Weight–Volume Relationships.
The unit weight of the soil is the weight of soil per unit volume. The most commonly used unit in the U.S. customary system is pounds per cubic foot (pcf), and the most commonly used unit in the SI system is kilonewtons per cubic meter (kN/m3). Other combinations of weight and volume units may be used in computations where consistent units are needed.
The unit weight, y, can be computed using one of the following relationships:
This expression for unit weight makes no assumption about the amount of water present in a sample of soil or rock, and is based simply on the weight and volume of the soil or rock.
The saturated unit weight is the unit weight of a fully saturated soil. In this case, no air or gas is present in the voids in the soil. An expression for the saturated unit, Ysat, is obtained by dividing the volume terms in the numerator and denominator of Eq. 3.4 by Vs and substituting the term for void ratio where appropriate: 
The specific gravity of the mineral grains, Gs, is the ratio of the unit weight of solids divided by the unit weight of water:
The values for specific gravity are usually in such a narrow range (i.e., 2.60 <Gs < 2.85) that an approximate value of 2.7 is usually assumed rather than performing the necessary laboratory tests for measurement.
It is convenient to rearrange the above relationship in the form
and substitute Eq. 3.7 into Eq. 3.5 to obtain an expression for Ysat
in terms of specific gravity, void ratio, and unit weight of water:
Equation 3.8 is in the form usually used in practice.
A useful expression for void ratio can be derived from the expressions for degree of saturation, water content, and specific gravity. The derivation is 
The dry unit weight, Yd, is the unit weight for the special case where Sr = 0. The dry unit weight is computed using
where the water content w is expressed as a decimal fraction. The above expression for dry unit weight is valid for any value of w. Another useful relationship for dry unit weight in terms of specific gravity, void ratio, and unit weight of water is
Note that if Sr is not 100% then Eq. 3.8 must be changed to
This is a general expression that is valid for all values of degree of saturation. When Sr is zero, this equation yields the dry unit weight, and when Sr is 100%, this equation yields the saturated unit weight.
The effective unit weight (also called the submerged unit weight)is defined as
where Ysat is the saturated unit weight.
Some instructors ask their students to memorize the six boxed equations above. All other weight–volume relationships can be derived from these equations.
Categories:
Soil
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