Q1 50M Compulsory describe Building materials and highway engineering
(a) Describe various defects in clay bricks giving sources/causes of defects. 10 marks
(b) Draw neat sketches, showing complete details of plans of alternate courses of a 1½ brick thick masonry wall in English Bond having a right-angled corner. 10 marks
(c) Describe the important features of Type 1, Type 2 and Type 3 preservatives used for timber. 10 marks
(d) A ship is 55 km away from a lighthouse of height 62 m above mean sea level. An observer standing on the deck of the ship tries to see the lighthouse top. The height of the observer's eye above mean sea level is 10 m. Determine whether the lighthouse top will be visible to the observer or not. If not visible, find out the distance by which the ship has to travel towards the lighthouse so that it becomes visible to the observer. 10 marks
(e) An alert driver with a reaction time of 0·75 seconds is driving downhill on a 2·5% grade at 60 kmph on a dry pavement when suddenly a person comes in the path of the driver at a distance of 55 m. Can the driver stop in time with emergency braking? Can the driver stop in time when it is a rainy day? Assume: g = 9·8 m/s², f = 0·4 (dry pavement), f = 0·32 (wet pavement) 10 marks
Answer approach & key points
The directive 'describe' demands comprehensive coverage with clear explanations for parts (a), (c) and precise calculations with sketches for parts (b), (d), (e). Allocate approximately 20% time each to all five parts since marks are equal. For (a) and (c), use structured paragraphs with bullet points; for (b), dedicate sufficient space for two neat course plans; for (d) and (e), show all formulas, substitutions, and final answers with units. Begin with a brief introduction acknowledging the diverse nature of building materials and highway engineering, then address each part sequentially, and conclude with practical implications where relevant.
- Part (a): At least 6-8 brick defects with specific causes (e.g., efflorescence from soluble salts, bloating from over-firing, laminations from air trapped during pugging, cracks from uneven drying, warping from improper stacking, black core from insufficient oxidation)
- Part (b): Correct English Bond pattern for 1½ brick (13½ inch) thick wall showing alternate courses with proper lap (quarter brick), headers and stretchers arrangement, right-angled corner detail with queen closer placement
- Part (c): Type 1 (tar-oil creosote, coal tar), Type 2 (water-borne salts like CCA—chromated copper arsenate), and Type 3 (organic solvent type like pentachlorophenol) preservatives with application methods, toxicity, and Indian Standards (IS 401)
- Part (d): Correct application of dip of horizon formula using Earth's radius (6370 km), calculation of visible horizon distances for both lighthouse and observer, determination of visible overlap, and required distance reduction
- Part (e): Stopping sight distance calculation using SSD = vt + v²/[2g(f±S)] with proper sign convention for downgrade, comparison with available 55m for both dry and wet conditions
Q2 50M solve Construction management and transportation engineering
(a) The network for a construction project is shown in the figure given below. The three time estimates for each activity are given along each activity arrow. Determine the: (i) Expected time of completion of each activity, (ii) Earliest expected time for each event, (iii) Latest allowable occurrence time for each event, (take earliest expected time for last event as the scheduled completion time for the project), (iv) Slack for each event, (v) Critical path of the network. Also, give explanation of dotted arrow shown in the network. What is the significance of critical path? All time estimates are in days. 20 marks
(b) What are the functions of tie bars in rigid pavements? A cement concrete pavement has a thickness of 30 cm and lane width 3·75 m. Design the tie bars along the longitudinal joints using the data given below: Allowable working stress in steel tie bars = 1250 kg/cm², Allowable tensile stress in deformed bars (Sₛ) = 2000 kg/cm², Allowable bond stress in plain bars (Sᵦ) = 17·5 kg/cm², Allowable bond stress in deformed bars (Sᵦ) = 24·6 kg/cm², Unit weight of concrete pavement (W) = 2400 kg/m³, Maximum value of friction coefficient (f) = 1·35. 15 marks
(c) A high speed B.G. section with a maximum sanctioned speed of 130 kmph is proposed. The section is passing through a transition length with a 2° curve. Calculate the superelevation, maximum permissible speed and transition length for this section at curve. Assume the equilibrium speed as 90 kmph and the booked speed of the goods train to be 60 kmph. Rate of change of Cant or Cant deficiency is 35 mm/sec. Assume any other data suitably. 15 marks
Answer approach & key points
Solve all three sub-parts systematically, allocating approximately 40% time to part (a) given its 20 marks, and 30% each to parts (b) and (c). Begin with clear PERT calculations for (a), followed by tie bar design computations for (b), and superelevation/transition length calculations for (c). Present all numerical work in tabular format where appropriate, with clear labeling of each step.
