UPSC Civil Engineering 2021 — Paper II

This multi-part question requires solving five distinct technical problems across building construction, project management, surveying, highway engineering, and railway engineering. Allocate approximately 2 minutes per mark (20 minutes per part), presenting each sub-part (a) through (e) as separate, clearly labelled sections. Begin with direct answers for theoretical parts, show complete numerical working for calculation-based parts, and ensure diagrams are neatly drawn with proper labelling.

• Part (a): Purpose of first coat plastering (keying surface, leveling, damp-proofing); formwork loads (fresh concrete weight, construction live loads, wind, vibration, impact); correct identification of pitched roof components (rafter, purlin, tie beam, king post/queen post)
• Part (b): Correct conversion from A-O-A to A-O-N network topology; accurate forward and backward pass calculations; identification of critical path with zero float activities
• Part (c): Application of sensitivity formula n = (S/R) × 206265 seconds; correct calculation of angle change from bubble displacement; derivation of radius of curvature R = S × D / α in arc-seconds
• Part (d): Definition of vertical curve as transition curve in elevation; significance for sight distance, comfort, drainage; correct geometric sketches for both summit curves (convex) and valley curves (concave) with tangent lengths
• Part (e): Application of Indian Railways tractive effort formula considering curve resistance (0.01° per degree), friction limitation, and speed-dependent factors; correct unit conversions for metre gauge conditions

This question demands solving three distinct numerical problems covering resource allocation in project management, highway geometric design, and surveying calculations. The answer should present each part sequentially with clear problem identification, application of correct formulae, systematic calculations, and final verification of results. Part (a) requires resource leveling/ smoothing with Gantt charts or histograms, Part (b) needs set-back distance calculations using IRC standards, and Part (c) involves reciprocal leveling and collimation error determination.

• Part (a): Resource allocation with unlimited resources (resource leveling) and limited resources (resource smoothing) using histograms, identification of peak demand and resource constraints
• Part (a): Clear advantages and disadvantages of both methods including cost implications, project duration impact, and resource utilization efficiency
• Part (b): Correct application of set-back distance formulae for SSD (m < R) and OSD cases, accounting for lane offset of 1.9 m from center line
• Part (c): Calculation of true staff readings using reciprocal leveling principles, elimination of collimation error, and determination of R.L. of B
• Part (c): Recognition that instrument at P gives true difference of level, while Q setup reveals collimation error through inconsistent readings

Begin with a brief introduction acknowledging the multi-disciplinary nature of the question spanning railway engineering, geodetic surveying, and infrastructure financing. Allocate approximately 40% effort to part (a) combining drainage sketches with curve clearance calculations, 30% to part (b) for the intervisibility problem with proper profile diagram, and 30% to part (c) for conceptual comparison of PPP models with a neat BOOT structure diagram. Conclude with a synthesis on integrated infrastructure planning.

• Part (a)(i): Surface water removal via side drains, catch water drains, and proper ballast section; sub-surface water removal via cross drains (drainage layer), pipe drains, and inverted filters with neat sectional sketches
• Part (a)(ii): Calculation of extra clearances on curves using IRC formulae: overthrow (C1), end-throw (C2), lean due to superelevation (C3), and shift; application to inside and outside platforms with 840mm height consideration
• Part (b): Application of line of sight formula considering earth's curvature and refraction (k=0.07); calculation of minimum height of sight line above peaks C and D; determination of non-intervisibility and scaffolding height at B using Indian Survey standards
• Part (c): Definition of infrastructure project with characteristics (public good nature, high capital cost, long gestation, externalities); systematic comparison of BOO vs BOOT on ownership, transfer, financing risk, and government role; typical BOOT structure diagram showing SPV, concessionaire, lenders, and government relationships
• Part (c) continued: Indian examples such as Delhi Metro (PPP variants), NHAI BOT projects, or airport privatization to illustrate BOOT application

Begin with a brief introduction acknowledging the multi-part nature of this pavement design, valuation, and materials question. For part (a), apply IRC:58 design methodology for dowel bars using the given radius of relative stiffness and wheel load, showing complete derivations for bearing, shear, and flexural stress checks. For part (b), prepare a discounted cash flow table year-wise for development costs and revenue realization, computing net present value and cost per m². For part (c)(i), enumerate ferro-cement advantages with specific justification for large tank feasibility, and for (c)(ii) label door components with correct technical terminology. Allocate approximately 40% time to part (a), 30% to part (b), and 30% combined to part (c), ensuring all numerical workings are clearly presented with stated assumptions.

