Q1 50M Compulsory discuss High strength concrete, hollow blocks, highway maintenance, pavement joints, remote sensing
(a) Briefly discuss why it is more advantageous to use high strength concrete for construction of high-rise buildings and large-span bridges as compared to normal strength concrete. (10 marks)
(b) Briefly discuss the advantages of using hollow concrete blocks for masonry works of a building as compared to stone or brick masonry works. (10 marks)
(c) Determine the total present worth of maintenance cost of a 4-lane highway using the capitalized equivalent approach.
The following costs are estimated for maintenance of the above highway :
(i) Periodic maintenance cost to be carried out at every five years = ₹ 2 crores
(ii) Annual maintenance cost = ₹ 0.06 crore
Assume the interest rate as 10% per year compounded annually. (10 marks)
(d) The laying temperature during the construction of plain cement concrete pavement of slab thickness 20 cm is 15 °C and the maximum slab temperature during the summer is used to be 45 °C. If the width of expansion joint gap is 2.5 cm, calculate the spacing between the expansion and contraction joints.
Assume the following data :
Coefficient of thermal expansion of concrete = 12×10⁻⁶ per °C
Unit weight of concrete = 2360 kg/m³
Allowable stress in cement concrete in tension = 0.8 kg/cm²
Coefficient of friction of the interface = 1.5 (10 marks)
(e) Explain the different types of resolutions in remote sensing with suitable examples. (10 marks)
Answer approach & key points
The directive 'discuss' for parts (a), (b), (e) requires balanced exposition with merits and contextual application, while parts (c) and (d) demand rigorous numerical solution. Allocate approximately 15% time each to (a), (b), (e) for conceptual depth; 25% each to (c) and (d) for calculations. Structure: begin with theoretical foundations for concrete technology and masonry, proceed through step-by-step engineering economics and pavement thermal analysis, conclude with remote sensing applications in Indian infrastructure monitoring.
- Part (a): High strength concrete advantages—reduced column sizes increasing floor area, lower dead load enabling taller structures, enhanced durability, reduced creep and shrinkage for bridges; mention M60-M100 grades used in Burj Khalifa and Bandra-Worli Sea Link
- Part (b): Hollow concrete block advantages—thermal insulation, sound absorption, 50% material saving, faster construction, lighter dead load reducing foundation cost; comparison with traditional Kota stone or Flemish bond brickwork
- Part (c): Capitalized equivalent calculation—convert periodic maintenance to equivalent annual cost using capital recovery factor, add annual maintenance, divide by interest rate; correct application of (A/P,10%,5) and final present worth formula
- Part (d): Expansion joint spacing from thermal expansion formula L = δ/(α×ΔT), contraction joint spacing from friction-stress equilibrium L = 2×σ×h/(μ×γ×100); correct unit conversions and temperature differential handling
- Part (e): Four resolution types—spatial (Landsat 30m vs Cartosat 2.5m), spectral (hyperspectral vs multispectral), radiometric (11-bit vs 8-bit), temporal (revisit period); Indian examples from NRSC/ISRO missions
Q2 50M solve Project management, traffic signal design, railway engineering
(a) A contractor intends to bid for erecting a statue at a square in an urban area. The various activities of the entire project are given below :
| Activity | Activity Name | Remark |
|----------|---------------|--------|
| A | Make statue | Starting activity |
| B | Lay foundation | Starting activity |
| C | Construct platform | Follows B (starts after laying foundation) |
| D | Erect statue | Finishing activity and follows A and C |
The project is expected to take 18 days to complete having a variance of 4 days. Determine in how many days the contractor would expect the project to be completed with a probability of 99%. For probability of 98.93%, the corresponding normal deviate Z value is +2.3 and for probability of 99.18%, Z value is +2.4. Further, if the contractor intends to complete the project in 17 days by crashing the activities, determine how much total project cost would the contractor expect. The normal and crash duration, and associated cost are given in the table below for various activities :
| Activity | Normal Activity | | Crash Activity | |
|----------|-----------------|---|----------------|---|
| | Duration (in days) | Cost (in ₹) | Duration (in days) | Cost (in ₹) |
| A | 8 | 6,000 | 5 | 9,000 |
| B | 4 | 2,000 | 3 | 4,000 |
| C | 8 | 5,000 | 7 | 5,500 |
| D | 6 | 3,000 | 3 | 7,500 |
For the entire project, the indirect cost is ₹ 500 per day. (20 marks)
(b) (i) A taxi driver was fined for crossing the traffic signal at right-angled road intersection. He claimed that the signal was faultily designed and the duration of amber light is not sufficient. Using the following data, verify the correctness of the driver's claim :
Road width at intersection = 20 m
Speed limit at road = 60 kmph
Amber light duration = 4.0 s
Comfortable deceleration = 3.0 m/s²
Car length = 4.0 m
Perception reaction time = 1.2 s (10 marks)
(ii) Explain with sketches how the subsurface drainage system is provided to lower the water table in road. (5 marks)
(c) Calculate the maximum number of wagons of weight 80 tonnes each that can be pulled by a locomotive having hauling capacity of 16 tonnes. The weight of the locomotive is 100 tonnes and the train has to run at a speed of 60 kmph on a straight level BG track. Assume rolling resistance of wagon and locomotive as 1.6 kg/tonne and 2.0 kg/tonne respectively.
