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Rock Mechanics and Rock Engineering

, Volume 50, Issue 10, pp 2695–2707 | Cite as

Analysis of the Seismic Performance of a Rock Joint with a Modified Continuously Yielding Model

Original Paper

Abstract

The problem of seismic wave transmission at a rock joint is a critical issue for aseismic affairs of underground rock engineering. Little attention has been given to the normal cyclic loading behavior of a joint during wave propagation. This paper introduces a modification to Cundall’s continuously yielding (CY) model. The original normal behavior of the CY model is upgraded by adding the capacity to account for sophisticated characteristics during normal cyclic loading. The proposed modified-CY (M-CY) model is verified through comparison with existing experimental data. The effects of various parameters in this M-CY model are discussed, indicating that the M-CY model is capable of fitting realistic test data. Subsequently, P-wave transmission across a M-CY joint is numerically performed and evaluated. The results show that the M-CY model exhibits more transmission and consequently less reflection than the linear model as the velocity magnitude of an incident impulse approaches its peak value. Furthermore, the compatibility of the joint under an incident P-wave can be revealed by the M-CY model. The seismic stability of the tailrace tunnel of the Baihetan Hydropower Plant, which is controlled by a large fault, is studied as an engineering application of the proposed model. Seismic analysis suggests that the tunnel’s main failure mode under an earthquake would be shear slip at the intersection of the tunnel ceiling and fault. A comparison between the proposed model and original CY model illustrates that the original model would give a failure mode that overestimates the fault opening during the earthquake.

Keywords

Seismic analysis Wave propagation Nonlinear joint Cyclic loading Continuously yielding model 

List of symbols

CY model

Continuously yielding model

\( {\text{en}} \)

Joint normal stiffness exponent of the CY model

\( {\text{es}} \)

Joint shear stiffness exponent of the CY model

\( d_{\text{m}} \)

Joint maximum closure

\( d_{{{\text{r}}\left( j \right)}} \)

Irrecoverable closure of loading path \( j \)

\( E \)

Young’s modulus

\( F \)

Tangent modulus governing parameter of the CY model

ISWZ

Interlayer shear weakness zone

\( k_{\text{n}} \)

Joint normal stiffness

\( k_{{{\text{ni}}\left( j \right)}} \)

Joint initial normal stiffness of loading path \( j \)

\( k_{\text{s}} \)

Joint shear stiffness

\( k_{\text{si}} \)

Joint initial shear stiffness

\( {\text{LP}}_{\left( j \right)} \)

Loading path \( j \)

M-CY model

Modified continuously yielding model

\( u_{\text{n}} \)

Joint normal displacement

\( u_{\text{s}} \)

Joint shear displacement

\( \alpha_{1} ,\alpha_{2} ,\beta_{1} ,\beta_{2} \)

Parameters of the M-CY model

\( \sigma_{\text{n}} \)

Joint normal stress

\( \sigma_{\text{s}} \)

Joint shear stress

Notes

Acknowledgements

This study was financially supported by the National Basic Research Program of China (no. 2015CB057905), the National Key R&D Program of China (no. 2016YFC0401803) and the National Natural Science Foundation of China (Nos. 51409263, 41672319 and 11472292).

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Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  • Zhen Cui
    • 1
    • 2
  • Qian Sheng
    • 1
  • Xianlun Leng
    • 1
  • Yalina Ma
    • 1
  1. 1.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina
  2. 2.PowerChina Huadong Engineering Corporation LimitedHangzhouChina

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