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Estimation of Elastic Moduli of Non-persistent Fractured Rock Masses

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Fig. 1
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Fig. 5

Notes

  1. The terms fracture, crack and joint will be used interchangeably as is often the case in the literature.

  2. For the open crack, a statement from Budiansky and O’Connell (1976) is quoted here for explanation: “Crack closure effects are ignored; that is, the cracks are assumed to have very small openings between their opposite faces, and the crack edges are considered to be blunt, so that sufficiently small stresses do not produce contact between crack faces”.

Abbreviations

E 0 :

Young’s modulus of intact rock

G 0 :

Shear modulus of intact rock

ν 0 :

Poisson’s ratio of intact rock

K n :

Fracture normal stiffness

K s :

Fracture shear stiffness

E :

Effective elastic modulus of fractured rock mass

E ⊥i (E ∥i ):

Effective elastic modulus of fractured rock mass in the normal (shear) direction of the ith fracture sets

G :

Effective shear modulus of fractured rock mass

ν :

Effective Poisson’s ratio of fractured rock mass

a :

Half-length of fracture

r :

The distance from fracture center along its length

ρ :

Fracture density, defined as the number of fracture central points per square meter

θ :

Angle between loading direction and normal direction of fracture plane

u :

Normal displacement jump of fracture faces

\(\overline{u}\) :

Average normal displacement jump of fracture faces

V :

Shear displacement jump of fracture faces

σ n :

Resolved normal stress on fracture from far-field stress

τ s :

Resolved shear stress on fracture from far-field stress

σ k :

Tension stress of fractures

σ p :

Normal stress acting on fracture faces

\(\overline{{\sigma_{p} }}\) :

Averaged normal stress acting on fracture faces

Τ :

Far-field shear stress

ΔΣ :

The total excess elastic strain energy due to the existence of fractures

ΔΣ fn :

The elastic strain energy stored in fracture due to normal stress

ΔΣ rn :

The excess elastic strain energy stored in rock due to normal stress

ΔΣ rs :

The elastic strain energy stored in rock due to shear stress

ΔΣ fs :

The excess elastic strain energy stored in fracture due to shear stress

A ∼ D :

Parameters of excess strain energy terms for non-uniform deformation mode

\(\overline{A} \sim \overline{D}\) :

Parameters of excess strain energy terms for uniform deformation mode

σ n1 σ k1 :

The subscript 1 denotes the ultimate quantities in integrals

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Acknowledgments

The authors gratefully acknowledge the support of the Chinese Fundamental Research (973) Program through Grant Nos. 2013CB03600 and 2015CB057900 and the support of the National Natural Science Foundation of China (Grant Nos. 51225902, 51004097 and 51309217).

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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, China

    J. P. Yang, W. Z. Chen, D. S. Yang & H. M. Tian

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

    W. Z. Chen

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  1. J. P. Yang
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  2. W. Z. Chen
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  3. D. S. Yang
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  4. H. M. Tian
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Correspondence to W. Z. Chen.

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Yang, J.P., Chen, W.Z., Yang, D.S. et al. Estimation of Elastic Moduli of Non-persistent Fractured Rock Masses. Rock Mech Rock Eng 49, 1977–1983 (2016). https://doi.org/10.1007/s00603-015-0806-y

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