Yahya Ghasemi Print III pdf

3.3.1.3. The air voids modulus 
The air void modulus is defined as the air void space ratio of the fines (ranging from 0.125 
mm to 4mm fractions) and course (>4 mm) portion of the particle system. It should be noted 
that the effect of properties of fine fractions portion is greater than the effect of coarse 
aggregates properties. Hence, the fineness modulus (Fm) of the fine/coarse aggregates is 
utilized as correction factor when defining the air voids modulus. A preliminary definition of 
the air voids modulus is (Mortsell et al., 1996): 
ܪ݉
=
ݒ
௦௔
(
ܪݏ
/(
ܨ݉
௦
)
଴
.
ହ
+
ܶݏ
) +
ݒ
௖௢
(
ܪ݌
/(
ܨ݉
௣
)
଴
.
ହ
+
ܶ݌
)
(3.20)
where v
sa
and v
co
are volume fraction of sand (0.125 – 4 mm) and volume fraction of coarse 
aggregates (>4 mm) respectively. Hs is air voids ratio in the sand (vol %), Hp is air voids ratio 
in the coarse aggregate, Ts is an aggregate parameter for the sand, Tp is an aggregate 
Flow rate

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23
Mix design approaches
parameter for the coarse aggregate, Fm
s
and Fm
p
are the fineness modulus for sand and coarse 
aggregates respectively. The aggregate parameters can be determined in different ways based 
on different conditions (Mortsell et al., 1996).
The physical interpretation of air voids modulus (Hm) according to the authors (Mortsell et 
al., 1999) is that it is equal to the paste volume (vol %) when the mix is changing from no 
slump to a small but measurable slump. 
3.3.1.4. Workability function for concrete 
The workability of the concrete can be measured using slump or flow table test and it can also 
be calculated based on the PMM as a function of the flow resistance of the matrix, the air 
voids modulus of the particle phase and the volume fraction of the matrix. The correlation 
between workability and volume fraction of the fluid phase is assumed to be S-shaped utilized 
by using the Tanh-function. Workability function Kp can be defined as: 
ܭ݌
=
(
݊ െ ݉
)(
݄ܶܽ݊
(2
ߙ
௞
(
ܨ݌ െ ܪ݉
)/100
െ
1) + 1
2
+
݉
(3.21) 
where 
m
and 
n
are lower and uppe
U DV\PSWRWH YDOXHV UHVSHFWLYHO\ Į
k
is expressed as the 
steepness of Kp function, Fp is volume fraction of fluid phase and Hm is the air void 
PRGXOXV7KHIDFWRUĮ
k
LVDIXQFWLRQRIWKHIORZUHVLVWDQFHUDWLRȜ
Q
:
ߙ
௞
=
ܣ
.
݁
ି஻ఒ
ೂ
(3.22)
where A and B are constants found by regression analysis.
The main application of the model is to adjust concrete mix design, from a workability point 
of view, when properties of proportions of the constituent materials are changed (Mortsell et 
al., 1996).