BAU Journal - Science and Technology
Volume 4 Issue 1
ISSN: 2959-331X
Article 3
December 2022
CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY
METHODS
Salem Abdelgader
Global Service Centre in MacGregor Company, Gdansk, Poland, salemsmoee4@gmail.com
Marzena Kurpinska
Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland,
marzena.kurpinska@pg.edu.pl
Hakim Abdelgader
Department of Civil Engineering, University of Tripoli, Tripoli, Libya, Faculty of Civil and Environmental Engineering,
Gdansk University of Technology, Gdansk, Poland, h.abdelgader@uot.edu.ly
Jamal Khatib
Faculty of Engineering, Beirut Arab University, j.khatib@bau.edu.lb
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Recommended Citation
Abdelgader, Salem; Kurpinska, Marzena; Abdelgader, Hakim; and Khatib, Jamal (2022) "CONCRETE MIX
DESIGN USING ABRAMS AND BOLOMEY METHODS," BAU Journal - Science and Technology: Vol. 4: Iss. 1,
Article 3.
DOI: https://doi.org/10.54729/MJPS9917
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Abdelgader et al.: CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY METHODS
1. INTRODUCTION
Environmental protection should be a priority in scientific research. This is especially
important for the field of concrete technology due to the repercussions of environmental pollution
as a result of CO2 emissions during cement production. If the production of one ton of cement
causes the emission of 600 kg of CO2 and the construction industry is responsible for 8% of total
CO2 emissions it belongs to look for optimal solutions in the production of cement but also in the
design of concrete. Scientifics have already taken up this challenge in concrete technology and
the results of the research are known, among others (Radhakrishna et al., 2020, Wang et al., 2018,
Brito et al., 2018, Chidiac et al., 2013, Popowics, 1998, Popowics, 1985).
The first methods of concrete design were the Abrams and Bolomey methods (Bulletin,
1924, Bolomey, 1935, Karni, 1974,Popovic et al., 1981, Kasperkiewicz, 1994). As these methods
are quite simple, they are still frequently used mainly in Europe (Abdelgader et al., 2020, Mishra
et. al., 2012, Brandt, 2009, Popovics and Ujhelvi, 2008, Ekinci et. al., 2006, Larrard, 1999). Based
on Bolomey's and Abrams’ formulas, many computer programs supporting concrete design were
created. Attempts were made fiew to modify these methods and the research results were
presented in the works (Wang et. al., 2018, Abdelgader et. al., 2013, Abdelgader et. al., 2012,
Nataraja et. al., 2012, Ramajane et. al., 2012, Brandt, 2009).
Wang et al., 2018 noticed that a concrete mixture with an optimum proportion of fine and
coarse aggregates guarantees high strength of concrete. The authors used the Bolomey method to
design concrete taking into account the appropriate regulations and grading requirements of the
aggregates in the China standards. After concrete test verification, the conclusion was made that
with the optimal combination of fine and coarse aggregates, concrete mix proportion is easy to
determine. In addition, the authors, based on the research, noticed that the obtained compressive
strength was higher by 20% than the designed one. It was assumed that this may be a guarantee
of high quality and durability of concrete.
Abdelgader at el., 2013, 2012 in their research took into account the fact that the properties
of fresh mix and hardened concrete are significantly related to their composition. The authors
referred to other concrete composition design methods such as ACI and BS methods are the most
commonly used. The presented research used the modified Bolomey method as The Three
Equations Method, which was illustrated in this paper, in addition to the assessment of the
laboratory results of concrete mixes produced by this method.
Nataraja and Sanjay, 2012 were dealing with the development of design concrete with
Bolomey and Abrams. This research used the impact of aggregate quality on concrete
compressive strength. Was researched to proportion mortar strengths to concrete compressive
strength and to impact abrasion resistance of the aggregate on the compressive strength of
concrete. The research used soapstone as well as granite stone as coarse aggregates. Based on the
results, correction to the published modified Bolomey equation is also suggested which can be
used for the design of concrete containing soapstone.
Rajamane at el., 2012 used the Bolomey equation has been used for relating the cement–
water ratio to the compressive strengths of concrete containing normal and lightweight aggregate
(LWA). It was found that this is basically a linear equation, not considering explicitly the
parameters relating to coarse aggregates. It has been shown the strengths of lightweight concrete
(LWC) containing LWA are influenced both by w/c ratio and the properties of the LWA. A
modified Bolomey method, considering indirectly the presence of LWA, is suggested, using the
experimental data.
