---
title: "Stress-strain of paste, aggregate, concrete"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:stress-strain-three-phase"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/stress-strain-three-phase
site: BCT Engineering
---

# Stress-strain of paste, aggregate, concrete

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

- Asked in: 2066 Chaitra (old course), 5 marks
- Video: [6. Stress strain curve of aggregate, cement paste and concrete | Graph | RCC GATE English lectures](https://www.youtube.com/watch?v=tP_Fn7Wp8b0) — The Civil Girl
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/stress-strain-three-phase
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Explain the stress-strain relationship of cement paste, aggregate and concrete based on the concept of concrete as a three phase system.

## Short answer

Aggregate is stiff and linear elastic; cement paste is less stiff but nearly linear. Concrete’s curved, non-linear curve comes from the weak interfacial transition zone, where elastic mismatch causes progressive bond and matrix cracking.

## Answer

Concrete is a three-phase system: **aggregate**, **hydrated cement paste** and the **interfacial transition zone (ITZ)** between them. The stress-strain behaviour of the composite is different from that of its parts.

```text
 stress
   |     /  aggregate: steep, linear, brittle
   |    /
   |   /          _.--'''--.   concrete: curved,
   |  /       _.-''          '.  slope between the two
   | /    _.-'
   |/  .-'     paste: gentler slope, linear, brittle
   |.-'     _____--------
   | _____---
   +----------------------------- strain
```

#### Aggregate
Linear elastic up to brittle failure; high strength and high modulus (typically 50 to 100 GPa), small strain at failure.

#### Hydrated cement paste
Also nearly linear up to failure and brittle, but of lower modulus (10 to 30 GPa) and strength; large strain capacity compared to aggregate.

#### Concrete
Although aggregate and paste each behave almost linearly, concrete gives a **curved, non-linear** curve. Its stiffness lies between that of paste and aggregate, and its strength is lower than that of the aggregate:
- The ITZ is porous and contains oriented Ca(OH)2 crystals and microcracks formed by bleeding water and shrinkage. It is the weakest link.
- Under load the elastic mismatch between the stiff aggregate and the softer paste causes stress concentration at the interface, so bond cracks grow from about 30% of $f_c$ and matrix cracks from about 50 to 75%.
- This progressive cracking gives the curved shape; the strain at the peak is about 0.002, and the descending branch shows that the failure is governed by the matrix and the ITZ, not by the strength of aggregate.

So the modulus of concrete lies between that of aggregate and paste, and the strength depends on the paste and ITZ quality rather than on the aggregate.

## Check yourself

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

1. The three phases of concrete are:
   A. cement, sand, water
   B. aggregate, hydrated paste and the interfacial transition zone
   C. gel, steel, air
   D. coarse, fine, filler
   Answer: B. ITZ is the weakest link. (Key point: Three phases)

2. Individually, aggregate and paste each show:
   A. nearly linear elastic, brittle behaviour
   B. highly curved behaviour
   C. ductile plastic yield
   D. no strength
   Answer: A. Their composite is curved. (Key point: Aggregate and paste)

3. Concrete's curved curve arises from:
   A. perfect elastic bonding
   B. aggregate crushing at low load
   C. progressive cracking at the ITZ and matrix due to elastic mismatch
   D. absence of paste
   Answer: C. Stress concentration at the interface grows bond cracks. (Key point: Why concrete is curved)

4. Concrete strength depends mainly on:
   A. aggregate strength alone
   B. steel
   C. colour
   D. paste and ITZ quality
   Answer: D. Failure is governed by matrix and ITZ. (Key point: Strength governed by)

## Related in Concrete Technology and Masonry Structure

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- [Concrete as a three phase system](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Athree-phase-system) — Concrete Technology and Masonry Structure, chapter 2, asked 5×
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