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A ring with a volume of 20 cm\(^3\) weighs 61 g. The ring is then completely filled with soil, and the total weight of the wet soil and ring equals 97.8 g. After the soil sample is oven-dried at 105°C for 24 hours, the ring and the dry soil sample weigh a total of 89 g. Given that the solid unit weight of the soil sample is 2.65 t/m\(^3\), calculate the following:

a) Natural unit weight of soil (\(\gamma_n\))
b) Natural water content of soil (\(w_n\))
c) Dry unit weight of soil sample (\(\gamma_d\))
d) Void ratio (\(e\))
e) Porosity (\(n\))
f) Volume of air (\(V_a\))
g) Calculate the final water content (\(w_f\)) and the final unit weight of the soil sample (\(\gamma_{n \, \text{final}} = \gamma_{\text{sat}}\)) when it is fully saturated, keeping the total volume constant.

Answer :

a) Natural Unit Weight of Soil (γn): 1.84 g/cm³

b) Natural Water Content of Soil (wn): 9.89%

c) Dry Unit Weight of Soil Sample (γd): 1.67 g/cm³

d) Void Ratio (e): 0.67

e) Porosity (n): 0.40

f) Volume of Air (Va): 1.978 cm³

g) Final Water Content (wf): 9.89% and Final Unit Weight of Saturated Soil (γn final = γsat): 1.85 g/cm³

How did we get these values?

To solve this problem, we'll need to apply various soil mechanics principles and equations. Let's start with each question:

a) Natural Unit Weight of Soil (γn):

The natural unit weight of soil is calculated using the formula:

γn = (Weight of soil in the ring + Weight of the ring) / Volume of the ring

γn = (97.8g - 61g) / 20cm³

γn = 36.8g / 20cm³

γn = 1.84 g/cm³

b) Natural Water Content of Soil (wn):

The natural water content of the soil can be calculated using the formula:

wn = [(Weight of soil in the ring - Weight of dry soil) / Weight of dry soil] × 100%

wn = [(97.8g - 89g) / 89g] × 100%

wn = (8.8g / 89g) × 100%

wn ≈ 9.89%

c) Dry Unit Weight of Soil Sample (γd):

The dry unit weight of the soil sample can be calculated using the formula:

γd = γn / (1 + wn)

γd = 1.84 g/cm³ / (1 + 0.0989)

γd ≈ 1.67 g/cm³

d) Void Ratio (e):

The void ratio (e) can be calculated using the formula:

e = (γd / γw) - 1

Where γw is the unit weight of water, which is approximately 1 g/cm³.

e = (1.67 g/cm³ / 1 g/cm³) - 1

e ≈ 0.67

e) Porosity (n):

The porosity (n) is related to the void ratio (e) as follows:

n = e / (1 + e)

n = 0.67 / (1 + 0.67)

n ≈ 0.40

f) Volume of Air (Va):

Va can be calculated using the formula:

Va = wn × Volume of soil in the ring

Va = 0.0989 × 20cm³

Va ≈ 1.978cm³

g) Final Water Content (wf) and Final Unit Weight (γn final = γsat):

When the soil is fully saturated while keeping the total volume constant, the final water content (wf) can be calculated using the formula:

wf = Va / (Volume of soil in the ring)

wf = 1.978cm³ / 20cm³

wf ≈ 0.0989 or 9.89%

The final unit weight (γn final = γsat) when fully saturated can be calculated as:

γn final = γd / (1 - wf)

γn final ≈ 1.67 g/cm³ / (1 - 0.0989)

γn final ≈ 1.85 g/cm³

So, the final unit weight of the saturated soil sample is approximately 1.85 g/cm³.

learn more about Porosity: https://brainly.com/question/13866233

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Rewritten by : Jeany

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