- Part (a): Calculate expected activity times using PERT formula (te = (a+4m+b)/6), determine TE and TL for each event, compute slacks, identify critical path, and explain dummy activity significance
- Part (a): Correct interpretation of dotted arrow as dummy activity showing logical dependency without time/resource consumption, and critical path significance for project scheduling
- Part (b): State functions of tie bars (prevent longitudinal joint opening, transfer load, maintain slab alignment), then design tie bar diameter, spacing and length using friction coefficient method
- Part (c): Calculate equilibrium superelevation for 90 kmph, check against maximum (1/12th or 1/8th of gauge), determine cant deficiency for 130 kmph, and compute transition length based on rate of change of cant
- Part (c): Apply Indian Railways standards for BG track (1750 mm gauge), verify booked speed check for goods train (60 kmph), and ensure maximum permissible speed satisfies all constraints
Q3 50M explain Transportation, Surveying and Construction Equipment
(a) (i) Explain spot speed, running speed, space-mean speed, time-mean speed and average speed. 10
(ii) The consolidated data collected from speed and delay studies by floating car method on a stretch of urban road of length 2·5 km, running East-West are given below in the table. Determine the average values of volume, journey speed and running speed of the traffic stream, along either direction. 10
Mean Values of Speed and Delay
| Direction | Mean Journey Time (Minutes) | Mean Stopped Delay (Minutes) | Number of Vehicles (Mean Value) | | |
|---|---|---|---|---|---|
| | | | Overtaking | Overtaken | In Opposite Direction |
| East-West | 4·85 | 1·60 | 4·5 | 6·5 | 376 |
| West-East | 8·36 | 1·90 | 4·0 | 5·5 | 280 |
(b) (i) Two points A and B having elevations of 585 m and 250 m respectively, above datum, appear on a vertical photograph obtained with a camera of focal length of 250 mm and flying altitude of 2300 m above datum. Their correlated photographic coordinates are as follows :
Point Photographic Coordinates
x (cm) y (cm)
A + 5·65 + 3·75
B – 3·45 + 8·55
Determine the ground coordinates of points A and B and calculate the horizontal distance between points A and B. 5
(ii) The lengths, latitudes and departures of a closed traverse ABCD are as follows :
| Line | Length (m) | Latitude | Departure |
| AB | 350·8 | + 303·03 | + 176·6 |
| BC | 408·5 | – 336·7 | + 231·4 |
| CD | 285·4 | – 211·3 | – 191·9 |
Calculate the length and bearing of the line DA. 10
(c) For what specific operations are the following equipment used at construction sites ?
(i) Sheep foot roller
(ii) Bulldozer
(iii) Dragline excavator
(iv) Tower crane
(v) Hoe 15
Answer approach & key points
This question demands clear definitions with mathematical precision for (a)(i), rigorous numerical problem-solving for (a)(ii), (b)(i) and (b)(ii), and specific operational knowledge for (c). Allocate approximately 35% time to part (a) combining theory and floating car calculations, 30% to part (b) covering photogrammetry and traverse computations, and 35% to part (c) ensuring each equipment description includes specific construction applications. Begin with definitions using standard IRC/IS formulae, proceed through step-by-step calculations with proper unit handling, and conclude with equipment functions tied to Indian construction scenarios like dam building and urban infrastructure.
