Geotechnical Engineering

DHARM

16 GEOTECHNICAL ENGINEERING

The value of γo is 1g/cm^3 or 1000 kg/m^3 or 9.81 kN/m^3.

Saturated Unit Weight

The ‘Saturated unit weight’ is defined as the bulk unit weight of the soil mass in the saturated
condition. This is denoted by the letter symbol γsat.

Submerged (Buoyant) Unit Weight

The ‘Submerged unit weight’ or ‘Buoyant unit weight’ of a soil is its unit weight in the sub-

merged condition. In other words, it is the submerged weight of soil solids (Ws)sub per unit of

total volume, V of the soil. It is denoted by the letter symbol γ′ :

γ′ =

()W

V

ssub ...(Eq. 2.10)

(Ws)sub is equal to the weight of solids in air minus the weight of water displaced by the solids.
This leads to :
(Ws)sub = Ws – Vs. γw ...(Eq. 2.11)
Since the soil is submerged, the voids must be full of water ; the total volume V, then,
must be equal to (Vs + Vw). (Ws)sub may now be written as :

(Ws)sub = W – Ww – Vs. γw

= W – Vw. γw – Vsγw

= W – γw(Vw + Vs)

= W – V. γw

Dividing throughout by V, the total volume,

()W

V

ssub = (W/V) – γ
w
or γ′ = γsat – γw ...(Eq. 2.12)
It may be noted that a submerged soil is invariably saturated, while a saturated soil
need not be sumberged.

Equation 2.12 may be written as a direct consequence of Archimedes’ Principle which
states that the apparent loss of weight of a substance when weighed in water is equal to the
weight of water displaced by it.

Thus, γ′ = γsat – γw

since these are weights of unit volumes.

Dry Unit Weight

The ‘Dry unit weight’ is defined as the weight of soil solids per unit of total volume ; the former

is obtained by drying the soil, while the latter would be got prior to drying. The dry unit weight

is denoted by the letter symbol γd and is given by :

γd =

WW

V

sd()or ...(Eq. 2.13)

Since the total volume is a variable with respect to packing of the grains as well as with
the water content, γd is a relatively variable quantity, unlike γs, the unit weight of solids.*

*The term ‘density’ is loosely used for ‘unit weight’ in soil mechanics, although the former really

means mass per unit volume and not weight per unit volume.