(a) (i) Explain with neat sketches, how surface and sub-surface water can be removed from a railway track. (ii) Two high level…

(a)(i) Removing surface and sub-surface water from a railway track (10 marks)

Surface water. The formation is given a cross-slope or camber (about 1 in 30 to 1 in 40) so that rain drains off to the sides. Side drains run along the cess, and catch-water drains on the uphill side of a cutting intercept run-off. Clean, well-graded ballast lets water pass quickly. Drains must be kept clear and given a continuous fall to an outfall.

Sub-surface water. Sub-surface drains are laid below the formation. A perforated or porous pipe (or a stone-filled French drain) lies in a trench that is lined or backfilled with graded filter material, and it discharges to a side drain through cross-drains. The filter has coarser material next to the pipe and finer material outside, so fines cannot wash in and clog it. A sand or blanketing layer under the ballast also cuts capillary rise and keeps the formation dry.

(a)(ii) Extra clearance for platforms on a 2° BG curve (10 marks)

R = 1,750/D = 875 m. Bogie centres B = 14.785 m, length L = 21.34 m, cant e = 100 mm, platform height h = 840 mm, and rail centre distance G = 1.750 m.

• Centre throw (inside) = B²/(8R) = 14.785²/(8 × 875) = 0.031 m = 31 mm.
• End throw (outside) = (L² − B²)/(8R) = (21.34² − 14.785²)/7,000 = 0.034 m = 34 mm.
• Lean due to cant at platform height = he/G = 840 × 100/1,750 = 48 mm. It tilts the coach towards the inside.

Inside platform: the lean adds to the centre throw, so extra clearance = 31 + 48 = 79 mm. Outside platform: the lean moves the coach away, so extra clearance = 34 − 48 = −14 mm, i.e. none is needed (the end throw is more than offset by the lean).

(This follows the usual sign logic; using G = 1.676 m changes the lean to 50 mm.)

(b) Intervisibility of A and B (15 marks)

For a point at distance d₁ from A and d₂ from B (km), the curvature and refraction correction relative to the chord AB is 0.0673d₁d₂ metres. Add it to the peak height and compare with the line of sight (LOS). D = 130 km.

Peak C (AC = 50, CB = 80): correction = 0.0673 × 50 × 80 = 269 m, so effective height = 308 + 269 = 577 m. LOS height = 225 + 935 × 50/130 = 585 m. LOS is 8 m above, so C is clear.

Peak D (AD = 90, DB = 40): correction = 0.0673 × 90 × 40 = 242 m, so effective height = 632 + 242 = 874 m. LOS height = 225 + 935 × 90/130 = 872 m. LOS is 2 m below, so D blocks the view.

A and B are not intervisible.

Scaffolding at B. Raise B by s so the LOS at D reaches 874.3 m: 225 + (935 + s) × 90/130 = 874.3, so 935 + s = 937.9 and s ≈ 2.9 m (about 3 m). C then also remains clear.

(c) Infrastructure project, BOO and BOOT (15 marks)

An infrastructure project is a capital-intensive, long-gestation asset that provides an essential public service, such as a road, port, airport, power plant, water supply or railway. It has long life, large sunk cost and wide social benefit.

BOO (Build–Own–Operate). The private developer builds, owns and operates the asset and keeps ownership permanently. There is no transfer to the government, and it carries all construction, operating and market risk. It suits merchant power plants.

BOOT (Build–Own–Operate–Transfer). The developer builds, owns and operates the asset only for a fixed concession period, recovers its investment and return through tolls or tariffs, and then transfers the asset to the government, usually free of cost. Risks are shared by contract, and the government carries the post-transfer risk. It suits toll roads, bridges and ports.

Typical BOOT structure. The government grants a concession to a special-purpose company. Sponsors put in equity and lenders provide debt. The company contracts a contractor for construction and an operator for O&M, and it collects user charges. At the end of the concession it hands the asset to the government.