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An Illustration of Determining Quantitatively the Rock Mass Quality Parameters of the Hoek–Brown Failure Criterion

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Abstract

In tunneling, determining quantitatively the rock mass strength parameters of the Hoek–Brown (HB) failure criterion is useful since it can improve the reliability of the design of tunnel support systems. In this study, a quantitative method is proposed to determine the rock mass quality parameters of the HB failure criterion, namely the Geological Strength Index (GSI) and the disturbance factor (D) based on the structure of drilling core and weathering condition of rock mass combined with acoustic wave test to calculate the strength of rock mass. The Rock Mass Structure Index and the Rock Mass Weathering Index are used to quantify the GSI while the longitudinal wave velocity (V p) is employed to derive the value of D. The DK383+338 tunnel face of Yaojia tunnel of Shanghai–Kunming passenger dedicated line served as illustration of how the methodology is implemented. The values of the GSI and D are obtained using the HB criterion and then using the proposed method. The measured in situ stress is used to evaluate their accuracy. To this end, the major and minor principal stresses are calculated based on the GSI and D given by HB criterion and the proposed method. The results indicated that both methods were close to the field observation which suggests that the proposed method can be used for determining quantitatively the rock quality parameters, as well. However, these results remain valid only for rock mass quality and rock type similar to those of the DK383+338 tunnel face of Yaojia tunnel.

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Fig. 1

Reproduced with permission from Marinos and Hoek (2000)

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Abbreviations

σ 1 :

The maximum effective stress

σ 3 :

The minimum effective stress

σ ci :

The uniaxial compressive strength of the intact rock

m i :

The Hoek–Brown constant of the intact rock

m b :

Extrapolates the intact rock constant m i to the rock mass

s :

The constant which depends upon the rock mass’s characteristics

a :

The constant which depends upon the rock mass’s characteristics

GSI:

Geological Strength Index

D :

Disturbance parameters

\( d_{\hbox{max} }^{{{\text{GSI}},L}} ,\,\,d_{\hbox{max} }^{{{\text{GSI}},F}} \) :

The difference between the maximum and minimum values of the GSI value of the Laisvall and Fictitious mine tunnel

\( d_{\hbox{max} }^{D,L} ,\,\,d_{\hbox{max} }^{D,F} \) :

The difference between the maximum and minimum values of the D value of the Laisvall and Fictitious mine tunnel

\( \bar{x} \) :

The average value of the GSI or D value

s :

The standard deviation of the GSI or D value

RSI:

Rock Mass Structure Index

RWI:

Rock Mass Weathering Index

RQD:

Rock Quality Designation

WI:

The weathering index of weathered rock mass

WI′:

The weathering index of fresh rock mass

(X) a :

The atomic proportion of element X

(X–O) b :

The bond strength of element X with oxygen

ρ :

The density of rock mass

δ :

The stress components of rock mass

u, v, w :

The displacements components of rock mass along with x, y, z directions

e :

The volumetric strain

λ :

Lame coefficient

G :

Modulus of rigidity

∇2 :

Laplace operator

V (p,s) :

The acoustic wave speed

V p :

The velocity of longitudinal wave

V s :

The velocity of transverse wave

E m :

The elasticity modulus

μ :

Poisson’s ratio

V p,UD :

The velocity of longitudinal wave in the rock mass before tunnel excavation

V p,D :

The velocity of longitudinal wave in the rock mass after tunnel excavation

E m,UD :

The elasticity modulus of rock mass before tunnel excavation

E m,D :

The elasticity modulus of rock mass after tunnel excavation

ζ :

The reduced ratio of velocity of longitudinal wave

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Acknowledgements

This study is financially supported by the National Natural Science Foundation of China (Grants No. 41672260) and the Natural Science Foundation Key Projects of Hubei Province (Grant No. 2013CFA110). The authors greatly appreciate the helpful comments and suggestions of the anonymous reviewers.

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Authors and Affiliations

  1. Faculty of Engineering, China University of Geosciences, Wuhan, People’s Republic of China

    Li Wu & Bo Li

  2. School of Mining and Geosciences, Nazarbayev University, Astana, 010000, Kazakhstan

    Amoussou Coffi Adoko

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  1. Li Wu
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  2. Amoussou Coffi Adoko
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Correspondence to Li Wu.

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Wu, L., Adoko, A.C. & Li, B. An Illustration of Determining Quantitatively the Rock Mass Quality Parameters of the Hoek–Brown Failure Criterion. Rock Mech Rock Eng 51, 1063–1076 (2018). https://doi.org/10.1007/s00603-017-1375-z

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