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An Experimental Study on the Pre-Peak Unloading Damage Evolution of Marble

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Abstract

The behavior of rock damage evolution under unloading conditions is of utmost importance for the analysis of the stress-induced failure of overstressed rock masses. In this paper, a new experimental approach, the incrementally cyclic loading–unloading pressure test (ICLUP test), is designed to quantify stress-induced micro-fracturing and fracturing under the condition of confining pressure reduction. The experimental results demonstrate that the pre-peak damage and deformation characteristics of marble specimens may be easily quantified by irreversible strains, and two damage stages, namely, the linear steady stage and the nonlinear unsteady stage, which are, respectively, represented as a linear steady rate and a nonlinear unsteady rate of damage evolution, occur along with the increase of unloading damage. The new model is proposed to describe the features of pre-peak unloading damage evolution, and the physical meanings and ranges of its material parameters are explained and analyzed. Furthermore, the evolution of volumetric dilation and elastic parameters which occurs along with the increase of unloading damage is revealed. Also discussed in this paper are the inhomogeneity and initial damage of specimens, as well as related research planned to be performed in the future.

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Abbreviations

D :

Damage variable

D 0 :

Initial damage

D ax :

Damage variable of axial strain

D lat :

Damage variable of lateral strain

D vol :

Damage variable of volumetric strain

E :

Young’s modulus

K :

Bulk modulus

G :

Shear modulus

t :

Damage proportion factor

α:

Linear damage rate

β:

Nonindependent model parameter

σ1 :

Axial stress or the maximum principal stress

\( \sigma_{3}^{0} \) :

Hydrostatic pressure

σ3 :

Lateral or minimum principal stress

Δσ1 :

Axial or maximum principal stress increment

Δσ2 :

Intermediate principal stress increment

Δσ3 :

Lateral or minimum principal stress increment

\( \varepsilon_{\text{ax}}^{\text{p}} \) :

Permanent axial strain

\( \varepsilon_{\text{lat}}^{\text{p}} \) :

Permanent lateral strain

\( \varepsilon_{\text{vol}}^{\text{p}} \) :

Permanent volumetric strain

\( \dot{\varepsilon }_{\text{v}}^{\text{p}} \) :

Volumetric plastic increment

\( \dot{\varepsilon }_{1}^{\text{p}} \) :

Axial plastic strain increment

\( \dot{\varepsilon }_{3}^{\text{p}} \) :

Lateral plastic strain increment

\( \Updelta \varepsilon_{1}^{\text{e}} \) :

Axial elastic strain increment

\( \Updelta \varepsilon_{3}^{\text{e}} \) :

Lateral elastic strain increment

ν:

Poisson’s ratio

Ψ:

Dilatancy angle

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Acknowledgments

The authors gratefully acknowledge the financial support from the National Special Funds of China for Major State Basic Research Project under Grant No. 2010CB732006 and the National Natural Science Foundation of China under Grant No. 51079144. The first author also wishes to thank Prof. Feng Dai (College of Water Resource and Hydropower, Sichuan University) for the helpful discussions on the work presented. Special thanks go to the two anonymous reviewers for their constructive comments.

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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, People’s Republic of China

    Shi-Li Qiu, Xia-Ting Feng, Jian-Qing Xiao & Chuan-Qing Zhang

  2. School of Civil Engineering and Architecture, Anyang Normal University, Anyang, 455000, People’s Republic of China

    Jian-Qing Xiao

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  1. Shi-Li Qiu
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  2. Xia-Ting Feng
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Correspondence to Shi-Li Qiu.

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Qiu, SL., Feng, XT., Xiao, JQ. et al. An Experimental Study on the Pre-Peak Unloading Damage Evolution of Marble. Rock Mech Rock Eng 47, 401–419 (2014). https://doi.org/10.1007/s00603-013-0394-7

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