Cement selection plays a crucial role in the performance of concrete structures[1], especially for large-scale
projects such as dams. For this purpose, three types of cement (X, Y, and Z) have been analyzed based on
their chemical composition and performance characteristics. The study evaluates their suitability for dam
construction by calculating (Silica Modulus, Alumina Modulus, and Hydraulic Modulus) and determining
the major cement compounds using Bogue’s equations.
Given Data:
Answer to the question no (i)
Silica modulus:
The Modulus of Silica (SM) is a key parameter in cement chemistry that represents the ratio of silicon dioxide
(SiO2) to the sum of alumina (Al2O3) and ferric oxide (Fe2O3) in the raw mix. It is a key factor in determining
the cement's reactivity, particularly in its setting and strength development properties.[2] The higher SM ratio
indicates an increase in resistance to chemical and atmospheric attack and a higher strength. A lower amount
of alumina also causes slow setting and slow hardening of cement. Depending on the cement type, the ratio
varies from 1.5 to 5.
It can be calculated using the formula:
𝐒𝐢𝐎𝟐
SM=
(𝐀𝐥𝟐𝐎𝟑+𝐅𝐞𝟐𝐎𝟑)
Alumina Modulus:
The alumina modulus, which is the ratio of alumina oxide to iron oxide, generally assists in determining
the temperature at which the liquid phase composition of clinker begins to form inside a kiln. It also
indicates the colour of the clinker produced.[3]A high ratio indicates a fast setting (higher thermal stress and
crack), and a too-low alumina ratio has low heat of hydration and low shrinkage. The range is 1.5 to 2.5.
It can be calculated using the formula:
𝐀𝐥𝟐𝐎𝟑
AM= 𝐅𝐞𝟐𝐎𝟑
Hydraulic Modulus:
The hydraulic modulus in cement refers to the ratio of the amounts of lime (CaO), to silica (SiO₂) , Alumina
(Al2O3), and Iron Oxide(Fe2O3) present in the cement composition. It indicates the proportion of lime that is
available to react with water and form cementitious compounds during hydration.[3]The range is 1.7 to 2.3 if
it is more than 2.4, then the concrete made expansion and shrinkage also lose volume stability[4]. If the HM
value is less than 1.7, then the resulting cement will have lower strength.
It can be calculated using the formula:
𝐂𝐚𝐎
HM=
𝑺𝒊𝑶𝟐+𝐀𝐥𝟐𝐎𝟑+𝐅𝐞𝟐𝐎𝟑
Calculation :
Cement X:
SM= 21/(7+6) =1.62
AM= 7/6= 1.17
HM= 58/(21+7+6) = 1.71
Cement Y:
9
SM= =0.53
14+3
AM= 14/3 =4.67
HM= 49/ (9+14+3) =1.88
Cement Z:
SM= 20/(5+2.5) = 2.67
AM= 5/2.5 =2.00
HM= 66/(20+5+2.5) = 2.40
Cement Type Silica Modulus (SM) Alumina Modulus (AM) Hydraulic Modulus (HM)
X 1.62 1.17 1.71
Y 0.53 4.67 1.88
Z 2.67 2.00 2.40
Answer to the question no (ii):
Bogue's equations estimate the major compounds in cement [5,6]
➢ C₃S (Tricalcium Silicate): Responsible for early strength gain.
➢ C₂S (Dicalcium Silicate): Responsible for late strength development.
➢ C₃A (Tricalcium Aluminate): Contributes to the early setting time and heat of hydration.
➢ C₄AF (Tetracalcium Alumino Ferrite): A minor component
that contributes to heat but does not directly improve strength and
forms similar hydration products to C3A with or without gypsum.
