Civil Engineering 2022 Paper I 50 marks Solve

Q7

(a) (i) Distinguish between discharge velocity and seepage velocity in the case of flow of water through soils. 5 (ii) A soil sample 90 mm high and 6000 mm² in cross-section was subjected to a falling head permeability test. The head fell from 500 mm to 300 mm in 1500 seconds. The permeability of the soil was 2.4×10⁻³ mm/s. Determine the diameter of the standpipe. 10 (b) Two parallel plates are moving in opposite direction with velocities 1 m/s and 2 m/s respectively. For the given coordinate system (shown below), draw the velocity and shear stress profile for positive and negative pressure gradient after obtaining the profile equations : 20 (c) Laboratory results of a soil have shown that its unconfined compressive strength is 120 kN/m². In a triaxial compression test, a specimen of the soil when subjected to a confining pressure of 40 kN/m² failed at an additional stress of 160 kN/m². Estimate the shearing strength of the same soil along a horizontal plane at a depth of 4 m at the site. The groundwater table is at a depth of 2·5 m from the ground level. Take the dry unit weight of the soil as 17 kN/m³ and specific gravity as 2·7. Also, assume the unit weight of water as 10 kN/m³. 15

हिंदी में प्रश्न पढ़ें

(a) (i) मृदा में जल के प्रवाह के लिए निस्सरण वेग और रिसन वेग में अंतर बताइए। (ii) 90 mm ऊँचाई और 6000 mm² अनुप्रस्थ परिच्छेद वाले एक मृदा प्रतिदर्श पर पतन दाबोच्चता पारगम्यतामापी परीक्षण किया गया। 1500 सेकंड में दाबोच्चता का पतन 500 mm से 300 mm हुआ। मृदा की पारगम्यता 2.4×10⁻³ mm/s थी। स्टैंडपाइप के व्यास को निर्धारित कीजिए। (b) दो समानांतर प्लेट विपरीत दिशा में क्रमशः 1 m/s और 2 m/s के वेग से चल रही हैं। परिच्छेदिका (प्रोफाइल) समीकरण प्राप्त करने के पश्चात्, धनात्मक और ऋणात्मक दाब प्रवणता के लिए, दी गई निर्देशांक पद्धति (नीचे दर्शाई गई) के लिए, वेग और अपरूपण प्रतिबल परिच्छेदिका (प्रोफाइल) अंकित कीजिए : (c) प्रयोगशाला परिणाम दर्शाते हैं कि एक मृदा की अपरिबद्ध संपीडन सामर्थ्य 120 kN/m² है। एक त्रि-अक्षीय संपीडन परीक्षण में, एक मृदा प्रतिदर्श जिस पर 40 kN/m² का परिरोधी दाब लगा था, वह 160 kN/m² के अतिरिक्त प्रतिबल पर विफल हो गया। स्थल की 4 m गहराई पर क्षैतिज तल पर इसी मृदा की अपरूपण सामर्थ्य का आकलन कीजिए। भूमजल स्तर, धरातल से 2·5 m नीचे है। मृदा का शुष्क एकक भार 17 kN/m³ और विशिष्ट घनत्व 2·7 लीजिए। जल का एकक भार 10 kN/m³ मान लीजिए।

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Approach

Begin with clear definitions distinguishing discharge and seepage velocity for part (a)(i), then solve the falling head permeability problem showing all substitutions. For part (b), derive the general Couette-Poiseuille flow equation first, then plot velocity and shear stress profiles for both pressure gradient cases with proper boundary conditions. Conclude with part (c) by determining soil parameters from given test data, calculating effective stress at 4m depth, and applying Mohr-Coulomb failure criterion. Allocate time proportionally: ~15% for (a)(i), ~20% for (a)(ii), ~40% for (b), and ~25% for (c).