Also, calculate the hauling capacity of the locomotive required if the train has to climb a gradient of 1 in 150 in 1° curve. (15 marks)
Answer approach & key points
Begin by identifying the critical path and calculating expected project duration with probability for part (a), then verify amber light timing using kinematic equations for part (b)(i), sketch subsurface drainage for (b)(ii), and finally compute hauling capacity and gradient resistance for part (c). Allocate approximately 40% time to part (a) due to its 20 marks and complexity involving PERT and crashing, 30% to part (b) combined, and 30% to part (c). Present all calculations systematically with clear labeling of each sub-part.
- Part (a): Identify critical path (B-C-D), calculate expected duration (18 days), determine Z-value for 99% probability (interpolate to Z=2.37), compute completion time (~22.7 days), perform crashing analysis by cost slope to reduce duration to 17 days at minimum additional cost including indirect costs
- Part (b)(i): Calculate stopping sight distance using perception-reaction time and braking distance, determine safe amber time using dilemma zone concept (ISD = v*t + v²/2a + vehicle length), compare with given 4.0s amber duration to verify driver's claim
- Part (b)(ii): Sketch longitudinal section showing perforated pipe, filter media, outlet structure, and lowered water table position with proper labeling for subsurface drainage in road construction
- Part (c): Calculate total train resistance on level track (rolling resistance of locomotive + wagons), equate to hauling capacity to find maximum wagons (16), then compute required hauling capacity for 1 in 150 gradient with 1° curve using Ruling Gradient formula including curve resistance (0.04% per degree)
Q3 50M calculate Surveying, Railway Engineering and Construction Materials
(a) (i) Observations were made with a theodolite from the points A and B of baseline AB having horizontal length of 200 m to the two inaccessible points P and Q at the same side of the line AB.
The following observations are done :
∠PAB = 80°, ∠QBA = 90°, ∠QAB = 50°, ∠PBA = 45°
The angle of elevation of P from A = 20°
The angle of elevation of Q from A = 12°
Calculate the horizontal distance PQ and difference in elevation between P and Q.
10
(ii) A pair of overlapping vertical photographs was taken with an aerial camera of focal length 150 mm from an altitude of 3000 m above datum. The mean principal base measured is equal to 80 mm. In the common overlap, a flagpole with its base 100 m above datum is observed. What will be the height of the flagpole if the parallax difference between the top and bottom point of the flagpole is 4·6 mm? Also, find the scale of photograph at datum and the distance covered by the aircraft between two successive exposures.
10
(b) (i) Explain the required properties of a good ballast material for railway track. Explain with reasons which ballast material is best suitable for high-speed railway track.
10
(ii) Calculate the minimum depth of ballast required for a broad gauge railway track having sleeper density of M+6, length of rail of 13·0 m and width of sleeper of 25 cm.
