Page 21 - ICJ Jan 2026

TECHNICAL PAPER

Subscripts, “sp” and “sA” are used to denote paste and 1
aggregate solid, respectively. The solid conductivity of concrete 0.9
is taken as arithmetic mean of above two conductivities i.e., 0.8
k s = 0.5 (k s1 + k s2 ). 0.7

The k sA is unknown, but knowing k s for various concrete 0.6
aggregates k sA can be estimated from following equation, when The fraction of enclosed pores (f ) 0.5 f = − 0.5178(w/c) + 1.1388
V p , V A , k sp , and k s are known, by a trial-and-error procedure or 0.4 R² = 0.9931
adopting any standard solution procedure for transcendental 0.3
equation. 0.2
0.1
(43) 0
0 0.2 0.4 0.6 0.8 1
[45]
The calculated k sA values for Korean aggregate and river sand w/c of concrete
for various paste contents range from 3.25 to 3.75 W/m.K with Figure 22: Fraction of enclosed pores of concrete against w/c
their average 3.58 W/m.K and CV of 6.3 %. The estimation shows
that k sA values are independent of paste content and depend value of 0.6, it is lower and the average value is 0.82; similarly,
upon aggregates and their combination. The calculated values the average value of f for w/c of 0.64 is 0.82. For w/c value of
for various aggregate combinations are given in Table 12. 0.9, the average f value is 0.67. Higher, the w/c, proportion
of interconnected capillary pores increases with respect to
When aggregate mineral sources are same and coincide with
any one of the combinations, the above k sA values in Table 12 proportion of gel pores, hence fraction of enclosed pores
can be used to estimate thermal conductivity of concrete. reduces. Fraction of enclosed pores f against w/c for concrete
When the source is partially known that one aggregate belongs is plotted in Figure 22, and a linear relationship seems to exist.
to quartzite origin and others are non-quartzite origin, then The Equation 44 with rounded coefficient and constant shows
the average of values in row 3 to row 6, i.e., 5.48 W/m.K is the proposed relationship, and can be used for estimating f. The
recommended as an approximate value of k sA . When both w/c value for f = 1 is 0.27 at 28 days age, i.e. matured concrete
the aggregates belong to non-quartzite aggregate, the and seems to be justifiable. The f is 1 for w/c values less than
recommended value of k sA is 4.57 W/m.K. If the sources of 0.27 with all gel pores. This equation is valid for normal concrete
aggregate are completely unknown, overall average value of where w/c is usually higher than 0.4, with upper limit as 1. The f
5.21 W/m.K may be used. is independent of all other factors.

The fraction of enclosed pores for paste is nearly 1 up to w/c 0.4 f = 1.14–0.52 (w/c) (44)
as most of the pores are gel pores. While, for mortar the f values Thus, with the knowledge of p, k s and f, the conductivity of
are lower. For concrete with w/c 0.4, the fraction of enclosed normal strength concrete can be calculated. An example is
pore f is independent of paste content in concrete as it is illustrated as follows:
dependent proportion of gel pores in paste. The average value
is 0.93. For concrete with different types aggregate with w/c A normal strength concrete having following mix proportion:
cement 380 kg/m , coarse aggregate 1150 kg/m , fine aggregate
3
3
Table 12: Solid conductivity of aggregate 750 kg/m , and w/c equals to 0.5. Aggregate sources are
3
combination in concrete limestone aggregate and sand are river sand. Estimates of dry
SR. COARSE AGGREGATE FINE AGGREGATE THERMAL and saturated thermal conductivity values are to be calculated
NO. CONDUCTIVITY OF for matured concrete (28 days age) as follows:
SOLID K sA (W/m.K)
1. Korean Aggregate Korean River sand 3.58 Volume of paste V p : (Neglecting the small initial chemical
2. Quartzite Quartzite Pit Sand 6.76 shrinkage in bulk) is . Porosity
3. Basalt Quartzite Pit Sand 5.63 (p) using Equations 39 and 40 is 0.145. The calculated values
4. Limestone Quartzite Pit Sand 4.32
are k sA = 4.02 W/m.K, V ps = (1 – 0.466)´0.311 = 0.166 and V agg = 1
5. Siltstone Quartzite Pit Sand 6.07
– V p = 1 – 0.311 = 0.689, = 0.194, = 0.806; k p = 1.4
6. Quartzite River Sand 5.93
W/m.K, with the known values k s for concrete using Equation
7. Basalt River Sand 5.17
43 is 3.23. The constants A 1 , B 1 etc. are calculated for p = 0.145,
8. Limestone River Sand 4.02
and are A 1 = 2.875; B 1 = 1.10; A 2 = 0.000792; and B 2 = 0.8255.
9. Siltstone River Sand 4.54
With these values of A 1 (p), B 1 (p), A 2 (p), and B 2 (p); λ 1d , and λ 2d , are
26 THE INDIAN CONCRETE JOURNAL | JANUARY 2026