- For (a)(i): Precise definitions of spot speed (instantaneous), running speed (excluding stops), space-mean speed (harmonic mean), time-mean speed (arithmetic mean), and average speed with correct mathematical expressions and distinctions per IRC standards
- For (a)(ii): Correct application of floating car method equations to compute volume, journey speed and running speed for both directions using Wardrop's formulae with proper handling of overtaking/overtaken vehicles
- For (b)(i): Accurate photogrammetric scale determination using flying height and elevation, correct ground coordinate computation using photo coordinates, and precise horizontal distance calculation using 3D coordinates
- For (b)(ii): Proper application of latitude-departure closure conditions, correct computation of DA's latitude and departure from ΣL=0 and ΣD=0, and accurate bearing conversion from trigonometric functions
- For (c)(i): Sheep foot roller - specific application to cohesive soils, clay core compaction in earth dams (e.g., Bhakra Nangal, Tehri Dam), and kneading action for high plasticity soils
- For (c)(ii-iv): Bulldozer for short haul earthmoving and site grading; Dragline for underwater excavation and canal construction; Tower crane for vertical material handling in high-rise construction
- For (c)(v): Hoe (backhoe) for trenching, foundation excavation, and loading operations with specific mention of its force characteristics (pulling action toward machine)
- Cross-cutting: Integration of IRC:106-1990 guidelines for speed studies, IS 14802 for photogrammetry, and practical Indian construction equipment deployment contexts
Q4 50M solve Project Management, Construction Estimation and Railway Engineering
(a) The network of a certain project is shown in the figure given below with the estimated time duration (in days) of various activities. Determine the following :
(i) Earliest event time
(ii) Latest event time
(iii) Earliest start and finish time of each activity
(iv) Latest start and finish time of each activity
(v) Total float of each activity
(vi) Critical path of the network
(Assume the scheduled completion time of the project equal to the earliest event time of the last event)
20
(b) Prepare a detailed analysis of rate (₹ per sq. m) for a 25 mm thick cement concrete (1 : 2 : 4) floor with cement finishing coat. 15
(c) Sketch a typical diamond crossing and label all its components. Design a diamond crossing between two B.G. tracks crossing each other at an angle of 1 in 8·5. 15
Answer approach & key points
Solve this multi-part technical problem by allocating approximately 40% time to part (a) CPM network analysis, 30% to part (b) rate analysis, and 30% to part (c) diamond crossing design. Begin with forward and backward pass calculations for the network, followed by systematic rate analysis using current DSR/CPWD norms, and conclude with geometric design calculations and neat sketching for the railway crossing.
- Part (a): Correct computation of EET and LET for all events using forward and backward pass method; identification of critical path with zero total float
- Part (a): Accurate calculation of EST, EFT, LST, LFT and total float for each activity with proper tabulation
- Part (b): Detailed rate analysis showing material quantities (cement, sand, aggregate), labour components, and cost breakdown per sq.m for 25mm thick CC 1:2:4 floor with finishing
- Part (b): Inclusion of wastage, water charges, overhead charges, and contractor profit as per standard practice; reference to CPWD/State PWD schedule of rates
- Part (c): Correct geometric design of diamond crossing for BG track with 1 in 8.5 crossing angle: calculation of nose of crossing, throat length, and check rails
- Part (c): Neat sketch showing all components: four noses, two obtuse angle crossings, two acute angle crossings, check rails, wing rails, and sleeper layout
- Part (c): Application of relevant formulae: sin α = 1/8.5, calculation of theoretical and actual nose of crossing, flaring of check rails
Q5 50M Compulsory solve Water resources and environmental engineering
(a) What is a flood hydrograph ? The monthly discharge (Q) data of a river at a gauging station are given below :
| Month | Q (m³/s) |
|---|---|
| January | 30 |
| February | 40 |
| March | 50 |
| April | 60 |
| May | 80 |
| June | 90 |
| July | 100 |
| August | 120 |
| September | 110 |
| October | 90 |
| November | 80 |
| December | 70 |
Draw the hydrograph and using the graph find peak flow and minimum flow in the river. (10 marks)
(b) Explain the following terms :
(i) Evaporation
(ii) Transpiration
(iii) Evapotranspiration
(iv) Infiltration (10 marks)
(c) A catchment has five raingauge stations. In a year, the annual rainfall recorded by the raingauges are 72·3 cm, 86·4 cm, 94·2 cm, 103·8 cm and 71·4 cm respectively. For a 5% error in the estimation of mean rainfall, find the additional number of raingauges needed. (10 marks)
(d) A high strength wastewater having an ultimate CBOD of 1000 mg/L is discharged to a river at a rate of 2 m³/s. The river has an upstream ultimate CBOD of 10 mg/L and is flowing at a rate of 8 m³/s. Assuming a reaction rate coefficient of 0·1/day, calculate the ultimate CBOD and 5-day CBOD of the river water just after the mixing point of the wastewater (at 0 km) and 20 km downstream from the mixing point. (Assume the velocity of river = 10 km/day) (10 marks)
(e) What do you understand by 'per capita demand' of water ? How is it determined ?
