Civil Engineering 2025 Paper I 50 marks Calculate

Q7

(a) A braced cut 7·0 m deep and 3·0 m wide is proposed in a cohesionless sand deposit. Assume that the first row of struts to be located at 0·5 m below ground level and the spacing of strut as 2·5 m as shown in the diagram. In the plan, the struts are placed at spacing of 2 m centre to centre. Using Peck's empirical relation for pressure diagram, determine the design loads in the struts. The properties of sand are as follows: Angle of shearing resistance = 30° Bulk density = 16·5 kN/m³ (b) A 5 m thick clay layer is subjected to drained condition both at top and bottom. It has few sand drains in square pattern. The spacing of sand drains are 3 m centre to centre. The coefficient of consolidation in vertical and radial directions are same and equal to 5 × 10⁻³ m²/day. The radius of the sand drains is 0·25 m. Assuming that there is no smear at the periphery of drain wells, it has been estimated that a given uniform surcharge would cause a total consolidation settlement of 200 mm without sand drains. Find the consolidation settlement of clay layer with same surcharge and sand drains, at times of 6 months, 9 months and one year. Draw the variation of settlement with time. (c) (i) A liquid whose specific gravity is 0·8 and dynamic viscosity is 1·8 poise, flows in a vertical pipe of 8 cm diameter. Pressure gauges in the pipe located 20 m apart indicate a pressure of 180 kPa at the upper end and a pressure of 360 kPa at the lower end. Calculate the flow rate and find the direction of the flow in the pipe. (Use Hagen-Poiseuille equation.) (ii) Water flows from A to B through a tapering pipe. The following data is given at section A and B: | Section | A | B | |---------|---|---| | Diameter of pipe | 12 cm | 10 cm | | Elevation | 100.000 m | 101.000 m | | Gauge pressure | 30 kPa | 20 kPa | Estimate the discharge in the pipe line. (Assume zero loss of energy between two sections.)

हिंदी में प्रश्न पढ़ें

(a) 7·0 m गहरी और 3·0 m चौड़ी एक बंधनयुक्त काट एक संसजन रहित बालू निक्षेप में प्रस्तावित है। मान लीजिए कि टेकों की प्रथम पंक्ति धरातल से 0·5 m नीचे लगानी है और आरेख में दर्शाए अनुसार टेकों का अंतराल 2·5 m है। अनुविन्यास में, टेकों को केंद्र से केंद्र के 2 m के अंतराल पर रखा गया है। दाब आरेख के लिए पैक के अनुभाविक संबंध का उपयोग करते हुए, टेकों में अभिकल्प भारों को निर्धारित कीजिए। बालू के गुणधर्म इस प्रकार हैं : अपरूपण प्रतिरोध का कोण = 30° स्थूल घनत्व = 16·5 kN/m³ (b) एक 5 m मोटी मृत्तिका परत शीर्ष और तली पर अपवाहित अवस्था में है। इसमें कुछ बालू नालियाँ वर्गाकार प्रारूप में हैं। बालू नालियों की केंद्र से केंद्र की दूरी 3 m है। संघनन गुणांक ऊर्ध्वाधर और त्रिजीय दिशाओं में समान है और 5 × 10⁻³ m²/दिन के बराबर है। बालू नालियों की त्रिज्या 0·25 m है। यह मानते हुए कि नाली कुओं की परिधि पर कोई स्मीयर नहीं है, यह आकलन किया गया कि एक प्रदत एकसमान अधिभार बालू नालियों के बिना 200 mm का सकल संघनन निष्पदन करेगा। इसी अधिभार और बालू नालियों के साथ मृत्तिका परत का संघनन निष्पदन 6 माह, 9 माह और 1 वर्ष के समय पर ज्ञात कीजिए। निष्पदन का समय के साथ विचरण दर्शाइए। (c) (i) एक द्रव, जिसका विशिष्ट घनत्व 0·8 और गतिक श्यानता 1·8 पॉइज़ है, 8 cm व्यास के एक ऊर्ध्वाधर पाइप में प्रवाहित होता है। पाइप में एक दूसरे से 20 m की दूरी पर लगे दाबमापी ऊपरी सिरे पर दाब 180 kPa और निचले सिरे पर दाब 360 kPa दर्शाते हैं। पाइप में प्रवाह दर की गणना कीजिए और प्रवाह की दिशा ज्ञात कीजिए। (हैगन-पॉइज़ुइल समीकरण का उपयोग कीजिए।) (ii) एक शुंडाकार पाइप में जल A से B तक प्रवाहित होता है। परिच्छेद A और B पर निम्नलिखित आँकड़े प्रदत हैं : | परिच्छेद | A | B | |---|---|---| | पाइप का व्यास | 12 cm | 10 cm | | ऊँचाई | 100.000 m | 101.000 m | | गेज दाब | 30 kPa | 20 kPa | पाइप लाइन में निस्सरण का आकलन कीजिए। (दो परिच्छेदों के बीच ऊर्जा ह्रास शून्य मान लीजिए।)

Evaluate your answer to this question → See all 2025 Civil Engineering questions

Directive word: Calculate

This question asks you to calculate. 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

Calculate the required quantities for all four sub-parts systematically. For (a), apply Peck's empirical relation for braced cut pressure distribution and determine strut loads using tributary area method. For (b), use Barron's theory for radial consolidation with sand drains, computing degree of consolidation at specified time intervals and plotting settlement-time curve. For (c)(i), apply Hagen-Poiseuille equation considering both pressure and elevation heads to find flow rate and direction. For (c)(ii), apply Bernoulli's equation between sections A and B to estimate discharge. Allocate approximately 30% time to part (a), 30% to part (b), 20% to (c)(i), and 20% to (c)(ii). Present calculations in sequential steps with clear identification of given data, formulae used, substitutions, and final results with proper units.

