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An uncompacted heap of soil has a volume of 10000 rm3 and void ratio of 1. If the soil is compacted to a volume of 7500 m3, then the corresponding void ratio of the compacted soil is _________. (round off to one decimal place)
Correct answer is '0.5'. Can you explain this answer?
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An uncompacted heap of soil has a volume of 10000 rm3 and void ratio o...
(Vs)heap = (Vs)compacted soil
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An uncompacted heap of soil has a volume of 10000 rm3 and void ratio o...
Given data:
Uncompacted soil volume (V) = 10000 m^3
Uncompacted soil void ratio (e) = 1
Compacted soil volume (Vc) = 7500 m^3
Explanation:
To find the corresponding void ratio of the compacted soil, we can use the relationship between void ratio and volume:
Void ratio (e) = (Volume of voids) / (Volume of solids)
Step 1: Find the volume of solids in the uncompacted soil
The volume of solids can be calculated using the given void ratio and the volume of the soil:
Volume of solids (Vs) = V / (1+e)
Substituting the given values, we get:
Volume of solids (Vs) = 10000 / (1+1) = 5000 m^3
Step 2: Find the volume of voids in the uncompacted soil
The volume of voids can be calculated by subtracting the volume of solids from the total volume:
Volume of voids (Vv) = V - Vs
Substituting the given values, we get:
Volume of voids (Vv) = 10000 - 5000 = 5000 m^3
Step 3: Find the volume of solids in the compacted soil
Since the volume of solids remains the same during compaction, the volume of solids in the compacted soil is also 5000 m^3.
Step 4: Find the volume of voids in the compacted soil
The volume of voids can be calculated by subtracting the volume of solids in the compacted soil from the total volume of the compacted soil:
Volume of voids in compacted soil (Vvc) = Vc - Vs
Substituting the given values, we get:
Volume of voids in compacted soil (Vvc) = 7500 - 5000 = 2500 m^3
Step 5: Find the void ratio of the compacted soil
Using the formula for void ratio, we can find the void ratio of the compacted soil:
Void ratio (ec) = Vvc / Vs
Substituting the values, we get:
Void ratio (ec) = 2500 / 5000 = 0.5
Therefore, the corresponding void ratio of the compacted soil is 0.5.
Uncompacted soil volume (V) = 10000 m^3
Uncompacted soil void ratio (e) = 1
Compacted soil volume (Vc) = 7500 m^3
Explanation:
To find the corresponding void ratio of the compacted soil, we can use the relationship between void ratio and volume:
Void ratio (e) = (Volume of voids) / (Volume of solids)
Step 1: Find the volume of solids in the uncompacted soil
The volume of solids can be calculated using the given void ratio and the volume of the soil:
Volume of solids (Vs) = V / (1+e)
Substituting the given values, we get:
Volume of solids (Vs) = 10000 / (1+1) = 5000 m^3
Step 2: Find the volume of voids in the uncompacted soil
The volume of voids can be calculated by subtracting the volume of solids from the total volume:
Volume of voids (Vv) = V - Vs
Substituting the given values, we get:
Volume of voids (Vv) = 10000 - 5000 = 5000 m^3
Step 3: Find the volume of solids in the compacted soil
Since the volume of solids remains the same during compaction, the volume of solids in the compacted soil is also 5000 m^3.
Step 4: Find the volume of voids in the compacted soil
The volume of voids can be calculated by subtracting the volume of solids in the compacted soil from the total volume of the compacted soil:
Volume of voids in compacted soil (Vvc) = Vc - Vs
Substituting the given values, we get:
Volume of voids in compacted soil (Vvc) = 7500 - 5000 = 2500 m^3
Step 5: Find the void ratio of the compacted soil
Using the formula for void ratio, we can find the void ratio of the compacted soil:
Void ratio (ec) = Vvc / Vs
Substituting the values, we get:
Void ratio (ec) = 2500 / 5000 = 0.5
Therefore, the corresponding void ratio of the compacted soil is 0.5.
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An uncompacted heap of soil has a volume of 10000 rm3 and void ratio of 1. If the soil is compacted to a volume of 7500 m3, then the corresponding void ratio of the compacted soil is _________. (round off to one decimal place)Correct answer is '0.5'. Can you explain this answer?
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