5
(c) Briefly discuss the effect of the following on the properties of mortar used for construction work :
(i) Alkali water and seawater
(ii) Low temperature
(iii) Sand and water
15
Answer approach & key points
This multi-part question requires solving numerical problems in (a)(i)-(ii), explaining concepts with calculations in (b)(i)-(ii), and discussing material properties in (c). Allocate approximately 35% time to part (a) for precise trigonometric calculations involving inaccessible point location and aerial photogrammetry; 30% to part (b) for ballast properties and depth calculation; and 35% to part (c) for comprehensive discussion on mortar deterioration factors. Begin each numerical part with clear diagram sketching, show all formulae with proper units, and conclude with practical implications for Indian railway/construction contexts.
- Part (a)(i): Apply sine rule to triangles PAB and QAB to find horizontal distances AP, BP, AQ, BQ; use these to determine PQ via coordinate geometry or cosine rule; calculate elevations using tangent of vertical angles and find elevation difference
- Part (a)(ii): Apply parallax-height relationship h = (H-h₁)×dp/(b+dp) for flagpole height; calculate photographic scale as f/H; determine air base and ground coverage using B = b×H/f
- Part (b)(i): List ballast properties (hardness, angularity, durability, drainage, elasticity); justify crushed stone as best for high-speed tracks citing Indian Railways specifications and reduced maintenance
- Part (b)(ii): Calculate sleeper density M+6 = 13+6 = 19 sleepers per rail length; apply ballast depth formula considering sleeper spacing and bearing area requirements for BG track
- Part (c): Discuss alkali/seawater effects (efflorescence, sulphate attack, corrosion); low temperature effects (retarded hydration, frost damage); sand/water effects (gradation, workability, strength, w/c ratio) with IS code references
Q4 50M compare Construction Equipment, Ferrocement and Traffic Engineering
(a) Compare the application of 'straight blade' and 'angle blade' of bulldozers for earthwork in a construction project. Determine the unit cost (₹/m³) for pushing the soil by a bulldozer for a canal construction project using the following data :
(i) Bulldozer cost = ₹ 4,000 per hour
(ii) Wages of operator = ₹ 150 per hour
(iii) Rated moldboard capacity in loose volume (blade load) = 4 cum
(iv) Swell factor for the soil = 1·25
(v) Hauling distance = 50 m
(vi) Operating time per hour for the bulldozer = 50 minutes
(vii) Forward speed of the bulldozer = 3 kmph
(viii) Reverse speed of the bulldozer = 6 kmph
(ix) Gear shifting time = 0·3 minute
20
(b) Answer the following in brief :
(i) Why is it advantageous to use ferrocement when the structural member is in tension?
(ii) What are the advantages of using ferrocement over reinforced concrete?
(iii) What are the advantages of using ferrocement in marine structures?
15
(c) The speed and delay study was conducted by floating car method during different round trips on a stretch of 3 km State highway. The data of the study is given below :
| Trip Number | Number of Vehicles | | |
| | In Opposite Direction | Overtaking | Overtaken |
| 1 | 140 | 30 | 16 |
| 2 | 130 | 22 | 17 |
| 3 | 180 | 18 | 19 |
Given that the floating car is moving at a constant speed of 30 kmph, calculate the following :
(i) Traffic stream variables for different trips
(ii) Speed-density and volume-density relationship
15
Answer approach & key points
Begin with a comparative analysis of straight blade versus angle blade bulldozers for part (a), followed by systematic numerical calculation of unit cost using the given operational parameters. For part (b), provide concise, technically precise answers on ferrocement properties and applications. For part (c), apply the floating car method equations to derive traffic stream variables and establish the Greenshields relationships. Allocate approximately 40% of effort to part (a) given its 20 marks, 30% to part (b) for 15 marks, and 30% to part (c) for 15 marks.