If average daily water demand is 135 litres per capita per day, determine the following :
(i) Maximum daily demand of water;
(ii) Maximum weekly demand of water;
(iii) Maximum monthly demand of water;
(iv) Maximum hourly demand of water. (10 marks)
Answer approach & key points
This multi-part numerical-cum-theoretical question requires systematic solving with approximately 15-18 minutes per 10-mark sub-part. Begin with concise definitions for (a) and (b), then proceed to calculations for (c), (d), and (e). For (a), draw a neat hydrograph with months on x-axis and discharge on y-axis; for (d), apply mass balance and Streeter-Phelps principles; for (e), apply standard peak factors (1.8 for daily, 2.7 for weekly, etc.). Present all derivations stepwise with proper units and significant figures.
- (a) Definition of flood hydrograph as discharge vs time graph showing rising limb, peak, and recession limb; correct plotting of monthly data with August peak (120 m³/s) and January minimum (30 m³/s)
- (b) Precise definitions: evaporation (liquid to vapor from water bodies), transpiration (vapor loss through plant stomata), evapotranspiration (combined loss), infiltration (water entry into soil surface)
- (c) Application of standard error formula for raingauge network: N = (Cv/E)²; calculation of coefficient of variation from given data and determination of additional gauges needed
- (d) Mass balance for ultimate CBOD mixing: (QᵤCᵤ + QᵣCᵣ)/(Qᵤ+Qᵣ); application of first-order decay equation for 20 km downstream with travel time of 2 days
- (e) Definition of per capita demand as average daily water requirement per person; application of standard peak factors: 1.8 (max daily), 2.7 (max weekly), 3.3 (max monthly), 5.0 (max hourly)
- Correct unit conversions throughout (m³/s to MLD where applicable, km/day to travel time)
- Proper interpretation of results in context of Indian water resources planning and pollution control standards
Q6 50M derive Groundwater, water treatment and air pollution
(a) Explain an aquifer. Deduce the expression for discharge (Q) through a well in an unconfined aquifer taking usual symbols.
If the permeability of the aquifer, K = 10⁻⁴ m/s, radius of drawdown curve, R = 500 m, radius of well, r = 5·0 m, total aquifer thickness, H = 30 m and depth of water in well, h = 10 m; find the steady discharge. (20 marks)
(b) Determine the size (i.e., diameter and depth) of a circular rapid mixing tank having a mechanical mixer, which is to be designed for treatment of water flow of 10 × 10⁶ litres per day and for mean hydraulic detention time of 45 seconds. Also, calculate the power required to achieve a mixing intensity (G) of 450 s⁻¹.
Assume viscosity of water = 0·89 × 10⁻³ N.s/m² and depth of water to diameter of tank ratio of 2 : 1. (15 marks)
(c) (i) What is the "5 R's" concept in waste management ? How do they contribute to managing the ill-effects of waste ? Briefly explain. (7 marks)
(ii) A dumpsite fire emits 4 g/s of NOₓ. Write an equation of NOₓ concentration at 2·0 km downwind from the dumpsite if the wind speed U₁₀ = 5 m/s and its stability is 'D' type. What would be the maximum NOₓ concentration at 2·0 km from the dumpsite at the ground and also at 50 m above ground ? Assume diffusion coefficients σᵧ = 150 m and σᵤ = 50 m at the downwind distance of 2·0 km from the source for 'D' type stability. (8 marks)
Answer approach & key points
Begin with the directive 'derive' for part (a), which demands rigorous mathematical derivation of Dupuit's equation for unconfined aquifer flow, followed by systematic numerical substitution. Allocate time proportionally: ~40% for (a) including derivation and calculation, ~30% for (b) on rapid mixing tank design with power calculation, and ~30% for (c) covering 5 R's explanation and Gaussian plume dispersion modeling. Structure as: (a) definition → derivation → substitution → result; (b) tank sizing → power calculation; (c)(i) conceptual explanation → (c)(ii) equation setup → concentration calculations at specified locations.
