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Types of unit weights in phase terms

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.

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.

Symbols: WsW_s = weight of solids, WwW_w = weight of water, W=Ws+WwW = W_s + W_w, VsV_s = volume of solids, VwV_w = volume of water, VaV_a = volume of air, Vv=Vw+VaV_v = V_w + V_a, V=Vs+Vw+VaV = V_s + V_w + V_a.

Unit weightMeaningExpression
Bulk (moist/total) unit weight γ\gammaTotal weight per unit total volumeγ=Ws+WwVs+Vw+Va\gamma = \dfrac{W_s + W_w}{V_s + V_w + V_a}
Dry unit weight γd\gamma_dWeight of solids per unit total volumeγd=WsVs+Vw+Va\gamma_d = \dfrac{W_s}{V_s + V_w + V_a}
Saturated unit weight γsat\gamma_{sat}Weight per unit volume when Va=0V_a = 0γsat=Ws+WwV\gamma_{sat} = \dfrac{W_s + W_w}{V} with Va=0V_a = 0
Submerged (buoyant) unit weight γ′\gamma'Effective weight under water per unit total volumeγ′=γsat−γw=Ws−VsγwV\gamma' = \gamma_{sat} - \gamma_w = \dfrac{W_s - V_s\gamma_w}{V}
Unit weight of solids γs\gamma_sWeight of solids per volume of solidsγs=WsVs=Gγw\gamma_s = \dfrac{W_s}{V_s} = G\gamma_w
Unit weight of water γw\gamma_wWeight of water per volume of waterγw=WwVw\gamma_w = \dfrac{W_w}{V_w} (9.81 kN/m³)

✓ Answer checked by Claude Opus 5.5 (high effort)

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