Particle breakage and energy dissipation of carbonate sands under quasi-static and dynamic compression

  • Yang XiaoEmail author
  • Zhengxin Yuan
  • Jian Chu
  • Hanlong Liu
  • Junyu HuangEmail author
  • S. N. Luo
  • Shun Wang
  • Jia Lin
Research Paper


Quasi-static and dynamic compression tests are conducted on carbonate sand using a Material Testing System and a modified split Hopkinson pressure bar, respectively. The particle size distributions (PSDs) of carbonate sand before and after loading are measured via laser diffractometry. The stress–strain curves demonstrate that the carbonate sand investigated in this study exhibits strain rate effects. The stress–strain curves show slightly different features for quasi-static and dynamic loading conditions. The particle breakage extent, which is quantified from the PSDs of the samples before and after loading, is investigated at different stress levels and input energy values. The breakage efficiency under the quasi-static loading condition is higher than that under the dynamic loading condition. As a result, the particle breakage extent is higher under the quasi-static loading condition than under the dynamic loading condition at the same stress level. Furthermore, the particle breakage modes are highly dependent on stress. The breakage modes under the dynamic loading condition change from attrition and abrasion at low stress levels, resulting in the appearance of plateaus in the grading curves, to fracture at high stress levels, resulting in the disappearance of plateaus in the grading curves.

Graphical abstract


Carbonate sand Dynamic response Energy efficiency Particle size distribution Particle breakage 

List of symbols

B15, B10, Bg, and Bf

Single-number breakage index

Br, BrE, IG, and BBI

Area ratio breakage index


Specific gravity


Uniformity coefficient


Particle diameters at 10% of the PSD (mm)


Particle diameters at 60% of the PSD (mm)


Axial strain of the sample

\( \dot{\varepsilon }_{a} \)

Axial strain rate of the sample (s−1)

\( \sigma_{a}^{\prime } \)

Axial stress of the sample (MPa)


Young’s modulus of the bar material (GPa)


Cross-sectional area of the bar material (mm2)


Elastic wave speed of the bar material (m/s)


Cross-sectional area of the sample (mm2)


Length of the sample (mm)


Strain of the incident bar


Strain of the transmission bar


Pulse duration (µs)


Particle diameter (mm)


Maximum particle diameter (mm)


Minimum particle diameter (mm)


Percentage finer (%)


Fractal dimension

\( \sigma_{ay}^{\prime } \)

Yield stress of the sample (MPa)


Breakage potential (mm)


Total breakage (mm)


Material constant


Material constant


Specific work \( \left( {{\text{MJ/m}}^{3} } \right) \)


Axial strain upon yielding


Threshold of the specific work \( \left( {{\text{MJ/m}}^{3} } \right) \)


Initial porosity


Compressibility index


Characteristic specific work \( \left( {{\text{MJ/m}}^{3} } \right) \)


Regression parameter



The authors would like to acknowledge the financial support from the 111 Project (Grant No. B13024), the National Natural Science Foundation of China (Grant Nos. 51678094, 51509024, 51578096), the Special Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2017T100681), and the project funded by the China Postdoctoral Science Foundation (Grant No. 2016M590864).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yang Xiao
    • 1
    • 2
    • 3
    Email author
  • Zhengxin Yuan
    • 2
  • Jian Chu
    • 4
  • Hanlong Liu
    • 2
  • Junyu Huang
    • 5
    Email author
  • S. N. Luo
    • 5
    • 6
  • Shun Wang
    • 7
  • Jia Lin
    • 7
  1. 1.Key Laboratory of New Technology for Construction of Cities in Mountain AreaChongqing UniversityChongqingPeople’s Republic of China
  2. 2.School of Civil EngineeringChongqing UniversityChongqingPeople’s Republic of China
  3. 3.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingPeople’s Republic of China
  4. 4.School of Civil and Environmental EngineeringNanyang Technological UniversitySingaporeSingapore
  5. 5.The Peac Institute of Multiscale SciencesChengduPeople’s Republic of China
  6. 6.Key Laboratory of Advanced Technologies of MaterialsMinistry of Education, Southwest Jiaotong UniversityChengduPeople’s Republic of China
  7. 7.Institute of Geotechnical Engineering, University of Natural Resources and Life SciencesViennaAustria

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