Novel Approach for Generating Homogeneous Samples for Discrete-Element-Method Studies

Acknowledgments

Notation

A_w

wall boundary area;

a_c

degree of anisotropy;

D_s

shear displacement;

d

branch vector joining the particle centers;

$\overline{e}$

average void ratio;

e₀

initial void ratio;

e_i

void ratio of the ith element;

e_t

target void ratio;

e_y

unit vector in the y-direction;

$F_c^y$

vertical force on the boundary;

f_ni

normal contact force at the ith boundary-particle contact point;

f_si

tangential contact force at the ith boundary-particle contact point;

k_n

normal stiffness;

k_s

tangential stiffness;

n_c

unit normal vectors of the contact;

n_g

number of grids;

n_l

layer number;

n_p

total particle number;

n_s

slipping contact number;

$\overline{r}$

average particle radius;

r_b

radius of interior particle;

r_w

radius of boundary particle;

S_c

slide fraction;

S_e

variance of the void ratio;

S_x

variance of the horizontal stress;

S_y

variance of the vertical stress;

T

layer thickness;

v

velocity of the boundary;

α

relaxation factor;

α_d

local damping coefficient;

δ

gap between layers;

Δδ_n

relative displacements in the normal direction;

Δδ_s

relative displacements in the tangential direction;

μ_g

interparticle friction coefficient;

${\varphi }_{\mu }$

interparticle friction angle;

ρ

particle density;

${\sigma }_1^i$

vertical stress of the ith element;

${\sigma }_3^i$

horizontal stress of the ith element;

σ_c

current confining pressure;

σ_t

target confining pressure;

Δt

timestep increment;

t_c

unit tangential vectors of the contact;

θ

angle between the normal contact and the x-direction; and

θ_c

principal direction of the strong contact forces.

References