---
title: "w/c ratio, porosity and Powers' concept"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:wc-ratio-porosity-powers"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/wc-ratio-porosity-powers
site: BCT Engineering
---

# w/c ratio, porosity and Powers' concept

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

- Asked in: 2066 Jestha (old course), 2+5+3 marks
- Video: [Gel/Space ratio in Hindi | Strength of Concrete | Concrete Technology](https://www.youtube.com/watch?v=VLpHeLv1F5A) — CIVILian
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/wc-ratio-porosity-powers
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Describe the effect of water-cement ratio on porosity of concrete. What is the concept of Powers to calculate porosity of concrete? Suggest the proper w/c ratio in view of durability of concrete as per weather condition.

## Short answer

Higher w/c increases capillary porosity, reducing strength and durability. Powers’ model: capillary porosity = (w/c – 0.36α) / (w/c + 0.32). For durability, w/c limits are 0.55 mild, 0.50 moderate, 0.45 severe, 0.40 extreme exposure.

## Answer

#### Effect of w/c ratio on porosity
Porosity of the paste is the volume of pores (gel pores plus capillary pores). Mixing water in excess of what hydration needs stays in the paste as capillary pores (empty or water-filled). About 0.23 of the cement mass is chemically combined and about 0.15 is held in gel pores, so full hydration needs $w/c \approx 0.38$. For higher $w/c$, the extra water makes capillary pores. With higher $w/c$:
- Capillary porosity is higher and pores are larger and interconnected.
- Strength falls and permeability rises sharply; a pore volume of about 25% and above makes capillaries continuous.
- Durability is therefore worse (carbonation, chloride and sulphate ingress, freeze-thaw).

#### Powers' concept
Powers and Brownyard treated the paste volume as cement + water, and found that hydrated cement (gel including gel pores) occupies about 2.06 times the volume of the cement. For 1 g cement, specific volume 0.319 cm$^3$:

$$
\begin{aligned} \text{Gel volume} &= 0.657\alpha, \qquad \text{Total paste} = 0.319 + w/c \\ \text{Capillary porosity } P_c &= \frac{w/c - 0.36\alpha}{w/c + 0.32} \end{aligned}
$$

Here $\alpha$ is degree of hydration. Capillary porosity is the space left in the paste after subtracting unhydrated cement and gel. Strength follows the gel/space ratio, $f_c = 240x^3$.

#### Proper w/c ratio for durability (IS 456, Table 5)
| Exposure | Maximum w/c (RCC) | Minimum cement (kg/m$^3$) |
|---|---|---|
| Mild | 0.55 | 300 |
| Moderate | 0.50 | 300 |
| Severe | 0.45 | 320 |
| Very severe | 0.45 | 340 |
| Extreme | 0.40 | 360 |

Thus a lower w/c (0.40 to 0.45) is required in marine, cold or aggressive environments, and 0.50 to 0.55 is acceptable for mild weather.

## Check yourself

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

1. Higher w/c ratio gives:
   A. more and larger capillary pores, lower strength and higher permeability
   B. fewer pores
   C. higher strength
   D. lower permeability
   Answer: A. Excess water leaves capillary pores. (Key point: Effect of high w/c)

2. Full hydration needs w/c of about:
   A. 0.10
   B. 0.80
   C. 0.38
   D. 1.00
   Answer: C. 0.23 chemically combined + 0.15 gel pore water. (Key point: Full hydration w/c)

3. Powers: hydrated cement occupies about ___ times cement volume:
   A. 1.0
   B. 2.06
   C. 0.319
   D. 5
   Answer: B. 1 g cement 0.319 cm^3 gives 0.657 cm^3 gel. (Key point: Powers gel volume)

4. For extreme exposure the max w/c is:
   A. 0.55
   B. 0.50
   C. 0.45
   D. 0.40
   Answer: D. Severity lowers the permitted w/c; mild 0.55. (Key point: IS 456 limits)

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