Civil Engineering 2023 Paper I 50 marks Solve

Q7

(a) A 3·0 m high sandy fill material was placed loosely at a relative density of 50%. Laboratory studies indicated that the maximum and minimum void ratios of the fill material are 0·90 and 0·52 respectively. Construction specifications required that the fill be compacted to a relative density of 80%. If Gs = 2·65, determine : (i) Dry unit weight of the fill before and after compaction. (ii) Final height of the fill after compaction. Take γw = 9·81 kN/m³. (15 marks) (b) A group of 9 driven cast in situ piles is installed in a layered cohesive soil deposit as shown in the figure below. Piles are 40 cm in diameter and 15 m long. The spacing between the piles is 1·2 m and the cutoff level is 2·0 m below the ground level. Determine the safe load of the piles with a factor of safety of 2·5. (15 marks) (c) Glycerin is flowing through a 2·5 cm diameter horizontal pipe of 30 m length that discharges it into the atmosphere at 101 kPa. The flow rate through the pipe is 0·05 litres/second. Dynamic viscosity (μ) and density of glycerin are 0·25 kg/m-s and 1250 kg/m³, respectively. Answer the following : (i) What is the absolute pressure at 30 m length just before the exit of pipe ? (ii) At what angle (θ) must the pipe be inclined downward from the horizontal for the pressure in the entire pipe to be atmospheric pressure and the flow rate to be maintained the same ? (20 marks)

हिंदी में प्रश्न पढ़ें

(a) एक 3·0 m ऊँचा बालुई भरण पदार्थ 50% सापेक्ष घनत्व पर असंहत रूप में रखा गया । प्रयोगशाला अध्ययन संकेत करते हैं कि भरण पदार्थ के अधिकतम और न्यूनतम रिक्त अनुपात क्रमशः: 0·90 और 0·52 हैं । निर्माण विनिर्देशों के अनुसार भरण को 80% के सापेक्ष घनत्व तक संहनित किया जाना है । यदि Gs = 2·65 है, तो निर्धारित कीजिए : (i) संहनन के पहले और बाद में भरण का शुष्क एकक भार । (ii) संहनन के बाद भरण की अंतिम ऊँचाई । γw = 9·81 kN/m³ लीजिए । (15 marks) (b) नीचे चित्र में दर्शाए अनुसार, स्व-स्थान ढली 9 प्रवेशित स्तंभों के एक समूह को एक स्तरित संसजनी मृदा निक्षेप में अधिष्ठापित किया गया है । स्तंभों का व्यास 40 cm और लम्बाई 15 m है । स्तंभों के बीच अंतराल 1·2 m है और विच्छेद तल भूमि तल से 2·0 m नीचे है । सुरक्षा गुणक 2·5 के साथ, स्तंभों के सुरक्षित भार को निर्धारित कीजिए । दृढ़ मृतिका Cᵤ = 50 kN/m² α = 0·9 γ = 18 kN/m³ मृदु मृतिका Cᵤ = 30 kN/m² α = 1·0 γ = 16 kN/m³ दृढ़ीय मृतिका Cᵤ = 90 kN/m² α = 0·5 γ = 20 kN/m³ स्तंभ समूह (15 marks) (c) एक 30 m लम्बे, 2·5 cm व्यास के क्षैतिज पाइप में ग्लिसरिन प्रवाहित है, जो इसे 101 kPa पर वायुमण्डल में निर्सरित करती है । पाइप में प्रवाह दर 0·05 लीटर/सेकण्ड है । ग्लिसरिन की गतिक श्यानता (μ) और घनत्व क्रमशः: 0·25 kg/m-s और 1250 kg/m³ हैं । निम्नलिखित के उत्तर दीजिए : (i) पाइप के निर्गम से तुरन्त पहले 30 m लम्बाई पर निरपेक्ष दाब क्या है ? (ii) पाइप को क्षैतिज से नीचे की ओर किस कोण (θ) से झुकाया जाए जिससे पूरे पाइप में दाब, वायुमण्डलीय दाब हो और प्रवाह दर समान बनी रहे ? (20 marks)

Evaluate your answer to this question → See all 2023 Civil Engineering questions

Directive word: Solve

This question asks you to solve. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Solve all three numerical parts systematically, allocating approximately 30% time to part (a) on soil compaction, 30% to part (b) on pile group capacity, and 40% to part (c) on pipe flow hydraulics. Begin each part with stated assumptions and formulae, proceed through step-by-step calculations with proper units, and conclude with clearly boxed final answers for each sub-part.

