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DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials

Abstract

The critical-state response of granular assemblies composed of elastic spheres under generalised three-dimensional loading conditions was investigated using the discrete element method (DEM). Simulations were performed with a simplified Hertz–Mindlin contact model using a modified version of the LAMMPS code. Initially isotropic samples were subjected to three-dimensional stress paths controlled by the intermediate stress ratio, \(b=[(\sigma '_{2}-\sigma '_{3})/\) \((\sigma '_{1}-\sigma '_{3})]\). Three types of simulation were performed: drained (with \(b\)-value specified), constant volume and constant mean effective stress. In contrast to previous DEM observations, the position of the critical state line is shown to depend on \(b\). The data also show that, upon shearing, the dilatancy post-peak increases with increasing \(b\), so that at a given mean effective stress, the void ratio at the critical state increases systematically with \(b\). Four commonly-used three-dimensional failure criteria are shown to give a better match to the simulation data at the critical state than at the peak state. While the void ratio at critical state is shown to vary with \(b\), the coordination number showed no dependency on \(b\). The variation in critical state void ratios at the same \(p'\) value is apparently related to the directional fabric anisotropy which is clearly sensitive to \(b\).

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Acknowledgments

The computing resources used included time on HECToR which was funded via EPSRC Grant EP/I006761/1. The cx1 cluster at Imperial College London was also used. Dr. Hanley would like to acknowledge funding from the Royal Commission for the Exhibition of 1851. The demonstration of the software package Stereo 32 [45] by Tom Shire of Imperial College is also appreciated.

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Correspondence to C. O’Sullivan.

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Huang, X., Hanley, K.J., O’Sullivan, C. et al. DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials. Granular Matter 16, 641–655 (2014). https://doi.org/10.1007/s10035-014-0520-6

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  • DOI: https://doi.org/10.1007/s10035-014-0520-6

Keywords

  • Discrete element method
  • Critical state
  • Intermediate stress ratio
  • Buckling
  • Failure criteria