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An Energy-Based Method to Determine Rock Brittleness by Considering Rock Damage

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Abstract

Accurate evaluations of rock brittleness are very significant in the engineering geology and geotechnical engineering fields. Most previous studies have adopted the stress–strain relationship to propose a series of indices for rock brittleness estimations but have seldom considered rock damage. Rock damage can be viewed as an energy dissipation process during rock deformation, which is closely related to rock brittleness. In this study, a new brittleness index (BI23) was proposed by considering rock damage, and the rock damage was calculated by the energy-based method. Then, the newly proposed rock brittleness index was validated by analyzing the variations in rock brittleness under increasing confining pressures and temperatures. The results indicate that the rock brittleness estimated by BI23 shows a significant drop in the case of increasing confining pressures and temperatures. To demonstrate its performance and advantages, a comparative study between the BI23 index and some previous indices was conducted by analyzing the stress–strain curves (SSC) of four rock types (e.g., limestone, marlite, feldspar lithic sandstone, and feldspathic quartz sandstone). The comparative study shows that the BI23 is able to produce more stable and consistent rock brittleness even for the same rock type under different tests, which is considered to be a major improvement over previous indices. Finally, the brittleness value distribution patterns of BI23 for normal and extreme conditions are discussed. It is suggested that the scope of rock brittleness evaluations under normal conditions should be defined to be between 0.5 (ductile) and 1 (brittle) in practical applications.

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Abbreviations

BI:

Brittleness index

BIs:

Brittleness indices

UCS:

Uniaxial compressive strength

SSC:

Stress–strain curve

CLT:

Cycling loading test

BTS:

Brazilian tensile strength

DM method:

Deformation modulus-based method

EN method:

Energy-based method

SS method:

Stress-based method

SA method:

Strain-based method

SEM:

Scanning electron microscope

E:

Loading elastic modulus

\(E_{0}\) :

Elastic modulus

M :

Post-peak elastic modulus

\(\rho\) :

Density

ν:

Poisson’s ratio

\(D_{i}\) :

Damage degree

\(U_{i}\) :

Total energy increment

\(U_{i}^{d}\) :

Dissipation energy

\(U_{i}^{e}\) :

Elastic energy increment

\(U_{T}^{d}\) :

Total dissipated energy

\(\sum U_{i}^{d}\) :

Accumulated dissipated energy

\(\sigma_{e}\) :

Stress at the elastic limit

\(\sigma_{p}\) :

Peak stress

\(\sigma_{r}\) :

Residual stress

\(\sigma_{1}\) :

Maximum principle stress

\(\sigma_{3}\) :

Minimum principle stress

\(\sigma_{3}\) :

Maximum tensile strength

\(\varepsilon_{e}\) :

Strain at the elastic limit

\(E_{d}\) :

Deformation energy

\(E_{G}\) :

Surface energy

\(\varepsilon_{p}\) :

Strain at the peak point

\(\varepsilon_{i}\) :

Irreversible deformation

\(\varepsilon_{r}\) :

Strain at the residual point

\(\varepsilon_{tot}\) :

Total strain at failure

\(\varepsilon_{el}\) :

Elastic strain at failure

\(W_{ir}\) :

Unrecoverable elastic energy

\(W_{pe}\) :

Pre-peak elastic strain energy

\(W_{r}\) :

Restore elasticity energy

\(W_{tos}\) :

Total strain energy

\(W_{el}\) :

Elastic energy at failure

\(W_{tot}\) :

Total energy at failure

\(W_{et}\) :

Total elastic energy

\(W_{er}\) :

Rupture energy

\(W_{e}\) :

Consumed elastic energy

\(W_{p}\) :

Dissipated plastic energy

\(dW_{r}\) :

Rupture energy increment

\(dW_{e}\) :

Unloading elastic energy increment

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Acknowledgements

This study has received financial support from the National Natural Sciences Foundation of China (Grant No. 42177159 & No. 41877253) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant No. CUG2106304). The supports are gratefully acknowledged.

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Authors and Affiliations

  1. School of Environmental Studies, China University of Geosciences, Wuhan, 430078, China

    Wei Wang, Yu Wang, Bo Chai, Linxiao Xing & Ziheng Xia

  2. Hubei Key Laboratory of Yangtze Catchment Environmental Aquatic Science, Wuhan, 430078, China

    Wei Wang & Bo Chai

  3. Three Gorges Research Center for Geohazards, Ministry of Education, Wuhan, 430074, China

    Juan Du

  4. Research Center for Geohazards Monitoring and Warning in Three Gorges Reservoir, Wanzhou, 404000, China

    Wei Wang, Bo Chai & Juan Du

  5. The Institute of Hydrogeology and Environmental Geology, CAGS, Shijiazhuang, 050061, China

    Linxiao Xing

  6. Technology Innovation Center of Geothermal & Hot Dry Rock Exploitation and Development, MNR, Shijiazhuang, 050061, China

    Linxiao Xing

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  1. Wei Wang
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  2. Yu Wang
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  3. Bo Chai
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Correspondence to Bo Chai.

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Wang, W., Wang, Y., Chai, B. et al. An Energy-Based Method to Determine Rock Brittleness by Considering Rock Damage. Rock Mech Rock Eng 55, 1585–1597 (2022). https://doi.org/10.1007/s00603-021-02727-1

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