(a) (i) Explain any two traffic surveys carried out to decide the geometric design features of a road. (5 marks) (ii) The…

(a)(i)

• Traffic volume survey: counts vehicles over a period, classified by type, direction, speed, lane occupancy and turning movements. It gives design volume, peak hour factor, average speed, lane demand and junction volumes. These values are used to fix number of lanes, lane width, acceleration and deceleration lanes, junction layout, and pavement capacity.
• Speed survey: measures spot speeds, running speeds, 85th percentile speed, and speed distribution at a section. It fixes design speed, horizontal and vertical curve radii, sight distance, superelevation, cross slope, and alignment features.

(a)(ii) Given v = 100 – 1·2 k, v in km/h, k in veh/km. Since 1·2 = 6/5, v = 100 – (6/5)k. This is a Greenshields linear speed-density relation for steady, uniform traffic on the section. Flow q = v k = k(100 – (6/5)k) = 100k – (6/5)k² veh/h. For maximum flow, differentiate q with respect to k and set derivative zero: dq/dk = 100 – (12/5)k = 0 k = 100/(12/5) = 125/3 veh/km. The second derivative d²q/dk² = –12/5 < 0, so this is a maximum. Then v = 100 – (6/5)(125/3) = 50 km/h. q(max) = 50 × 125/3 = 6250/3 veh/h. Free-flow speed = 100 km/h at k = 0; jam density = 100/(6/5) = 250/3 veh/km at v = 0. Critical values are half free-flow speed and half jam density. The critical density is the density at maximum flow, and the critical speed is the speed at that density. Diagrams to draw:

• Speed-density: axes k horizontal, v vertical; straight line from (0, 100) to (250/3, 0); mark critical point (125/3, 50).
• Flow-density: axes k horizontal, q vertical; parabola q = 100k – (6/5)k², zero at k = 0 and 250/3, vertex at (125/3, 6250/3).
• Speed-flow: axes v horizontal, q vertical; from k = (100 – v)/(6/5), q = v(250/3 – (5/6)v), zero at v = 0 and 100, vertex at (50, 6250/3).

(b) Point A is on ground, so its staff reading is normal. Points B to F are on the ceiling, so their staff readings are inverted and are taken as negative. The height of instrument is the elevation of the line of sight. All readings are in metres to three decimals. A: RL = 100·500 m; BS = +1·234 m; HI = 100·500 + 1·234 = 101·734 m. B: FS = –1·782 m; RL = 101·734 – (–1·782) = 103·516 m; BS = –1·345 m; HI = 103·516 – 1·345 = 102·171 m. C: FS = –1·830 m; RL = 102·171 + 1·830 = 104·001 m; BS = –1·730 m; HI = 104·001 – 1·730 = 102·271 m. D: FS = –2·000 m; RL = 102·271 + 2·000 = 104·271 m; BS = –2·056 m; HI = 104·271 – 2·056 = 102·215 m. E: FS = –2·340 m; RL = 102·215 + 2·340 = 104·555 m; BS = –2·156 m; HI = 104·555 – 2·156 = 102·399 m. F: FS = –2·780 m; RL = 102·399 + 2·780 = 105·179 m. Regular checks: Number of BS = number of FS = 5. ΣBS = 1·234 – 1·345 – 1·730 – 2·056 – 2·156 = –6·053 m. ΣFS = –1·782 – 1·830 – 2·000 – 2·340 – 2·780 = –10·732 m. ΣBS – ΣFS = 4·679 m. RL(F) – RL(A) = 105·179 – 100·500 = 4·679 m. Check satisfied. Final levels: B = 103·516 m, C = 104·001 m, D = 104·271 m, E = 104·555 m, F = 105·179 m.

(c) Bulking of sand is the increase in bulk volume of sand when a small amount of water is present. In dry sand, particles are in contact and voids are air-filled. When damp, a thin water film forms on each particle; surface tension creates menisci between particles, pushing them apart and trapping air. This increases the total volume occupied by the same mass of sand. At saturation, voids are filled with water and the volume returns to the dry volume. Bulking is most pronounced for fine sand because its large surface area holds more water film. Sketches:

• Draw three containers: dry sand with particles touching and air voids; damp sand with water films and larger voids, higher level; saturated sand with water filling voids, level back to dry level.
• Draw a curve of bulking percentage against moisture content: starts at 0 for dry sand, rises to a maximum of about 30–40% for fine sand, 20–25% for medium sand, and 10–15% for coarse sand at about 5–10% moisture, then falls to 0 at saturation. Effect on concrete mix:
• If sand is measured by volume, bulking makes a bucket or pan contain less solid sand and more air/water than intended. The concrete will have lower sand content, more voids, and its workability/consistency will be affected; strength and durability may fall.
• Moist sand also carries water; if mixing water is not reduced, the water-cement ratio increases, causing shrinkage, permeability, and strength loss.
• Therefore sand should be weighed, or its measured volume should be corrected by the bulking percentage, and the moisture content should be accounted for in the water addition.