140
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
commonly used gradations of coarse aggregates are in good agreement with the
Fuller curves. Thereafter, during establishing the 3D mesoscopic concrete model,
the distribution of coarse aggregates sizes can be determined by different gradation
curves.
The relatively simple shape of coarse aggregates, i.e., the sphere coarse aggregates,
is discussed in this section. Firstly, generating the random numbers to determine
the location of sphere coarse aggregates center (x 0 , y 0 , z 0 ), and the dropping area
of coarse aggregates is limited in the first octant for convenient modelling. Then,
the sphere coarse aggregates are dropped according to the distribution of coarse
aggregates sizes of the actual concrete specimens and gradation curve. The diameter
and radius of coarse aggregates to be dropped is denoted by D 0 and R 0 , respectively.
Before dropping the coarse aggregates, it is necessary to judge whether the following
boundary conditions are satisfied
⎧
⎨
⎩
X min ≤ (x 0 + R 0 ) ≤ X max
Y min ≤ (y 0 + R 0 ) ≤ Y max
Z min ≤ (z 0 + R 0 ) ≤ Z max
(5.2)
where X min , Y min , Z min and X max , Y max , Z max are the boundary for cuboid dropping area of the coarse aggregates. If the location of coarse aggregates does not
satisfy above boundary conditions, the new random numbers will be regenerated
until Eq. (5.2) is satisfied.
In order to avoid the invasion between the dropped coarse aggregates (x 0 , y 0 , z 0 )
and the previous ones (x i , y i , z i ), the distance between the new coarse aggregates and
existing one must be greater than the sum of two spheres radius, i.e.,
R 0 + R i ≤ L D
(5.3)
where R i is the radius of any coarse aggregate which has been dropped, and L D
represents the distance between the two sphere coarse aggregates, which can be
expressed as
L D =
(x 0 − x i )
2
+ (y 0 − y i )
2
+ (z 0 − z i )
2
(5.4)
When the new coarse aggregates meet boundary conditions and are not invaded
by other existing coarse aggregates, they can be dropped until the required volume
fraction is satisfied. When the concrete model is relatively large, the computational
payload attributed to the invasion judgment will be increased significantly as more
and more coarse aggregates are dropped, seriously slowing down the modelling
speed. Aiming to improve the efficiency of dropping coarse aggregates and modelling
speed, the methods of block modelling and dropping coarse aggregates according
to their particle sizes are adopted at present. The block modelling breaks the whole
dropping area into several parts, a larger concrete model is divided into several
smaller concrete models, and dropping coarse aggregates is conducted within each
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
commonly used gradations of coarse aggregates are in good agreement with the
Fuller curves. Thereafter, during establishing the 3D mesoscopic concrete model,
the distribution of coarse aggregates sizes can be determined by different gradation
curves.
The relatively simple shape of coarse aggregates, i.e., the sphere coarse aggregates,
is discussed in this section. Firstly, generating the random numbers to determine
the location of sphere coarse aggregates center (x 0 , y 0 , z 0 ), and the dropping area
of coarse aggregates is limited in the first octant for convenient modelling. Then,
the sphere coarse aggregates are dropped according to the distribution of coarse
aggregates sizes of the actual concrete specimens and gradation curve. The diameter
and radius of coarse aggregates to be dropped is denoted by D 0 and R 0 , respectively.
Before dropping the coarse aggregates, it is necessary to judge whether the following
boundary conditions are satisfied
⎧
⎨
⎩
X min ≤ (x 0 + R 0 ) ≤ X max
Y min ≤ (y 0 + R 0 ) ≤ Y max
Z min ≤ (z 0 + R 0 ) ≤ Z max
(5.2)
where X min , Y min , Z min and X max , Y max , Z max are the boundary for cuboid dropping area of the coarse aggregates. If the location of coarse aggregates does not
satisfy above boundary conditions, the new random numbers will be regenerated
until Eq. (5.2) is satisfied.
In order to avoid the invasion between the dropped coarse aggregates (x 0 , y 0 , z 0 )
and the previous ones (x i , y i , z i ), the distance between the new coarse aggregates and
existing one must be greater than the sum of two spheres radius, i.e.,
R 0 + R i ≤ L D
(5.3)
where R i is the radius of any coarse aggregate which has been dropped, and L D
represents the distance between the two sphere coarse aggregates, which can be
expressed as
L D =
(x 0 − x i )
2
+ (y 0 − y i )
2
+ (z 0 − z i )
2
(5.4)
When the new coarse aggregates meet boundary conditions and are not invaded
by other existing coarse aggregates, they can be dropped until the required volume
fraction is satisfied. When the concrete model is relatively large, the computational
payload attributed to the invasion judgment will be increased significantly as more
and more coarse aggregates are dropped, seriously slowing down the modelling
speed. Aiming to improve the efficiency of dropping coarse aggregates and modelling
speed, the methods of block modelling and dropping coarse aggregates according
to their particle sizes are adopted at present. The block modelling breaks the whole
dropping area into several parts, a larger concrete model is divided into several
smaller concrete models, and dropping coarse aggregates is conducted within each