Page 297 - Mechanics of Asphalt Microstructure and Micromechanics

Applications of Discrete Element Method 289

This relationship is also applicable to the force-displacement relationship in the tan-
gent direction. From this relationship the following equations can be obtained:
A
[] [
[]
A
kk B] kk B [ ]
k = n n k = s s (9-4a, b)
n
s
B
A
A
k [] + k [ B] k [] + k k []
n n s s
9.2.2.2 Hertz Contact Model
Contact normal secant stiffness:
⎛ 2 G 2 R ⎞
K = ⎜ ⎟ U n
n
⎜ 31( − ν ⎟ ) ⎠ (9-5)
⎝

Contact shear tangent stiffness:
⎛ ( 2 ) 13 ⎞
/
⎜ 2 G 3 1 ( − ν ) R ⎟ 13
/
k = ⎜ ⎟ F n (9-6)
s
⎜ 2 − ν ⎟ i
⎝ ⎠
More details about the formulations can be found from the PFC3D manuals.
9.2.2.3 Parallel Bond Model
Bonding model is another key model in PFC3D. It is only formed between proximate
particles (not between balls and walls), and continues to exist until broken, which hap-
pens when its strengths are exceeded.
PFC3D 3.0 supports two bonding models: contact bond model and parallel bond
model. The parallel bond model can transfer momentums.
The parallel bond acts over a circular cross-section as shown (Figure 9.4), which en-
ables it to transmit both a force and a momentum. Another important feature of parallel
FIGURE 9.4 Schematic of B
parallel bond (Itasca
Consulting Group, 2005).
A
(A) (C) (B)
x n x x
i i i i

n
M i
F n n
i M i
2R
s
F i

L