https://doi.org/10.1007/s00603-020-02192-2

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