DEM simulation of shear vibrational fluidization of granular material

Abstract

Fluidization of dry granular material is the transition from a solid state to a liquid state when sufficient energy is applied during vibration. This behavior is important because it is closely related to deformations of geotechnical structures during an earthquake. The scientific challenge lies in the understanding on how strain localization is related to the fluidization zone during the entire shearing process. Despite the importance of the mechanical behavior of granular material during fluidization, it cannot be easily characterized using traditional direct shear test. In this paper, 2D DEM model is firstly conduct, shear vibrational fluidization is defined for dry granular material, and the discrete element method has been used to simulate the direct shear test on granular material under vibrational loading during shearing. The peak, residual and vibro-residual shear strength envelopes have been obtained from the numerical simulations. Three distinct zones have been identified in the upper shear box based on the observed changes in volumetric strain before vibration. During vibration, fluidization occurs in the three zones with the characteristics that the shear stress, porosity, volumetric strain, and the coordination number drop to relatively lower values. During vibration, material becomes denser than the critical state, and strain localization has been relieved. Densification of the material at the shear zone leads to a strengthening of the material which increases the shearing resistance after vibration. Furthermore, a comparison of the 2D and 3D simulations is performed. Results reveal that the motion of particles in the out-of-plane direction in the 3D simulations lead to smoother shear stress and more consistent with the experimental result.

Appendix: Servomechanism for computing and controlling the wall-based stress state

Throughout the loading process, the top normal stress is kept constant by adjusting the top loading wall velocity using a numerical servomechanism. The servomechanism implements the following algorithm [20]. The equation for wall velocity $\dot{u}^{w}$ is calculated in Eq. A1:

$$ \dot{u}^{w} = G\left( {\sigma^{\text{measured}} - \sigma^{\text{required}} } \right) = G\Delta \sigma $$

(A1)

where the superscript $w$ represents wall, $\sigma^{\text{measured}}$ is the contact pressure of the wall which is measured during shearing, $\sigma^{\text{required}}$ is the required contact pressure that we set, $G$ is a calculated parameter that is estimated from Eqs. A2–A6.

The maximum increment in wall force arising from the wall movement in one time step is calculated from Eq. A2:

$$ \Delta F^{w} = k_{n}^{c} N_{c} \dot{u}^{w} \Delta t $$

$$ k_{n}^{c} = \frac{{k_{n}^{b} k_{n}^{w} }}{{k_{n}^{b} + k_{n}^{w} }} $$

(A2)

where $N_{c}$ is the number of contacts on the wall, $k_{n}^{c}$ is the average combined normal stiffness of the two contacting entities (ball-to-wall), $k_{n}^{b}$ and $k_{n}^{w}$ are the normal stiffness of the ball and the wall, respectively, the superscript symbol $b$ represents balls, $\Delta t$ is the DEM simulation time step. Therefore, the change in the average wall stress is calculated from Eq. A3:

$$ \Delta \sigma^{w} = \frac{{k_{n}^{c} N_{c} \dot{u}^{w} \Delta t}}{A} $$

(A3)

where A is the wall area. For stability, the absolute value of the change in wall stress must be less than the absolute value of the difference between the measured and required stresses. In practice, a relaxation factor $\alpha$ is used such that the stability requirement becomes that:

$$ \left| {\Delta \sigma^{w} } \right| < \alpha \left| {\Delta \sigma } \right| $$

(A4)

Substituting Eqs. A1 and A3 into Eq. A4 yields:

$$ \frac{{k_{n}^{c} N_{c} \dot{u}^{w} \Delta t}}{A} < \alpha \left| {\Delta \sigma } \right| $$

(A5)

The “gain” parameter $G$ is determined using Eq. A6:

$$ G = \frac{\alpha A}{{k_{n}^{c} N_{\text{c}} \Delta t}} $$

(A6)

Here, α is the relaxation factor which is equal to 0.5, A is the area of the top plane, in the 2D numerical model, A is the area of the top loading plane, which is equal to the length of the top loading plane multiplies by the width of the box. In current study, A = 60 mm × 60 mm.