Original Paper

Granular Matter

, Volume 14, Issue 6, pp 733-747

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Two-dimensional discrete element modelling of bender element tests on an idealised granular material

  • J. O’DonovanAffiliated withDepartment of Civil and Environmental Engineering, Imperial College London
  • , C. O’SullivanAffiliated withDepartment of Civil and Environmental Engineering, Imperial College London Email author 
  • , G. MarketosAffiliated withDepartment of Civil and Environmental Engineering, Imperial College London


The small-strain (elastic) shear stiffness of soil is an important parameter in geotechnics. It is required as an input parameter to predict deformations and to carry out site response analysis to predict levels of shaking during earthquakes. Bender element testing is often used in experimental soil mechanics to determine the shear (S-) wave velocity in a given soil and hence the shear stiffness. In a bender element test a small perturbation is input at a point source and the propagation of the perturbation through the system is measured at a single measurement point. The mechanics and dynamics of the system response are non-trivial, complicating interpretation of the measured signal. This paper presents the results of a series of discrete element method (DEM) simulations of bender element tests on a simple, idealised granular material. DEM simulations provide the opportunity to study the mechanics of this testing approach in detail. The DEM model is shown to be capable of capturing features of the system response that had previously been identified in continuum-type analyses of the system. The propagation of the wave through the sample can be monitored at the particle-scale in the DEM simulation. In particular, the particle velocity data indicated the migration of a central S-wave accompanied by P-waves moving along the sides of the sample. The elastic stiffness of the system was compared with the stiffness calculated using different approaches to interpreting bender element test data. An approach based upon direct decomposition of the signal using a fast-Fourier transform yielded the most accurate results.


Discrete element simulation Stiffness Shear wave Small strain