Foundation, Concrete and Earthquake Engineering

What is gel/space ratio? Its significance in concrete strength prediction

Gel/space ratio

The ratio of volume occupied by hydrated cement paste to the aggregated volume of capillary pores and hydrated cement paste is known as gel/space ratio. It is denoted by r. Powers (1958) found that compressive strength of concrete is 34000 r3 psi (234 r3 MPa) and interestingly he found no influence of mix proportion of concrete and age of it on strength prediction. To realize the definition and significance of gel/space ratio it is required to discuss about volume of hydration product.

Volume of hydration produts

The total space available to occupy by productsof hydration is the summation of absolute volume of fresh cement and the volume of mixing water. Of these, if small loss of water under the contraction of the cement paste and that due to bleeding is ignored, the water consumed by chemical reaction with C2S and C3S was found to be 21 and 24 percent (very roughly) of the mass of two respective silicates. If the final reaction of hydrate C4AF is

The respective figures of C3AF and C3A are 37 and 40 percent. Equation (1) is also vary approximately due to our inadequate knowledge of stoichiometry of the hydration products and cannot be ascertained the amount of chemically combined water. Non-evaporable water determined under specific conditions is considered as 23% if anhydrous cement (measured by mass); in case of type II, moderate sulfate resistant cement, this value may be 18%. The specific gravity of hydration products of cement becomes such that the resulting volume is more than absolute volume of anhydrous cement.
Volume of hydration product of cement
The average value of specific gravity of hydration product in saturated structure, inclusive of pores available in the possible densest structure, is 2.16. Here we are providing a demonstration of calculation of volume change during hydration.

Example 1.0

Mass of cement=100 g
Specific gravity of cement=3.15
That is absolute volume of hydrated cement=100/3.15=31.8 ml
Volume of non-evaporable water= 23ml (23% of mass of cement)
Volume of solid product of hydration of cement=31.8+0.23 X 100 (1-0.254)
=48.9 ml

The cement paste at this condition has characteristic porosity around=28%

That is 

Where wg=volume of gel water 
i.e, wg=48.9X0.28+0.28Xwg
or, wg=19ml

Thus the volume of hydrated cement paste=48.9+19=67.9 ml 

The summary of the example 1 can be drawn as in table-1
Volume of hydration product
From table -1 it can be concluded that
Total volume of water in the mix=23+19=42 ml
Water/cement ration= 42/100=0.42 (by mass)

Water/cement ration= 42/31.8=1.32 (by volume)
Actual volume cement+water=31.8+42=73.8 ml

Volume reduction during hydration=73.8-67.9= 5.9 ml
Volume of hydration products for 1 ml of dry cement=67.9/31.8=2.13 ml

Example 1.0 is ideal condition, where hydration is assumed to occur in sealed container where no water movement is allowed whether into or away from the system. It is interesting to note that reduction in volume by value 5.9 stand for empty capillary pores dispersed in the hydrated cement paste.

Effect of temperature on gel/space ratio

We know a higher temperature at the time of placing of concrete and maintaining or allowing during setting, definitely increase strength at very early stage; followed by often adverse effect on strength at and after 7 days. This is due to rapid initial reaction that occur during hydration leading to formation of hydration product of poorer quality; a poor physical structure having more pores.

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