Key points expected

  • Part (a)(i): Clear distinction between discharge velocity (v = Q/A, Darcy's velocity) and seepage velocity (vs = v/n, actual pore velocity) with v = n×vs relationship and physical interpretation through void ratio/porosity
  • Part (a)(ii): Correct application of falling head permeability formula k = (aL/At)ln(h1/h2), proper unit consistency, and solving for standpipe diameter d = √(4a/π) yielding approximately 7.6 mm
  • Part (b): Derivation of velocity profile u(y) = -(1/2μ)(dp/dx)(Hy-y²) + (U2-U1)(y/H) + U1 with U1 = -1 m/s, U2 = 2 m/s, H = gap height; shear stress τ = μ(du/dy); profiles for dp/dx > 0 (adverse) and dp/dx < 0 (favorable) showing possible flow reversal
  • Part (c): Determination of cohesion c = 60 kN/m² and friction angle φ = 30° from unconfined (qu = 2c) and triaxial tests; calculation of total stress, pore pressure (u = 15 kN/m²), and effective stress σ' = 53 kN/m² at 4m depth; final shear strength τf = c + σ'tanφ
  • Part (c) continued: Proper unit weight calculations using γsat = (G+e)γw/(1+e) with e determined from γd = Gγw/(1+e), ensuring submerged unit weight γ' = γsat - γw for stress below water table

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Precisely defines discharge vs seepage velocity with porosity relationship; correctly identifies Couette-Poiseuille flow superposition; accurately applies Mohr-Coulomb and effective stress principle for part (c); no conceptual errors in any sub-partBasic definitions correct but misses physical significance of seepage velocity; derives flow equation with minor sign errors; identifies soil strength parameters but confuses total and effective stress conceptsConfuses discharge and seepage velocity or omits porosity relationship; fails to recognize combined Couette-Poiseuille flow; applies total stress instead of effective stress in shear strength calculation
Numerical accuracy20%10All calculations correct: standpipe diameter ~7.6 mm with proper significant figures; velocity profile coefficients accurate; soil parameters c=60 kPa, φ=30° exactly; effective stress and shear strength calculations precise to appropriate decimal placesCorrect methodology but arithmetic errors in one sub-part (e.g., wrong log calculation or unit conversion); soil parameters approximately correct but rounding errors; final answer within 10% of correct valueMajor calculation errors in multiple sub-parts; incorrect formula substitution; order of magnitude errors in permeability or shear strength; missing units or inconsistent unit usage
Diagram quality20%10Clear velocity and shear stress profiles for part (b) with labeled axes, boundary conditions (U1=-1, U2=2), inflection points marked; distinct curves for positive and negative dp/dx showing parabolic nature and possible reverse flow; neat freehand or scaled drawingProfiles drawn but missing key features like boundary velocity values or pressure gradient labels; sketches recognizable but poorly scaled; missing one of the two required cases (positive or negative dp/dx)No diagrams for part (b) despite explicit requirement; or unrecognizable sketches without proper labeling; straight line profiles showing fundamental misunderstanding of viscous flow
Step-by-step derivation20%10Complete Navier-Stokes reduction for part (b) starting from ∂²u/∂y² = (1/μ)(dp/dx), integration with constants C1, C2 determined from no-slip at y=0 (u=U1) and y=H (u=U2); clear substitution in falling head formula; systematic Mohr's circle construction for part (c)Final equations correct but skips key integration steps or boundary condition application; presents results without showing intermediate algebra; correct methodology but condensed derivationJumps to final formula without derivation; no boundary condition application shown; incorrect integration or algebraic manipulation; simply states answers without process
Practical interpretation20%10Interprets seepage velocity significance for piping/erosion in Indian dams (e.g., Tehri); explains Couette flow relevance to lubrication or groundwater flow; relates calculated shear strength to foundation design or slope stability for typical Indian soil conditionsBrief mention of practical relevance without specific examples; generic statements about soil strength or flow applications; no connection to Indian engineering contextPurely academic treatment with no physical interpretation; fails to explain why results matter; no engineering judgment or application context provided

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