24-MMP-A5 Surface Mining Methods and Design · December 2018
Question 17 of 27
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper: Surface Mining Methods and Design (09-MMP-A5), National Exam, December 2018 — 20 pages, compulsory Question 1 (40 marks, parts 1.1–1.8) plus THREE of five optional Questions 2–6 (20 marks each) normally constitute a complete paper. As a study resource, this solution answers Question 1 in full AND all five optional Questions 2–6.
Reference texts: Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (3rd ed.) — truck-shovel match factor, dragline stripping geometry, capital cost indexes, open-pit scheduling; SME Mining Engineering Handbook (3rd ed.) — equipment costing, mine dewatering, cost-index escalation.
Given. Pit width (coal-floor width) W=40 m; overburden depth D=25 m; highwall angle 63° (adds width at the top of the cut); coal-face angle 90° (vertical, no added width, per the exam’s simplification); swell factor 0.25; spoil angle of repose 35°; max stacking distance from highwall edge=75 m (Q3.4); dragline floor sits at the original ground surface, 25 m above the coal seam floor.
Find. Cut cross-sectional area; loose spoil-pile area; spoil pile height above the coal floor; operational stacking height above the dragline’s own floor; horizontal offset between the dumping point and the pile peak — all per 1 m of strike length.
Check — the spoil pile is modelled here as a free-standing, symmetric (isosceles) pile with BOTH faces at the 35° angle of repose, the standard simplified model for a "simple side casting" cross-section when the exam does not supply a spoil-shape figure. A pile leaning against the previous spoil (one face steeper/vertical) would give a taller, narrower result; the symmetric assumption is stated explicitly here and carried consistently through 3.8–3.9.
Approach. Trapezoid geometry for the cut (highwall batter on one side, vertical coal face on the other); apply swell to get the loose spoil area; solve the isosceles-triangle spoil pile (base angle = angle of repose) for its base and height from that area; convert to the two required reference elevations.
3.8.1 — cut area. The highwall batters back by D/tan(63°) over the cut depth, adding that much extra width at the top; the coal-face side stays vertical (0 added width): $$\text{top offset} = \dfrac{25}{\tan 63^\circ} = 12.74\text{ m}, \quad \text{top width} = 40+12.74=52.74\text{ m}$$ $$A_{cut} = \dfrac{(52.74+40)}{2}\times 25$$ $$\boxed{A_{cut} = 1159.2\text{ m}^2}$$ (m³ per m of strike length).
3.8.2 — spoil pile area. Apply the swell factor to the cut volume: $$A_{spoil} = A_{cut}(1+0.25) = 1159.2 \times 1.25$$ $$\boxed{A_{spoil} = 1449.0\text{ m}^2}$$
3.8.3 — spoil pile height above coal floor. For a symmetric triangular pile of area A with both base angles φ=35°: $$A = \left(\dfrac{b}{2}\right)^2\tan\phi \;\Rightarrow\; \dfrac{b}{2}=\sqrt{\dfrac{A}{\tan\phi}}=\sqrt{\dfrac{1449.0}{\tan 35^\circ}}=45.49\text{ m}$$ $$h_{pile} = \dfrac{b}{2}\tan\phi = 45.49\times\tan35^\circ$$ $$\boxed{h_{pile} = 31.85\text{ m above the coal-seam floor}}$$ (base width b=91.0 m).
3.8.4 — operational stacking height above dragline floor. The dragline sits at the original ground surface, 25 m above the coal floor, so the height it must actually LIFT material above its own working level is the pile height less that 25 m: $$h_{op} = h_{pile} - D = 31.85 - 25$$ $$\boxed{h_{op} = 6.85\text{ m above the dragline floor}}$$
3.8.5 — horizontal offset, dump point to pile peak. The dragline’s maximum stacking distance from the highwall edge is 75 m (Q3.4); the pile’s peak, for a symmetric pile with its near toe at the edge, sits at half the base width: $$\Delta x = d_{stack} - \dfrac{b}{2} = 75 - 45.49$$ $$\boxed{\Delta x \approx 29.5\text{ m}}$$ — the dragline is currently dumping about 29.5 m beyond where the pile’s eventual peak will sit, i.e. it is still building the FAR flank of the pile at this point in the operation.
