Yahya Ghasemi Print III pdf

3.2. Particle packing theory
In order to produce an optimized concrete product, it is vital to select an acceptably accurate 
packing model for estimation of packing density. As a principal, particle packing models aim 
to define the size distribution curve in a way that results in high packing thus leaving less 
volume of voids to be filled with paste. However, it should be mentioned that maximizing 
packing density does not necessarily guarantee a workable mixture (Kwan and Mora, 2002).
This is considered for example in 4C user manual (2009) by suggesting that for making a 
workable concrete, the maximum packing density should be avoided. While it is known that 
the optimum packing is not equal to maximum packing, the approach to deciding an optimum 
packing is not clear. 
The packing density of a granular mix is defined as the solid volume in a unit total volume
which is equal to ratio of bulk density to the relative density of the solids. 
ߙ
=
ߩ
௕
ߩ
௦
(3.3) 
w
KHUH Į LV SDFNLQJ GHQVLW\ 7KH
packing density can also be defined in relation to void 
content: 
ߙ
= 1
െ ݁
(3.4)

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17
Mix design approaches
It should be mentioned that almost all of the particle packing models are fundamentally rely
on the following geometry based equations (De Larrard, 1999; Furnas, 1929): 
ߙ
௧
=
ߚ
ଵ
1
െ ݕ
ଶ
Large particles are dominant (1)
(3.5) 
ߙ
௧
=
1
ݕ
ଵ
+ (
ݕ
ଶ
ߚ
ଶ
)
Small particles are dominant (2)
(3.6) 
w
KHUHĮ
t
LVFDOFXODWHGSDFNLQJGHQVLW\RIDPL[WXUHȕ
1
is the packing density of the larger size 
FODVV ȕ
2
is the packing density of the small size class 2,y
1
is the volume fraction of size 
class 1 and y
2
is the volume fraction of size class 2 where for two size classes y
1
+y
2
=1.
Eq. (3.5) is valid in case that the amount of large particles is dominating the particle structure 
where small particles are filling the voids between the larger particles, on the other hand, Eq.
(3.6) deals with a situation where the amount of small particles is dominating and large