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Methodology for Establishing Comprehensive Stress Paths in Rocks During Hollow Cylinder Testing

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Abstract

We here systematically investigated the methodology for establishing comprehensive stress paths with the aim of developing hollow cylinder apparatuses for rock mechanics. The research was based on the stress combination in element of hollow cylinder sample with varied loading analysis treatment. For this purpose, we discussed the mechanism underlying the variations in principal stress magnitude and principal stress rotation. The orientation angle of the major principal stress was defined in an alternative prospect. Then a series of stress paths was introduced, including the hydrostatic pressure stress path, principal stress magnitude variation stress path on the deviatoric plane, pure principal stress rotation stress path, and the complex stress path coupling the variation in the magnitude of principal stress and principal stress rotation effect. The comprehensive stress paths were analyzed with rock mechanical theory and a mathematical approach. The suggested loading methods were examined using simulation loading tests, laboratory case tests and special case verification. The results showed successful completion of different stress paths. The proposed methodology was first investigated systematically in rock mechanics, contributing to development of the new hollow cylinder apparatus and complex rock engineering simulation.

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Abbreviations

\(F\), \({M_{\text{t}}}\), \({P_{\text{e}}}\), \({P_i}\) :

Vertical load, torque, external radial pressure, and internal radial pressure on HCA specimen

\({\tilde {\sigma }_z}\), \({\tilde {\sigma }_r}\), \({\tilde {\sigma }_\theta }\), \({\tilde {\tau }_{z\theta }}\) :

Vertical stress, radial stress, circumferential stress, and shear stress in HCA specimen

\({\sigma _z}\), \({\sigma _r}\), \({\sigma _\theta }\), \({\tau _{z\theta }}\) :

Average vertical stress, radial stress, circumferential stress, and shear stress in a continuum

\({R_{\text{e}}}\) :

External specimen radii

\({R_{\text{i}}}\) :

Internal specimen radii

\(\sigma _{z}^{\prime }\) :

Principal stress corresponding to the vertical stress

\(\sigma _{\theta }^{\prime }\) :

Principal stress corresponding to the circumferential stress

\(\alpha\) :

Rotation angle of the major principal stress axis

\({\sigma _{13}}\), \({\sigma _{31}}\), \({\tau _{13}}\),\({\tau _{31}}\) :

Opposite normal stresses and shear stresses in Mohr circle

\({\sigma _1}\), \({\sigma _2}\), \({\sigma _3}\) :

Major, intermediate, and minor principal stresses

\(\delta\) :

Rotation angle between \({\sigma _1}\) and \({\sigma _{13}}\) in Mohr circle

\({\theta _\sigma }\) :

Lode angle

\({{\mathbf{\sigma }}_{ij}}\) :

Cauchy stress tensor

\({{\mathbf{S}}_{ij}}\) :

Stress deviator tensor

\({S_1}\), \({S_2}\), \({S_3}\) :

Major, intermediate, and minor principal stress deviators

\({J_2}\) :

Second deviatoric stress invariant

\(p\) :

Hydrostatic pressure

\(b\) :

Intermediate principal stress coefficient

\(q\) :

Equivalent shear stress

\(\dot {\alpha }\) :

Rotation rate of the major principal stress axis

\(R\) :

The downward thrust of piston rod produced by oil pressure

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Acknowledgements

We gratefully acknowledge financial support from the National Science Foundation of China (NSFC) (51704097, 51427803 and 51404240), the Scientific Instrument Developing Project of Chinese Academy of Sciences (YZ201553 and YZ201344), China National Key Basic Research Program under Grant No. 2014CB046902, the Key Opening Laboratory Project for Deep Mining Construction at Henan province (2015 KF-06), the Key Scientific Research Project of Henan Higher Education Institutions (16A560004) and Dr. Fund Projects of Henan Polytechnic University (B2016-65). Besides, the authors are also grateful to the editor Giovanni Barla and the anonymous reviewers for their many helpful comments, which have greatly improved this paper.

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Authors and Affiliations

  1. International Joint Research Laboratory of Henan Province for Underground Space Development and Disaster Prevention, School of Civil Engineering, Henan Polytechnic University, Jiaozuo, 454000, Henan, China

    Zhen Li

  2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Hui Zhou, Yue Jiang, Dawei Hu & Chuanqing Zhang

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  1. Zhen Li
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Correspondence to Zhen Li or Hui Zhou.

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Li, Z., Zhou, H., Jiang, Y. et al. Methodology for Establishing Comprehensive Stress Paths in Rocks During Hollow Cylinder Testing. Rock Mech Rock Eng 52, 1055–1074 (2019). https://doi.org/10.1007/s00603-018-1628-5

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