Dynamic Weakening of Sandstone Subjected to Repetitive Impact Loading

  • L. H. Tong
  • Yang Yu
  • S. K. Lai
  • C. W. Lim
Original Paper


Dynamic weakening is commonly observed when stone is subjected to a single or repetitive impact loading. In a series of impact loading experiments conducted using the split Hopkinson pressure bar system with external confinement pressure, we observe evident nonlinear dynamic response for each impact loading, an accompanying dynamic weakening effect, and significant plastic deformation of the specimen. The dynamic response can be predicted accurately by the nonlinear granular model (Johnson and Jia in Nature 437:871–874, 2005). In the framework of statistics, an analytical model for dynamic weakening is proposed and it suggests that the weakening effect is induced by the increasing number of broken inter-particle bonds after impact. This is related to a decrease in the dynamic modulus that can be described by introducing a confinement pressure-dependent energy portion parameter \(\mu\). A further nonlinear analysis of the experimental data provides detailed insights into the nonlinear dynamic response. The proposed weakening mechanism is based on inter-particle statistics and it comprises a wealth of dynamic regimes, including modulus softening and damage evolution, which can be extended to other granular materials but not limited to rocks.


Dynamic weakening Impact loads Sandstone Nonlinear response 



The work described in this paper was supported by the National Natural Science Foundation of China (Grants nos. 11602210 and 11702095), Jiangxi Science Fund for Distinguished Young Scholars (Grant no. 2018ACB21024), and the Matching Grant from the Hong Kong Polytechnic University (Project no. 4-BCDS).


