3D continuum-discrete coupled modelling of triaxial Hopkinson bar tests on rock under multiaxial static-dynamic loads

W. R. Hu, K. Liu, D. O. Potyondy, Q. B. Zhang

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36 Citations (Scopus)


Rock engineering projects at depth are frequently subjected to dynamic loadings under in-situ stress state, and the studies should be conducted to decipher the coupled effect of confining pressure and strain rate on the behaviour of rocks. The triaxial Hopkinson bar system has been applied to investigate the responses of materials to the coupled multiaxial static-dynamic loads. In this study, a three-dimensional (3D) continuum-discrete coupled method is employed to establish a numerical-based triaxial Hopkinson bar system, and the steel bars and a cubic specimen are modelled by continuum zones and bonded-particle material, respectively. Firstly, the detailed numerical modelling is performed to verify some prerequisites and uncertainties in the experiments, including stress wave propagation and attenuation in three directions, dynamic stress equilibrium, boundary effects, interfacial frictions, and controversial methodologies for applying confining pressure, by using the flat-joint model and parallel bond model. Then, both experimental tests and numerical modelling are carried out on sandstone under multiaxial pre-stress conditions (i.e., uniaxial, biaxial and triaxial compression) followed by dynamic loads. The dynamic responses of rock, including stress-strain curves, dynamic strength, energy evolutions, and damage patterns, exhibit confinement dependence, which is in good agreement with experimental observations. Under uniaxial compression, the specimens are broken into fragments by multiple fractures; while under biaxial compression, two symmetrically distributed V-shaped damage zones form near the free surfaces. Under triaxial compression, the degree of damage is substantially reduced, and microcrack localisation zones are initiated from the surface, propagate to the interior and eventually form macroscopic fractures. Moreover, a series of numerical simulations is conducted to investigate the strain rate dependence of sandstone under multiaxial load conditions. Both dynamic strength and peak lateral dynamic stresses increase with increasing strain rate. The increase of dynamic strength and failure strain becomes obvious at high strain rates with the enhancement of lateral confinement.

Original languageEnglish
Article number104448
Number of pages21
JournalInternational Journal of Rock Mechanics and Mining Sciences
Publication statusPublished - Oct 2020


  • Continuum-discrete coupled method
  • Dynamic loads
  • Flat-joint model
  • Multiaxial confinement
  • Triaxial Hopkinson bar

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