Volume of gel divided by the sum of gel and capillary pore volumes

Volume of gel divided by volume of unhydrated cement

Volume of water divided by volume of cement

Volume of capillary pores divided by volume of gel

Why does strength increase when x increases?

Gel fills pores, so the solid fraction rises

Water content in the paste increases

What does the cubic relation f_c = 240 x^3 imply?

A small rise in x gives a large strength gain

As w/c increases at full hydration, x and strength:

Both fall (e.g. 0.914 at 0.40 to 0.715 at 0.60)

The maximum value of x and its strength is:

1.0, giving 240 MPa intrinsic strength

2071 Chaitra · 6 marks

Effect of gel/space ratio on strength

Short answer

Strength follows fc = 240x³ MPa, where x = gel/(gel+capillary pores). A higher x from lower w/c or greater hydration fills more voids, sharply raising strength. Examples: w/c 0.40 gives 183 MPa, 0.60 gives 87.7 MPa at full hydration.

Explain the effect of gel/space ratio on the theoretical strength of concrete.

The gel/space ratio $x$ is the ratio of the volume of hydrated cement (gel) to the sum of the volume of gel and capillary pores (the space available to it):

x = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}

Powers found by tests on mortar cubes that strength depends on $x$ rather than on age, as:

f_c = 240\,x^3\ \text{MPa}

Effect

When $x$ increases, the pores are filled by gel, the solid fraction rises and strength increases. The relation is a cubic, so a small increase in $x$ makes a large strength gain.
$x$ increases with the degree of hydration $\alpha$ (better curing, more age, finer cement, higher temperature) and falls with higher $w/c$ .
Examples at $w/c = 0.5$ : $\alpha = 0.5$ gives $x = 0.498$ and $f_c = 29.7$ MPa; $\alpha = 1.0$ gives $x = 0.802$ and $f_c = 123.9$ MPa.

$w/c$	$x$ at full hydration	$f_c$ (MPa)
0.40	0.914	183.1
0.50	0.802	123.9
0.60	0.715	87.7

Maximum $x$ is 1.0 (when all space is filled), which gives the 240 MPa intrinsic strength.
The values are for paste; in concrete the actual strength is lower because of air voids, ITZ and aggregate, but the trend is the same and it explains why strength falls with w/c and rises with curing.

✓ Answer checked by Claude Sonnet 5.5

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Effect of gel/space ratio on strength

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