• Part (a): Calculation of load transfer capacity (40% of 5000 kg = 2000 kg), determination of dowel bar diameter using bearing stress criterion (σb = P/(d×h) ≤ 100 kg/cm²), spacing based on relative stiffness (l = 80 cm), and verification against shear (1000 kg/cm²) and flexural (1400 kg/cm²) stress limits with joint width 2.0 cm
• Part (a): Selection of standard dowel bar size (typically 25-32 mm diameter) and spacing (250-300 mm), with 50% load transfer efficiency assumption and check for concrete bearing stress using Bradbury's or IRC:58 recommendations
• Part (b): Year-wise development cost outflow (10%, 15%, 20%, 55% of Rs. 100 × 60,000 = Rs. 6,00,000) and revenue inflow from plot sales (10%, 20%, 20%, 30%, 20% of 60,000 m² at Rs. 5000/m²), discounted at 7% to find NPV and cost per m²
• Part (c)(i): Ferro-cement advantages—thin sections (10-25 mm), high strength-to-weight ratio, crack resistance due to distributed reinforcement, no formwork needed, cost-effectiveness for small tanks; justification for 25,000+ litre tanks requires thickness increase, stiffener rings, and waterproofing treatment
• Part (c)(ii): Correct labeling of door components—styles (vertical), rails (horizontal), mullions (intermediate vertical), panels, stiles, top rail, bottom rail, lock rail, meeting stiles, hinges, latch/lock hardware

Begin with the directive 'calculate' for the numerical parts (a), (b), (c), and (e), while 'discuss' applies to part (d). Allocate approximately 20% time to each sub-part given equal 10-mark weighting. Structure as: direct calculations for (a), (b), (c), (e) with clear steps, followed by a descriptive response for (d) on indicator organisms. No conclusion needed; present each part separately with clear labeling.

• Part (a): Apply superposition principle to 1-hour unit hydrograph; convolute with 70 mm and 40 mm rainfall excesses lagged by 1 hour; identify peak DSR ordinate in m³/s
• Part (b): Apply risk formula R = 1 - (1-1/T)^n where T=25 years, n=3 years; calculate exact probability of overtopping in third year specifically, not cumulative
• Part (c): Use Khosla's theory for exit gradient; apply G_E = (H/d) × (1/π√λ) where λ = (1+√(1+α²))/2 and α = b/d; substitute b=50m, d=5m, H=5m
• Part (d): Define indicator organism; list 4-5 ideal characteristics (e.g., consistently present in feces, non-pathogenic, easy to detect); name E. coli and Streptococcus faecalis or Coliform bacteria
• Part (e): Apply Manning's equation Q = (1/n) × A × R^(2/3) × S^(1/2) for full circular pipe; explain 150 mm minimum prevents clogging by solids and maintains self-cleansing velocity

Begin with a clear statement of given data and design criteria for both tanks in part (a). Allocate approximately 40% of effort to part (a) as it carries 20 marks, with detailed step-by-step calculations for rectangular and circular tank dimensions, followed by verification checks for retention time, horizontal velocity and weir overflow rate. For part (b) (15 marks), explain the theoretical basis for BOD/COD relationship, then enumerate practical reasons for divergence including biodegradability limitations, toxic substances, and microbial kinetics. For part (c) (15 marks), present the cropping pattern data clearly, apply sequential monthly water balance calculations accounting for crop water requirements, effective rainfall, canal losses (15%) and reservoir losses (10%) to determine storage capacity. Conclude with a summary table comparing both tank designs and key insights on BOD/COD differences.

