Paper I — Q8
(a) At a site, fine sand exists to a depth of 10 m and below this lies a soft clay layer 7·0 m thick. Water table is 4·0 m below…
At a site, fine sand exists to a depth of 10 m and below this lies a soft clay layer 7·0 m thick. Water table is 4·0 m below the ground surface. Saturated unit weight of sand is 20·0 kN/m³ and the wet unit weight above the water table is 18 kN/m³. The water content of the normally consolidated clay is 42%, liquid limit is 46% and the specific gravity of the solid particles is 2·75. The proposed construction will transmit a net stress of 130 kN/m² at the centre of the clay layer. Find the average settlement of the clay layer. 15 marks
A strip footing of width 2·8 m as shown in the figure is founded at a depth of 2·5 m below the ground surface in a C – φ soil. Water table is at a depth of 6 m below the ground surface. The average moist weight of soil above the water table is 18 kN/m³. Determine the ultimate bearing capacity, net ultimate bearing capacity, net allowable bearing pressure and the load/m for a factor of safety of 2·5. Use the general shear failure theory of Terzaghi. Given : For φ = 30°, Nc = 37·2 Nq = 22·5 Nγ = 19·7 What will be the percent decrease in ultimate bearing capacity if during the flooding, water level rises 2 m above around surface ? 15 marks
Water at 20°C flows through a pipe of inlet diameter of 10 cm and passes further through a circular nozzle of diameter 2·5 cm, exits into the air as a jet, and strikes a vertical plate as shown in the figure. A force, F = 100 N is required to hold the plate stationary. Assuming steady, frictionless, one-dimensional flow and densities of water and mercury as 1000 kg/m³ and 13550 kg/m³ respectively, answer the following : Determine the velocities at sections ① and ②.
Determine the mass flow rate of water.
Determine the mercury manometer reading 'h'. 20 marks
हिंदी में प्रश्न पढ़ें
एक स्थल पर, 10 m गहराई तक महीन बालू है और इसके नीचे 7·0 m मोटी मृद् मृत्तिका परत है । भौम जल स्तर भूमि तल से 4·0 m नीचे है । बालू का संतृप्त एकक भार 20·0 kN/m³ है और भौम जल स्तर से ऊपर आर्द्र एकक भार 18 kN/m³ है । सामान्य रूप से संघनित मृत्तिका का जलांश 42%, द्रव सीमा 46% है और ठोस कणों का विशिष्ट घनत्व 2·75 है । प्रस्तावित निर्माण, मृत्तिका परत के मध्य पर 130 kN/m² का निवल प्रतिबल प्रेषित करेगा । मृत्तिका परत का औसत निष्पदन ज्ञात कीजिए । 15 marks
2.8 m चौड़ी एक पट्टी पाद (फुटिंग) को चित्र में दर्शाए अनुसार एक C - φ मृदा में भूमि तल से 2.5 m नीचे आधारित किया गया है। भौम जल स्तर भूमि तल से नीचे 6 m गहराई पर है। भौम जल स्तर से ऊपर मृदा का औसत आर्द्र भार 18 kN/m³ है। 2.5 के एक सुरक्षा गुणक के लिए चरम धारण क्षमता, निवल चरम धारण क्षमता, निवल अनुमेय धारण दाब और भार/मीटर निर्धारित कीजिए। टेरज़ाघी के सामान्य अपरूपण विफलन सिद्धांत का उपयोग कीजिए। प्रदत्त : φ = 30° के लिए, Nc = 37.2 Nq = 22.5 Nγ = 19.7 यदि बाढ़ के दौरान, जल स्तर भूमि तल से 2 m ऊपर हो जाता है तो चरम धारण क्षमता में प्रतिशत कमी क्या होगी ? पाद (फुटिंग) ←B = 2.8 m→ φ = 30° γ = 18 kN/m³ C = 40 kN/m² 15 marks
10 cm के अंतर्गम व्यास के एक पाइप से 20°C पर जल प्रवाहित है और आगे यह 2·5 cm व्यास के एक वृत्ताकार नोजल से गुजरते हुए वायु में एक जेट की तरह बाहर निकलता है और चित्र में दर्शाए अनुसार एक उर्ध्वाधर प्लेट से टकराता है। प्लेट को स्थिर रखने के लिए एक बल, F = 100 N आवश्यक है। प्रवाह को अपरिवर्ती, घर्षण रहित, एक-विमीय प्रवाह और जल तथा पारे के घनत्व क्रमशः: 1000 kg/m³ और 13550 kg/m³ मानते हुए, निम्नलिखित के उत्तर दीजिए : परिच्छेद ① और ② पर वेग निर्धारित कीजिए।
जल की द्रव्यमान प्रवाह दर निर्धारित कीजिए।
पारा मैनोमीटर पाठ्यांक 'h' निर्धारित कीजिए। 20 marks
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 showing a pile group embedded in a three-layer cohesive soil profile:
- Ground level and water table: The ground level is at the top with a groundwater table symbol located at the ground surface.
- Soil strata (depths shown on the vertical 'Depth (m)' axis on the left):
- Top layer: Firm Clay of thickness 3 m (from depth 0 to 3 m), with properties Cu = 50 kN/m^2, alpha = 0.9, and gamma = 18 kN/m^3.
- Middle layer: Soft Clay of thickness 9 m (from depth 3 m to 12 m), with properties Cu = 30 kN/m^2, alpha = 1.0, and gamma = 16 kN/m^3.
- Bottom layer: Stiff Clay of thickness 5 m (from depth 12 m to 17 m), with properties Cu = 90 kN/m^2, alpha = 0.5, and gamma = 20 kN/m^3.
- