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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_{sat} = 101.2 \text{ pcf}[/tex].

Find:

i. Dry unit weight ([tex]\gamma_{dry}[/tex])

ii. Void ratio ([tex]e[/tex])

iii. Weight of the water ([tex]W_w[/tex])

Answer :

Given soil properties and conditions, the calculated values of weight are:

  • i. γ_dry = 107.39 pcf,
  • ii. e = 0.593,
  • iii. W_w = 144.6 lb/ft³.

(i) To find the dry unit weight (γ_dry), we can use the formula γ_dry = γ_sat / (1 + e), where γ_sat is the saturated unit weight (given as 101.2 pcf) and e is the void ratio. With the void ratio given as 0.593, the dry unit weight is calculated as 101.2 / (1 + 0.593) = 107.39 pcf.

(ii) The void ratio (e) can be determined using the relationship e = (G_s * w) / (1 + w), where G_s is the specific gravity of solids (2.72) and w is the water content (64.9% or 0.649 as a decimal). Substituting these values gives e = (2.72 * 0.649) / (1 + 0.649) = 0.593.

(iii) To find the weight of the water (W_w), we can use the formula W_w = γ_w * V, where γ_w is the unit weight of water (62.4 pcf) and V is the volume of the saturated soil. The volume V can be calculated as the product of the depth (12 ft) and the cross-sectional area.

Given the cross-sectional area is not provided, it cannot be directly calculated, but assuming a unit width (1 ft) gives V = 12 ft³. Therefore, W_w = 62.4 pcf * 12 ft³ = 144.6 lb/ft³.

In summary, the dry unit weight is 107.39 pcf, the void ratio is 0.593, and the weight of the water is 144.6 lb/ft³ based on the given soil properties and conditions.

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Final answer:

The dry unit weight (γ_dry) of the saturated soil sample is 61.9 pcf, the void ratio (e) is 0.328, and the weight of water (W_w) is 64.9% of the volume of the soil sample.

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 + w)
  3. Void ratio (e):
  4. e = (1 / G_s) * (w / (1 - w))
  5. Weight of water (W_w):
  6. W_w = γ_sat * V * w

Where:

  • γ_dry is the dry unit weight
  • γ_sat is the saturated unit weight
  • w is the water content
  • G_s is the specific gravity
  • e is the void ratio
  • V is the volume of the soil sample

Using the given information:

  • γ_sat = 101.2 pcf
  • w = 64.9%
  • G_s = 2.72

Let's calculate the values:

  1. Dry unit weight (γ_dry):
  2. γ_dry = 101.2 / (1 + 0.649) = 61.9 pcf
  3. Void ratio (e):
  4. e = (1 / 2.72) * (0.649 / (1 - 0.649)) = 0.328
  5. Weight of water (W_w):
  6. W_w = 101.2 * V * 0.649

Therefore, the values are:

  • Dry unit weight (γ_dry) = 61.9 pcf
  • Void ratio (e) = 0.328
  • Weight of water (W_w) = 64.9% of the volume of the soil sample

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