---
title: "Abrams' law of concrete strength"
subject: "Concrete Technology and Masonry Structure"
chapter: 3
key: "semester_5/concrete_technology_and_masonry_structure:abrams-law"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/abrams-law
site: BCT Engineering
---

# Abrams' law of concrete strength

Concrete Technology and Masonry Structure · Chapter 3: Mix design of concrete and property of green concrete

- Asked in: 2082 Bhadra, 3 marks
- Video: [Water Cement Ratio | WC Ratio | Abram's WC Ratio Law | Cement Test](https://www.youtube.com/watch?v=S2wuzwK9AxI) — Cement Plant Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/abrams-law
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-3

## Question

Describe Abrams' law of concrete.

## Short answer

Abrams' law states that concrete strength is inversely proportional to the water-cement ratio: f_c = A / B^{w/c}. Lower w/c yields higher strength because excess water leaves capillary pores. Valid for fully compacted workable mixes.

## Answer

**Abrams' law** (D. A. Abrams, 1918) states that for a given set of materials and age, the strength of fully compacted concrete is inversely related to the water-cement ratio: the **lower the w/c ratio, the higher the strength**.

$$
f_c = \frac{A}{B^{\,w/c}}
$$

where $f_c$ is the compressive strength, $w/c$ is the water-cement ratio by mass, and $A$, $B$ are empirical constants depending on the cement, age, curing and testing (Abrams: $A = 96.5$ MPa, $B = 7$ for 28 days).

```text
 f_c
  |\
  | `.
  |   `-.
  |      `--.____
  +----------------> w/c
```

**Explanation**: only about 0.23-0.38 of the cement mass of water is needed for hydration; the extra water evaporates leaving capillary pores, which weaken the paste, so strength falls rapidly as w/c increases. The law is valid only for workable mixes that can be fully compacted.

## Check yourself

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

1. Abrams' law states that for given materials and age, strength
   A. increases with w/c
   B. is independent of w/c
   C. depends only on aggregate size
   D. decreases as w/c increases
   Answer: D. Lower w/c gives higher strength. (Key point: Statement)

2. Why does strength fall as w/c rises?
   A. Extra water evaporates leaving capillary pores
   B. More cement is hydrated
   C. Aggregates become stronger
   D. Water adds to the strength gel
   Answer: A. Only about 0.23-0.38 of cement mass of water is needed; the rest leaves pores. (Key point: Why strength falls)

3. The law is valid only for mixes that are
   A. dry and uncompacted
   B. workable and fully compacted
   C. over-vibrated
   D. segregated
   Answer: B. It assumes full compaction of plastic mixes. (Key point: Validity)

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