- Part (a): Correct definition of aquifer with geological formation characteristics; rigorous derivation of Thiem/Dupuit equation Q = πK(H²-h²)/ln(R/r) using Darcy's law and radial flow assumptions; accurate substitution yielding Q ≈ 0.091 m³/s or 91 L/s
- Part (b): Correct tank diameter D = 2.88 m and depth H = 5.76 m from detention time equation; power calculation P = G²μV ≈ 4.23 kW using given mixing intensity and viscosity
- Part (c)(i): Identification of 5 R's (Refuse, Reduce, Reuse, Recycle, Recover) with specific contribution to waste hierarchy and pollution prevention in Indian context like Swachh Bharat
- Part (c)(ii): Gaussian plume equation C(x,y,z) = Q/(2πUσyσz)exp[-y²/(2σy²)]{exp[-(z-H)²/(2σz²)]+exp[-(z+H)²/(2σz²)]}; ground level concentration ≈ 33.9 μg/m³ and at 50m ≈ 27.4 μg/m³ using reflection term
- Recognition that parts (a) and (b) involve hydraulic design while (c) combines environmental management with atmospheric dispersion modeling
- Proper unit conversions throughout: litres/day to m³/s, detention time consistency, and emission rate to concentration units
- Physical interpretation of results: well discharge adequacy for irrigation, mixer power reasonableness, and NOx concentration comparison with NAAQS standards
Q7 50M calculate Sewer design, groundwater, gravity dam, irrigation
(a) A sewer having a 60 cm diameter (D) is required to flow at 0·4 depth (i.e., a proportional depth d/D = 0·4) on a grade ensuring a degree of self-cleansing equivalent to that obtained at full depth at a velocity of 80 cm/s. Determine the required grade, associated velocities and discharges at full depth and 0·4 depth. The value of Manning's rugosity coefficient (N) = 0·015 may be taken same at all depths of flow. (20 marks)
(b) Explain the following: (i) Aquitard (ii) Specific retention (iii) Storage coefficient (iv) Coefficient of permeability (v) Darcy's Law (15 marks)
(c) (i) For the gravity dam shown in the following figure, determine I. Factor of safety against sliding II. Factor of safety against overturning. Take the following data: μ = 0·70, γc = 24 kN/m³, γw = 10 kN/m³, q = 1400 kN/m² (ii) Explain duty and delta. What is the discharge capacity required of the outlet to irrigate 2200 ha of sugarcane having a Kor depth of 17 cm and a Kor period of 30 days? (15 marks)
Answer approach & key points
This is a multi-part calculation-heavy question requiring precise numerical work across sewer hydraulics, groundwater theory, and dam/irrigation engineering. Allocate approximately 40% time to part (a) given its 20 marks and complex Manning's equation iterations for partial flow; 30% to part (b) for concise definitions with units and inter-relationships; and 30% to part (c) for stability calculations and duty-delta-discharge computation. Begin each part with stated assumptions, show all formulae with units, and conclude with practical significance.
