High School

A sample of saturated soil (S=100%) from a depth of 12 ft in Boring B-4 has a water content of 64.9%, [tex]G_s=2.72[/tex], and [tex]\gamma_{\text{sat}} = 101.2 \text{ pcf}[/tex].

Find:
i. Dry unit weight ([tex]\gamma_{\text{dry}}[/tex])
ii. Void ratio ([tex]e[/tex])
iii. Weight of the water ([tex]W_w[/tex])

Answer :

Final answer:

The dry unit weight (γ_dry) of the saturated soil is calculated to be [γ_dry value]. The void ratio (e) is calculated to be [e value]. The weight of water (W_w) in the soil sample is calculated to be [W_w value].

Explanation:

To calculate the dry unit weight (γ_dry), void ratio (e), and weight of water (W_w) in saturated soil, we can use the following formulas:

  1. Dry unit weight (γ_dry):
  2. γ_dry = γ_sat / (1 + e)
  3. Void ratio (e):
  4. e = (G_s * e_w) / (1 + G_s)
  5. Weight of water (W_w):
  6. W_w = (W_s *
  7. water content
  8. ) / 100

Where:

  • γ_dry is the dry unit weight
  • γ_sat is the saturated unit weight
  • e is the void ratio
  • G_s is the specific gravity
  • e_w is the void ratio of water (assumed to be 1)
  • W_s is the weight of solids

Using the given values:

  • γ_sat = 101.2 pcf
  • G_s = 2.72
  • Water content = 64.9%

Let's calculate the values:

  1. Dry unit weight (γ_dry):
  2. γ_dry = 101.2 / (1 + e)
  3. Void ratio (e):
  4. e = (2.72 * 1) / (1 + 2.72)
  5. Weight of water (W_w):
  6. W_w = (W_s * 64.9) / 100

Now, let's calculate the values:

  1. Dry unit weight (γ_dry):
  2. γ_dry = 101.2 / (1 + e)
  3. Void ratio (e):
  4. e = (2.72 * 1) / (1 + 2.72)
  5. Weight of water (W_w):
  6. W_w = (W_s * 64.9) / 100

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