(a) The consolidated undrained (CU) tests were performed on the four over-consolidated clay samples obtained from a site. The pre-consolidation pressure was 650 kN/m². The results of triaxial test in CU condition are as follows:
| Test sample | Cell

Question

(a) The consolidated undrained (CU) tests were performed on the four over-consolidated clay samples obtained from a site. The pre-consolidation pressure was 650 kN/m². The results of triaxial test in CU condition are as follows:
| Test sample | Cell pressure kN/m² | Deviator stress kN/m² | Pore pressure kN/m² | Remark |
|-------------|---------------------|----------------------|---------------------|--------|
| 1 | 100 | 290 | – 40 | All the tests were performed in CU condition. The deviator stress and pore pressure were at failure. |
| 2 | 200 | 430 | – 20 | |
| 3 | 400 | 600 | 50 | |
| 4 | 600 | 840 | 110 | |
Determine the effective shear strength parameters. Draw the variation of pore pressure parameter 'A' (at failure) with over-consolidation ratio.

(b) A 250 mm diameter concrete pile 8 m long was driven by a double-acting hammer. The driving was carried out by a short dolly and cushion. The average penetration recorded in the last five blows was 3.0 mm per blow. Determine the safe pile load. As per IS 2911 (Part I) – 1979, the coefficient of restitution of the materials under impact for double-acting hammer striking on steel anvil and driving RCC pile is 0.5. The rated energy of hammer is 16.5 kJ and mass of hammer is 22 kN. Assume that only 90% of the rated energy is consumed. The density of RCC pile may be considered as 25 kN/m³. Assume the factor of safety as 2.5.

(c) (i) In a horizontal, rectangular channel, the sluice gate is opened. A hydraulic jump is formed downstream of the sluice gate.
The depth of water before jump is 0.8 m and specific energy before jump is 12.0 m.
Find the sequent depth of the jump and energy lost in the jump.
What is the initial Froude number ? Classify the jump based on the results obtained in the problem.

(ii) A runoff river plant is proposed to generate hydroelectric power. The net head available is 30 m. The river carries a sustainable flow of 30 m³/s in dry weather. Determine the maximum generating capacity. Daily load pattern indicates 20 hrs of average load and 4 hrs of peak load. Estimate the volume of pondage to be provided to supply the daily demand.
Assume load factor = 85%, Efficiency = 80%.

UPSC Answer Check · Accepted Answer

Solve all four sub-parts systematically, allocating approximately 35% time to part (a) due to its analytical complexity involving CU test data interpretation, 25% to part (b) for pile driving calculations using Hiley's formula, 25% to part (c)(i) for hydraulic jump computations, and 15% to part (c)(ii) for hydropower capacity and pondage estimation. Begin each sub-part with stated assumptions, show complete derivations with formulae, present calculations in tabular form where appropriate, and conclude with clearly boxed final answers with proper units.
- Part (a): Calculate effective stresses (σ'₃ = σ₃ - u) and plot Mohr-Coulomb envelope to determine c' and φ'; compute pore pressure parameter A = Δu/Δσ₁ at failure for each sample and plot A vs OCR relationship showing negative values for over-consolidated clays
- Part (b): Apply Hiley's formula Qup = ηₕWₕH/(S + C/2) with proper substitutions for hammer efficiency (0.9), coefficient of restitution (0.5), temporary compression (C), and pile elastic compression; determine safe load by applying FOS = 2.5
- Part (c)(i): Use specific energy equation E = y + V²/2g to find velocity and Froude number; apply hydraulic jump equations y₂ = (y₁/2)(√(1+8Fr₁²)-1) and EL = (y₂-y₁)³/(4y₁y₂); classify jump based on Fr₁ range (undular/weak/oscillating/stable/strong)
- Part (c)(ii): Calculate average power P = ηρgQH/1000 in kW; determine installed capacity using load factor; compute pondage volume as difference between peak flow demand and dry weather flow integrated over peak hours, accounting for continuous generation
- Correct interpretation of negative pore pressure in over-consolidated clays indicating dilatant behavior during shear
- Proper handling of units (kN, kPa, mm, m) and conversion factors throughout all calculations
- Clear presentation of Mohr's circles or stress paths for part (a) and schematic of hydraulic jump for part (c)(i)

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies that effective stress analysis requires subtracting pore pressures; recognizes negative A values indicate dilatancy in over-consolidated clays; applies proper Hiley's formula variant for double-acting hammer; uses correct hydraulic jump and specific energy relationships; understands load factor vs plant factor distinction for hydropower	Minor errors in concept application such as using total stresses instead of effective stresses for Mohr-Coulomb, or confusing single-acting vs double-acting hammer energy transfer, or misidentifying jump classification ranges	Fundamental conceptual errors like plotting total stress Mohr circles, using wrong formula (e.g., Engineering News formula instead of Hiley's), or calculating Froude number with wrong depth/velocity relationship
Numerical accuracy	20%	10	Precise calculations with c' ≈ 0-20 kPa and φ' ≈ 25-30° from Mohr-Coulomb envelope; A values correctly computed as -0.138, -0.047, 0.083, 0.131; safe pile load ≈ 450-500 kN; y₂ ≈ 4.2-4.5 m, EL ≈ 8-9 m, Fr₁ ≈ 4.5-5.0 (stable jump); installed capacity ≈ 6-7 MW, pondage ≈ 0.8-1.0 Mm³	Minor arithmetic errors or rounding differences (±10%) in final values, or correct method with one substitution error in intermediate steps	Significant calculation errors (>20% deviation), wrong order of magnitude, or missing critical factors like hammer efficiency or coefficient of restitution in pile formula
Diagram quality	20%	10	Neat Mohr-Coulomb plot with properly scaled axes, four Mohr circles at failure, clear envelope line showing c' intercept and φ' angle; A vs OCR plot with negative-positive transition; labeled hydraulic jump schematic; all diagrams with titles, axes labels, and units	Diagrams present but with scaling issues, missing labels, or hand-sketched without proper geometric construction for Mohr circles	Missing required diagrams, or diagrams that misrepresent physical relationships (e.g., positive A values plotted without acknowledging negative range for over-consolidated clay)
Step-by-step derivation	20%	10	Explicit statement of all formulae (Terzaghi's effective stress principle, Skempton's A parameter, Hiley's equation with all terms defined, Belanger's jump equations, hydropower equations); clear tabulation of intermediate values; logical flow from given data to final answer with no skipped steps	Some formulae implied rather than stated, or minor steps combined without explicit demonstration, but overall logic traceable	Missing derivations, 'black box' calculations with unexplained numbers, or illogical sequencing that prevents verification of method
Practical interpretation	20%	10	Interprets negative pore pressure and dilatancy implications for field behavior; discusses pile driving efficiency factors and site-specific adjustments; explains jump classification significance for stilling basin design; relates pondage calculation to Indian river hydrology and peaking power requirements (e.g., NHPC operational practices)	Brief mention of practical relevance without elaboration, or generic statements about safety factors without context-specific insight	Purely mathematical treatment with no physical interpretation, or incorrect practical conclusions (e.g., suggesting negative A indicates measurement error rather than dilatancy)

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