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Obtaining Constitutive Relationship for Rate-Dependent Rock in SHPB Tests

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Abstract

A large number of tests have recently been conducted with the Split Hopkinson pressure bar (SHPB) method to determine the characteristics of rock dynamics. However, it is still impossible to get test results at a perfect constant strain rate from this set-up owing to the rate dependency of rock materials. For instance in most cases, dynamic behavior of rock can only be described with an average strain rate. The results from these methods, including rich strain rate information, frequently tend to be inexplicable or self-contradictory. The obtained stress–strain curves can then never be directly treated as constitutive curves as in static tests. In this paper, the reasons behind the controversial stress–strain results with current methods are analyzed. In addition, the requirement for the rock specimen to deform at a constant strain rate is demonstrated after theoretical analysis of correlations among specimen, deforming stress, incident stress, reflected stress and transmitted stress. With test results from SHPB by pulse shaper and special shape striker methods, the requirement is verified. Finally, the method of 3D scattergram considering stress–strain–strain rate simultaneously is brought up to get constitutive relationships of rate-dependent rock. The new method gives reasonable predictions for constitutive relationships of rock at different strain rates. At the same time, the new method has fewer requirements and has a wider application scope for SHPB tests.

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Acknowledgments

Financial support from the National Natural Science Foundation of China (50904079, 50934006) and PhD Programs Foundation of Chinese Education Ministry (200805331143) are greatly acknowledged. Our thanks are due to Prof Jian Zhao at Swiss Federal Institute of Technology Lausanne and Prof Richard Durham at the University of Western Australia for their help in the improvement of the paper. Also, the authors express their acknowledgements to the anonymous reviewers for their precious comments.

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Authors and Affiliations

  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Zilong Zhou, Xibing Li, Zhouyuan Ye & Kewei Liu

  2. School of Energy and Safety Engineering, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, People’s Republic of China

    Zhouyuan Ye

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  1. Zilong Zhou
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  2. Xibing Li
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  3. Zhouyuan Ye
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Correspondence to Xibing Li.

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Zhou, Z., Li, X., Ye, Z. et al. Obtaining Constitutive Relationship for Rate-Dependent Rock in SHPB Tests. Rock Mech Rock Eng 43, 697–706 (2010). https://doi.org/10.1007/s00603-010-0096-3

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  • DOI: https://doi.org/10.1007/s00603-010-0096-3

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