Brandt, 2009 in the book presented a modified Bolomey method for the practical prediction
of compressive strength at the age of 28 days. He assumed that compressive strength is mainly on
one parameter: this is the water/cement ratio. Traditional formulae described by Bolomey
described were have been transformed on the Three Equations method.
In this paper, the authors presented the results of laboratory tests, comparing both methods
of concrete design, including the modified Bolomey method. Concrete with assumed compressive
strength 25, 30, 35, 40, and 45 MPa was researched. The compositions of concretes were
compared and calculated according to two methods. The research was conducted in the laboratory
using two types of samples: cubic 15x15x15cm for compressive strength tests and cylinders ϕPublished by Digital Commons @ BAU, 2022
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BAU Journal - Science and Technology, Vol. 4, Iss. 1 [2022], Art. 3
15cm, h-30cm for the splitting strength tests using the Brazilian method. The obtained test results
can be the basis for future modifications of the concrete design methods, taking into account
additives and admixtures, and can be the basis for the application of artificial neural networks
(ANN) to design the composition of concrete.
2. METHODOLOGY
2.1 Materials
The local materials used from Northern Poland and portland ordinary CEM I 42.5R
type Portland cement were used. The physical properties of cement are presented in Tab.1.
Table 1: Physical properties of cement
Cement
Type
Setting
Start Time
[min]
Setting
End
Time
[min]
155
195
CEM I 42.5R
Compressive
Strength
[MPa]
After
2 [days]
After 28
[days]
30.2
57.3
Blaine
Fineness
[cm2/g]
Loss of
Ignition
[%]
Water
Demand
[%]
3504
3.4
27.5
The natural rounded, washed aggregate was used in the research Fig.1. The graining
of the aggregates is shown in Fig. 2. Clean water was used without impurities. Admixtures
and additives in this research were not used.
a) sand 0-2mm
b) gravel 2-8mm
c) gravel 8-16mm
Fig.1: The aggregate using in research.
Fig.2: Granular gradient curve for mix aggregates.
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DOI: 10.54729/MJPS9917
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Abdelgader et al.: CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY METHODS
2.2 Methods
2.2.1 Design of concrete composition according to Abrams's Law and the modified
Bolomey method (Three Equations).
The design steps of the composition of the concrete mix according to the
Abrams law were as follows: 1/ definition of compressive strength 𝑓′𝐶 ; 2/ definition
of the required workability (medium and very high); 3/ the Abrams equation used to
𝑊
design the compressive strength of concrete, through cement/water ratio ( 𝐶 ),
according to the Eq. (1).
𝑓′𝐶 =
𝐴
(1)
𝑊
( )
𝐵 𝐶
where A, and B are empirical constants, W – water, C- cement.
These formulae used with appropriate calibration of constants A and B, allowing
for local conditions, specified properties of components (aggregate), quality of curing,
etc. Based on 28 days of compressive strength, other mechanical parameters like
splitting strength be calculated from standardized formulae. All calculations of the
results was presented in Tab. 4.
The design steps of the composition of the concrete mix according to the
Bolomey method the steps were as follows: 1/ definition of compressive strength 𝑓′𝐶 ';
2/ definition of the required workability (medium and very high); 3/ the Bolomey
method as Three Equation used to design the compressive strength of concrete,
through cement/water ratio (W/C), according to Eq. (2) and (3).
The modified Bolomey method by Brandt 2009, is based on the solution of three
linear equations, which expressed strength, materials density, and water requirements
of particular fractions of aggregate. The compressive strength was calculated after the
so-called Bolomey formula from Eq. (2-5) as follows:
1
𝑓 ′ 𝐶 = 𝐴1 ⋅ (𝑊/𝐶 − 0.5)
1
𝑓′𝐶 = 𝐴2 ⋅ (𝑊/𝐶 + 0.5)
for w/c > 0.4
(2)
for w/c ≤ 0.4
(3)
where: 𝑓′𝐶 – characteristic compressive strength, C- cement, W-water and both
constants A1 and A2 considered after the quality of cement and aggregate.
The value of the coefficients A1 and A2 depend on the cement's compressive
strength and aggregate shape. It is done by defining them from Tab. 2, where the coarse
aggregate used in the concrete mixtures was rounded shape and the compressive
strength of the cement type is CEM I 42.5R. The value of each of the coefficients was:
A1 = 20 MPa and the coefficient A2 =13 MPa.
Table 2: Coefficient of A1 and A2 values.
