Yahya Ghasemi Print III pdf

3.1. Ideal size distribution curve
As mentioned, the idea of composing an ideal particle size distribution (PSD) curve for 
aggregates was first introduced by Fuller and Thompson (1907). The concept behind ideal 
size distribution curve lies in reducing void content of the packed aggregates, since at constant 
water content, mixes with higher packing will have more available water as lubricant between 
particles. The Fuller curve deals with continuous grading curve ranging from 250 
ȝ
m to the 
maximum size. As a result, Fuller curve is less suitable for self-compacting concrete (SCC)
and high strength concrete (HSC)
ZKHUH ILQHV ZLWK VL]H RI OHVV WKDQ ȝ
m is commonly 
used and also mixes made with gap-graded crushed aggregates, as an example Fuller curve 
cannot be used for a material ranging from 4 to16 mm since the diameter of the small class is 
not considered by the approach. In that sense, grading by Fuller curve represents a special 
case. In a more general case, packing equation were derived by Andreasen and Andersen
(1930), it is suggested that to obtain optimum packing (less voids), the particle size 
distribution should be calculated based on the following equation. 
ܲ
(
ܦ
) = (
ܦ
ܦ
௠௔௫
)
௤
(3.1) 
where P is the fraction that can pass the sieve with opening D, D
max
is maximum particle size 
of the mix and parameter q has value ranging from 0 to 1. According to (Andreasen and 
Andersen, 1930), value of 0.37 for q will result in optimum packing while the Fuller curve 
can be obtained by using q=0.5. 
The A&A curve (Andreasen and Andersen, 1930) was later on modified to account for the 
minimum particle size (Dmin) in the mix by Funk and Dinger (1994). The modified A&A 
curve can be calculated based on the following equation: 
ܲ
(
ܦ
) =
ܦ
௤
െ ܦ
௠௜௡
௤
ܦ
௠௔௫
௤
െ ܦ
௠௜௡
௤
(3.2) 
It should be mentioned that the value of 
q
is commonly decided based on experience and/or 
on qualitative empirically obtained values judged by the type of aggregates - crushed or 
natural- (Gram et. al., 2017) or their place of mother rock origin (e.g. a certain q value for 
aggregates from Norway).
Figure 3.2. shows ideal curves obtained from Fuller, A&A and modified A&A approaches. 

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Mix design approaches
Figure 3.2. Ideal curves according to Fuller, Andreasen & Andersen, and modified A&A (Funk and 
Dinger). For maximum and minimum 
SDUWLFOH VL]HRI PP DQG ȝP
respectively. (Fennis and 
Walraven, 2012) 
While ideal size distribution are practical and easy to use, they don’t take into account the 
interaction between the particles and other factors that affect the packing e.g. shape, surface 
texture, etc.