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TECHNICAL PAPER

2
C 1 (0.0484) = 1.32 × 0.0484 – 0.12 × 0.0484 + 0.10 = 0.1025 Starting by assuming the value of k s = 8.7, the values λ 1d , λ 2d ,
λ 1s , and λ 2s are calculated. Consequently, calculated value is
2
D 1 (0.0484) = – 1.38 × 0.0484 + 0.78 × 0.0484 + 0.84 = 0.8745
obtained as f = 0.995. The estimated values of k ed and k es are
2
C 2 (0.0484) = – 0.165 × 0.0484 + 0.479 × 0.0484 = 0.0228 8.58 and 8.64 W/m.K respectively. Thus, k s = 8.7 and f = 0.995 are
deemed appropriate.
D 2 (0.0484) = e – 0.0484 = 2.7182 – 0.0484 = 2.6698
Hence, = C 1 (0.0484) k s + D 1 (0.0484) = 0.1025 × 5 + 0.8745 = Values of k s and f calculated in similar manner as above for
1.387; λ 1s = 0.7210 various rocks are given in Table 3. The fraction of enclosed
pores for rocks ranges from 0.774 to 0.996, with an average
value of 0.870 and coefficient of variation of 8.1 %. Rocks thus
have mostly enclosed pores. This is expected as pores in rocks
Experimentally obtained k ed and k es values, 3.22 and 4.69, can be are likely to be formed due to contraction of the material from
used to obtain f as follows,
molten state to solid state in case of igneous rocks and during
sedimentation process in sedimentary rocks. The conductivity
[43]
of rocks reported by Marshal for some rocks are; Quartz:
5.17 W/m.K, Granite: 2.908 W/m.K, Dolomite: 4.43 W/m.K,
Limestone: 3.23 W/m.K, Basalt: 1.710 W/m.K, Marble:
Now
2.454 W/m.K, and Feldspar: 2.326 W/m.K. The state of moisture
condition of the specimen is likely to be close to dry state,
k ed (estimated) = k s ( ) = 5.0 × 0.0779 (1–0.8326) × 0.9446 0.8326
however, neither their porosities nor their saturated conductivity

= 3.11;
is known, although values reported like those are given in
k es (estimated) = k s ( ) = 5.0 × 0.7210 (1–0.8326) × 0.9453 0.8326 Table 3.
= 4.52
5.3 Thermal conductivity of concrete
These values are different from experimental k ed and k es values,
hence proceed to next iteration to estimate k s and f, Aggregate constitutes the major volumetric component in
ordinary concrete occupying about 70 % of the volume. Hence,
aggregate contributes maximum to thermal conduction in
concrete. Coarse aggregate constitutes about 45 % by volume
in normal strength concrete while the fine aggregate may
constitute 25 % in the 70 % volume. Coarse aggregate and
The average of the two values above is k s (new); i.e., k s (new) = fine aggregate may be having different rock sources hence
[k s (new – dry) + k s (new – sat)] / 2 = 5.185 conductivity of the solid in concrete may depend upon their

mineralogical compositions.
For this case, λ 1d = 0.0754; λ 2d = 0.9445; λ 1s = 0.7112; λ 2s = 0.9445;
f =0.834 Table 4 shows the thermal conductivities of a concrete sample
in dry and saturated states along with permeable porosity. The
(1–0.834) 0.834
k ed (estimated) = 5.185 × 0.0754 × 0.9445 = 3.22 concrete was cast with different types of aggregates with OPC
k es (estimated) = 5.185 × 0.7112 (1–0.834) × 0.9445 0.834 = 4.67 cement, fine aggregate, and coarse aggregates proportioned
These two estimated values nearly match with the experimental Table 3: Estimated k and f values of some rock
values, however estimation of k s (new) from these two values lead aggregate s
to k s (new) = 5.20. One can check that k s = 5.20 and f = 0.834
converge and are the estimated true values of solid conductivity ROCK TYPE k s (W/m.K) f
and fraction of enclosed pores. Basalt 4.173 0.902
Limestone 1 3.552 0.947
Similarly, for another case of quartzite rock for which, dry
and saturated conductivities and porosity are 8.58 W/m.K, Limestone 2 4.781 0.895
Sandstone 1 10.60 0.774
8.64 W/m.K and 0.30 % respectively. For p = 0.003, A 1 (0.003),
B 1 (0.003), A 2 (0.003), B 2 (0.003), C 1 (0.003), D 1 (0.003), C 2 (0.003), and Sandstone 2 5.176 0.839
D 2 (0.0003) are calculated and given below, Shale 5.210 0.833
Siltstone 1 6.00 0.815
A 1 (0.003) B 1 (0.003) A 2 (0.003) B 2 (0.003) C 1 (0.003) D 1 (0.003) C 2 (0.003) D 2 (0.003) Siltstone 2 5.658 0.826

2.289 1.148 0.00031 1.006 0.09998 0.842 0.00144 2.715 Quartzite 8.697 0.996

THE INDIAN CONCRETE JOURNAL | JANUARY 2026 21