DEM simulations of shear modulus and damping ratio of sand with emphasis on the effects of particle number, particle shape, and aging

In this study, the nonlinear, Hertz-Mindlin contact model and clumped particles were used in the discrete element method simulations of cyclic shear tests to obtain the shear modulus G and damping ratio D at a wide range of strain levels. The simulated G and D, which demonstrated similar behavior as observed by the experiments, can be derived from either (1) the traced energy or (2) the resulting hysteresis loop. As the particle number N-p in the numerical sample increased (i.e., the ratio of the particle size to the sample size decreased) while other sample parameters were fixed, including the same sample size and void ratio, the resulting G decreased whereas D increased. Increasing particle numbers indeed led to a decrease in the associated contact normal forces among particles, which in turn lowered the contact stiffness and therefore the shear modulus of the sample. The D responses were the results of interaction between the stored energy, which was related to the shear modulus, and the energy that mainly dissipated at the weak contacts where the contact normal forces F-n were smaller than the associated mean value F-n mean. The G and D values of the samples became similar and almost independent of N-p when N-p was greater than 32,000 where the ratio of D-50 to the sample size was 0.029. Hence, this particle number was used in the simulations to obtain unbiased results. The G and D values can also be increased and decreased, respectively, by increasing the particle aspect ratio (i.e., by decreasing sphericity). The simulations regarding aging effects on G and D replicated the experimental observations. The contact normal forces among particles were found to become more homogenized after aging. This in turn increased the shear modulus and led to increasing contact normal forces at weak contacts, thereby reducing the frictional loss and damping ratio. The aged and unaged samples had similar shear moduli and damping ratios as the strain levels gradually increased. This is simply because contact forces homogenized during aging were progressively destroyed by subsequent shearing and associated structural changes.