Question

A bord and pillar panel initially has an extraction ratio of 0.15. After widening galleries, the extraction ratio changes to 0.25. Using the tributary area method, the percentage change in pillar stress (rounded off to two decimals) is __________.

Hint:

As extraction ratio increases, pillar area decreases and pillar stress increases sharply.

Answer 1

Correct Answer: 13

Pillar stress under tributary method:
\[ \sigma_p = \frac{\sigma_v}{1 - e}, \] where $e$ = extraction ratio.
Initial extraction ratio:
\[ e_1 = 0.15 \quad \Rightarrow \quad \sigma_{p1} = \frac{\sigma_v}{0.85}. \]
Final extraction ratio:
\[ e_2 = 0.25 \quad \Rightarrow \quad \sigma_{p2} = \frac{\sigma_v}{0.75}. \]
Percentage change:
\[ % \Delta \sigma = \frac{\sigma_{p2} - \sigma_{p1}}{\sigma_{p1}} \times 100. \]
\[ = \frac{\frac{\sigma_v}{0.75} - \frac{\sigma_v}{0.85}}{\frac{\sigma_v}{0.85}} \times 100. \]
Simplify:
\[ = \left( \frac{0.85 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.10}{0.75} \right) \times 100. \]
\[ = 13.33%. \]
\[ \boxed{13.33%} \quad (\text{acceptable range: } 13.00\text{–}14.00) \]