---
title: "Types of unit weights in phase terms"
subject: "Soil Mechanics"
chapter: 2
key: "semester_4/soil_mechanics:unit-weights-phase-relations"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/unit-weights-phase-relations
site: BCT Engineering
---

# Types of unit weights in phase terms

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

- Asked in: 2076 Baisakh, 2 marks
- Video: [SOIL MECHANICS ǀ Derivation of Functional Relations ǀ Bulk, Dry, Saturated and Submerged Density](https://www.youtube.com/watch?v=rZEmI8yKk8M) — Civil_O_Graphy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/unit-weights-phase-relations
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-2

## Question

Name the different types of unit weights used in soil mechanics and express them in terms of weights and volumes of soil solid, void water and void air.

## Short answer

Bulk unit weight is (Ws+Ww)/V, dry unit weight is Ws/V, saturated unit weight is (Ws+Ww)/V with no air, submerged unit weight is gamma_sat minus gamma_w, solids unit weight is Ws/Vs equals G gamma_w, and water unit weight is Ww/Vw.

## Answer

Symbols: $W_s$ = weight of solids, $W_w$ = weight of water, $W = W_s + W_w$, $V_s$ = volume of solids, $V_w$ = volume of water, $V_a$ = volume of air, $V_v = V_w + V_a$, $V = V_s + V_w + V_a$.

| Unit weight | Meaning | Expression |
|---|---|---|
| Bulk (moist/total) unit weight $\gamma$ | Total weight per unit total volume | $\gamma = \dfrac{W_s + W_w}{V_s + V_w + V_a}$ |
| Dry unit weight $\gamma_d$ | Weight of solids per unit total volume | $\gamma_d = \dfrac{W_s}{V_s + V_w + V_a}$ |
| Saturated unit weight $\gamma_{sat}$ | Weight per unit volume when $V_a = 0$ | $\gamma_{sat} = \dfrac{W_s + W_w}{V}$ with $V_a = 0$ |
| Submerged (buoyant) unit weight $\gamma'$ | Effective weight under water per unit total volume | $\gamma' = \gamma_{sat} - \gamma_w = \dfrac{W_s - V_s\gamma_w}{V}$ |
| Unit weight of solids $\gamma_s$ | Weight of solids per volume of solids | $\gamma_s = \dfrac{W_s}{V_s} = G\gamma_w$ |
| Unit weight of water $\gamma_w$ | Weight of water per volume of water | $\gamma_w = \dfrac{W_w}{V_w}$ (9.81 kN/m³) |

## Check yourself

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

1. Bulk unit weight is:
   A. Ww/Vw
   B. Ws/V
   C. Ws/Vs
   D. (Ws+Ww)/(Vs+Vw+Va)
   Answer: D. Total weight per total volume. (Key point: Bulk unit weight)

2. Dry unit weight is:
   A. Ws/Vs
   B. Ws/(Vs+Vw+Va)
   C. (Ws+Ww)/V
   D. Ww/V
   Answer: B. Weight of solids per unit total volume. (Key point: Dry unit weight)

3. Submerged unit weight is:
   A. gamma_sat + gamma_w
   B. gamma - gamma_d
   C. gamma_d - gamma_w
   D. gamma_sat - gamma_w
   Answer: D. Buoyancy reduces saturated unit weight by gamma_w. (Key point: Submerged unit weight)

4. The unit weight of solids is:
   A. Ws/V
   B. G x gamma_w = Ws/Vs
   C. Ww/Vw
   D. gamma_sat - gamma_w
   Answer: B. gamma_s = Ws/Vs = G gamma_w. (Key point: Unit weight of solids)

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