Coal pillar load calculation by pressure arch theory

The pressure arch theory is used to calculate the load that a coal pillar can withstand before it collapses. The formula for calculating the load is:

P = K * (σh)^2 / (2 * (1 - sin²θ))

Where:
P = Load on the pillar (in pounds)
K = Constant (usually around 0.6)
σ = Stress on the pillar (in pounds per square foot)
h = Height of the pillar (in feet)
θ = Angle of internal friction of the coal (in degrees)

An example of how to use this formula to calculate the load on a coal pillar is as follows:

A coal pillar has a height of 200 feet and an angle of internal friction of 30 degrees. The stress on the pillar is 500 pounds per square foot. Using the formula above, we can calculate the load on the pillar as follows:

P = K * (σh)^2 / (2 * (1 - sin²θ))
P = 0.6 * (500 * 200)^2 / (2 * (1 - sin²30))
P = 0.6 * (100,000 * 100,000) / (2 * (1 - (0.5)²))
P = 0.6 * 10,000,000,000 / 0.75
P = 8,000,000,000 pounds

So the load on the pillar is 8,000,000,000 pounds.
Please note that these are rough calculations and may not be accurate for all situations, real-world calculations are done by experts and take into account many other factors

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