• Part (a): Correct application of surface overflow rate formula (Q/As = 20 m/d) to determine plan areas; calculation of rectangular tank dimensions (L:B = 3:1, SWD = 3.5m) yielding L ≈ 55 m, B ≈ 18.3 m; circular tank diameter ≈ 35.7 m with SWD = 4.0 m
• Part (a): Verification of retention time (3-5 hours), horizontal velocity (<10 m/h), and weir overflow rate (6-10 m³/h/m) with clear pass/fail assessment; overall dimensions including inlet/outlet zones each equal to SWD
• Part (b): Explanation that COD measures total oxidizable matter while BOD measures only biodegradable fraction; reasons for BOD < COD including: presence of refractory organic compounds, toxic/inhibitory substances, insufficient acclimatization period, nitrification interference, and soluble non-biodegradable organics
• Part (b): Reference to typical BOD/COD ratios (0.4-0.8 for municipal wastewater, lower for industrial wastewater) and significance for treatment plant design
• Part (c): Monthly water balance computation: Crop water requirement (CWR) = CWR peak × kc × area; net irrigation requirement = CWR - effective rainfall; gross irrigation = net/(1-canal losses); reservoir yield accounting for 10% losses; storage capacity as maximum cumulative deficit
• Part (c): Application to typical Indian cropping pattern (e.g., kharif paddy + rabi wheat) with proper unit conversions (ha-m or Mm³) and final reservoir capacity determination

This is a multi-part numerical and descriptive problem requiring systematic solving. Allocate approximately 40% time to part (a) as it carries the highest marks (20) and involves comprehensive drain design using Lacey's regime theory; 30% each to parts (b) and (c). Begin with clear problem statements for each part, show all formulae with their sources, present step-by-step calculations with proper units, and conclude with practical significance of results.

• Part (a): Correct application of drainage coefficient to compute discharge Q = C×A = 0.06×(576×10⁴)/(24×3600) m³/s; application of Lacey's regime equations (P = 4.75√Q, R = 5V²/2f, S = f^(5/3)/(3340×Q^(1/6))) to determine trapezoidal section dimensions with 1:1 side slopes
• Part (b): Application of Thiem's equation for unconfined aquifer: Q = πK(h₂²-h₁²)/ln(r₂/r₁) to determine hydraulic conductivity K, then using same equation with r = well radius (0.25 m) to find drawdown in pumping well; or alternatively using Dupuit equation
• Part (c): Definition of grit as heavy inorganic solids (sand, gravel, silt, egg shells, coffee grounds) with particle size > 0.15 mm and specific gravity 2.4-2.65; explanation of grit removal necessity to prevent abrasion of pumps/mechanical equipment, pipe clogging, and reduction of digester volume
• Part (c): Explanation that velocity control devices (proportional flow weirs, Parshall flumes, venturi flumes, or sutro weirs) are essential in unaerated chambers to maintain 0.15-0.3 m/s velocity for grit settling while keeping organic matter in suspension; contrast with aerated chambers where air diffusion creates controlled rolling action making velocity devices redundant
• Integration: Recognition that Lacey's silt factor f=1.0 indicates medium silt typical of Indian alluvial plains, and that drainage design must account for monsoon intensity patterns in waterlogged areas like the Indo-Gangetic basin

Calculate the synthetic unit hydrograph coefficients Ct and Cp in part (a) using Snyder's method with given basin parameters; describe the sanitary landfill components with a neat schematic in part (b); and outline the EIA 2006 clearance process stepwise in part (c). Allocate approximately 40% time to numerical calculations in (a), 30% to diagram and description in (b), and 30% to procedural explanation in (c).

• Part (a): Correct application of Snyder's synthetic unit hydrograph equations to calculate Ct = tpR/(C₁(L.Lc)^0.3) and Cp = qpR.tR/(C₂.A)
• Part (a): Accurate substitution of values: L=125 km, Lc=90 km, A=3000 km², tR=12 h, tpR=34 h, qpR=135 m³/s.cm with proper unit handling
• Part (b): Description of sanitary landfill components: liner system, leachate collection, gas collection, cover system, monitoring wells
• Part (b): Schematic diagram showing cross-section with proper labeling of all functional layers and drainage systems
• Part (c): Sequential steps of EIA 2006: screening, scoping, public consultation, appraisal by EAC, final EC with conditions, post-clearance monitoring
• Part (c): Mention of category A/B projects, TOR preparation, 30-day public hearing notice, and validity period of clearance