- Part (a): Comparison of straight blade (U-blade for heavy digging, crowding, short hauls) versus angle blade (side casting, ditching, spreading, longer hauls) with specific construction applications
- Part (a): Correct calculation of production rate considering blade load, swell factor, cycle time (forward haul + reverse return + gear shifting), and operating efficiency
- Part (a): Accurate unit cost computation by combining ownership/operating costs with hourly production output
- Part (b): Ferrocement's tensile advantage due to high specific surface area of mesh reinforcement, crack control, and distributed micro-cracking behavior
- Part (b): Ferrocement advantages over RC—thinner sections, no cover requirements, impermeability, impact resistance, and suitability for prefabrication
- Part (b): Marine applications—corrosion resistance of galvanized mesh, resistance to chloride penetration, repairability, and performance in splash zones
- Part (c): Correct application of floating car method equations: traffic volume, average travel time, and mean speed calculations for each trip
- Part (c): Derivation of speed-density (linear) and volume-density (parabolic) relationships using fundamental diagram principles
Q5 50M Compulsory solve Hydrology, groundwater, water and wastewater treatment
(a) A box culvert has an expected life of 10 years.
(i) If the acceptable risk of at least one event exceeding the culvert capacity during the design life is 5 percent, what design period should be used?
(ii) What is the chance that the box culvert designed for an event of this return period will not have its capacity exceeded for 50 years?
10
(b) A well fully penetrates a 50 m thick confined aquifer. After a long period of pumping at a constant rate of 0·10 m³/s, the drawdowns at distances of 50 m and 150 m from the well are observed to be 3 m and 1·2 m respectively. With the help of a sketch, determine the hydraulic conductivity and the transmissivity.
10
(c) Enumerate any five adverse effects of reservoir sedimentation. How can it be reduced?
10
(d) The BOD of wastewater sample incubated @ 30 °C for 1 day was 120 mg/L. Find 5-day BOD @ 20 °C and estimate the percent of unoxidized BOD @ 20 °C after 20 days. Take rate constant as 0·1/day @ 20 °C.
10
(e) Explaining the process of composting municipal solid wastes, discuss the important design considerations of aerobic composting.
10
Answer approach & key points
This is a multi-part numerical and descriptive problem requiring systematic solving of five distinct sub-parts. Allocate approximately 20% time to each part: (a) risk analysis using probability concepts, (b) Thiem's equation application with sketch, (c) enumeration with mitigation measures, (d) BOD kinetics with temperature correction, and (e) composting process explanation with design considerations. Begin with clear identification of given data, apply appropriate formulae with proper units, and conclude with practical significance for Indian water resources and waste management contexts.
- (a)(i) Apply risk formula R = 1 - (1 - 1/T)^n to find design return period T ≈ 195 years for 5% risk over 10 years
- (a)(ii) Calculate probability of non-exceedance as (1 - 1/195)^50 ≈ 77% for 50-year period
- (b) Apply Thiem's steady-state equation with sketch showing confined aquifer, well, and observation wells; compute K ≈ 4.17×10⁻⁴ m/s and T ≈ 2.08×10⁻² m²/s
- (c) List five effects: reduced storage capacity, upstream flooding, delta formation, turbine abrasion, and ecological impacts; suggest watershed management, check dams, and sediment flushing
- (d) Apply temperature correction k₃₀ = k₂₀ × θ^(T-20) with θ=1.047, then L₀ = BOD₁/(1-e^(-kt)), compute 5-day BOD₂₀ ≈ 162 mg/L and unoxidized % after 20 days ≈ 13.5%
- (e) Explain composting phases (mesophilic, thermophilic, maturation) with C/N ratio control, moisture 50-60%, aeration, and turning frequency for aerobic design
Q6 50M solve Hydrology, rainfall-runoff, wastewater treatment, sewer design, water treatment
(a) A storm over a catchment of area 5 km² had a duration of 14 hours. The mass curve of rainfall of the storm is as follows:
| Time from Start of Storm, t (h) (1) | Accumulated Rainfall (cm) (2) |
|-------------------------------------|-------------------------------|
| 0 | 0 |
| 2 | 0·6 |
| 4 | 2·8 |
| 6 | 5·2 |
| 8 | 6·7 |
| 10 | 7·5 |
| 12 | 9·2 |
| 14 | 9·6 |
If the φ index for the catchment is 0·4 cm/h, determine (i) the effective rainfall (ER) hyetograph and (ii) the volume of direct runoff from the catchment due to the storm. Show clearly one set of calculations and summarize your results in a tabular form. (iii) Also, plot the effective rainfall hyetograph.