  1. Brown ET (2012) Progress and challenges in some areas of deep mining. Min Technol 121:177–191. CrossRefGoogle Scholar
  2. Brunet T, Jia X, Johnson PA (2008) Transitional nonlinear elastic behaviour in dense granular media. Geophys Res Lett. CrossRefGoogle Scholar
  3. Chen R, Li K, Xia KW, Lin YL, Yao W, Lu FY (2016) Dynamic fracture properties of rocks subjected to static pre-load using notched semi-circular bend method. Rock Mech Rock Eng 49:3865–3872. CrossRefGoogle Scholar
  4. Chen R, Yao W, Lu F, Xia K (2018) Evaluation of the stress equilibrium condition in axially constrained triaxial SHPB tests. Exp Mech 58:527–531. CrossRefGoogle Scholar
  5. Dai F, Xu Y, Zhao T, Xu NW, Liu Y (2016) Loading-rate-dependent progressive fracturing of cracked chevron-notched Brazilian disc specimens in split Hopkinson pressure bar tests. Int J Rock Mech Min Sci 88:49–60. CrossRefGoogle Scholar
  6. Du HB, Dai F, Xia KW, Xu NW, Xu Y (2017) Numerical investigation on the dynamic progressive fracture mechanism of cracked chevron notched semi-circular bend specimens in split Hopkinson pressure bar tests. Eng Fract Mech 184:202–217. CrossRefGoogle Scholar
  7. Du HB, Dai F, Xu Y, Liu Y, Xu HN (2018) Numerical investigation on the dynamic strength and failure behavior of rocks under hydrostatic confinement in SHPB testing. Int J Rock Mech Min Sci 108:43–57. CrossRefGoogle Scholar
  8. Espindola D, Galaz B, Melo F (2012) Ultrasound induces aging in granular materials. Phys Rev Lett 109:158301. CrossRefGoogle Scholar
  9. Frew DJ, Akers SA, Chen W, Mark LG (2010) Development of a dynamic triaxial Kolsky bar. Meas Sci Technol 21:105704. CrossRefGoogle Scholar
  10. Hokka M, Black J, Tkalich D, Fourmeau M, Kane A, Hoang NH, Li CC, Chen WW, Kuokkala VT (2016) Effects of strain rate and confining pressure on the compressive behavior of Kuru granite. Int J Impact Eng 91:183–193. CrossRefGoogle Scholar
  11. Huang R, Zhao J, Ju N, Li G, Lee ML, Li Y (2013) Analysis of an anti-dip landslide triggered by the 2008 Wenchuan earthquake in China. Nat Hazards 68:1021–1039. CrossRefGoogle Scholar
  12. Huang S, Mohanty B, Xia K (2017) A multi-particle crushing apparatus for studying rock fragmentation due to repeated impacts. Rev Sci Instrum 88:125114. CrossRefGoogle Scholar
  13. Jia X (2004) Codalike multiple scattering of elastic waves in dense granular media. Phys Rev Lett 93:154303. CrossRefGoogle Scholar
  14. Johnson PA, Jia X (2005) Nonlinear dynamics, granular media and dynamic earthquake triggering. Nature 437:871–874. CrossRefGoogle Scholar
  15. Johnson PA, Savage H, Knuth M, Gomberg J, Marone C (2008) Effects of acoustic waves on stick-slip in granular media and implications for earthquakes. Nature 451:57. CrossRefGoogle Scholar
  16. Kaiser PK, Cai M (2012) Design of rock support system under rockburst condition. J Rock Mech Geotech Eng 4:215–227. CrossRefGoogle Scholar
  17. Li X, Zhou Z, Lok T-S, Hong L, Yin T (2008) Innovative testing technique of rock subjected to coupled static and dynamic loads. Int J Rock Mech Min Sci 45:739–748. CrossRefGoogle Scholar
  18. Li H, Xiang X, Jianchun L, Jian Z, Bo L, Yaqun L (2011) Rock damage control in bedrock blasting excavation for a nuclear power plant. Int J Rock Mech Min Sci 48:210–218. CrossRefGoogle Scholar
  19. Li X, Gong F, Tao M, Dong L, Du K, Ma C, Zhou Z, Yin T (2017) Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: a review. J Rock Mech Geotech Eng 9:767–782. CrossRefGoogle Scholar
  20. Li SH, Zhu WC, Niu LL, Yu M, Chen CF (2018) Dynamic characteristics of green sandstone subjected to repetitive impact loading: phenomena and mechanisms. Rock Mech Rock Eng 51:1921–1936. CrossRefGoogle Scholar
  21. Melosh HJ (1979) Acoustic fluidization: a new geologic process? J Geophys Res Solid Earth 84:7513–7520. CrossRefGoogle Scholar
  22. Melosh HJ (1996) Dynamical weakening of faults by acoustic fluidization. Nature 379:601–606. CrossRefGoogle Scholar
  23. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364. CrossRefGoogle Scholar
  24. Weng L, Li X, Taheri A, Wu Q, Xie X (2018) Fracture evolution around a cavity in brittle rock under uniaxial compression and coupled static-dynamic loads. Rock Mech Rock Eng 51:1–15. CrossRefGoogle Scholar
  25. Wu BB, Kanopoulos P, Luo XD, Xia KW (2014) An experimental method to quantify the impact fatigue behavior of rocks. Meas Sci Technol 25:075002. CrossRefGoogle Scholar
  26. Wu BB, Yao W, Xia KW (2016) An experimental study of dynamic tensile failure of rocks subjected to hydrostatic confinement. Rock Mech Rock Eng 49:3855–3864. CrossRefGoogle Scholar
  27. Xia K, Yao W (2015) Dynamic rock tests using split Hopkinson (Kolsky) bar system—a review. J Rock Mech Geotech Eng 7:27–59. CrossRefGoogle Scholar
  28. Xia KW, Huang S, Marone C (2013) Laboratory observation of acoustic fluidization in granular fault gouge and implications for dynamic weakening of earthquake faults. Geochem Geophys Geosyst 14:1012–1022. CrossRefGoogle Scholar
  29. Xu Y, Dai F (2018) Dynamic response and failure mechanism of brittle rocks under combined compression-shear loading experiments. Rock Mech Rock Eng 51:747–764. CrossRefGoogle Scholar
  30. Xu Y, Dai F, Xu NW, Zhao T (2016) Numerical investigation of dynamic rock fracture toughness determination using a semi-circular bend specimen in Split Hopkinson pressure bar testing. Rock Mech Rock Eng 49:731–745. CrossRefGoogle Scholar
  31. Zhou YX, Xia K, Li XB, Li HB, Ma GW, Zhao J, Zhou ZL, Dai F (2012) Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. Int J Rock Mech Min Sci 49:105–112. CrossRefGoogle Scholar
  32. Zhu WC, Bai Y, Li XB, Niu LL (2012) Numerical simulation on rock failure under combined static and dynamic loading during SHPB tests. Int J Impact Eng 49:142–157. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • L. H. Tong
    • 1
    • 2
  • Yang Yu
    • 1
    • 2
  • S. K. Lai
    • 3
    • 4
  • C. W. Lim
    • 5
    • 6
  1. 1.Institute of Geotechnical Engineering, School of Civil Engineering and ArchitectureEast China Jiaotong UniversityNanchangPeople’s Republic of China
  2. 2.Jiangxi Key Laboratory of Infrastructure Safety and Control in Geotechnical EngineeringEast China Jiaotong UniversityNanchangPeople’s Republic of China
  3. 3.Department of Civil and Environmental EngineeringThe Hong Kong Polytechnic UniversityKowloonPeople’s Republic of China
  4. 4.The Hong Kong Polytechnic University Shenzhen Research InstituteShenzhenPeople’s Republic of China
  5. 5.Department of Architecture and Civil EngineeringCity University of Hong KongKowloonPeople’s Republic of China
  6. 6.City University of Hong Kong Shenzhen Research InstituteShenzhenPeople’s Republic of China

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