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Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4387–4402 | Cite as

Numerical Study on Anisotropy of the Representative Elementary Volume of Strength and Deformability of Jointed Rock Masses

  • Zhengzhao LiangEmail author
  • Na Wu
  • Yingchun Li
  • Hong Li
  • Wanrun Li
Original Paper
  • 203 Downloads

Abstract

Representative elementary volume (REV) is a significant parameter in analyzing the size effect and the continuous media theory of natural jointed rock masses. Generalized RVEs, which include the REV of jointed rock masses (RREV) and the REV of mechanical parameters of jointed rock masses (PREV), were introduced and investigated based on the anisotropy of natural jointed rock masses. A two-dimensional model was developed based on the available geology, material heterogeneity and Monte Carlo simulation of joint network. The size effect and anisotropy of the elastic modulus and the uniaxial compressive strength (UCS) of jointed rock masses were investigated, and then, the PREV was determined. Numerical results showed that the PREVs for both the elastic modulus and UCS exhibited strong anisotropy. The RREV dimension was determined as 14 × 14 m based on the PREV of different rotational directions. The equivalent mechanical parameters of the elastic modulus and UCS were determined for different rotational directions. It is suggested that the anisotropy of the PREV should be considered when the RREV and corresponding equivalent mechanical parameters are assessed.

Keywords

Jointed rock masses Scale effect Anisotropy Representative elementary volume (REV) 

Abbreviations

\(\mu\)

Various mechanical parameters of individual elements

\(\mu_{\text{o}}\)

Mean mechanical parameters of individual elements

\(m\)

Heterogeneity index

\(E\)

Elastic modulus of the damaged elements

\(E_{\text{o}}\)

Elastic modulus of the undamaged elements

\(D\)

Damage variable

\(\lambda\)

Residual strength coefficient

\(f_{\text{to}}\)

Uniaxial tensile strength

\(f_{\text{tr}}\)

Residual tensile strength

\(\varepsilon_{\text{to}}\)

Threshold strain

\(\varepsilon_{\text{tu}}\)

Ultimate tensile strain

η

Ultimate strain coefficient

\(\sigma_{1}\)

Maximum principal stress

\(\sigma_{3}\)

Minimum principal stress

\(f_{\text{co}}\)

Uniaxial compressive strength

\(\varphi\)

Internal friction angle of element

\(f_{\text{cr}}\)

Residual uniaxial compressive strength

\(\varepsilon_{\text{co}}\)

Compressive strain at the elastic limit

\(K_{i}\)

Variation coefficient with model size i

\(A_{i}\)

Mechanical parameter with model size i

\(\bar{A}_{i}\)

Average mechanical parameter with model size greater than or equal to i

\({\text{RREV}}\)

Representative elementary volume of jointed rock masses

\({\text{PREV}}\)

Representative elementary volume of mechanical parameter of jointed rock masses

Notes

Acknowledgements

This study is supported by the National Natural Science Foundation of China (Grant No. 51779031 and 51678170).

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Zhengzhao Liang
    • 1
    Email author
  • Na Wu
    • 1
  • Yingchun Li
    • 1
  • Hong Li
    • 1
  • Wanrun Li
    • 1
  1. 1.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina

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