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Analysis of EDZ Development of Columnar Jointed Rock Mass in the Baihetan Diversion Tunnel

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Abstract

Due to the time dependency of the crack propagation, columnar jointed rock masses exhibit marked time-dependent behaviour. In this study, in situ measurements, scanning electron microscope (SEM), back-analysis method and numerical simulations are presented to study the time-dependent development of the excavation damaged zone (EDZ) around underground diversion tunnels in a columnar jointed rock mass. Through in situ measurements of crack propagation and EDZ development, their extent is seen to have increased over time, despite the fact that the advancing face has passed. Similar to creep behaviour, the time-dependent EDZ development curve also consists of three stages: a deceleration stage, a stabilization stage, and an acceleration stage. A corresponding constitutive model of columnar jointed rock mass considering time-dependent behaviour is proposed. The time-dependent degradation coefficient of the roughness coefficient and residual friction angle in the Barton–Bandis strength criterion are taken into account. An intelligent back-analysis method is adopted to obtain the unknown time-dependent degradation coefficients for the proposed constitutive model. The numerical modelling results are in good agreement with the measured EDZ. Not only that, the failure pattern simulated by this time-dependent constitutive model is consistent with that observed in the scanning electron microscope (SEM) and in situ observation, indicating that this model could accurately simulate the failure pattern and time-dependent EDZ development of columnar joints. Moreover, the effects of the support system provided and the in situ stress on the time-dependent coefficients are studied. Finally, the long-term stability analysis of diversion tunnels excavated in columnar jointed rock masses is performed.

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Abbreviations

\(C_{0}\) :

Cohesion of the basalt rock (MPa)

\(C_{{{\text{j}}3}}\) :

Cohesion of the horizontal joint inside a column (MPa)

\({\text{d}}\sigma\) :

Stress increment (MPa)

\(E_{1}\) :

Elastic moduli of the basalt perpendicular to the column axis (GPa)

\(E_{2}\) :

Elastic moduli of the basalt parallel to the column axis (GPa)

\(f_{\text{j1}}^{\text{s}}\) :

Shear criterion of joint between columns (MPa)

\(f_{\text{j1}}^{\text{t}}\) :

Tension criteria of joint between columns (MPa)

\(f_{\text{j2}}^{\text{s}}\) :

Shear criterion of plumose joint inside a column (MPa)

\(f_{\text{j2}}^{\text{t}}\) :

Tension criteria of plumose joint inside a column (MPa)

\(f_{\text{j3}}^{\text{s}}\) :

Shear criteria for the horizontal joint inside a column (MPa)

\(f_{\text{j3}}^{\text{t}}\) :

Tension criteria for the horizontal joint inside a column (MPa)

\(G\) :

Shear modulus of the basalt (GPa)

\(h_{{{\text{j}}3}}\) :

Shear-tensile boundary mixed criteria for the horizontal joint inside a column (MPa)

\({\text{JCS}}^{\text{j1}}\) :

Joint wall compressive strength of joint between columns (MPa)

\({\text{JCS}}^{\text{j2}}\) :

Joint wall compressive strength of plumose joint inside a column (MPa)

\({\text{JRC}}^{\text{j1}}\) :

Joint roughness coefficient of joint between columns

\({\text{JRC}}^{\text{j2}}\) :

Joint roughness coefficient of plumose joint inside a column

\(\left[ K \right]\) :

Global stiffness matrix (MPa)

\(K_{\text{JRC}}\) :

Time-dependent degradation coefficients of joint roughness coefficient

\(K_{{\varphi_{r} }}\) :

Time-dependent degradation coefficients of residual friction angle

\(\left[ {R^{ji} } \right]\) :

Transformation matrix of the ith set of joint planes (MPa)

\(r\) :

Tunnel radius (m)

\(\delta\) :

Wall displacement of tunnel (mm)

\(\phi_{0}\) :

Internal friction angle of the basalt (°)

\(\phi_{{{\text{j}}3}}\) :

Internal friction angle of the horizontal joint inside a column (°)

\(\phi_{\text{m}}^{\text{j1}}\) :

Friction angle considering dilatancy effects of joint between columns (°)

\(\phi_{\text{m}}^{\text{j2}}\) :

Friction angle considering dilatancy effects of plumose joint inside a column (°)

\(\phi_{\text{r}}^{\text{j1}}\) :

Residual friction angle of joint between columns (°)

\(\phi_{\text{r}}^{\text{j2}}\) :

Residual friction angle of plumose joint inside a column (°)

\(\sigma_{3'3'}^{\text{j1}}\) :

Normal stress on the joint between columns (MPa)

\(\sigma_{3'3'}^{\text{j2}}\) :

Normal stress on the plumose joint inside a column (MPa)

\(\sigma_{3'3'}^{\text{j3}}\) :

Normal stress on the horizontal joint inside a column (MPa)

\(\sigma_{\text{j1}}^{\text{t}}\) :

Tensile strength of joint between columns (MPa)

\(\sigma_{\text{j2}}^{\text{t}}\) :

Tensile strength of plumose joint inside a column (MPa)

\(\sigma_{\text{j3}}^{\text{t}}\) :

Tensile strength of the horizontal joint inside a column (MPa)

\(\sigma_{\text{t}}\) :

Tensile strength of the basalt rock (MPa)

\(\varepsilon\) :

Strain tensor of the columnar jointed rock mass (MPa)

\(\varepsilon^{\text{I}}\) :

Strain tensor of the intact rock (MPa)

\(\varepsilon^{\text{J}}\) :

Strain tensor of the joints (MPa)

\(\varepsilon_{\text{a}}\) :

Threshold strain that rock mass entered an acceleration stage (mm/m)

\(\varepsilon_{\text{s}}\) :

Threshold strain that rock mass entered a stabilization stage (mm/m)

\(\varepsilon_{\text{t}}\) :

Tunnel strain (mm/m)

\(\tau_{\text{j1}}\) :

Shear stress on the joint between columns (MPa)

\(\tau_{\text{j2}}\) :

Shear stress on the plumose joint inside a column (MPa)

\(\tau_{\text{j3}}\) :

Shear stress on the horizontal joint inside a column (MPa)

\(\upsilon_{1}\) :

Poisson’s ratio of the basalt perpendicular to the column axis

\(\upsilon_{2}\) :

Poisson’s ratio of the basalt parallel to the column axis

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Acknowledgments

Financial support from the National Natural Science Foundation of China under Grant no. 11232014 is gratefully acknowledged. The authors also thank Professors Y. L. Fan, X. D. Zhu, and A. C. Shi for their kind help for the field investigation, and the China Three Gorges Project Corporation for their technical assistance. In addition, the authors would like to acknowledge two anonymous reviewers for their helpful suggestions and comments.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, People’s Republic of China

    Xian-Jie Hao, Xia-Ting Feng, Quan Jiang & Shao-Jun Li

  2. School of Resources and Civil Engineering, Northeastern University, Shenyang, 110004, People’s Republic of China

    Cheng-Xiang Yang

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  1. Xian-Jie Hao
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Correspondence to Xia-Ting Feng.

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Hao, XJ., Feng, XT., Yang, CX. et al. Analysis of EDZ Development of Columnar Jointed Rock Mass in the Baihetan Diversion Tunnel. Rock Mech Rock Eng 49, 1289–1312 (2016). https://doi.org/10.1007/s00603-015-0829-4

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  • DOI: https://doi.org/10.1007/s00603-015-0829-4

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