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

(ii) The relationship between speed and density for a given section of road was found to be v = 100 – 1·2 k, where v is speed in kmph an

Question

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

(ii) The relationship between speed and density for a given section of road was found to be v = 100 – 1·2 k, where v is speed in kmph and k is the density in vehicles per km. Calculate the speed and density in which maximum flow could occur. Also draw the speed-density, speed-flow and flow-density diagrams indicating critical values. (15 marks)

(b) Starting from ground point A having elevation of 100·500 m, levels from points B to F were taken inside a tunnel. The points B to F were marked in the ceiling of the tunnel keeping the staff inverted. Above staff readings were observed during the survey.

Calculate the levels of all the points marked inside the tunnel. Also apply the regular checks for calculations. (15 marks)

(c) Explain in brief (with neat sketches), the Phenomenon of Bulking of Sand. How does bulking of sand affect the concrete mix ? (15 marks)

UPSC Answer Check · Accepted Answer

This multi-part question requires solving numerical problems in (a)(ii) and (b) while explaining concepts in (a)(i) and (c). Allocate approximately 35% time to (a)(ii) for its 15 marks involving traffic flow calculations and three diagrams, 30% to (b) for the 15-mark levelling problem with inverted staff, 20% to (c) for the 15-mark bulking explanation with sketches, and 15% to (a)(i) for the 5-mark traffic survey description. Begin with clear statements of given data, show all formulae and substitutions, and conclude with practical implications.
- (a)(i): Identification and explanation of any two relevant traffic surveys (e.g., speed and delay study, origin-destination survey, traffic volume study, spot speed study) with their specific application to geometric design
- (a)(ii): Derivation of q = vk, calculation of optimum speed v₀ = vₘ/₂ = 50 kmph, optimum density k₀ = kⱼ/₂ = 41.67 veh/km, and maximum flow qₘₐₓ = vₘkⱼ/₄ = 2083.33 veh/hr using v = 100 - 1.2k
- (a)(ii): Correct plotting of three fundamental diagrams (speed-density, speed-flow, flow-density) with proper axes, curves, and critical values marked (vₘ, kⱼ, qₘₐₓ, v₀, k₀)
- (b): Application of inverted staff correction (reading subtracted from height of instrument), correct calculation of HI at each setup, and computation of levels for points B through F with proper sign convention
- (b): Application of arithmetic check (ΣBS - ΣFS = Last RL - First RL) and closure check for the levelling operation
- (c): Explanation of bulking phenomenon due to surface moisture forming films around sand particles, increase in volume by 20-40% at 5-8% moisture content, and peak bulking at 4-6% moisture
- (c): Neat sketches showing dry sand, moist sand with water films causing particle separation, and fully saturated sand where bulking disappears
- (c): Effects on concrete mix: reduced strength if volume batching used without correction, need for weight batching or bulking factor adjustment, and field practices in Indian construction sites

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates flawless understanding of Greenshields' linear speed-density model, fundamental traffic flow relationships, tunnel levelling with inverted staff, and bulking mechanism; correctly identifies free-flow speed (100 kmph) and jam density (83.33 veh/km) from given equation; explains why bulking occurs at specific moisture content due to surface tension	Shows basic understanding of traffic flow theory and levelling principles but makes minor errors in identifying parameters (e.g., confuses vₘ with v₀) or incomplete explanation of bulking mechanism; understands inverted staff concept but applies sign convention inconsistently	Fundamental misconceptions about traffic flow relationships (e.g., treats v = 100-1.2k as flow equation), fails to recognize inverted staff requires subtraction rather than addition, or describes bulking incorrectly as chemical reaction rather than physical phenomenon
Numerical accuracy	20%	10	All calculations precise to three decimal places where appropriate; correct values: v₀ = 50 kmph, k₀ = 41.67 veh/km, qₘₐₓ = 2083.33 veh/hr; tunnel levels computed with consistent precision and correct arithmetic/closure checks within permissible limits	Correct methodology with minor arithmetic errors (e.g., calculation errors in multiplication/division, rounding errors); or correct final answers with some intermediate steps missing; checks applied but with computational errors	Major calculation errors in deriving optimum conditions (e.g., incorrect differentiation or algebraic manipulation), wrong formula application (using q = v + k), or completely incorrect level calculations with wrong sign conventions
Diagram quality	20%	10	Three traffic flow diagrams (v-k, v-q, q-k) drawn to scale with proper axes labels, correct parabolic/linear curves, and all critical values clearly indicated; bulking sketches show particle-level mechanism with water films; neat, labeled diagrams with proper proportions	Diagrams present but with minor flaws: missing labels, incorrect curve shapes (e.g., straight line for q-k relationship), or bulking sketches lacking clarity on particle separation mechanism; freehand sketches acceptable but poorly proportioned	Missing diagrams, incorrect fundamental shapes (e.g., speed-flow curve decreasing throughout), unlabeled axes, or sketches that fail to illustrate the actual bulking phenomenon; diagrams drawn without any relation to calculated values
Step-by-step derivation	20%	10	Clear derivation of q = v(100-1.2v)/1.2 or equivalent, explicit differentiation dq/dk = 0 to find optimum conditions, all HI calculations shown with inverted staff correction clearly explained; each level computation shown with rise/fall or height of instrument method	Derivation present but skips key steps (e.g., jumps to final formula without showing substitution), or uses alternative correct method (e.g., vertex of parabola formula) without explanation; levelling calculations shown but with condensed steps	No derivation shown—only final answers stated; or incorrect derivation with wrong calculus steps; tunnel levels presented as final values without any intermediate calculations or explanation of methodology
Practical interpretation	20%	10	Relates traffic flow results to highway capacity design (LOS E/F at qₘₐₓ), discusses implications of tunnel survey accuracy for construction alignment, explains field correction methods for bulking in concrete batching plants (weight batching preferred, or percentage correction for volume batching), cites IRC or MORTH relevance	Brief mention of practical relevance without elaboration; generic statements about importance of accurate surveys or concrete quality without specific connection to calculated results; mentions bulking correction but without quantitative adjustment	No practical interpretation provided; or irrelevant discussion unrelated to the specific problems solved; fails to recognize that maximum flow represents capacity, or that bulking affects mix proportioning in field concrete

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