Question:
The centre-to-centre size of coal pillars developed in Board and Pillar mining is 40 m x 40 m working at 280 m depth has 4.0 m wide galleries. What area of roof does a pillar support according to tributary area theory?
The centre-to-centre size of coal pillars developed in Board and Pillar mining is 40 m x 40 m working at 280 m depth has 4.0 m wide galleries. What area of roof does a pillar support according to tributary area theory?
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Don't get confused by extra information.
The Tributary Area Theory is very straightforward: the supported area is simply the centre-to-centre pillar spacing squared (for a square grid).
The gallery width would be needed to find the actual size of the pillar itself (Pillar size = Centre distance - Gallery width).
The depth would be needed to calculate the stress on the pillar (Stress = Overburden Pressure * Tributary Area / Pillar Area).
The Tributary Area Theory is very straightforward: the supported area is simply the centre-to-centre pillar spacing squared (for a square grid).
The gallery width would be needed to find the actual size of the pillar itself (Pillar size = Centre distance - Gallery width).
The depth would be needed to calculate the stress on the pillar (Stress = Overburden Pressure * Tributary Area / Pillar Area).
Updated On: Jul 2, 2026
- 4480 sq.m
- 1936 sq.m
- 1600 sq.m
- 1296 sq.m
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
We need to calculate the area of the roof supported by a single coal pillar using the Tributary Area Theory.
Step 2: Key Formula or Approach:
The
Tributary Area Theory (TAT) is a simple method for estimating the load on a pillar.
It assumes that each pillar supports the weight of the overlying rock in a "tributary area" that extends halfway to each adjacent pillar.
In a regular grid of pillars, this tributary area is simply the centre-to-centre distance between pillars multiplied in both directions.
\[ \text{Tributary Area} = (\text{Centre-to-centre distance})_1 \times (\text{Centre-to-centre distance})_2 \]
Step 3: Detailed Explanation:
The problem gives the following data:
- Centre-to-centre size of pillars = 40 m x 40 m
- Depth = 280 m (This is extra information, not needed for calculating the area).
- Gallery width = 4.0 m (This is also extra information).
According to the Tributary Area Theory, the area of roof supported by one pillar is equal to the square of the centre-to-centre distance.
\[ \text{Area Supported} = 40 \, \text{m} \times 40 \, \text{m} = 1600 \, \text{m}^2 \]
Step 4: Final Answer:
The area of roof a pillar supports according to the tributary area theory is 1600 sq.m.
This corresponds to option (C).
We need to calculate the area of the roof supported by a single coal pillar using the Tributary Area Theory.
Step 2: Key Formula or Approach:
The
Tributary Area Theory (TAT) is a simple method for estimating the load on a pillar.
It assumes that each pillar supports the weight of the overlying rock in a "tributary area" that extends halfway to each adjacent pillar.
In a regular grid of pillars, this tributary area is simply the centre-to-centre distance between pillars multiplied in both directions.
\[ \text{Tributary Area} = (\text{Centre-to-centre distance})_1 \times (\text{Centre-to-centre distance})_2 \]
Step 3: Detailed Explanation:
The problem gives the following data:
- Centre-to-centre size of pillars = 40 m x 40 m
- Depth = 280 m (This is extra information, not needed for calculating the area).
- Gallery width = 4.0 m (This is also extra information).
According to the Tributary Area Theory, the area of roof supported by one pillar is equal to the square of the centre-to-centre distance.
\[ \text{Area Supported} = 40 \, \text{m} \times 40 \, \text{m} = 1600 \, \text{m}^2 \]
Step 4: Final Answer:
The area of roof a pillar supports according to the tributary area theory is 1600 sq.m.
This corresponds to option (C).
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