---
title: "Theoretical maximum dry density"
subject: "Soil Mechanics"
chapter: 5
key: "semester_4/soil_mechanics:theoretical-maximum-dry-density"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/theoretical-maximum-dry-density
site: BCT Engineering
---

# Theoretical maximum dry density

Soil Mechanics · Chapter 5: Soil Compaction

- Asked in: 2078 Chaitra, 1 marks
- Video: [Soil Maximum Dry Density and Factor Affecting Soil Compaction](https://www.youtube.com/watch?v=4GOow-36dK4) — Harris Ramli
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/theoretical-maximum-dry-density
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-5

## Question

Describe theoretical maximum dry density.

## Short answer

Theoretical maximum dry density is the dry density at zero air voids (S=100%), given by γ_d = Gγ_w/(1+wG). It sets an upper bound; actual compaction always leaves 2–5% air, so the compaction curve lies below the zero air void line.

## Answer

The **theoretical maximum dry density** is the dry density that a soil would have if all air were removed from the voids, i.e. at $S = 100\%$ for the given water content. It is represented by the zero air void (ZAV) line:
$$
\gamma_{d,max(theory)} = \frac{G\gamma_w}{1 + wG}
$$
It is an upper limit of dry density: the actual compaction curve always lies below it, since in practice 2 - 5% air remains in the soil.

## Check yourself

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

1. Theoretical maximum dry density corresponds to:
   A. OMC
   B. S = 50%
   C. S = 100% (no air in voids)
   D. Zero water content
   Answer: C. It is the dry density with all air removed. (Key point: Meaning)

2. Which is the correct formula?
   A. gw/(1+wG)
   B. G*gw/(1+e)*w
   C. G*gw/(1+wG)
   D. G*gw*(1+wG)
   Answer: C. ZAV: gd = G gw / (1 + wG). (Key point: Formula)

3. Real compaction curves lie:
   A. On the ZAV line
   B. Below the ZAV line since 2-5% air remains
   C. Above the ZAV line
   D. Crossing the ZAV line
   Answer: B. Air cannot be fully expelled so the curve stays below. (Key point: Practical)

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