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TECHNICAL PAPER

The r m and p obtained through the model can be subsequently (12)
used in Equation 7 to predict the strength of paste, mortar, or
concrete etc. However, for concrete the equation proposed in the earlier
[15]
paper by Kumar and Bhattacharjee is given in Equation 13,
(8)
(13)
The r m was further related to w/c, mean cement particle size where, k is a constant and takes care of unaccounted factors, f ca ,
D and age t as derived through geometric modelling. The
equations for r 0.5 with these factors are given in Equations 9, f e , f a and f T are multiplying factors to take into consideration of
the effects of aggregate type, exposure to acidic environment,
(9) age and exposure temperature, respectively.
where, To revisit Abrams’ Law, i.e., strength of a cement-based material
reduces with w/c, the p and r 0.5 , were related to w/c through
(9a) Equations 2 and 9. The empirical constants in the equations
were worked out from experimental data generated across
(9b) several research studies [15-19] . The main variables in Equations
11, 12, and 13, which are related to w/c include cement/
In above equations, the constants a 1 , a 2 , a 3 and a 4 are 1184.6, – cementitious content, degree of hydration/age, total porosity,
161.7, 123.0 and – 7.4, respectively for OPC paste. and r 0.5 . For F = 0, K 1 and K 2 in Equations 11 and 12 are identical
and consequently the variation of strength depends on the
For fly ash admixed paste, mortar etc. similar relationship can common factor, C α (1 –p)/(r 0.5 ) , in all the three equations. For
½
also be obtained , e.g., for fly ash mortar gel porosity is related a given age, α c would thus vary only with C (1 – p)/(r 0.5 ) . Thus,
[18]
½
to water to binder ratio is as follows, the pattern of variation of σ c with w/c would be similar for
paste mortar and concrete. The variation of σ c with w/c for four
cases as shown in Figures 6 to 9 corroborates the postulation
of Abrams’ Law. Hence a more fundamental understanding of
where, the constants k 1 , k 2 , k 3 , k 4 and k 5 are 600.72, – 270.73, Abrams’ Law is provided through models based on porosity and

[20]
257.44, – 23.56, and – 30.82 respectively for cement fly ash pore size distribution .

mortar. The above expression was obtained after removing The measured porosity and pore size distribution (PSD)
few extreme data and the corresponding coefficient of are known to vary depending on the experimental method
determinations was 73 %. Capillary pores in fly ash mortar tend employed . While MIP measures an equivalent pore-entry
[21]
to get segmented early and capillary pore entry radius vanishes, radius and the porosity of intrudable pores only, it covers
thus resulting in r m = r m (gel).
maximum range of pore sizes when compared with other
The uniaxial compressive strength of cement-based composites methods. In contrast, water permeable pores measured through
including concrete is governed by tensile failure along the boiling water test as per ASTM C642-21, provides the total
direction normal to compressive load, induced owing to permeable pore volume and generally yields higher porosity
Poisson’s effect. Hence, extending the idea illustrated in values. However, the theoretically estimated total porosity often
Equation 7, the compressive strength σ can be expressed as overestimates the water permeable porosity measured through
[22]
given in Equation 10 [15,19] , cold and boiling water tests as per ASTM C642-21 .
(10) 4. ADVENT OF ADMIXTURES AND STRENGTH

The K in Equation 10, accounts for a factor relating compressive During the early 1960s, synthetic polymers began to make
strength to tensile strength, E 0 , T 0 etc., and other unaccounted inroads into many domestic and industrial applications.
factors, depending upon method of tests. Elastic modulus This development led to the synthesis and introduction of
and surface energy of pore free solids include solid phase of more efficient water-reducing agents (WRAs) for concrete.
aggregates, un-hydrated cement and products of hydration. Sulphonated melamine formaldehyde (SMF) and sulphonated
Further separation of K into factors resulted in Equation 11 naphthalene formaldehyde (SNF) condensates were widely
[19]
for OPC paste and Equation 12 for OPC-fly ash paste and adopted as water reducing agents (WRA). Owing to their larger
cement-sand mortar. molecular size compared with lignosulphonates - derived from
natural plant sources and obtained as by-products of the paper
(11) industry - SNF and SMF could be adsorbed by cementitious

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