Key points expected

  • Part (a): Correct application of relative density formula to find void ratios before and after compaction, then dry unit weight using γd = Gs·γw/(1+e), and height reduction using mass conservation
  • Part (a)(ii): Calculation of final height using relationship H2 = H1 × (1+e2)/(1+e1) based on constant mass and plan area
  • Part (b): Determination of individual pile capacity in layered clay using α-method for skin friction and bearing capacity for base, then application of group efficiency factors for 3×3 pile group
  • Part (b): Consideration of block failure mode versus individual pile failure for closely spaced piles (spacing/diameter = 3)
  • Part (c)(i): Application of Hagen-Poiseuille equation for laminar flow to find pressure drop, verification of Reynolds number, and calculation of absolute pressure at pipe exit
  • Part (c)(ii): Derivation of required inclination angle using energy equation where pressure gradient due to elevation head balances viscous losses, maintaining same flow rate

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: relative density-void ratio relationships for part (a); α-method skin friction and end bearing for piles in layered clay with proper group efficiency for part (b); Hagen-Poiseuille laminar flow with Reynolds number verification and Bernoulli energy equation for part (c)Uses correct basic formulae but makes minor errors in conceptual application such as wrong group efficiency factor, incorrect flow regime assumption, or missing mass conservation principleFundamental conceptual errors like treating relative density as density, using Terzaghi's bearing capacity for piles without modification, or applying turbulent flow equations for clearly laminar conditions
Numerical accuracy25%12.5All calculations precise to 3 significant figures with correct unit conversions (cm to m, litres/s to m³/s), consistent use of γw = 9.81 kN/m³, and accurate arithmetic throughout; final answers clearly stated with proper unitsGenerally correct calculations with minor arithmetic errors or inconsistent significant figures; correct methodology but slips in decimal placement or unit conversionsMajor calculation errors, wrong unit conversions (e.g., missing 10⁻³ for flow rate), inconsistent use of water unit weight, or answers without units
Diagram quality10%5Clear sketch for part (b) showing 3×3 pile group arrangement with dimensions (spacing 1.2m, diameter 0.4m), cutoff level at 2m, and layered soil profile with thicknesses; labeled free-body diagram for part (c) showing inclined pipe with pressure and elevation headsBasic diagram present but missing key dimensions or labels; rough sketch without proper scale indication or missing soil layer identificationNo diagrams where required (especially for pile group geometry), or completely misleading sketches that contradict problem statement
Step-by-step derivation25%12.5Each sub-part shows complete derivation: stated given data, formula with standard symbols, substitution with units, intermediate results, and final answer; logical flow with cross-referencing between related calculations (e.g., void ratio to unit weight to height)Some steps shown but with gaps in derivation, missing intermediate steps, or unclear logical progression; formulae stated but substitution not fully shownOnly final answers with no working, or working that cannot be followed; jumps between unrelated equations without explanation
Practical interpretation20%10Interprets results practically: comments on significant height reduction in compaction for highway embankments; discusses whether group or individual failure governs pile design; explains why glycerin requires laminar flow analysis and implications for industrial pipe design; references relevant IS codes (IS 2911 for piles, IS 2720 for compaction)Brief mention of practical relevance without elaboration; generic statements about construction quality or fluid transport without specific connection to calculated resultsNo interpretation of what results mean practically, or irrelevant commentary that does not address the engineering significance of the numerical answers

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Civil Engineering 2023 Paper I