20
(b) (i) Using the data pertaining to a wastewater treatment plant, determine the quantity of sludge produced per day:
Wastewater flow = 10 MLD
Suspended solids (SS) in raw wastewater = 250 mg/L
Efficiency of PST = 62%
Sludge concentration = 5%
Volatile solids (VS) = 60%
Specific gravity of VS = 0·980
Fixed solids = 40%
Specific gravity of fixed solids = 2·65
10
(ii) A 30 cm diameter circular sewer is laid in a section where invert slope is 1 in 500. Determine the velocity and sewage flow in the section and check for self-cleansing velocity. Take Manning's coefficient as 0·015. Assume that the sewer is running full.
5
(c) (i) Explain the problems encountered during the operation of filters in water treatment and suggest how these are controlled.
10
(ii) Enumerate the factors to be considered while designing an intake structure. Sketch a river intake and name its components.
5
Answer approach & key points
This is a multi-part numerical and descriptive problem requiring systematic solving. Allocate approximately 40% time to part (a) given its 20 marks and computational intensity; 30% to part (b) covering sludge production and sewer hydraulics; and 30% to part (c) on filter operation problems and intake design. Begin with clear problem statements, show all calculations with proper units, present results in tabular form as demanded, and conclude with practical interpretations relevant to Indian water infrastructure contexts.
- For (a): Correctly derive incremental rainfall from mass curve, compute φ-index based effective rainfall hyetograph by subtracting 0.4 cm/h losses, identify periods with zero/positive ER, and calculate total direct runoff volume = Σ(ER) × catchment area
- For (a)(iii): Plot ER hyetograph with time on x-axis and intensity (cm/h) on y-axis, showing only bars where rainfall intensity exceeds φ-index
- For (b)(i): Calculate mass of SS removed = 10 MLD × 250 mg/L × 0.62, then sludge volume using specific gravity of solids mixture (weighted average of VS and FS) and 5% concentration
- For (b)(ii): Apply Manning's equation V = (1/n)R^(2/3)S^(1/2) for full circular sewer, compute discharge Q = VA, and compare velocity with self-cleansing criterion (typically 0.6-0.75 m/s for sanitary sewers)
- For (c)(i): Explain filter problems (mud balls, cracking, air binding, sand incrustation) with specific control measures (surface washing, backwashing rate adjustment, filter media replacement)
- For (c)(ii): Enumerate intake design factors (water quality, flood levels, navigation, ice, future demand) and sketch river intake showing components like screen, sump, pump house, and approach channel
Q7 50M calculate Environmental and Irrigation Engineering
(a) The data related to the activated sludge process is given below:
Population = 500000
Wastewater contribution = 150 lpcd
BOD of settled wastewater = 200 mg/L
Effluent BOD required = 30 mg/L
Using the data, find the design parameters as mentioned below (Take F/M = 0·2, MLSS = 3000 mg/L, SVI = 100, where MLSS = Mixed liquor suspended solids, SVI = Sludge volume index):
(i) Volume of aeration
(ii) Efficiency
(iii) Volumetric loading
(iv) Return sludge ratio
(v) Hydraulic retention time (HRT)
20 marks
(b) An unlined irrigation channel in an alluvium of median size 0·30 mm is of trapezoidal section with bed width = 3·0 m, side slope = 1·5 H : 1 V and longitudinal slope = 0·00035. If this channel carries a discharge of 1·5 m³/s at a depth of 0·8 m, then determine—
(i) the average bed shear stress due to flow;
(ii) the shear stress due to grains;
(iii) the shear stress due to bed forms.
Take γ = 9790 N/m³.
15 marks
(c) Define waterlogging. Enumerate any four causes of waterlogging. What are the effects of waterlogging? Describe any five control measures for waterlogging.
