(a) A two-lane State Highway in plain terrain, with cutting section having camber of 2·0%, negotiates a curve of radius 480 m. Design superelevation and explain the process of attaining designed superelevation with the help of neat sketches. 15 marks

Question

(b) (i) The following consecutive readings were observed, on a continuously sloping ground, with the help of a 4·0 m staff and a dumpy level. If the reduced level of first point is 99·000 m, calculate the level of last point by entering the readings in level book. Also apply the usual checks. 10 marks
3·815, 2·500, 1·335, 2·980 and 0·800 m

(ii) The maximum quantity of water to be discharged by the side drains on both sides of a highway section is 1·8 m³/s. Design rectangular side drains for the following conditions. Both drains carry equal discharge.
Maximum permissible velocity of flow = 0·8 m/s
Roughness coefficient = 0·03 10 marks

(c) The project of constructing a small road in a rural area consists of various activities as given in the table below. The time (in weeks) and cost (₹ in lakh) required for completion of each activity is also given.

| Activity | Normal Time (Weeks) | Normal Cost (₹ in lakh) |
|----------|---------------------|-------------------------|
| 1-3 | 9 | 90 |
| 1-2 | 12 | 180 |
| 2-3 | 18 | 210 |
| 3-4 | 20 | 360 |

The construction of road started from 1st January. The project was reviewed after 13 weeks and the following conditions were observed:
(i) Activities 1 – 2 and 1 – 3 are completed as originally planned.
(ii) Activity 2 – 3 is in process and will require 19 more weeks to complete.
(iii) Activity 3 – 4 has not started.

Based on the above review after 13 weeks, formulate a new project including all activities.

Will the project be completed by 15th August of the same year?

If the project is to be completed in 49 weeks, determine how much activity 3 – 4 is to be crashed and what will be the increase in project cost?

Assume crash cost for activity 3 – 4 is ₹ 450 lakh and crash time is 17 weeks. 15 marks

UPSC Answer Check · Accepted Answer

Design requires systematic problem-solving with calculations and sketches. Allocate ~30% time to part (a) superelevation design with rotation diagrams, ~35% to part (b) numerical problems (levelling and drain design), and ~35% to part (c) CPM crashing analysis. Begin with clear problem statements, show all formulae with IRC/IS codes, present stepwise calculations, and conclude with practical feasibility checks.
- Part (a): Calculate superelevation for R=480m using IRC formula e=V²/225R, check against maximum 7% and 10% limits, apply ruling speed of 80 kmph for State Highway, and explain rotation about centre-line with inner edge depressed and outer edge raised
- Part (a): Draw three neat sketches showing (i) normal camber section, (ii) transition start with outer edge raised, (iii) full superelevation with rotated section
- Part (b)(i): Enter readings in standard level book format with BS, IS, FS columns, calculate rises and falls, verify ΣBS-ΣFS=Last RL-First RL=ΣRise-ΣFall, determine final RL
- Part (b)(ii): Apply Manning's equation V=(1/n)R^(2/3)S^(1/2) for rectangular drain, assume b=2y or given proportions, calculate dimensions for Q=0.9 m³/s per drain, check velocity < 0.8 m/s
- Part (c): Draw original network, identify critical path 1-2-3-4 (50 weeks), formulate revised network after 13 weeks with remaining durations, calculate new completion date and compare with 15th August (32 weeks from 1st Jan)
- Part (c): Determine crash requirement for 49-week completion, calculate cost slope for activity 3-4, find crash weeks needed and additional cost

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies IRC:38 for superelevation limits and rotation methods; uses standard levelling terminology (BS, FS, IS, HI) correctly; applies Manning's equation with appropriate hydraulic radius for rectangular sections; constructs accurate CPM network with proper critical path identification and crashing logic	Uses correct basic formulae but with minor errors in IRC code application or hydraulic radius definition; network drawn but critical path identification may have errors; understands levelling procedure but confuses rise/fall method with height of instrument	Fundamental conceptual errors such as using wrong superelevation formula, treating Manning's n incorrectly, or completely misunderstanding CPM methodology with wrong activity dependencies
Numerical accuracy	20%	10	All calculations precise: superelevation value with proper limiting checks, levelling arithmetic with exact RL to 3 decimals, drain dimensions satisfying Q and V constraints, CPM time analysis with correct crash cost computation (₹90 lakh per week for activity 3-4)	Correct methodology with minor arithmetic slips in one or two parts; final answers slightly off but approach verifiable; rounding errors in significant figures	Major calculation errors in multiple parts, wrong unit conversions, or completely incorrect final answers without working checks
Diagram quality	20%	10	Three clear superelevation sketches showing rotation stages with dimensions and slopes; neat level book tabulation with proper columns; network diagram with nodes, activities, durations, and critical path highlighted; drain cross-section with flow depth and freeboard	Diagrams present but lacking clarity or incomplete annotations; sketches show concept but missing key dimensions; network drawn but without proper activity-on-arrow or activity-on-node conventions	Missing essential diagrams, illegible sketches without labels, or no attempt at network representation despite question requirements
Step-by-step derivation	20%	10	Every formula stated before substitution (e=V²/225R, e_max=0.07, Manning's equation, cost slope formula); clear logical flow from given data to solution; arithmetic checks shown for levelling; crashing steps enumerated with time-cost trade-offs	Formulae mentioned but derivation skips some intermediate steps; working shown but not always logically sequenced; checks mentioned but not fully executed	No formulae stated, jumps to final answers, or working so disorganized that verification is impossible
Practical interpretation	20%	10	Interprets superelevation attainment for construction sequencing; discusses drain freeboard and maintenance access; clearly states project cannot meet 15th August deadline (requires 51 weeks vs 32 available); identifies minimum 49-week completion needs 2-week crash on activity 3-4 at ₹180 lakh additional cost; suggests practical alternatives	States conclusions but with limited practical context; mentions deadline issues but calculation errors affect validity; cost implications stated without sensitivity analysis	No interpretation of results, ignores deadline feasibility question, or provides conclusions contradicted by own calculations

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