---
title: "Toughness index, activity, air content"
subject: "Soil Mechanics"
chapter: 2
key: "semester_4/soil_mechanics:short-note-toughness-activity"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/short-note-toughness-activity
site: BCT Engineering
---

# Toughness index, activity, air content

Soil Mechanics · Chapter 2: Solids- Water –Air Relations and Index properties of soils

- Asked in: 2078 Chaitra, 4 marks
- Video: [soil mechanics important numerical | finding plasticity index | toughness index of the soil .](https://www.youtube.com/watch?v=ZvSVor4M9Pc) — pushpa thapa
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/short-note-toughness-activity
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-2

## Question

Describe toughness index, coefficient of curvature, activity of soil and air content.

## Short answer

Toughness index is Ip/If and measures shear strength at plastic limit. Coefficient of curvature is D30 squared over D10 times D60, with 1 to 3 indicating well graded. Activity is Ip divided by clay fraction, classifying swelling potential. Air content is Va/V or n(1-S).

## Answer

#### Toughness index ($I_t$)
The ratio of plasticity index to flow index:
$$
I_t = \frac{I_p}{I_f}
$$
It measures the shear strength of soil at the plastic limit. Typical values are 0 to 3; low values mean the soil is friable and has low toughness.

#### Coefficient of curvature ($C_c$)
A shape parameter of the grain size curve:
$$
C_c = \frac{D_{30}^2}{D_{10} \times D_{60}}
$$
A well-graded gravel or sand has $C_c$ between 1 and 3.

#### Activity of soil ($A$)
The ratio of the plasticity index to the percent of clay-size particles (< 2 micron):
$$
A = \frac{I_p}{\%\ \text{clay fraction}}
$$
$A < 0.75$ inactive (kaolinite), 0.75 - 1.25 normal (illite), $> 1.25$ active (montmorillonite). It indicates the swelling potential.

#### Air content ($a_c$)
The ratio of volume of air to total volume of the soil:
$$
a_c = \frac{V_a}{V}
$$
Also $a_c = n(1 - S)$, where $n$ is porosity and $S$ is the degree of saturation.

## Check yourself

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

1. Toughness index is:
   A. Ip/If
   B. If/Ip
   C. Ip x If
   D. wL - wP
   Answer: A. It= Ip/If, a measure of shear strength at the plastic limit. (Key point: Toughness index)

2. Coefficient of curvature is:
   A. D10/D60
   B. D60/D10
   C. D30^2/(D10 x D60)
   D. D30/(D10 x D60)
   Answer: C. Cc = D30^2/(D10 D60); well-graded soil has Cc between 1 and 3. (Key point: Coefficient of curvature)

3. A soil with activity A > 1.25 is:
   A. Active with high swelling potential like montmorillonite
   B. Inactive like kaolinite
   C. Normal like illite
   D. Non-plastic
   Answer: A. A = Ip / % clay; above 1.25 is active. (Key point: Activity)

4. Air content ac equals:
   A. Vw/V
   B. Va/Vv
   C. Va/V = n(1-S)
   D. Va/Vs
   Answer: C. Air content is air volume over total volume, equal to n(1 - S). (Key point: Air content)

## Related in Soil Mechanics

- [Index tests for soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aindex-tests-list) — Soil Mechanics, chapter 2, asked 2×
- [Pycnometer data, water content, γsub](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Apycnometer-water-content-submerged) — Soil Mechanics, chapter 2
- [Placement water content](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aplacement-water-content) — Soil Mechanics, chapter 5
- [Compacted soil 17 kN/m³, OWC 16%](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amax-dry-weight-17-void-ratio) — Soil Mechanics, chapter 5, asked 2×
- [Compacted soil 18 kN/m³, porosity and ZAV](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amax-dry-weight-18-porosity-zav) — Soil Mechanics, chapter 5, asked 2×
- [Index and engineering properties](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aindex-vs-engineering-properties) — Soil Mechanics, chapter 2, asked 4×

## Related in other subjects

- [Coefficient of restitution; car on track](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Adirect-central-impact-restitution-car-track) — Applied Mechanics (Dynamics), chapter 2
- [Double ring infiltrometer, phi-index versus W-index](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adouble-ring-phi-vs-w-index) — Engineering Hydrology, chapter 3
- [Insulating layer: minimum outside heat transfer coefficient](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ainsulating-layer-min-outside-h-300c) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2×
- [Insulation layer: minimum outside heat transfer coefficient](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Ainsulation-min-outside-h-270c-70c) — Fundamental of Thermodynamics & Heat Transfer, chapter 7, asked 2×