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Civil Engineering 2023 Paper I 50 marks Solve

Paper I — Q7

(a) A 3.0 m high sandy fill material was placed loosely at a relative density of 50%. Laboratory studies indicated that the…

(a)
(i)

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 : 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. [Figure: water table at ground level; firm clay 0–3 m, cu = 50 kN/m², α = 0.9, γ = 18 kN/m³; soft clay 3–12 m, cu = 30 kN/m², α = 1.0, γ = 16 kN/m³; stiff clay 12–17 m, cu = 90 kN/m², α = 0.5, γ = 20 kN/m³; pile cap with its base 2 m below ground] 15 marks

(c)
(i)

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 : 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
(i)

(क) 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 रिक्ति 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 : 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 अंक)

(ख) नीचे चित्र में दर्शाए अनुसार, स्व-स्थान ढली 9 प्रवेशित स्थूणाओं के एक समूह को एक स्तरित संसजनी मृदा निक्षेप में अधिष्ठापित किया गया है । स्थूणाओं का व्यास 40 cm और लम्बाई 15 m है । स्थूणाओं के बीच अंतराल 1.2 m है और विच्छेद तल भूमि तल से 2.0 m नीचे है । सुरक्षा गुणक 2.5 के साथ, स्थूणाओं के सुरक्षित भार को निर्धारित कीजिए । [चित्र: भौम जल स्तर भूमि तल पर; दृढ़ मृत्तिका 0–3 m, cu = 50 kN/m², α = 0.9, γ = 18 kN/m³; मृदु मृत्तिका 3–12 m, cu = 30 kN/m², α = 1.0, γ = 16 kN/m³; दुर्नम्य मृत्तिका 12–17 m, cu = 90 kN/m², α = 0.5, γ = 20 kN/m³; स्थूणा-टोपी का आधार भूमि से 2 m नीचे] (15 अंक)

(ग) एक 30 m लम्बे, 2.5 cm व्यास के क्षैतिज पाइप में ग्लिसरीन प्रवाहित है, जो इसे 101 kPa पर वायुमण्डल में निस्सरित करती है । पाइप में प्रवाह दर 0.05 लीटर/सेकण्ड है । ग्लिसरीन 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 तुरंत 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, वायुमंडलीय दाब हो और प्रवाह दर समान बनी रहे ? (20 अंक)

Q7 of the 2023 UPSC Mains Civil Engineering Paper I, as printed
The question as printed in the 2023 Civil Engineering paper
Evaluate your answer to this question → See all 2023 Civil Engineering questions

The figure this question refers to, in words

The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.

(b) A cross-sectional diagram of a shallow strip footing and soil layers:

  • Ground surface is shown as a horizontal line with hatch marks below it.
  • The footing is an inverted T-shaped strip footing with width at the base B = 2.8 m.
  • Depth of foundation from the ground surface to the base of the footing is 2.5 m.
  • Water table is indicated by an inverted triangle with horizontal lines at a depth of 6 m below the ground surface.
  • Soil properties are given as: phi = 30 degrees, moist unit weight gamma = 18 kN/m^3, and cohesion C = 40 kN/m^2.

Model answer

Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.

(a) Sand fill: compaction from D_r = 50% to 80%

Relative density D_r = (e_max − e)/(e_max − e_min), with e_max − e_min = 0.38.

Before: e₁ = 0.90 − 0.50 × 0.38 = 0.71. After: e₂ = 0.90 − 0.80 × 0.38 = 0.596.

(i) Dry unit weight γ_d = G_s γ_w/(1 + e), with G_s γ_w = 2.65 × 9.81 = 25.997 kN/m³. Before compaction γ_d1 = 25.997/1.71 = 15.20 kN/m³. After compaction γ_d2 = 25.997/1.596 = 16.29 kN/m³.

(ii) The solid volume per unit plan area is constant, so H₂/(1 + e₂) = H₁/(1 + e₁). H₂ = 3.0 × 1.596/1.71 = 2.80 m (a settlement of 0.20 m). Check: H₂ = H₁ γ_d1/γ_d2 = 3.0 × 15.20/16.29 = 2.80 m.

(b) Safe load of the pile group

Piles run from the cut-off level (2 m) to 17 m depth: 1 m in firm clay, 9 m in soft clay and 5 m in stiff clay (1 + 9 + 5 = 15 m). I take the tip to be in the stiff clay. Perimeter = π × 0.4 = 1.2566 m, base area = π × 0.4²/4 = 0.1257 m².

