Page 6 - ICJ Jan 2026

TECHNICAL PAPER

1960s . Kantro and Copeland, almost during the same period,
[7]
reported the results of an experimental study of over 13 years, to
establish the amounts of chemically combined water with major
compounds of cement. Equation 1 and Table 1 outline these
[7]
findings .
(1)
where, W n is the chemically combined water, C is the quantity
of cement, while compound quantities are (C 3 S), (C 2 S), etc.,
and a 1 , a 2, a 3, a 4 are amount of water bound to each major
Versatile concrete compound of cement on complete hydration. The values of a 1,
a 2, a 3, a 4 were determined experimentally and the results are
shown in Table 1. Based on this finding and assuming a typical
Figure 5: 3D representation of concrete performance domain composition of cement with 48 % C 3 S, 25 % C 2 S, 11 % C 3 A and
9 % C 4 AF, at complete hydration, chemically combined water
When ductility and crack arresting properties are desired for cement works out to be approximately 0.23 gm per gm of
[7]
fibres of appropriate elastic moduli, either solo or in hybrid cement . Powers and Brownyard also estimated the density of
combinations, are used. The third dimension of performance hydration products, i.e. C-S-H gel and Ca(OH) 2 , by using helium
of concrete composite is its long-term behavior, including pycnometry. Based on density and mass of hydration products,
resistance to creep, fatigue and material degradation resulting equations for total porosity, gel porosity, and capillary porosity
in the deterioration of elements under service exposure, were proposed by Powers and are given in Equations 2 to 4.
particularly in very severe aggressive environments. Concrete
composites can be designed for a desired maintenance-free (2)
intended design life through design for endurance against
fatigue and deterioration through service-life-based design
procedures, tailored to the exposure environment [7-11] . Therefore, (3)
the performance of concrete can be represented in a three-
dimensional space as shown in Figure 5, wherein, performance
requirements are correlated with material system design, the (4)
[1]
system can be designed as per requirement of performance .
However, current code provisions are mostly prescriptive, and It is evident that the OPC paste is porous, and the pores
research is required to develop reliable procedures. Against
this backdrop, some research are presented in the following constitute inherent flaw in the solid system that results in
sections. discrepancy between theoretically estimated tensile strength
considering Van der Waals bond strength, and the strength that
[7]
is realized in practice .
3. REVISITING ABRAMS’ LAW FROM A
MICRO-STRUCTURAL PERSPECTIVE The discrepancy between the measured and the theoretically
estimated strength of brittle materials such as glass, with the
Several micro-structure models of hydrated OPC paste have former being much lower than the latter one, was explained by
been proposed based on observations from various analytical - Griffith in 1920s through his fracture theory. Fracture of material
experimental techniques. The most accepted model postulates
a layered sheet like structure for C-S-H, which is gelatinous, Table 1: Chemically combined water [7]
i.e., having a gel structure. The layers of C-S-H are bonded by
Van der Waals forces and have inter layer spaces filled with gel w/c RATIO
water. These spaces constitute the gel porosity and is estimated a 1 0.4 0.4 0.6 0.8 0.4
to be typically 28 %. The thickness of the inter layer space (1 YEAR) (6½ YEARS) (6½ YEARS) (6½ YEARS) (13 YEARS)
estimated using adsorption isotherms and BET method is about a 1 0.228 0.234 0.238 0.234 0.230
15 Å, after Powers and Brownyard . Powers also identified the a 2 0.168 0.178 0.198 0.197 0.196
[7]
presence of capillary pores having larger sizes, i.e., the empty
a 3 0.429 0.504 0.477 0.509 0.522
spaces left behind by unreacted water upon evaporation.
Powers’ works were mostly reported during the late 1940s to the a 4 0.132 0.158 0.142 0184 0.109

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