Question

In a bord and pillar panel, a square pillar of size 35 m \( \times \) 35 m (centre to centre) is extracted to form four equal square-shaped stooks as shown. The width of each gallery and crosscut is 5 m. The height of the working seam is 3 m. The reduction in safety factor after pillar splitting by using Bieniawski’s pillar strength formula, in %, is _______ (rounded off to 2 decimal places).

Bieniawski's pillar strength formula is given by \( S_p = S_1 \left( 0.64 + 0.36 \frac{w}{h} \right) \), where \( S_1 \) is the strength of a 0.9 m\(^3\) coal block, \( w \) is the pillar width, and \( h \) is the mining height.

Hint:

Bieniawski’s pillar strength formula helps estimate the safety factor by considering the width and height of the pillar, and the strength of the coal. After pillar splitting, the safety factor typically reduces due to a decrease in pillar width.

Answer 1

Correct Answer: 0.6

Solution:

1. Initial Pillar Dimensions and Area:

Centre-to-centre dimension of initial pillar = 35 m × 35 m
Width of gallery/crosscut = 5 m
Actual width of initial pillar (w₁) = 35 − 5 = 30 m
Area of initial pillar (A₁) = (30)² = 900 m²

2. Dimensions and Area of the Stooks:

Width of each stook (w₂) = (30 − 5) / 2 = 12.5 m
Area of each stook (A_stook) = (12.5)² = 156.25 m²
Total area of four stooks (A₂) = 4 × 156.25 = 625 m²

3. Mining Height:

Height of the working seam (h) = 3 m

4. Bieniawski’s Pillar Strength Formula:

S_p = S₁ [0.64 + 0.36 (w / h)]

5. Initial Pillar Strength (S_p1):

S_p1 = S₁ [0.64 + 0.36 × (30 / 3)]
S_p1 = S₁ (0.64 + 3.6) = 4.24 S₁

6. Strength of Each Stook (S_p2):

S_p2 = S₁ [0.64 + 0.36 × (12.5 / 3)]
S_p2 = S₁ (0.64 + 1.50) = 2.14 S₁

7. Safety Factor Comparison:

Initial safety factor (SF₁) ∝ S_p1 × A₁ = 4.24 S₁ × 900

Safety factor after splitting (SF₂) ∝ S_p2 × A_stook × 4
SF₂ = 2.14 S₁ × 156.25 × 4 = 1337.5 S₁

Ratio of safety factors:

SF₂ / SF₁ = 1337.5 / (4.24 × 900)
SF₂ / SF₁ ≈ 0.3505

8. Percentage Reduction in Safety Factor:

Reduction = (1 − 0.3505) × 100
Reduction ≈ 64.95 %

Final Answer:
The reduction in safety factor is 64.95 %.