• C₃S (Alite): 4.07(CaO) - 7.60(SiO₂) - 6.72(Al₂O₃) - 1.43(Fe₂O₃) - 2.85(SO₃)
• C₂S (Belite): 2.87(SiO₂) - 0.754(C₃S)
• C₃A (Aluminate): 2.65(Al₂O₃) - 1.69(Fe₂O₃)
• C₄AF (Ferrite): 3.04(Fe₂O₃)
Calculation:
Cement X
➢ C₃S = 4.07(58) - 7.60(21) - 6.72(7) - 1.43(6) - 2.85(1) = 236.06 - 159.6 - 47.04 - 8.58 - 2.85 =
18%
➢ C₂S = 2.87(21) - 0.754(17.99) = 60.27 - 13.56 = 46.7%
➢ C₃A = 2.65(7) - 1.69(6) = 18.55 - 10.14 = 8.41%
➢ C₄AF = 3.04(6) = 18.24%
Cement Y:
➢ C₃S = 4.07(49) - 7.60(9) - 6.72(14) - 1.43(3) - 2.85(2.5) = 199.43 - 68.4 - 94.08 - 4.29 - 7.125
= 25.53%
➢ C₂S = 2.87(9) - 0.754(25.535) = 25.83 - 19.25 = 6.59%
➢ C₃A = 2.65(14) - 1.69(3) = 37.1 - 5.07 = 32.03%
➢ C₄AF = 3.04(3) = 9.12%
Cement Z:
➢ C₃S = 4.07(66) - 7.60(20) - 6.72(5) - 1.43(2.5) - 2.85(2) = 268.62 - 152 - 33.6 - 3.575 - 5.7 =
73.74%
➢ C₂S = 2.87(20) - 0.754(73.745) = 57.4 - 55.60 = 1.8%
➢ C₃A = 2.65(5) - 1.69(2.5) = 13.25 - 4.225 = 9.02%
➢ C₄AF = 3.04(2.5) = 7.6%
Summary of Bogue’s Compound Composition
Cement Type C₃S (%) C₂S (%) C₃A (%) C₄AF (%)
X 18.0 46.7 8.41 18.24
Y 25.53 6.59 32.03 9.12
Z 73.74 1.8 9.02 7.6
Interpretation & Selection of Cement for Dam Construction
Performance Characteristics
1. Temperature Rise
o C₃A and C₄AF compounds produce heat quickly during hydration, contributing to the
concrete's temperature rise.[7], [8]
o Cement Y has the highest C₃A (32.03%) and would therefore generate the most heat.
o Cement Z has slightly higher C₃A than Cement X, so it will also generate moderate heat.
o Cement X has a balanced heat generation due to moderate C₃S and lower C₃A.
2. Compressive Strength
o High C₃S gives early strength, while high C₂S gives later strength.[7-9]
o Cement Z will develop strength the fastest due to high C₃S (73.74%).
o Cement X has a balanced early (C₃S) and later strength (C₂S = 46.7%).
o Cement X, with 18.13% C₃S, and Cement Y, with 30.52%, will have lower early strength
compared to Cement Z.
o Cement Y has low C₂S, so long-term strength may be an issue.
o Cement Z's lower C₂S (0.81%) will result in a concrete mix that achieves high early
strength but slower long-term strength development.
3. Permeability
o Lower C₃A makes cement more resistant to sulfate attack.[11]
o Cement Z has lower C₃A (9.02%), making it resistant to chemical attack.
o Cement Y has the highest C₃A (32.03%), making it less durable and higher permeability.
o Cement X has moderate C₃A, making it a balanced choice.
o Cement Z has a higher C₃S content, which will help reduce permeability, making it the
least permeable of the three.
Answer to the question no : iii
Final Recommendation
For dam construction, we need high durability, low permeability, and resistance to sulfate attack.
For dam construction, high early strength, durability, and low permeability are essential to ensure the
structure's long-lasting performance.