15 marks
Answer approach & key points
This is primarily a calculation-based question demanding precise numerical solutions for (a) activated sludge design parameters (20 marks) and (b) channel shear stress components (15 marks), followed by a descriptive part (c) on waterlogging (15 marks). Allocate approximately 40% time to part (a) for computing volume, efficiency, volumetric loading, return sludge ratio and HRT using F/M ratio and SVI relationships; 30% to part (b) for applying Einstein-Barbarossa or Engelund-Hansen partitioning of shear stress in alluvial channels; and 30% to part (c) for defining waterlogging with Indian examples like Punjab-Haryana canal commands, listing causes (seepage, poor drainage, heavy rainfall, obstruction), effects (salinity, reduced crop yield) and control measures (bio-drainage, interceptor drains, lining, crop rotation, tubewell drainage). Present calculations with clear formula statements, unit conversions, and final boxed answers.
- Part (a): Correct computation of wastewater flow (75 MLD), aeration tank volume using F/M = Q×S₀/(V×X), efficiency via BOD removal, volumetric loading as Q×S₀/V, return sludge ratio from SVI and mass balance, and HRT as V/Q
- Part (b): Calculation of total bed shear stress τ₀ = γRS, grain shear stress τ' using Einstein's approach or Engelund's τ' = γR'S where R' = 11d₆₅, and bed form shear stress τ'' = τ₀ − τ' for d₅₀ = 0.30 mm
- Part (c): Precise definition of waterlogging (water table within root zone), four causes including canal seepage in Indo-Gangetic plains, effects on soil aeration and crop productivity
- Part (c): Five control measures with specificity—surface drainage, subsurface drainage (mole drains in black cotton soils), interceptor drains, canal lining with CC/HDPE, and bio-drainage using Eucalyptus in Rajasthan
- Appropriate unit handling throughout: m³ for volume, hours for HRT, N/m² for shear stress, dimensionless ratios for efficiency and return sludge ratio
Q8 50M solve Hydraulic Structures and Environmental Engineering
(a) The figure shows an overflow spillway which is 40 m high. At the design energy head of 2·5 m over the spillway, determine—
(i) the sequent depths;
(ii) the energy loss;
(iii) the percentage of initial energy lost
for the hydraulic jump formed on a horizontal apron at the toe of the spillway.
20 marks
(b) 20 MLD of water with 80 mg/L of suspended solids is treated with alum [Al₂(SO₄)₃ · 14·3H₂O] dose of 60 mg/L. Find the quantity of sludge produced assuming that sufficient natural alkalinity is available. Take specific gravity of sludge as 1·04 and removal efficiency as 60%.
15 marks
(c) Explaining the procedure for developing a wind rose, discuss the applications of wind rose using a typical sketch.
15 marks
Answer approach & key points
This question requires solving three distinct problems: (a) hydraulic jump calculations for spillway energy dissipation (40% time, 20 marks), (b) sludge production calculation in water treatment (30% time, 15 marks), and (c) explaining wind rose construction with diagram (30% time, 15 marks). Begin with clear problem identification for each part, show all formulae with standard notation (Froude number, sequent depth equation, sludge mass balance), execute calculations systematically, and conclude with physical interpretation of results.
- For (a): Apply specific energy equation to find velocity at spillway toe; calculate Froude number and use Belanger's momentum equation for sequent depths y₁ and y₂; determine energy loss ΔE = (y₂-y₁)³/(4y₁y₂) and percentage loss
- For (a): Correct identification that total head = 40 + 2.5 = 42.5 m, velocity V₁ = √(2g×42.5), and critical assessment of whether apron is truly horizontal or needs correction
- For (b): Calculate suspended solids removed (80 × 0.6 = 48 mg/L), alum reaction stoichiometry with alkalinity, sludge mass using specific gravity 1.04, and convert to daily volume in m³/day
- For (c): Explain wind rose construction procedure: collect wind speed/direction data, create 16-point compass sectors, calculate frequency percentages, draw radial plot with concentric circles representing frequency
- For (c): Sketch standard wind rose showing calm percentage, prevailing wind direction, and applications: air pollution dispersion modeling (e.g., NTPC thermal plant siting), airport runway orientation, urban planning for Delhi/Mumbai airshed management
- Cross-cutting: Unit consistency throughout (MLD to m³/s, mg/L to kg/m³), proper significant figures, and physical reasonableness checks on all numerical answers