---
title: "Effect of gel/space ratio on strength"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:gel-space-ratio-effect"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/gel-space-ratio-effect
site: BCT Engineering
---

# Effect of gel/space ratio on strength

Concrete Technology and Masonry Structure · Chapter 4: Properties of hardened concrete

- Asked in: 2071 Chaitra, 6 marks
- Video: [Water Cement Ratio and Gel Space Ratio - Properties of Concrete - Advanced Concrete Technology](https://www.youtube.com/watch?v=rPn734g3Psw) — Ekeeda
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/gel-space-ratio-effect
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

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

## 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.

## Answer

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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Gel/space ratio is:
   A. Volume of gel divided by volume of unhydrated cement
   B. Volume of water divided by volume of cement
   C. Volume of gel divided by the sum of gel and capillary pore volumes
   D. Volume of capillary pores divided by volume of gel
   Answer: C. It compares gel to the total space available to it (gel + capillary pores). (Key point: Definition)

2. Why does strength increase when x increases?
   A. Gel fills pores, so the solid fraction rises
   B. Water content in the paste increases
   C. Unhydrated cement increases
   D. Aggregate size becomes larger
   Answer: A. Higher x means pores are filled by gel, giving a denser, stronger paste. (Key point: Why strength rises)

3. What does the cubic relation f_c = 240 x^3 imply?
   A. Strength is proportional to x
   B. A small rise in x gives a large strength gain
   C. Strength is independent of x
   D. Strength is highest at low x
   Answer: B. Because of the power of 3, small changes in x change strength strongly. (Key point: Cubic effect)

4. As w/c increases at full hydration, x and strength:
   A. Both rise
   B. x rises but strength falls
   C. Both stay unchanged
   D. Both fall (e.g. 0.914 at 0.40 to 0.715 at 0.60)
   Answer: D. More water means more capillary space, so x and strength fall. (Key point: Effect of w/c)

5. The maximum value of x and its strength is:
   A. 0.5, giving 120 MPa
   B. 1.0, giving 100 MPa
   C. 1.0, giving 240 MPa intrinsic strength
   D. 2.0, giving 480 MPa
   Answer: C. When all space is filled with gel, x = 1 and f_c = 240 MPa. (Key point: Maximum x)

## Related in Concrete Technology and Masonry Structure

- [Gel/space ratio and strength (550 gm cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-550g) — Concrete Technology and Masonry Structure, chapter 4, asked 3×
- [Gel/space ratio and strength (600 gm cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Agel-space-ratio-600g) — Concrete Technology and Masonry Structure, chapter 4, asked 3×
- [Theoretical strength of moist cured concrete (1 kg cement)](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Atheoretical-strength-1kg-cement) — Concrete Technology and Masonry Structure, chapter 4
- [Effect of water cement ratio on strength](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Awc-ratio-effect-strength) — Concrete Technology and Masonry Structure, chapter 3, asked 4×