College

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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

#SPJ9

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada