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Displacement Forecasting Method in Brittle Crack Surrounding Rock Under Excavation Unloading Incorporating Opening Deformation

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Abstract

Splitting failure, which is recognized as a special engineering geology phenomenon, occurs continually in the brittle rock mass of caverns during underground excavation. In this paper, a splitting model of linear slippage crack groups is built with fracture mechanics, energy analysis, and crack extension theories. Considering intrinsic cracks in rock mass and change of outer stress, intrinsic cracks propagate into macroscopical splitting cracks that are approximately parallel to the side wall of caverns. The splitting criterion of cavern rock mass and the method for predicting displacement in view of splitting opening displacement are proposed. In the end, the forecasting method is applied to the Jinping-I Hydropower Station, underground caverns engineering in China, the splitting failure zone and forecasting displacement are accordant with the monitoring data. The new forecasting displacement method is proven to contribute to the construction of similar underground caverns.

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Abbreviations

\(c\) :

Half of the initial crack length

\(l_{0}\) :

Half of the wing crack length

\(w\) :

Half of the neighboring crack space

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

Lateral deformation of brittle rock mass

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

Lateral deformation (external far-field force)

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

Lateral opening deformation (microcrack propagation)

\(U\) :

Complementary energy of system

\(P\) :

Generalized force

\(\Delta\) :

Generalized displacement

\(\Delta U_{\text{e}}\) :

Strain energy of element

\(\sigma_{i}\) :

Horizontal stress of element

\(\Delta V_{i}\) :

Element volume

\(\sigma_{1}\) :

Maximum compressive stress

\(\sigma_{2}\) :

Intermediate compressive stress

\(\sigma_{3}\) :

Lateral compressive stress

\(\sigma_{n}\) :

Normal stress

\(\phi\) :

Internal friction angle

\(\tau^{*}\) :

Effective shear stress

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

Stress intensity factor

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

Fracture toughness

Γ:

Density function of splitting opening deformation

\(E_{0}\) :

Modulus of deformation in undisturbed surrounding rock

\(K_{I}\) :

Modulus of deformation in excavated surrounding rock

\(\theta\) :

Angle between initial crack surface and horizontal direction

\(\upsilon\) :

Poisson’s ratio

\(\chi\) :

Initial crack density

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Acknowledgments

The authors express sincere appreciation to anonymous reviewers for their valuable comments on improving this study. The study is jointly supported by grants from the National Natural Science Foundation of China (Grant No. 41372294, 41002098 and 41102184), Program for Changjiang Scholars and Innovative Research Team in University of China (No. IRT13075), Shandong Province Transportation Science and Technology Project (Grant No. 2008Y002) and China Scholarship Council.

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Authors and Affiliations

  1. School of Civil Engineering, Shandong Jianzhu University, Jinan, 116024, China

    X. J. Li

  2. Geotechnical and Structural Engineering Research Center, Shandong University, Jinan, 250061, China

    W. M. Yang

  3. Institute for Infrastructure and Environment, University of Edinburgh, Edinburgh, EH9 3JL, UK

    L. G. Wang

  4. School of Geosciences, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JW, UK

    I. B. Butler

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  1. X. J. Li
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Correspondence to L. G. Wang.

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Li, X.J., Yang, W.M., Wang, L.G. et al. Displacement Forecasting Method in Brittle Crack Surrounding Rock Under Excavation Unloading Incorporating Opening Deformation. Rock Mech Rock Eng 47, 2211–2223 (2014). https://doi.org/10.1007/s00603-014-0599-4

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