Aggregate shape
Rounded
Angular
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Variable (A)
Compressive strength of cement (MPa)
32.5
42.5
52.5
A1
18.0
20.0
21.0
A2
12.0
13.0
14.5
A1
24.0
22.0
20.0
A2
16.0
14.5
13.5
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BAU Journal - Science and Technology, Vol. 4, Iss. 1 [2022], Art. 3
By means of the second equation Eq.(4), it is possible to calculate the amount
of water required to obtain the required consistency of the concrete mix. In our case,
medium and very high consistency were adopted.
𝑊 = 𝐶 ⋅ 𝑤𝐶 + 𝐴 ⋅ 𝑤𝐴
(4)
where: W- water, A – aggregate, C – cement, wc i wA - index by Stern, for cement and
water respectively. Index by Stern is the water needed to moisten 1 kg of the
specified aggregate fraction to obtain the required consistency and workability.
Table 3: Water index by Stern for aggregate (wA) and cement (wc)
Sieve size
(mm)
Workability
Medium
Very High
16 – 31.5
0.016
0.022
8 – 16
0.020
0.027
4–8
0.026
0.034
2–4
0.032
0.044
1–2
0.043
0.058
0.5 – 1
0.058
0.077
0.25 – 0.5
0.084
0.112
0.125 – 0.25
0.122
0.151
0 - 0.125
0.239
0.296
cement wc
0.275
0.310
In this Bolomey method, the unknown values were W/C, C-cement and Aaggregate. As in other methods minimum amount of cement and aggregate grading
were imposed by standard regulations.
The third equation takes into account the sum of the volumes of all components
which should be 1 m3. The formula is as follows Eq.(5):
𝐶
𝜌𝐶
+
𝐴
𝜌𝐴
+ 𝑤 = 1.0 [m3 ]
(5)
Where: C-cement and A-aggregate and 𝜌𝐶 and 𝜌𝐴 are specific densities of cement and
aggregate, respectively.
The results of the calculation are presented in Table 5
2.2.2 Experimental Tests
In this study, designs of concrete mixes with assumed strengths of 25, 30, 35,
40 and 45 MPa were made. Moreover, calculations of the concrete composition were
made taking into account two cases of concrete mix liquidity. It was assumed that the
mixes will have medium and very high workability. Two methods of concrete design
were used: the modified Bolomey method (Three Equation), therefore the
composition of the mixtures is significantly different in both cases. The compositions
of individual concretes are presented in Tab. 4 and Tab. 5. In total, 20 mixes were
designed. From each mixture, 6 cubic samples about dimensions 150 mm x 150 mm
x150 mm were made for the compressive strength test within 28 days and 3
cylindrical ϕ150mm x h300 mm samples for the splitting strength test using the
Brazilian method.
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DOI: 10.54729/MJPS9917
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Abdelgader et al.: CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY METHODS
Concrete components were mixed in a mechanical mixer. The consistency was
measured by the slump test (Fig.3). Then the mix was placed in PVC molds and
compacted on a vibrating table for 2 min, according to EN 12390-1. Samples were
stored until testing in a special room with a humidity of 90±5% (Fig.4). Test
specimens were stored for 24 h in molds at the temperature of 20 ± 2 °C, followed
until testing time by subsequent storage in a special room with a humidity of 95–
100% and a temperature of 20 ± 2 °C. One hour before the test, the specimens were
taken out from the chamber and left to dry in the air at a temperature of 20±2°C,
according to EN 12390-2:2019. The compressive strength of each concrete was tested
on cubic samples according to EN 12390-3 by means of an Advantest 9 Controls
machine (Advantest 9, Controls, San Maurizio Canavese, Italy) with a maximum
pressure force of 3000 kN according to EN 12390-4, Fig.5. Compressive strength was
tested according to EN 12390-3:2019 and was determined as an arithmetic mean of
six measurements, along with the calculation of standard deviation of each batch. The
tensile strength of concrete with the Brazilian method was made according to EN
12390-6, Fig.6.
Fig.3: The slump
test.
Fig.4: Curing the
concrete samples.
Fig.5: The
compressive
strength test.
Fig.6: The splitting
test.
