Question 9 of 11: Dragline Side-Casting Geometry and Capability Check

Question 4: Dragline Side-Casting Geometry and Capability Check (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.

4.1 – 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 (overburden depth, pit width, required spoil-pile height), whether that specific machine's reach and stacking capability can physically complete the planned cut, exactly the check performed numerically in 4.6 below.

Given. Tub diameter $=20$ m; positioning $=75\%$ of tub diameter from centreline to high-wall edge; operating radius $=70$ m; pit width $W=40$ m; overburden (cut) 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 thickness $=3$ m.

Find. The tub-positioning offsets (4.2.2–4.2.3), the swelled volume of a unit sample (4.3.1), the cut/spoil cross-section geometry for a 1 m wide slice (4.5.1–4.5.6), and whether this dragline can complete the cut as specified (4.6–4.7).

1. 4.2.2 – Tub-positioning offsets. Positioning $=75\%$ of the 20 m tub diameter, from centreline to 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. 4.2.3 – Dragline reach. The 70 m operating radius is measured from the centreline; reach beyond the high-wall edge: $$\text{reach}=70-15=\boxed{55\text{ m}}$$
3. 4.3.1 – Swelled volume. $$V_{broken}=V_0(1+SF)=1\times(1+0.25)=\boxed{1.25\text{ m}^3}$$ – swell inflates volume (or, per unit length, area), not linear dimensions directly.
4. 4.5.1 – 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. 4.5.2 – Spoil pile area. The swell factor inflates the cross-sectional area of the cast material by $(1+SF)$: $$A_{spoil}=A_{cut}(1+SF)=1000\times1.25=\boxed{1250\ \text{m}^2\text{/m}}$$
6. 4.5.3 – Spoil pile height above coal seam floor. Modelling the swelled spoil as a symmetric triangular pile at its natural angle of repose $\phi$, area $A=h^2/\tan\phi$, so $h=\sqrt{A\tan\phi}$. This gives the pile height above the OVERBURDEN floor (top of coal); the coal seam floor (true final pit bottom, once the 3 m coal seam itself is later removed) sits a further 3 m below: $$h_{spoil}=\sqrt{1250\times\tan35^\circ}=29.6\text{ m}\qquad h_{above\ coal\ floor}=29.6+3=\boxed{32.6\text{ m}}$$
7. 4.5.4 – Height of spoil above the dragline tub base. The tub sits on the original ground surface, i.e. a level $D=25$ m above the overburden floor: $$h_{above\ tub}=h_{spoil}-D=29.6-25=\boxed{4.6\text{ m}}$$
8. 4.5.5 – 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 vertical rise the bucket must lift and cast through, from the overburden floor to the pile crest: $$h_{op}=h_{spoil}=\boxed{29.6\text{ m}}\quad\text{vs. the machine's rated 12 m}$$
9. 4.5.6 – Horizontal reach factor. Half-base of the symmetric spoil triangle, plus the pit width, gives the horizontal distance from the high-wall crest (dig point) to the pile crest (dump point): $$\text{half-base}=\dfrac{h_{spoil}}{\tan\phi}=\dfrac{29.6}{\tan35^\circ}=42.3\text{ m}$$ $$\text{reach factor}=W+\text{half-base}=40+42.3=\boxed{82.3\text{ m}}$$

4.6 – Capability check. Unlike a larger dragline with a 90 m operating radius considered elsewhere in this course (for which the same 82.3 m reach factor is comfortably inside the machine's reach), THIS machine's 70 m operating radius is 12.3 m SHORT of the 82.3 m horizontal reach factor – it cannot physically reach the required dump point. The operational stacking height is also 29.6 m against a rated maximum of only 12 m – exceeded by 17.6 m. Both checks fail: the dragline can neither reach the required dump point nor stack the swelled spoil to the height this single-pass cross-section demands, so it CANNOT complete the mining plan as specified without modification.

4.7 – Auxiliary methods/equipment. Because BOTH reach and stacking height fall short (unlike a reach-only or stack-only shortfall), the fix must address both: (i) an advanced bench (Question 1.4.3) – pre-strip part of the overburden column with a dozer/scraper so the dragline only casts the lower portion, which reduces both the spoil volume (lowering the required pile height) AND the horizontal distance the remaining material must be cast; (ii) a chop-down two-pass technique (Question 1.4.4) by the same dragline, splitting the single 25 m cut into two shallower lifts, each individually within the machine's reach and stacking envelope; or (iii) a dedicated secondary machine (dozer, or a stacking conveyor/spreader) to re-handle and push the spoil pile further back and lower its effective crest height, extending the machine's effective reach at the cost of extra handling. Given the size of BOTH shortfalls here (12.3 m reach, 17.6 m stacking height), a combination of (i) advanced bench and (ii) chop-down is the more realistic fix than re-handling alone.