Calculating Degree of Saturation from Proctor Test Data

The degree of saturation ($S$) indicates how much of the soil's void volume is filled with water. We can calculate it using the results from a Proctor compaction test and the soil's specific gravity.

Key Formulas

• The relationship between dry density ($ \rho_d $), specific gravity ($G_s$), void ratio ($e$), and density of water ($ \rho_w $):

  $ \rho_d = \frac{G_s \rho_w}{1+e} $

• The relationship between degree of saturation ($S$), void ratio ($e$), water content ($w$), and specific gravity ($G_s$):

  $ S e = w G_s $

• Assume the density of water, $ \rho_w = 1 \text{ gm/cc} $.

Step 1: Calculate the Void Ratio (e)

We use the maximum dry density ($ \rho_d $) and specific gravity ($G_s$) to find the void ratio ($e$).

Given:

• $ \rho_d = 1.8 \text{ gm/cc} $
• $ G_s = 2.7 $

Rearranging the first formula:

$ 1+e = \frac{G_s \rho_w}{\rho_d} $

Substitute the values:

$ 1+e = \frac{2.7 \times 1}{1.8} $

$ 1+e = 1.5 $

$ e = 1.5 - 1 = 0.5 $

Step 2: Calculate the Degree of Saturation (S)

Now use the calculated void ratio ($e$), Optimum Moisture Content ($w$), and specific gravity ($G_s$) in the second formula.

Given:

• $ e = 0.5 $
• $ w = 15\% = 0.15 $
• $ G_s = 2.7 $

Rearranging the formula $ S e = w G_s $:

$ S = \frac{w G_s}{e} $

Substitute the values:

$ S = \frac{0.15 \times 2.7}{0.5} $

$ S = \frac{0.405}{0.5} $

$ S = 0.81 $

To express this as a percentage:

$ S = 0.81 \times 100\% = 81\% $

The degree of saturation for this soil at maximum dry density is 81%.