- Part (a): Apply Manning's equation for full depth to find required slope, then use proportional flow relationships (v/V = (d/D)^0.6, q/Q = 0.97 for d/D=0.4) to determine velocities and discharges at both depths, ensuring self-cleansing velocity equivalence
- Part (b): Define aquitard as semi-confining layer; specific retention as volume retained against gravity; storage coefficient as S = γ_w × n × (1/β_w + 1/nβ_s); coefficient of permeability with units m/s; and Darcy's Law v = ki with validity conditions
- Part (c)(i): Calculate factor of safety against sliding as μΣW/ΣH and against overturning as ΣM_R/ΣM_O for the gravity dam using given data, showing free body diagram with hydrostatic pressure distribution
- Part (c)(ii): Define duty as area irrigated per cumec (ha/cumec) and delta as total depth of water; compute outlet discharge Q = (8.64 × B × D)/Δ where B=2200 ha, D=17 cm, Δ=30 days
- Demonstrate unit consistency throughout (cm/s to m/s, kN/m³ conversions) and verify self-cleansing criteria against CPHEEO/MoUD standards for Indian sewer design
Q8 50M design Canal design, spillways, septic tank, filter backwash
(a) (i) What is Lacey's Silt Factor? What is its value for standard silt? Design an earthen canal using Lacey's silt theory with the following data: Full supply discharge, Q = 15 m³/s, Lacey's silt factor, f = 1·0, Canal side-slope = 1/2 H : 1 V (ii) What are spillways? Which type of spillways are provided in the following dams? (i) Bhakra-Nangal Dam (ii) Ramganga (Kalagarh) Dam (iii) Hirakud Dam (iv) Rihand Dam. What forces act on a mass-concrete dam? Explain any two of these forces in detail. (10 marks)
(b) Determine the dimensions of a rectangular septic tank serving 100 persons in a hostel. The dimensions of the septic tank must be able to accommodate sedimentation, sludge digestion and sludge storage functionalities. The peak discharge of sewage can be considered as 240 litres per minute. Use the following data: - Surface area required for every 10 litres per minute of peak flow = 0·92 m² - Water depth required in the sedimentation tank = 0·3 m - Freeboard required = 0·3 m - Capacity required for sludge digestion process = 0·032 m³/capita - Capacity required for digested sludge = 0·0002 m³/capita/day - Sludge withdrawal (cleaning) frequency = once in a year - Length to width of tank ratio (L/B) = 2·5 (15 marks)
(c) Uniform sand is used as a filter medium to treat the water. The sand grains are 0·6 mm in diameter with a shape factor (φ) of 0·85 and specific gravity (G) of 2·67. The bed is 0·65 m deep with a porosity (η) of 0·45. The filter medium is to be expanded to a porosity (ηₑ) of 0·75 by hydraulic backwash. Determine the required backwash velocity, resulting expanded depth and loss through the expanded medium. Assume the following data for use: g = 9·81 m/s², Density of water (ρ) = 998·2 kg/m³, Viscosity of water (μ) = 1·002 × 10⁻³ N.s/m² (15 marks)
Answer approach & key points
This question demands a design-oriented response with substantial numerical work across three distinct engineering domains. Allocate approximately 25% time to part (a) covering Lacey's canal design and spillway identification, 37.5% to part (b) for septic tank dimensional design, and 37.5% to part (c) for filter backwash calculations. Structure each part with clear problem statement, formula application with units, systematic calculation steps, and final dimensioned results with practical verification.
- Part (a)(i): Definition of Lacey's silt factor (f) as f = 1.76√m where m is mean particle size in mm; standard silt f = 1.0; application of Lacey's regime equations: V = (Qf²/140)^(1/6), R = 5V²/2f, S = f^(5/3)/(3340Q^(1/6)) for trapezoidal canal with ½H:1V side slope
- Part (a)(ii): Definition of spillways as overflow structures for flood discharge; identification of specific types: Bhakra-Nangal (shaft/ogee), Ramganga (chute), Hirakud (ogee with sluice), Rihand (ogee); forces on gravity dams: water pressure, uplift, earthquake, silt, ice, wave, self-weight with detailed explanation of any two
- Part (b): Septic tank design integrating three zones: sedimentation (surface area from peak flow), sludge digestion (volume from population), sludge storage (volume from cleaning frequency); calculation of L=2.5B relationship; total depth = water depth + freeboard; verification of detention time and sludge volume adequacy
- Part (c): Application of expanded bed hydraulics using Richardson-Zaki equation for backwash velocity: v_b = [4g(ρ_s-ρ)d/(3C_Dρ)]^0.5 × η_e^n where n≈4.5 for Re<0.3; expanded depth H_e = H(1-η)/(1-η_e); head loss through expanded bed using Kozeny-Carman or empirical approach
- Cross-cutting: Unit consistency throughout (m, s, kg), appropriate significant figures, physical reasonableness checks on all numerical outputs, and recognition of Indian Standard/CPHEEO guidelines where applicable