A soil is at a void ratio e = 0.90 with a specific gravity of the solid particles Gs = 2.70.

(a) Calculate the upper and lower limits for the water content w.
(b) Compute the mass of water in 100 cm3 sample of the soil at this e when saturation S = 50%. Note rhow = 1 g/cm3 .

The correct answers are:

a. % w = 33.3%

b. mass of water = 45g

Explanation:

First, let us define the parameters in the question:

void ratio e  = =  

Specific gravity =  

% Saturation S = × =   ×

water content w =   =

a) To calculate the lower and upper limits of water content:

when S = 100%, it means that the soil is fully saturated and this will give the upper limit of water content.

when S < 100%, the soil is partially saturated, and this will give the lower limit of water content.

Note; S = 0% means that the soil is perfectly dry. Hence, when s = 1 will give the lowest limit of water content.

To get the relationship between water content and saturation, we will manipulate the equations above;

w =  

Recall; mass = Density × volume

w =

From eqn. (2)   =

∴

putting eqn. (6) into (5)

w =

Again, from eqn (1)

substituting into eqn. (7)

∴

With eqn. (7), we can calculate

upper limit of water content

when S = 100% = 1

Given,

∴

∴ %w = 33.3%

Lower limit of water content

when S = 1% = 0.01

∴ % w = 0.33%

b) Calculating mass of water in 100 cm³ sample of soil ( )

Given, , S = 50% = 0.5

%S = × = ×

0.50 =

mass of water =

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