3. RESULTS
Table 4 presents the results of calculations by the Abrams law for the composition of
concrete classes 25, 30, 35, 40 and 45 MPa, as well as the results of compressive and splitting
strength tests. Mainly the content of cement in the composition of concrete as the main component
generating CO2 emissions was analyzed. As for the correlation between the cement content and
the compressive strength, it can be seen that in the case of concrete of the 25MPa class, the
obtained strength was 8% lower than that designed for the medium workability and 21.6% lower
in the case of workability very high. The W/C ratio = 0.78, while the cement content for the
assumed workability was 180 kg/m3 and 225 kg/m3, respectively. On the basis of the obtained test
results, it can be concluded that the W/C ratio calculated according to the formula Eq. (1) is too
high, therefore the concrete strength was lower than required. In the case of the designed concrete
strength class of 30, 35, 40 and 45 MPa, higher results, even up to 17%, were obtained. The
smallest difference between the design strength and the actual strength tested on the samples
concerned the strength of 30 and 35 MPa and ranged from 0% to 12%. So it can be said that in the
range of 30-35 MPa, the Abrams law turned out to be the best for design. The tests of concrete
splitting strength showed that the test results for individual classes ranged from 1.7 MPa to 3.5
MPa and differed, depending on the workability, from average and very high, from 3% to 15%,
respectively.
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BAU Journal - Science and Technology, Vol. 4, Iss. 1 [2022], Art. 3
Table 4: Calculation results and compressive and splitting strength tests according to Abram's
method.
Type of
workability
Design
compressive
strength (MPa)
Water to
Cement (W/C)
Cement
content
(kg/m3)
Aver.
compressive
strength after 28
days (MPa)
Aver. splitting
strength after
28 days (MPa)
Medium
25
0.78
180
23.0
2.0
Very high
25
0.78
225
19.6
1.7
Medium
30
0.68
219
29.8
2.2
Very high
30
0.68
271
31.6
2.5
Medium
35
0.60
264
39.3
3.0
Very high
35
0.60
325
37.8
2.9
Medium
40
0.53
323
47.0
3.3
Very high
40
0.53
393
43.3
3.2
Medium
45
0.46
414
49.6
3.4
Very high
45
0.46
497
52.0
3.5
Table 5 shows the results of calculations and laboratory tests according to the Bolomey
method. It can be noticed that in the case of calculations made with this method, the W/C ratio for
the design strength is much lower than that calculated according to the Abrams method and
amounts to W/C = 0.57. As you might expect, the compressive strength was much higher than the
designed one, because by as much as 45%. Consumption of cement for class 25 and medium and
very high workability was 286 kg/m3 and 351 kg/m3, respectively. For the designed concrete
strengths of 30, 35, 40 and 45 MPa, the W/C index decreased from 0.5 to 0.33, and along with that,
the cement content increased from 356 kg/m3 to 982 kg/m3. The strength was higher from 37% to
57%. The splitting strength ranged from 2.5 to 4.4 MPa. It can be clearly stated that the calculation
according to the Bolomey method (Three Equations) generates a very high consumption of
cement, and does not cause growth significantly increase the strength of the concrete.
Table 5: Calculation results and compressive and splitting strength tests according to Bolomey
method.
Aver.
compressive
strength after
28 days (MPa)
Aver. splitting
strength after
28 days (MPa)
286
36.1
2.5
0.57
351
36.4
3.1
30
0.50
356
41.1
3.1
Very high
30
0.50
432
44.7
2.6
Medium
35
0.44
451
49.7
3.0
Very high
35
0.44
538
52.9
2.9
Medium
40
0.39
579
55.7
4.1
Very high
40
0.39
678
52.7
3.7
Medium
45
0.33
879
58.4
4.3
Very high
45
0.33
983
62.3
4.4
Design
compressive
strength (MPa)
Water to
Cement
(W/C)
Cement
content
(𝑘𝑔∕m3 )
Medium
25
0.57
Very high
25
Medium
Type of
workability
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DOI: 10.54729/MJPS9917
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Abdelgader et al.: CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY METHODS
Figure 7 shows the change in compressive and splitting strength depending on the change in the
W/C ratio.
Fig.7: Relationship between the compressive and splitting strength and W/C ratio for medium and very
high workability according to Bolomey method's and Abrams law.
Figure 8 shows the relationship of compressive strength with the W/C ratio for medium and
very high workability, determined according to Bolomey method and Abrams's law. The figure
shows the compressive strength vs. cement consumption. From the results obtained, it can be seen
that the Abrams law is characterized by a better optimal consumption of cement vs. compressive
strength, especially above a compressive strength of 25 MPa.
Fig.8: Relationship of compressive strength vs. cement consumption with the W/C ratio.
