An oven tin containing a sample of moist soil was weighed and had a mass of 37.82 g; the empty tin had a mass of 16.15 g. After drying, the tin and soil were weighed again and had a mass of 34.68 g.
Assuming GS = 2.70, determine the void ratio of the soil if the air-void content is:
Zero
5%
need help when the void content is 5%!
Void ratio, e, is the volume of voids, Vv, divided by the soil volume Vs.
Total mass, M=37.82-16.15=21.67
Mass of solids, Ms=34.68-16.15=18.53
Gs=S.G. of soil particles = 2.7
=>
Vol of soil,
Vs=Ms/Gs=18.53/2.7=6.863 mL
air-void content, ac=0
=>
all voids are filled with water, or soil is saturated => Vv=Vw
Vol of water,
Vw=(M-Ms)/ρw=(21.67-18.53)/1=3.14
(a)
Void ratio,
e=Vv/Vs=Vw/Vs=3.14/6.863=0.458
(b)
Air-void content,
ac=Va/Vv=5%
=>
Vv=Va/ac
=Vw/(1-ac)
=3.14/(1-0.05)
=3.305
e=Vv/Vs=3.305/6.863=0.482
To determine the void ratio of the soil when the air-void content is 5%, we need to calculate the volume of the solids, the volume of air, and the volume of water in the soil.
First, we need to find the mass of water in the initial sample. The mass of the moist soil is 37.82 g, and the mass of the dry soil is 34.68 g. Therefore, the mass of water can be calculated as follows:
Mass of water = Mass of moist soil - Mass of dry soil
= 37.82 g - 34.68 g
= 3.14 g
Next, we need to determine the volume of water in the soil by using the specific gravity (GS) of the soil. The specific gravity is the ratio of the weight of a given volume of soil to the weight of the same volume of water. In this case, the specific gravity (GS) is given as 2.70.
Volume of water = Mass of water / (Density of water x GS)
= 3.14 g / (1 g/cm3 x 2.70)
= 1.18 cm3
Now, let's calculate the volume of solids in the soil. The mass of dry soil is 34.68 g. To determine the volume of solids, we need to know the specific gravity of solids (GSS). Assuming that GSS is 2.70:
Volume of solids = Mass of dry soil / (Density of water x GSS)
= 34.68 g / (1 g/cm3 x 2.70)
= 12.84 cm3
To find the volume of air in the soil, subtract the sum of the volume of water and the volume of solids from the total volume:
Volume of air = Total volume - Volume of solids - Volume of water
When the air-void content is 5%, the volume of air is calculated as follows:
Volume of air = (5/100) x (Volume of solids + Volume of water)
= (5/100) x (12.84 cm3 + 1.18 cm3)
= 0.693 cm3
Finally, we can compute the void ratio using the following formula:
Void ratio = Volume of air / Volume of solids
Void ratio = 0.693 cm3 / 12.84 cm3
Void ratio ≈ 0.054
Therefore, when the air-void content is 5%, the void ratio of the soil is approximately 0.054.
To determine the void ratio of the soil when the air-void content is 5%, we need to calculate the total volume of the soil and the volume of air voids.
Given data:
GS (Specific Gravity) = 2.70
Mass of empty tin (m_empty) = 16.15 g
Mass of tin with moist soil (m_moist) = 37.82 g
Mass of tin with dried soil (m_dried) = 34.68 g
Air-void content (AVC) = 5%
Step 1: Calculate the mass of water (m_water) in the soil.
m_water = m_moist - m_dried
m_water = 37.82 g - 34.68 g
m_water = 3.14 g
Step 2: Calculate the mass of solids (m_solids) in the soil.
m_solids = m_dried - m_empty
m_solids = 34.68 g - 16.15 g
m_solids = 18.53 g
Step 3: Calculate the volume of water (V_water) in the soil.
V_water = m_water / (GS * density_water)
density_water = 1000 kg/m3 (density of water)
V_water = 3.14 g / (2.70 * 1000 kg/m3)
V_water = 0.00116 m3
Step 4: Calculate the volume of solids (V_solids) in the soil.
V_solids = m_solids / (GS * density_water)
V_solids = 18.53 g / (2.70 * 1000 kg/m3)
V_solids = 0.00686 m3
Step 5: Calculate the air-void volume (V_air) in the soil.
V_air = AVC * (V_water + V_solids)
V_air = 0.05 * (0.00116 m3 + 0.00686 m3)
V_air = 0.00061 m3
Step 6: Calculate the total volume of the soil (V_total).
V_total = V_water + V_solids + V_air
V_total = 0.00116 m3 + 0.00686 m3 + 0.00061 m3
V_total = 0.00863 m3
Step 7: Calculate the void ratio (e).
e = V_air / V_solids
e = 0.00061 m3 / 0.00686 m3
e ≈ 0.089
Therefore, the void ratio of the soil when the air-void content is 5% is approximately 0.089.