PSI - Issue 37

Koji Uenishi et al. / Procedia Structural Integrity 37 (2022) 404–409 Uenishi and Xi / Structural Integrity Procedia 00 (2022) 000 – 000

408

5

3. Discrete modeling Secondly, the open source discrete element code ESyS-Particle (Weatherley et al., Version 2.3.5, 2021) is used to numerically support the outcome of the experimental observations. The code ESyS-Particle, often employed in the analysis of dynamic fracture in solid materials (see e.g. Debski and Klejment, 2021), has been first applied to our problem of a granular slope under dynamic impact by Tsukasa Goji in his master thesis submitted to the Graduate School of Engineering of the University of Tokyo in 2019. As in the above experiments, each granular particle has a diameter of 8 mm and mass of 0.146 g, and it is subjected to gravity. The contact model used in the two-dimensional simulations can have linear springs in each of the normal and shear directions of contact (1.0  10 6 N/m so that each particle can bear the effect of gravity), without any dashpot, and the coefficient of static and dynamic friction is assumed to be 0.3. In the calculations, for instance, when two particles are in contact, a shear spring is generated at the point of contact. Then, forces from neighboring particles cause the two particles in consideration to start sliding over each other with the shear spring withstanding the motion. When the shear force reaches the normal force multiplied by the friction coefficient, dynamic sliding is assumed to be initiated. In this way, not only frictionless behavior but also static and dynamic frictional deformation of granular media can be effectively simulated (Weatherley et al., Version 2.3.5, 2021). The slope is surrounded by rigid walls except for the top free surface on which a flying object modeling the free-falling steel ball impinges (Fig. 4(b) simulating the case shown in Fig. 3). The linear spring constant for the wall-particle contact is set to 1.0  10 6 N/m. For a reference purpose, the case without the retaining wall is also simulated (Fig. 4(a)). The numerically generated snapshots in Fig. 4 indicate that the computational results compare well with the experimental ones and the dynamics of granular media may be more clearly identified in the calculations if the parameters required for the numerics are cautiously and appropriately chosen. For example, in Fig. 4(a), unidirectional stress transfer as well as the opening just below the position of dynamic impact is well reproduced (compare the snapshots with Fig. 2 top). Similarly, in Fig. 4(b), the confining effect of the retaining wall, stress transfer along the top free surface and the slope face, and buckling-like jump of the particles on the top free surface seem to be properly simulated (see Fig. 3). Additional calculations on the dynamics of a vertical granular slope with a vertical retaining wall can also produce comparable results, and not only the effects of material stiffness but also those of more distinct inhomogeneities like cavities and seismic barriers placed in granular slopes have been preliminarily evaluated already.

a

b

Steel ball

50 mm

Retaining wall

4 m/s

0

Buckling-like jump

Concentrated stress transfer

Stress transfer

Stress transfer scattered

Opening below the impact point, resulting in mass flow

Fig. 4. Distributions of velocity magnitude due to dynamic impact, generated by the open source code ESyS-Particle for (a) unconfined and (b) confined granular slopes. The dynamics suggested by the discrete element method, with numerical parameters carefully selected and calibrated, compares well with the one postulated from the experimental observations. The diameter of every particle in the granular slope is 8 mm as in the experiments, and the temporal interval between each snapshot is 3000  s.