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4.2.2. Layer theories
Water and paste layer theories can be used as a basis for compiling a mix design. The main
difference between the water and paste layer theories roots in the way that the theories view
concrete mixtures, water layer theory considers concrete as a mixture of particles and water
while paste layer theory divides concrete in two phases of paste and aggregates. Water/paste
layer theories are less used in literature and practice comparing to particle packing theory
since the measurement of surface area is complex, expensive and in cases inaccurate. The
water/paste layer theories were not directly used in this document but rather explained to
33
Methods
emphasize the research gap concerning measurement of specific surface area (SSA).
Calculation of SSA based on particle size distribution curve and the conditions for replacing
assumed spherical shape of particles with other polyhedrons is described in Section 3.3.2 and
Papers III & IV.
34
Experimental results
5. EXPERIMENTAL RESULTS
The following chapter includes the results that were used in compiling the appended papers.
The data were obtained either in laboratory, by calculation or extracted from papers published
by other researchers.
Papers I & II focus on the subject of particle packing and the accuracy of three of the
developed models namely modified Toufar, CPM and 4C, see Sections 3.2 and 3.3. Papers III
& IV deal with estimation of specific surface area and its application in water/paste layer
theories as described in Section 3.3.2.
5.1. Packing models study
Figure 5.1. shows a typical result of packing density study (more results can be found in
Papers I & II) for binary mixes obtained from the laboratory experiment versus modified
Toufar model, 4C and CPM. The volume share of fines in the mixture was increased by 10%
in each step.
The interactions of particles were utilized in 4C software by means of
ȝ
-values (see Section
3.2.2). For sensitivity analysis purposes, three different
ȝ
-values of 0.07, 0.05, and 0.03 were
assigned to the model. Results from CPM were calculated by assigning compression index
K
equal to 4.1 which represents loose packing.
The models’ estimation had a point to point deviation of 0.5 % to 5.8 % in packing density
comparing to the laboratory data.
35
Experimental results
Figure 5.1. Loose packing density of a binary mix from Riksten quarry in Sweden, CPM, modified
Toufar and 4C models
ZLWKWKUHHGLIIHUHQWȝYDOXHV
vs. lab data.
As it can be seen in Figure 5.1, using different models will lead to different proportions of
aggregates for any given mixture. The difference also exists in estimation of maximum
packing density depending on which model was used where CPM slightly overestimates
packing values comparing to modified Toufar. Moreover, while the models tend to agree on
the packing density as the finer material becomes dominant in the mixture (above 60% of fine
content), the difference between estimated packing density becomes larger on the coarse side
(left side) of the diagram.
It was concluded that generally in the tests performed, the accuracy of CPM and modified
Toufar increase as the ratio between fines mean diameter to the coarse mean diameter
decreases. On the contrary 4C shows better agreement with the test results for higher mean
size ratios. For more detailed results see Paper II.
Figure 5.2. shows the total comparison of differences between measured and calculated
packing densities. Considering all the data obtained in the laboratory, Modified Toufar
showed 1.72 % mean difference while the mean difference for CPM and 4C were 1.79 % and
1.84 % respectively. It should be mentioned that the comparison was done on 4C with
ȝYDOXH
of 0.07 as it is suggested by 4C manual for aggregates originated in Scandinavia.
0,5
0,55
0,6
0,65
0,7
0,75
0,8
0
20
40
60
80
100
P
ac
ki
ng D
ensi
ty
% Fine / total volume
Riksten Crushed 0-2 + Riksten Crushed 8-16
4C
μ
=0.07
4C
μ
=0.05
Lab
Toufar
CPM
4C
μ
=0.03
36
Experimental results
Figure 5.2. Comparison of difference between calculated and measured values based on loose packing
for Modified Toufar, CPM and 4C (see also Paper II).
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