(a) What are the approximate limits of chemical (oxide) composition in hydraulic cement ? Also state the function of oxides in…

(a) Oxide composition of hydraulic cement and function of each oxide

Approximate limits are: lime CaO 60–67%, silica SiO₂ 17–25%, alumina Al₂O₃ 3–8%, iron oxide Fe₂O₃ 0.5–6%, magnesia MgO 0.1–4%, sulphur trioxide SO₃ 1–3%, and alkalis (Na₂O + K₂O) 0.4–1.3%.

Functions: CaO is the main oxide; it forms the silicates and aluminates that give strength, but excess free lime causes unsoundness. SiO₂ forms C₃S and C₂S, which give strength. Al₂O₃ forms C₃A, which gives quick setting and high early heat. Fe₂O₃ forms C₄AF, acts as a flux and gives the grey colour. MgO in excess causes delayed expansion. SO₃, from gypsum, controls the setting of C₃A and prevents flash set. Alkalis in excess can cause efflorescence and alkali–aggregate reaction.

(b) Work Breakdown Structure (WBS)

(i) A WBS is a hierarchical, deliverable-oriented decomposition of the whole project scope into smaller components until work packages are reached that can be estimated, scheduled, assigned and controlled. The sketch is a tree: Level 1 is the project; Level 2 has the major deliverables (planning, design, construction, commissioning); Level 3 has the work packages (foundation, superstructure, finishing, services); Level 4 has the activities (excavation, reinforcement, concreting, curing). Each package has a responsible person, a budget and a duration, and the 100% rule requires that the lower levels add up to the whole scope without overlap.

(ii) A WBS can be classified by project phase, by product or system, by geography or by organisation. For a metro corridor, a phase-based WBS is Planning, Design, Construction and Commissioning. Construction can then be split by system (civil works, track, traction, signalling), by location (station 1, station 2, tunnel section) or by contractor. The scope stays the same and only the cut changes with the management purpose.

(c) Workability of concrete

Workability is the ease with which fresh concrete can be mixed, transported, placed and compacted with minimum segregation and bleeding. It depends on the water–cement ratio, aggregate grading and shape, cement content, admixtures and temperature.

Slump test procedure: place a clean, oiled cone (300 mm high, 200 mm bottom and 100 mm top diameter) on a flat, non-absorbent plate. Fill it in three layers of about equal depth, tamping each layer 25 times with a 16 mm rod. Strike off the top, then lift the cone vertically in 5–10 seconds. Measure the subsidence of the concrete from the cone height; this is the slump in mm. Slump also shows the shape of failure (true, shear or collapse).

(d) Track material for 100 km of new track (doubling)

Doubling means laying a second track of 100 km, which is one track with two rails. Rail length = 13 m, so rail lengths per line = 100 000/13 = 7692.3.

Rails = 2 × 7692.3 ≈ 15 385 rails of 13 m.

Sleeper density (n + 4) per rail length with n = 13 gives 17 sleepers per rail. Sleepers = 7692.3 × 17 ≈ 1 30 770 sleepers, at spacing 13/17 = 0.765 m c/c (clear gap 0.765 − 0.25 = 0.515 m for the 250 mm sleeper width).

Joints ≈ 15 385 (one at the end of each rail). Fish plates = 2 per joint ≈ 30 770 and fish bolts with nuts = 4 per joint ≈ 61 540.

Sleeper fittings at 4 per sleeper (e.g. clips or dog spikes) ≈ 5 23 080. Ballast cannot be quantified because the depth and formation width are not given.

(e) Bearings of a regular hexagon

Each interior angle = 120°. For the traverse ABCDEF taken clockwise, each fore bearing is the previous one + 180° − 120° = +60°. (For an anticlockwise traverse, subtract 60° instead.)

Fore bearings: AB 120°, BC 180°, CD 240°, DE 300°, EF 0° (360°), FA 60°.

Back bearings (± 180°): AB 300°, BC 0°, CD 60°, DE 120°, EF 180°, FA 240°.

Diagonals: BE is the long diagonal, parallel to CD, so its bearing is 240°. In triangle ABF, angle ABF = 30°, and the bearing of BA is 300°, so the bearing of BF = 300° − 30° = 270°. (Using coordinates with side 1: B(0.866, −0.5), E(−0.866, −1.5), F(−0.866, −0.5) gives the same results.)