Key points expected

  • Part (a): Correct application of Peck's empirical pressure envelope (0.65γH·Ka for cohesionless sand), calculation of active earth pressure coefficient Ka = tan²(45°-φ/2) = 1/3, determination of pressure intensity, and computation of strut loads using tributary area method for three strut levels
  • Part (b): Application of Barron's equal strain theory for radial consolidation, calculation of drain spacing ratio n = re/rw = 6, time factor Tr = cvt/de², degree of consolidation Ur for radial drainage, combined degree of consolidation U = 1-(1-Uv)(1-Ur), and settlement at 6, 9, 12 months with plotted curve
  • Part (c)(i): Correct application of Hagen-Poiseuille equation Q = (πΔp*D⁴)/(128μL) with proper unit conversion (poise to Pa·s, cm to m), consideration of total head including elevation head to determine flow direction from lower to higher pressure when piezometric head is evaluated
  • Part (c)(ii): Application of Bernoulli's equation between sections A and B with continuity equation, proper accounting of velocity heads (VA²/2g and VB²/2g), elevation heads, and pressure heads to solve for discharge Q
  • Proper unit conversions throughout: poise to Pa·s, kPa to Pa, cm to m, days to years for consolidation calculations
  • Clear presentation of diagrams: pressure envelope for braced cut in (a), settlement-time curve for (b), and energy grade line sketch for (c)(ii)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies Peck's empirical relation for braced cuts, Barron's radial consolidation theory for sand drains, Hagen-Poiseuille equation for laminar pipe flow, and Bernoulli's equation for tapering pipe flow; recognizes that flow direction in (c)(i) depends on total head not pressure aloneIdentifies most concepts correctly but makes minor errors in theory selection (e.g., uses Terzaghi's 1D consolidation instead of Barron's theory, or omits velocity head in Bernoulli's equation); understands basic principles but applies them inconsistentlyConfuses fundamental concepts (e.g., uses Rankine's theory instead of Peck's empirical approach, applies Darcy's law instead of Hagen-Poiseuille, or completely misses radial consolidation effects); demonstrates lack of understanding of geotechnical and fluid mechanics principles
Numerical accuracy20%10All calculations accurate to appropriate significant figures: Ka = 0.333, pressure intensity ≈ 25.03 kPa, strut loads correctly computed; n = 6, Ur values accurate, settlements at 6, 9, 12 months precisely calculated; flow rate in (c)(i) ≈ 1.96×10⁻⁴ m³/s with correct direction; discharge in (c)(ii) ≈ 0.015 m³/sGenerally correct approach with minor calculation errors (e.g., arithmetic mistakes in strut load distribution, slight errors in time factor calculation, or unit conversion errors that don't affect order of magnitude); final answers close to expected valuesMajor numerical errors including wrong formula substitutions, incorrect unit conversions (e.g., missing 10⁻⁴ factor in viscosity), order-of-magnitude mistakes, or completely wrong final answers; demonstrates poor quantitative problem-solving ability
Diagram quality20%10Clear, labeled diagrams: trapezoidal pressure envelope for braced cut with strut positions marked, settlement-time curve with proper axes (time in months/days, settlement in mm) showing asymptotic approach to 200mm, and energy grade line diagram for (c)(ii) showing datum, EGL and HGLDiagrams present but with minor deficiencies: missing labels, incorrect proportions, or poorly scaled axes; pressure diagram shows correct shape but strut positions unclear; settlement curve present but time axis improperly scaledMissing essential diagrams, or diagrams that are misleading/wrong (e.g., triangular pressure distribution instead of Peck's trapezoidal envelope, no settlement-time plot, or completely incorrect energy line representation); diagrams fail to support the solution
Step-by-step derivation20%10Systematic presentation: given data clearly listed, formulae stated before substitution, all intermediate steps shown (calculation of Ka, pressure intensity, tributary areas for each strut; n, Tr, Ur, U, settlement ratios; Reynolds number check for laminar flow assumption; continuity and Bernoulli equations solved simultaneously)Most steps shown but with gaps in derivation (e.g., jumps from formula to final answer without intermediate calculation, or omits verification of laminar flow condition); generally followable but requires examiner to fill in missing stepsDisorganized working with no clear structure, missing essential steps, or 'magical' appearance of numbers without explanation; impossible to follow logic or verify calculations; demonstrates poor examination technique
Practical interpretation20%10Interprets results in engineering context: discusses why Peck's empirical approach is conservative for deep excavations in urban areas like Delhi Metro cuts; explains how sand drains accelerate consolidation for highway embankments on soft clays; comments on laminar flow verification and practical limits of Hagen-Poiseuille; notes energy losses in real tapering pipesBrief mention of practical relevance without elaboration (e.g., states sand drains 'speed up consolidation' without explaining mechanism or typical applications; or notes flow is laminar without discussing Reynolds number significance)Purely mathematical treatment with no physical interpretation; fails to recognize that calculated strut loads are design values, or that settlement-time relationship shows typical consolidation behavior; no connection to real-world civil engineering practice

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 2025 Paper I