Building Materials, Third Edition

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Let C = weight of cement in g, Vc = specific volume of cement ml/g, and W 0 = volume of mixing
water in ml.
Assuming 1 ml of cement on hydration produces 2.06 ml of gel.
Volume of gel =C x 0.319 x 2.06 = 0.657 C
Space available = C x 0.319 + W 0

Gel-space ratio =

€

 0

0.657 C

0.319 C W

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Let a = fraction of cement that has hydrated.
Volume of gel = C × a
× 0.319 × 2.06 = 0.657 Ca
Space available =C × 0.319 × a
+ W 0

Gel space ratio =

h

h 0

0.657 C
0 .319 C W
The limitation of this theory is that the theoretical strength
of concrete is much more than the actual strength of concrete.
In the above theory it has been assumed that the concrete is
perfectly homogeneous and flawless. But the presence of flaws
like cracks, voids, bleeding channels, rupture of bond due to
drying shrinkage and temperature stresses reduce the strength.
Griffith has done lot of work on this line and his theory is
gaining popularity. His work is based on these flaws.

Example 10.1 Calculate the gel space ratio and theoretical
strength of a sample of concrete made with 500 g of cement
with w/c ratio as 0.55,

1. On full hydration


2. On 75% hydration

Solution
W 0 = 500 × 0.55 = 275 ml

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Gel-space ratio =



22

 0

0.657 C 0.657 500

0.756

0.319 C W 0.319 500 275

Theoretical strength of concrete = 240 (0.756)^3 = 103.72 N/mm^2

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