Question 12 of 13: Dragline Side-Casting Geometry

Question 6: Dragline Side-Casting Geometry (20 marks, optional)

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.

6.1 – Range diagram. A range diagram is a to-scale plot of a dragline's working envelope – digging depth, dumping radius and dumping height, all measured from the machine's own centreline/tub – used to check, for a given pit geometry, whether that specific machine's reach and stacking capability can physically complete a planned cut, exactly the numerical check performed in 6.5–6.6 below.

Given. Tub diameter $=20$ m; positioning $=75\%$ of tub diameter from centreline to high-wall edge; operating radius $=90$ m; pit width $W=40$ m; overburden depth $D=25$ m; swell factor $SF=0.25$; angle of repose $\phi=35^{\circ}$; rated (max) stacking height $=12$ m; high-wall slope $=63^{\circ}$; coal seam $=3$ m.

Find. The tub-positioning offsets and reach (6.2), the swelled unit volume (6.3.1), the cut/spoil cross-section geometry for a 1 m slice (6.5.1–6.5.6), and whether the dragline can complete the cut as specified (6.6–6.7).

1. 6.2.2 – Tub-positioning offsets. Positioning $=75\%$ of the 20 m tub diameter, measured from the dragline centreline to the high-wall edge: $$d_{centreline}=0.75\times20=\boxed{15\text{ m}}$$ Distance from the high-wall edge to the NEAREST tub edge (tub radius $=10$ m): $$d_{edge}=15-10=\boxed{5\text{ m}}$$
2. 6.2.3 – Dragline reach. The 90 m operating radius is measured from the centreline; the reach beyond the high-wall edge is: $$\text{reach}=90-15=\boxed{75\text{ m}}$$
3. 6.3.1 – Swelled volume. $$V_{broken}=V_0(1+SF)=1\times(1+0.25)=\boxed{1.25\text{ m}^3}$$ – swell inflates volume (area, per unit length), not any linear dimension directly.
4. 6.5.1 – Cut area (1 m slice). Modelling the cut as the rectangular overburden block removed ahead of the coal (pit width × overburden depth): $$A_{cut}=W\times D=40\times25=\boxed{1000\ \text{m}^2\text{/m}}$$
5. 6.5.2 – Spoil pile area. The swell factor inflates the cast material's cross-sectional area by $(1+SF)$: $$A_{spoil}=A_{cut}(1+SF)=1000\times1.25=\boxed{1250\ \text{m}^2\text{/m}}$$
6. 6.5.3 – Spoil pile height above coal seam floor. Modelling the swelled spoil as a symmetric triangular pile at its angle of repose $\phi$ ($A=h^2/\tan\phi$), $h_{spoil}$ is measured above ORIGINAL GRADE (where the tub sits); the coal seam floor lies a further $D+\text{seam}$ below that grade: $$h_{spoil}=\sqrt{A_{spoil}\tan\phi}=\sqrt{1250\times\tan35^{\circ}}=29.6\text{ m above grade}$$ $$h_{above\ coal\ floor}=h_{spoil}+D+\text{seam}=29.6+25+3=\boxed{57.6\text{ m}}$$
7. 6.5.4 – Height of spoil above the dragline tub base. The tub itself sits on original grade – the SAME reference plane the spoil pile rises from – so this is simply the pile's own height above grade: $$h_{above\ tub}=h_{spoil}=\boxed{29.6\text{ m}}$$ (distinct from 6.5.3 only because that result adds the $D+\text{seam}=28$ m the coal floor sits below the tub's own level).
8. 6.5.5 – Operational stacking height. Distinct from the manufacturer's RATED stacking height (a boom-geometry spec, 12 m, measured above the machine's own working level), the OPERATIONAL stacking height is the actual total vertical rise the bucket must lift and cast through: $$h_{op}=h_{spoil}=\boxed{29.6\text{ m}}\quad\text{vs. the machine's rated 12 m}$$
9. 6.5.6 – Horizontal reach factor. Half-base of the symmetric spoil triangle, plus the pit width, gives the horizontal distance from the high-wall crest to the pile crest: $$\text{half-base}=\dfrac{h_{spoil}}{\tan\phi}=\dfrac{29.6}{\tan35^{\circ}}=42.3\text{ m}$$ $$\text{reach factor}=W+\text{half-base}=40+42.3=\boxed{82.3\text{ m}}$$

6.6 – Capability check. The 82.3 m horizontal reach factor is comfortably within the machine's 90 m operating radius, so REACH is adequate. The operational stacking height, however, is 29.6 m against a rated maximum of only 12 m – exceeded by 17.6 m. The dragline can reach the required dump point but cannot stack the swelled spoil to the height this single-pass cross-section demands, so it CANNOT complete the mining plan as specified without modification.

6.7 – Auxiliary methods/equipment. Since the shortfall is stacking height, not reach, the standard fixes (Question 1.6.2–1.6.3) are: (i) advanced bench mining – pre-strip part of the overburden column with a dozer/scraper so the dragline only casts the lower portion, reducing the spoil volume (and hence pile height) it must place in a single pass; (ii) a pullback (re-handle) pass – the dragline retreats and re-handles previously cast material to push the pile further back and lower its effective working height, at the cost of extra cycle time; or (iii) a secondary machine (dozer or a smaller spreader/conveyor) dedicated to redistributing the upper part of the spoil pile so the dragline's own single-lift stacking height stays within its 12 m rating.