---
title: "Compacted soil 18 kN/m³, porosity and ZAV"
subject: "Soil Mechanics"
chapter: 5
key: "semester_4/soil_mechanics:max-dry-weight-18-porosity-zav"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/max-dry-weight-18-porosity-zav
site: BCT Engineering
---

# Compacted soil 18 kN/m³, porosity and ZAV

Soil Mechanics · Chapter 5: Soil Compaction

- Asked in: 2074 Bhadra, 3 marks
- Video: [Maximum Dry Unit Weight and Optimum Moisture Content |Compaction Test Calculations| Compaction Curve](https://www.youtube.com/watch?v=culCiOfbScs) — Master Civil Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/max-dry-weight-18-porosity-zav
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-5

## Question

The maximum dry unit weight of a compacted soil mass is found to be 18 kN/m³ with optimum water content being 15%. Find the values of porosity and degree of saturation of this compacted soil. Also, find the value of the maximum dry unit weight on the zero air void line at that optimum water content. Take specific gravity of soil solid as 2.7.

## Short answer

Given γ_d = 18 kN/m³, w = 15%, G = 2.7: void ratio e = 0.4715, porosity n = 0.4715/1.4715 = 32.0%, degree of saturation S = 85.9%. Zero air void dry unit weight = 18.85 kN/m³.

## Answer

#### Given
$\gamma_{d} = 18$ kN/m³, $w = 15\%$, $G = 2.7$, $\gamma_w = 9.81$ kN/m³.

#### Void ratio and porosity
$$
e = \frac{G\gamma_w}{\gamma_d} - 1 = \frac{2.7 \times 9.81}{18} - 1 = 0.4715
$$
$$
n = \frac{e}{1+e} = \frac{0.4715}{1.4715} = 0.320 = 32.0\%
$$

#### Degree of saturation
$$
S = \frac{wG}{e} = \frac{0.15 \times 2.7}{0.4715} = 0.859 = 85.9\%
$$

#### Zero air void unit weight
$$
\gamma_{d,zav} = \frac{G\gamma_w}{1 + wG} = \frac{2.7 \times 9.81}{1 + 0.15 \times 2.7} = \frac{26.49}{1.405} = 18.85\ \text{kN/m}^3
$$

**Answer: $n = 32.0\%$, $S = 85.9\%$, $\gamma_{d,zav} = 18.85$ kN/m³.**

## Check yourself

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

1. Porosity from void ratio:
   A. n = 1+e
   B. n = e*(1+e)
   C. n = 1/e
   D. n = e/(1+e)
   Answer: D. n = e/(1+e). (Key point: Porosity)

2. With G = 2.7 and gd = 18, e = 0.4715, n is:
   A. 24%
   B. 68%
   C. 32%
   D. 47%
   Answer: C. 0.4715/1.4715 = 0.32. (Key point: Value)

3. S = wG/e = 0.15*2.7/0.4715 is about:
   A. 59%
   B. 85.9%
   C. 75%
   D. 100%
   Answer: B. 0.405/0.4715 = 0.859. (Key point: Saturation)

4. ZAV unit weight at w = 15%, G = 2.7 is about:
   A. 20.0
   B. 26.5
   C. 18.0
   D. 18.85
   Answer: D. 26.49/1.405 = 18.85. (Key point: ZAV)

## Close variants set in other exams

- [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×

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