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24-MMP-A5 Surface Mining Methods and Design · May 2014

Question 7 of 11: Dragline Range Diagram — Simple Side Casting

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A5 Surface Mining Methods and Design, 2014-May. 3 hours duration, closed book; one hand-written 8.5×11 inch reference sheet and an approved Casio or Sharp calculator permitted. Question 1 is compulsory (40 marks, all six parts 1.1–1.6); a candidate then selects THREE of Questions 2–6 (each worth 20 marks).

Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (dragline stripping systems, truck-shovel productivity, mine cost estimation — the primary reference throughout this paper); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design, 3rd ed. (block-model economics, floating/moving-cone algorithm, the Lerchs–Grossmann graph-theoretic pit-optimization method, annual push-back scheduling); Kennedy, B.A. (ed.), Surface Mining, 2nd ed., SME (dragline range-diagram geometry, stripping methods); Lerchs, H. & Grossmann, I.F. (1965), “Optimum Design of Open-Pit Mines,” CIM Bulletin, 58, 47–54.

Question 2: Dragline Range Diagram — Simple Side Casting (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Dragline: tub diameter 18 m, rated operating radius 95 m, positioning factor 75% of tub diameter, spec stacking height 12 m, digging depth 35 m. Ground/spoil geometry: highwall 63°, coal face 90° (vertical, “to simplify”), spoil-pile slope 35°, swell factor 0.25, overburden depth 30 m, pit width 45 m. All quantities are computed per lineal metre of cut (i.e. as a cross-sectional area, numerically equal to a volume/m).

Given data
QuantitySymbolValue
Tub diameterDt18 m
Operating radius (spec)Rspec95 m
Positioning factor—75% of Dt
Stacking height (spec)Hs,spec12 m
Highwall angleα63°
Spoil-pile slopeβ35°
Swell factorSF0.25
Overburden depthOB30 m
Pit widthW45 m

Find. The cut and spoil-pile cross-sectional areas, spoil-pile height, the dragline’s calculated stacking height and operating radius for this geometry, the horizontal reach factor, and (2.2) whether simple side-casting alone can complete the strip.

original ground leveldragline tubhighwall 63°coal face (90°)pit floor / coal seam topcut (OB = 30 m, W = 45 m)spoil pile, 35° both sidesR(calc) ≈ 127 m45 m pit width
Range-diagram section, drawn to the calculated geometry: highwall (63°) → coal face (vertical) → spoil pile (35° both sides). The dragline tub sits 13.5 m back from the highwall crest.

Approach. Build the cut cross-section as a trapezoid (pit-width base, highwall batter on one side, vertical coal face on the other) over the overburden depth; scale the spoil pile up by the swell factor and close it as a symmetric 35° triangular dump; then compare the resulting reach and stacking-height requirements against the machine’s spec to see whether simple side-casting is geometrically sufficient.

  1. Positioning distance (crest to tub centre). $d_{pos} = 0.75 \times 18\ \text{m} = 13.5\ \text{m}$.
  2. 2.1.2 — Cut area. The cut is a trapezoid: pit-width base $W$, height $OB$, one side battered at the highwall angle $\alpha$ (horizontal run $= OB/\tan\alpha$), the other side the vertical coal face (zero offset). $$\Delta x_{hw} = \frac{OB}{\tan\alpha} = \frac{30}{\tan(63^\circ)} = 15.29\ \text{m}, \qquad \text{top width} = W + \Delta x_{hw} = 60.29\ \text{m}$$ $$A_{cut} = \tfrac{1}{2}(W + \text{top width})\,OB = \tfrac{1}{2}(45+60.29)(30) = \boxed{1579\ \text{m}^2/\text{m}}$$
  3. 2.1.3 — Spoil-pile area. Loose (swelled) volume per metre of cut: $$A_{spoil} = A_{cut}(1+SF) = 1579 \times 1.25 = \boxed{1974\ \text{m}^2/\text{m}}$$
  4. 2.1.4 — Spoil-pile height. Model the dump as a symmetric triangle with both flanks at the angle of repose $\beta = 35^\circ$: base $= 2H_{sp}/\tan\beta$, so $A_{spoil} = H_{sp}^2/\tan\beta$. $$H_{sp} = \sqrt{A_{spoil}\tan\beta} = \sqrt{1974 \times \tan(35^\circ)} = \boxed{37.2\ \text{m}} \qquad (\text{base} = 2H_{sp}/\tan\beta = 106.2\ \text{m})$$
  5. 2.1.5 — Stacking height (calculated). The spoil-pile BASE sits in the previous cut’s void, i.e. $OB=30$ m below the original ground surface, so the crest height above original grade — the figure comparable to the machine’s spec value — is $$H_{s,calc} = H_{sp} - OB = 37.2 - 30 = \boxed{7.2\ \text{m}}$$ This is below the spec value of 12 m, so stacking height is not the binding constraint here.
  6. 2.1.7 — Operating radius (calculated). The tub sits $d_{pos}=13.5$ m back from the highwall crest (solid-ground side); the farthest point the bucket must reach to place spoil at the pile’s crest (centred on the base, which starts at the coal-face edge, top width from the crest) is $$R_{calc} = d_{pos} + \text{top width} + \tfrac{1}{2}\text{base} = 13.5 + 60.29 + 53.1 = \boxed{126.9\ \text{m}}$$
  7. 2.1.6 — Horizontal reach factor. $$\text{reach factor} = \frac{R_{calc}}{R_{spec}} = \frac{126.9}{95} = \boxed{1.34}$$ A factor above 1.0 means the required reach EXCEEDS the machine’s rated operating radius — this dragline cannot place all the spoil from this position by simple side casting alone.
Final results — Question 2.1
QuantityResult
2.1.2 Cut area1579 m²/m
2.1.3 Spoil-pile area1974 m²/m
2.1.4 Spoil-pile height37.2 m (base 106.2 m)
2.1.5 Stacking height (calculated)7.2 m (spec 12 m — OK)
2.1.6 Horizontal reach factor1.34 (> 1.0 — reach exceeded)
2.1.7 Operating radius (calculated)126.9 m (spec 95 m)
Check: the range-diagram geometry (tub position relative to the highwall crest, and a symmetric 35° spoil triangle) is the standard textbook construction for this class of problem; the exam’s own figure (drawn by the candidate in 2.1.1) would fix the exact reference points. The reach-factor conclusion (>1.0, side-casting alone insufficient) is not sensitive to small changes in exactly where along the spoil base the “crest” point is taken, since the shortfall is 34%, well outside plotting tolerance.

2.2 — Auxiliary methods. Because the calculated reach (126.9 m) exceeds the rated operating radius (95 m) by 34%, this dragline cannot complete the strip by simple side casting from a single tub position and needs one of the standard auxiliary techniques: (a) extended-bench or advanced-bench mining (Question 1.2.2/1.2.3) — stand the dragline on a partially-stripped bench above the seam to add both reach and stacking height without a bigger machine; (b) pre-stripping with an auxiliary stripping shovel or dozer to remove and rehandle the top slice of overburden onto a bench, shortening the depth the dragline itself must cover in one pass; (c) extended-bench with a pull-back/rehandle pass, where the dragline first casts as far as its reach allows, then rehandles the near-highwall portion of that spoil a second time onto the growing pile crest, trading extra rehandle cost for the reach it cannot achieve directly; or (d) tandem/dual dragline operation, where a second, smaller machine works the key cut or rehandles spoil while the main dragline continues primary casting. All trade extra capital or rehandle cost for the additional 30–35 m of effective reach/height this geometry is short.