➢ Cement Z is the best option for dam construction. Its high C₃S content (73.74%) ensures fast
strength development, making it suitable for structures requiring rapid hardening. Its lower C₂S
content (1.8%) indicates that it may have lower late strength, but for a dam, achieving high early
strength and minimising permeability are more critical. Cement Z’s combination of high early
strength and lower permeability makes it ideal for harsh dam environments, where water exposure
and structural integrity over time are key concerns and advantages for dam construction. The high
C₃S and low C₃A content in Cement Z contribute to a denser concrete matrix with lower
permeability. Lower C3A minimises the risk of excessive heat generation and sulfate attack, making
it more durable in the long term[8]. This is particularly important for dams, which are exposed to
water and varying environmental conditions[12]. This makes it highly resistant to water
penetration, ensuring the dam's long-term durability and providing good resistance to chemical
attack.
➢ Cement X has a balanced composition, providing a good combination of early and late strength due
to its higher C₂S content. However, its lower C₃S content makes it less suitable for applications
requiring rapid strength development like dams[13].
➢ Cement Y has a high C₃A content, which leads to the early setting time and heat of hydration[12],
[14] but may result in cracking due to rapid heat generation, making it less ideal for large-scale
applications like dam construction, where controlled hydration and heat generation are critical to
prevent cracking.
Final Conclusion:
Thus, Cement Z is the most appropriate choice for dam construction, given its performance characteristics,
including strength, heat generation, and low permeability, making it highly durable for such demanding
applications.
References:
[1] T. U. Mohammed, A. Hasnat, S. Sharkia, P. Hasan, B. K. M. A. Islam, and S. Sharkia, ‘Advancing and
Integrating Construction Education, Research & Practice’. [Online]. Available:
https://www.researchgate.net/publication/220018676
[2] M. M. Yadollahi, A. Benli, and R. Demirboʇa, ‘The effects of silica modulus and aging on
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[3] M. S. Kirgiz, ‘Use of ultrafine marble and brick particles as raw materials in cement
manufacturing’, Materials and Structures/Materiaux et Constructions, vol. 48, no. 9, pp. 2929–
2941, Sep. 2015, doi: 10.1617/s11527-014-0368-6.
[4] M. Schneider, M. Romer, M. Tschudin, and H. Bolio, ‘Sustainable cement production-present and
future’, 2011, Elsevier Ltd. doi: 10.1016/j.cemconres.2011.03.019.
[5] H. F. W. Taylor, ‘Modification of the Bogue calculation’.
[6] ‘bogue1929’.
[7] N. Li, L. Xu, R. Wang, L. Li, and P. Wang, ‘Experimental study of calcium sulfoaluminate cement-
based self-leveling compound exposed to various temperatures and moisture conditions:
Hydration mechanism and mortar properties’, Cem Concr Res, vol. 108, pp. 103–115, Jun. 2018,
doi: 10.1016/j.cemconres.2018.03.012.
[8] by Ahmadreza Sedaghat et al., ‘Cement Heat of Hydration and Thermal Control’, 2016.
[9] E. L’Hôpital, B. Lothenbach, D. A. Kulik, and K. Scrivener, ‘Influence of calcium to silica ratio on
aluminium uptake in calcium silicate hydrate’, Cem Concr Res, vol. 85, pp. 111–121, Jul. 2016, doi:
10.1016/j.cemconres.2016.01.014.
[10] G. Álvarez-Pinazo et al., ‘In-situ early-age hydration study of sulfobelite cements by synchrotron
powder diffraction’, Cem Concr Res, vol. 56, pp. 12–19, 2014, doi:
10.1016/j.cemconres.2013.10.009.
[11] S. I. Pavlenko, ‘Fine-grained concrete containing spoils from open cuts and hydroremoved ash
from thermal power plants of Ekibastuz as aggregates’.
[12] H. F. W. . Taylor, Cement chemistry. T. Telford, 1998.
[13] H. G. Van Oss and A. C. Padovani, ‘R E S E A R C H A N D A N A L Y S I S Cement Manufacture and
the Environment Part I: Chemistry and Technology’, 2002. [Online]. Available:
http://mitpress.mit.edu/JIEhttp://minerals.usgs.gov/minerals
[14] L. Lavagna and R. Nisticò, ‘An Insight into the Chemistry of Cement—A Review’, Jan. 01, 2023,
MDPI. doi: 10.3390/app13010203.
