---
title: "Hardness, toughness and aggregate blend"
subject: "Transportation Engineering I"
chapter: 6
key: "semester_6/transportation_engineering_i:hardness-toughness-blend"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/hardness-toughness-blend
site: BCT Engineering
---

# Hardness, toughness and aggregate blend

Transportation Engineering I · Chapter 6: Highway Materials

- Asked in: 2079 Jestha, 2+6 marks
- Video: [Aggregates - Crushing Test, Abrasion Test - Highway Materials - Transportation Engineering - I](https://www.youtube.com/watch?v=Jfjl2CNmAi4) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/hardness-toughness-blend
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-6

## Question

Define Hardness and Toughness of aggregate along with example of the test to determine below. Determine the best proportion of Aggregates A and B (P and Q) given below that will produce an aggregate blend meeting the given specification limits using graphical method.

| IS Sieve Size (mm) | Aggregate P (% passing) | Aggregate Q (% passing) | Specification limit |
|---|---|---|---|
| 25.0 | 100 | 100 | 100 |
| 19.0 | 100 | 95 | 95 - 100 |
| 9.5 | 80 | 55 | 60 - 75 |
| 4.75 | 60 | 35 | 40 - 55 |
| 2.36 | 55 | 15 | 30 - 40 |
| 0.60 | 25 | 10 | 12 - 22 |
| 0.075 | 5 | 9 | 3 - 10 |

## Short answer

Hardness is resistance to wear (Los Angeles abrasion test); toughness is resistance to impact (aggregate impact value test). The graphical blending method shows the allowable proportion of aggregate P is 37.5% to 62.5%, controlled by the 2.36 mm sieve. Thus the best blend is P:Q = 50:50.

## Answer

#### Hardness and toughness
- **Hardness** is the resistance of aggregate to wear (abrasion and attrition) by the rubbing action of vehicle wheels. Test: **Los Angeles abrasion test** (limit about 30% for a wearing course) or the Deval attrition test.
- **Toughness** is the resistance of aggregate to failure by impact (sudden shock) from moving loads. Test: **aggregate impact value test** (AIV not more than 30% for a wearing course; 45% for base).

#### Aggregate blend by graphical method
**Given**: Aggregates P and Q with a specified grading envelope. Let $x$ be the fraction of P and $(1-x)$ the fraction of Q. At every sieve:

$$
\text{Passing}_{mix} = x\,P + (1-x)\,Q
$$

In the graphical method for two aggregates, the % passing of Q is marked on the left vertical axis (0% P) and that of P on the right vertical axis (100% P), and a straight line joins the two points for each sieve. The specification limits are marked on each sieve line, and the vertical band common to all the lines gives the allowable range of the proportion of P. The same range is obtained by solving for $x$ at each sieve:

$$
x_{min} = \frac{L - Q}{P - Q},\qquad x_{max} = \frac{U - Q}{P - Q}
$$

| Sieve (mm) | P | Q | Spec | Allowed proportion of P |
|---|---|---|---|---|
| 25.0 | 100 | 100 | 100 | any |
| 19.0 | 100 | 95 | 95-100 | 0 to 100% |
| 9.5 | 80 | 55 | 60-75 | 20 to 80% |
| 4.75 | 60 | 35 | 40-55 | 20 to 80% |
| 2.36 | 55 | 15 | 30-40 | **37.5 to 62.5%** |
| 0.60 | 25 | 10 | 12-22 | 13.3 to 80% |
| 0.075 | 5 | 9 | 3-10 | any |

**Common range**: P between **37.5% and 62.5%** (controlled by the 2.36 mm sieve), so Q is between 62.5% and 37.5%.

**Best proportion: the mid-point, P : Q = 50 : 50.** Check:

| Sieve (mm) | 25 | 19 | 9.5 | 4.75 | 2.36 | 0.60 | 0.075 |
|---|---|---|---|---|---|---|---|
| Blend 50:50 | 100 | 97.5 | 67.5 | 47.5 | 35.0 | 17.5 | 7.0 |
| Spec | 100 | 95-100 | 60-75 | 40-55 | 30-40 | 12-22 | 3-10 |
| Within? | yes | yes | yes | yes | yes | yes | yes |

**Answer: Aggregate P : Aggregate Q = 50 : 50** (any proportion of P between about 38% and 62% satisfies the specification, and 50% gives a gradation near the middle of the envelope).

## Check yourself

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

1. Toughness of aggregate is resistance to
   A. Wear by abrasion, tested by Los Angeles
   B. Weathering, tested by soundness
   C. Failure by impact from moving loads, tested by aggregate impact value
   D. Shape, tested by flakiness
   Answer: C. Toughness is impact resistance; hardness is wear resistance. (Key point: Toughness)

2. In the blending method, the passing percentage of the mix at a sieve is
   A. P + Q
   B. x P - (1 - x) Q
   C. P / Q
   D. x P + (1 - x) Q
   Answer: D. x is the fraction of P and 1 - x of Q. (Key point: Blend equation)

3. Which sieve controls the allowable range of P?
   A. 2.36 mm, giving 37.5% to 62.5%
   B. 19 mm
   C. 0.075 mm
   D. 25 mm
   Answer: A. x_min = (30-15)/(55-15) = 0.375 and x_max = (40-15)/40 = 0.625. (Key point: Controlling sieve)

4. What proportion P : Q is adopted?
   A. 37.5 : 62.5 only
   B. 50 : 50, the mid-point of the range
   C. 100 : 0
   D. 80 : 20
   Answer: B. The mid-point gives gradation near the centre of the envelope. (Key point: Best proportion)

## Related in Transportation Engineering I

- [Hardness test of aggregate](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Ahardness-test) — Transportation Engineering I, chapter 6, asked 3×
- [Mixing three gravel quarries to specification](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-65k-gravel-blend) — Transportation Engineering I, chapter 6
- [Aggregate impact value test](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Aimpact-value) — Transportation Engineering I, chapter 6, asked 3×
- [Aggregate crushing value test](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Acrushing-value) — Transportation Engineering I, chapter 6, asked 7×
- [Soundness test of aggregate](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Aaggregate-soundness-test) — Transportation Engineering I, chapter 6, asked 3×

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