---
title: "Gel/space ratio and strength (600 gm cement)"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:gel-space-ratio-600g"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/gel-space-ratio-600g
site: BCT Engineering
---

# Gel/space ratio and strength (600 gm cement)

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

- Asked in: 2071 Shrawan, 4 marks
- 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-600g
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Calculate the gel/space ratio and the theoretical strength of a sample concrete made with 600 gm of cement with 0.45 water/cement ratio, on full hydration and at 60 percent hydration.

## Short answer

Gel/space ratio x = 0.657α / (0.319α + w/c); strength = 240x³ MPa. At full hydration (α=1), x = 0.854, strength 149.7 MPa. At 60% hydration, x = 0.615, strength 55.7 MPa.

## Answer

Powers' model gives the strength of concrete in terms of the **gel/space ratio** $x$:

$$
x = \frac{\text{volume of gel}}{\text{volume of gel} + \text{capillary pores}} = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}
$$

where $\alpha$ is the degree of hydration and $w/c$ the water-cement ratio by mass. The numbers come from cement of specific gravity about 3.14: 1 g of cement has 0.319 cm$^3$ volume and produces gel of $2.06\times0.319 = 0.657$ cm$^3$ (including gel pores). Compressive strength:

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

(240 MPa is the intrinsic strength of the gel; it varies from about 234 to 255 MPa for different cements.) The ratio $x$ does not depend on the mass of cement; the mass is only needed to give volumes.

#### Given
Cement = 600 g, $w/c = 0.45$, so water = $0.45\times600 = 270$ g. Volume of cement $= 600\times0.319 = 191.4$ cm$^3$; gel at full hydration $= 600\times0.657 = 394.2$ cm$^3$.

#### Full hydration ($\alpha = 1$)
$$
\begin{aligned} x &= \frac{394.2}{191.4+270} = \frac{394.2}{461.4} = 0.854 \\ f_c &= 240\times0.854^3 = 149.7\ \text{MPa} \end{aligned}
$$

#### 60% hydration ($\alpha = 0.6$)
$$
\begin{aligned} x &= \frac{0.6\times394.2}{0.6\times191.4+270} = \frac{236.5}{384.8} = 0.615 \\ f_c &= 240\times0.615^3 = 55.7\ \text{MPa} \end{aligned}
$$

**Answer: gel/space ratio 0.854 and strength 149.7 MPa at full hydration; 0.615 and 55.7 MPa at 60% hydration.** The result is independent of the 600 g mass because only the ratio $w/c$ matters.

## Check yourself

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

1. The Powers gel/space ratio is:
   A. 0.319 alpha / (0.657 alpha + w/c)
   B. 0.657 alpha / (0.657 alpha + w/c)
   C. 0.657 alpha / (0.319 alpha + w/c)
   D. 0.657 / (0.319 + alpha)
   Answer: C. Gel volume 0.657 alpha per gram over gel plus capillary space (0.319 alpha + w/c). (Key point: Gel/space formula)

2. Strength from the gel/space ratio x is given by:
   A. f_c = 240 x^3 MPa
   B. f_c = 240 x MPa
   C. f_c = 240 x^2 MPa
   D. f_c = x^3/240 MPa
   Answer: A. Powers found f_c = 240 x^3, where 240 MPa is the intrinsic strength of gel. (Key point: Strength relation)

3. Why does the 600 g mass not change the result?
   A. Because 600 g is a standard value fixed by Powers
   B. Because strength depends on the water mass only
   C. Because the mass changes gel and space by different factors
   D. x depends only on w/c and alpha; mass cancels in the ratio
   Answer: D. Both gel and space volumes scale with cement mass, so it cancels; only w/c matters. (Key point: Mass independence)

4. At full hydration with w/c 0.45, x and strength are about:
   A. 0.615 and 55.7 MPa
   B. 0.854 and 149.7 MPa
   C. 0.802 and 123.9 MPa
   D. 1.0 and 240 MPa
   Answer: B. x = 0.657/(0.319+0.45) = 0.854; f_c = 240 x 0.854^3 = 149.7 MPa. (Key point: Result)

## Close variants set in other exams

- [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×

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