Single pile, shaft (α c_u L, with c_u in kN/m² and L in m): 0.9 × 50 × 1 + 1.0 × 30 × 9 + 0.5 × 90 × 5 = 45 + 270 + 225 = 540 kN/m. Shaft = 540 × 1.2566 = 678.6 kN.

Base = 9 c_u A_b = 9 × 90 × 0.1257 = 101.8 kN. Q_u(single) = 780.4 kN.

Sum of individual piles: 9 × 780.4 = 7023 kN.

Block failure (3 × 3 group, spacing 1.2 m): B = 2 × 1.2 + 0.4 = 2.8 m, perimeter 11.2 m. Shaft = 11.2 × (50 × 1 + 30 × 9 + 90 × 5) = 11.2 × 770 = 8624 kN. Base = 9 × 90 × 2.8² = 6350 kN. Q_u(block) = 14 974 kN.

The smaller value governs, so the individual-pile action controls and the group efficiency is taken as 1. Q_safe = 7023/2.5 = 2809 kN (about 312 kN per pile). The 2 m of soil above the cut-off level contributes no resistance.

Diagram: Pile group in layered clay: section with layers and cut-off level, and plan showing block perimeter

(c) Glycerin flow in a horizontal pipe

Q = 0.05 L/s = 5 × 10⁻⁵ m³/s; D = 0.025 m; A = 4.909 × 10⁻⁴ m². V = Q/A = 0.1019 m/s. Re = ρVD/μ = 1250 × 0.1019 × 0.025/0.25 = 12.7, so the flow is laminar and Hagen–Poiseuille applies.

(i) Δp = 128 μLQ/(πD⁴) = 128 × 0.25 × 30 × 5 × 10⁻⁵/(π × 3.906 × 10⁻⁷) = 39 115 Pa = 39.1 kPa. The velocity head is equal at both ends of a uniform pipe, so the pressure at the upstream end, 30 m before the exit, is p = 101 + 39.1 = 140.1 kPa (absolute). At the exit itself the pressure is 101 kPa.

(ii) Head loss h_f = Δp/(ρg) = 39 115/(1250 × 9.81) = 3.19 m. For pressure to be atmospheric throughout, gravity alone drives the flow: L sin θ = h_f, so sin θ = 3.19/30 = 0.1063 and θ = 6.1° downward.

How this answer will be evaluated

What earns full marks: All parts show complete derivation, correct units, and explicit checks; neat sketches and code references present.

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Find the dry unit weights before and after compaction and the final height of the fill. 15 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • e₁ = 0.71 and e₂ = 0.596 from the relative-density relation
    • γ_d = G_sγ_w/(1 + e): 15.20 and 16.29 kN/m³
    • Constant solid volume: H₂ = H₁(1 + e₂)/(1 + e₁)
    • H₂ = 2.80 m

    Loses marks

    • Using moist unit weight or forgetting the constant-solids principle.

    Earns more

    • Marks for void ratios, unit weights and height.

    Extra mark

    • Cross-checking H₂ with the ratio of dry unit weights.
  2. (b) Find the safe load of the 9-pile group in layered clay with FS = 2.5. 15 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Shaft resistance Σ α c_u L × perimeter = 678.6 kN per pile
    • Base resistance 9 c_u A_b = 101.8 kN; Q_u = 780.4 kN
    • Block capacity (B = 2.8 m) = 14 974 kN exceeds 9 × 780.4 = 7023 kN
    • Q_safe = 7023/2.5 ≈ 2809 kN

    Loses marks

    • Measuring layer lengths from the ground instead of the cut-off level.

    Earns more

    • Marks for layer-wise shaft, base, block check and safe load.

    Extra mark

    • Stating that the smaller value governs, so efficiency is 1.
  3. (c) Find the pressure at the upstream end and the inclination that makes the pipe pressure atmospheric throughout. 20 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • V = 0.1019 m/s and Re = 12.7, so laminar
    • Hagen–Poiseuille Δp = 39.1 kPa
    • p_upstream = 101 + 39.1 = 140.1 kPa absolute
    • sin θ = h_f/L = 3.19/30, θ = 6.1° downward

    Loses marks

    • Using the Darcy friction factor from turbulent charts without checking Re.

    Earns more

    • Marks for the laminar check, Δp, absolute pressure and the angle.

    Extra mark

    • Noting that the exit pressure is 101 kPa.
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