Question

If the specific gravity of soil solids is 2.6, and water content is 90.51% for a given soil whose degree of saturation is 60%, its void ratio will be

Answer 1

VR ≈ 6.04

Step-by-step explanation:

To calculate the void ratio of a soil, we need to know the volume of voids (Vv) and the volume of solids (Vs). The void ratio (e) is defined as the ratio of the volume of voids to the volume of solids:

⇒ e = Vv / Vs

Given the specific gravity of soil solids (Gs) as 2.6, the water content (w) as 90.51%, and the degree of saturation (S) as 60%, we can determine the void ratio as follows:

1) Calculate the dry unit weight of the soil (γd):

⇒ γd = Gs * γw

Here, γw is the unit weight of water, which is approximately 9.81 kN/m³.

2) Calculate the moist unit weight of the soil (γm):

⇒ γm = γd * (1 + w)

Here, w is the water content expressed as a decimal (90.51% = 0.9051).

3) Calculate the saturated unit weight of the soil (γsat):

⇒ γsat = γw * (1 + w)

Here, γw is the unit weight of water.

4) Calculate the volume of water (Vw):

⇒ Vw = γw * w / γw

The unit weights cancel out, leaving Vw as the volume of water.

5) Calculate the volume of solids (Vs):

⇒ Vs = (1 - w) - Vw

Here, (1 - w) represents the volume of the soil solids in the moist state.

6) Calculate the volume of voids (Vv):

⇒ Vv = S * Vw

7) Calculate the void ratio (e):

⇒ e = Vv / Vs

By following these steps and plugging in the given values, you can determine the void ratio of the soil.

To calculate the void ratio, we need to follow the steps outlined in the previous response using the given values. Let's go through the calculations:

Given:

• Specific gravity of soil solids (Gs) = 2.6
• Water content (w) = 90.51%
• Degree of saturation (S) = 60%

Step 1: Calculate the dry unit weight (γd)

γw = 9.81 kN/m³ (unit weight of water)

γd = Gs * γw = 2.6 * 9.81 kN/m³ = 25.506 kN/m³

Step 2: Calculate the moist unit weight (γm)

γm = γd * (1 + w) = 25.506 kN/m³ * (1 + 0.9051) = 48.625 kN/m³

Step 3: Calculate the saturated unit weight (γsat)

γsat = γw * (1 + w) = 9.81 kN/m³ * (1 + 0.9051) = 18.72505 kN/m³

Step 4: Calculate the volume of water (Vw)

Vw = γw * w / γw = 9.81 kN/m³ * 0.9051 / 9.81 kN/m³ = 0.9051 m³

Step 5: Calculate the volume of solids (Vs)

Vs = (1 - w) - Vw = (1 - 0.9051) - 0.9051 = 0.0899 m³

Step 6: Calculate the volume of voids (Vv)

Vv = S * Vw = 0.6 * 0.9051 m³ = 0.54306 m³

Step 7: Calculate the void ratio (e)

e = Vv / Vs = 0.54306 m³ / 0.0899 m³ ≈ 6.04

Therefore, the void ratio of the given soil is approximately 6.04.

Answer 2

Step-by-step explanation:

To calculate the void ratio of the soil, we can use the following formula:

Void ratio (e) = (G_s * e_s) / (1 + e_w)

Where:

G_s = specific gravity of soil solids

e_s = void ratio of soil solids

e_w = void ratio of water

Given:

Specific gravity of soil solids (G_s) = 2.6

Water content = 90.51% (or 0.9051 in decimal form)

Degree of saturation = 60% (or 0.6 in decimal form)

To find the void ratio of water (e_w), we can use the formula:

e_w = (1 / (1 + w)) - 1

where w is the water content.

Calculating the void ratio of water:

e_w = (1 / (1 + 0.9051)) - 1

= 0.9051 / (1 + 0.9051) - 1

= 0.9051 / 1.9051 - 1

= 0.9051 / 0.9051

= 1 - 1

= 0

Since the water content is 90.51%, the void ratio of water is 0.

Now we can calculate the void ratio of the soil:

e = (G_s * e_s) / (1 + e_w)

= (2.6 * e_s) / (1 + 0)

Given that the degree of saturation (S) is 60% (or 0.6), we know that:

S = (e - e_w) / (e_s - e_w)

0.6 = (e - 0) / (e_s - 0)

e_s = 0.6 * e

Substituting this into the void ratio equation:

e = (2.6 * 0.6 * e) / (1 + 0)

e = (1.56 * e) / 1

1 = 1.56 * e

e = 1 / 1.56

e ≈ 0.641

Therefore, the void ratio of the given soil is approximately 0.641.