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BAU Journal - Science and Technology, Vol. 4, Iss. 1 [2022], Art. 3
4. CONCLUSIONS
Based on the obtained test results concretes with specific compressive strength: 25, 30, 35,
40 and 45 MPa and the assumed medium and very high workability, it can be concluded that there
are significant differences depending on the design method used. Basic differences characterizing
Abrams's law and Bolomey methods can be formulated.
1- Both methods are easy to apply and are therefore widely used mainly in Europe.
2- The analysis of the cement content in the composition of 1m3 of the mixture showed very large
differences depending on the calculation method used. The cement content calculated
according to the Abrams method ranged from 180 kg/m3 (25MPa) to 497 kg/m3 (45MPa)
depending on the class and determined according to the Bolomey method from 286 kg/m3
(25MPa) to 983 kg/m3 (45MPa).
3- By analyzing the results of the compressive strength tests, it was confirmed that the compressive
strength depends on the water/cement ratio. In the case of applying the Abrams law, the W/C
ratio was from 0.78 and decreased to 0.46, while the compressive strength was from 19.6 MPa
to 52.0 MPa, respectively. The W/C ratio for concretes designed according to the Bolomey
method was lower varied from 0.57 to 0.33, while the compressive strength was from 36.1 MPa
to 62.3 MPa.
4- In designing concrete, the selection of the design method is important due to the possibility of
calculation of the concrete mix composition and obtaining the precisely and compliant with the
requirements strength. The calculation method should allow the most precise prediction of
concrete strength. Based on the research, it was noticed that the standard deviation of the results
did not exceed 2% in any case (for 6 samples tested for each class and for each assumed
workability). In the case of the designed concrete strength class of 30, 35, 40 and 45 MPa,
higher results, even up to 17%, were obtained. The smallest difference between the design
strength and the actual strength tested on the samples concerned the strength of 30 and 35 MPa
and ranged from 0% to 12%. According to Bolomey method the strength was higher from 37%
to 57% when analyzing research for all concrete classes. So the endurance was significantly
overstated.
5- Compressive strength vs. cement consumption showed that the Abrams law is characterized by
optimal cement consumption, especially when determining the composition of concretes with
compressive strength above 25 MPa. It can be said that in the range of 30-35 MPa, the Abrams
law turned out to be the best for design.
6- The tests of concrete splitting strength calculated by Abrams law ranged from 1.7 MPa to 3.5
MPa and differed, depending on the workability from 3% to 15%, respectively, while according
to the Bolomey method the splitting strength ranged from 2.5 to 4.4 MPa and results differed
to 15%.
7- A cement content of more than 450 kg/m3 is not desirable, primarily from an environmental and
economic point of view.
8- It can be clearly stated that the calculation according to the modified Bolomey method (Three
Equations) generates a very high consumption of cement, and does not cause growth
significantly increase the strength of the concrete.
An example is the designed concrete class of 45 MPa. In this case, the amount of cement
according to the calculations was 983 kg/m3 and the compressive strength in this case was 62.3
MPa.
9- Probably the use of chemical admixtures along with the correction of the water content would
increase the strength concrete calculated according to both methods. However, attention should
be paid to the fact that concrete admixtures are selected depending on the type and amount of
cement. Therefore the cement content in 1m3 mix concrete is also important for economic
reasons, because the higher the cement content, the greater the admixture consumption.
10- Summarizing the above, bearing in mind the protection of the environment, it is necessary to
select the appropriate methods of concrete design, taking into account cement admixtures and
substitutes.
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DOI: 10.54729/MJPS9917
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Abdelgader et al.: CONCRETE MIX DESIGN USING ABRAMS AND BOLOMEY METHODS
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doi.org/10.1051/matecconf/201823802009.
- EN 12390-1 Concrete tests-Shape, dimensions and other requirements concerning test samples.
- EN 12390-3 Concrete tests -Compressive strength of the samples
- EN 12390-4 Concrete tests-Compressive strength. Universal testing machines specification
Published by Digital Commons @ BAU, 2022
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BAU Journal - Science and Technology, Vol. 4, Iss. 1 [2022], Art. 3
- EN 12390-2 Testing hardened concrete. Making and curing specimens for strength tests.
- EN 12390-3 Testing Hardened Concrete-Part 3: Compressive Strength of Test Specimens.
- EN 12390-6 Testing hardened concrete-Part 6: Tensile splitting strength of test specimens.
https://digitalcommons.bau.edu.lb/stjournal/vol4/iss1/3
DOI: 10.54729/MJPS9917
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