Ratcheting of Granular Materials

We investigate the quasistatic mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasiperiodic ratchetlike behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows exploration of the role of friction in the permanent deformation of unbound granular materials subjected to cyclic loading.

Figure 1

(a) Horizontal stress versus shear strain in the first $40$ cycles; (b) permanent (plastic) strain ${\gamma }_N$ after $N$ cycles versus the number of cycles; (c) stress against the volume fraction in the first $40$ cycles; (d) volume fraction ${\Phi }_N$ after $N$ cycles versus number of cycles.

Figure 2

Plastic deformation per cycle for different loading amplitudes. The calculations are performed on six different samples, each with 400 polygons.

Figure 3

(a) Each point represents the normal and tangential force at one contact normalized by $\ell p_0$. The dashed line shows the sliding condition $|f_t|=\mu f_n$; (b) and (c) show trajectories of the contact force of two selected sliding contacts. The dots denote the times $t=0,0.5t_0,\dots ,2t_0$ in unit of the period $t_0$; (d) shows plastic deformation $\xi$ at the contact shown in (c).

Figure 4

The arrows represents the field $\overrightarrow{u}$ of the plastic deformations accumulated at the contacts during one cycle: $\overrightarrow{u=500({\xi }_{N+1}-{\xi }_N)}$, where ${\xi }_N$ is the plastic displacement after $N$ cycles.

Figure 5

Fraction of sliding contacts $n_s$ in the ratcheting regime for $\Delta {\sigma }_y/p_0=0.424$ (dash-dotted line), 0.0707 (dashed line), 0.007 07 (dotted line), and 0.000 707 (solid line)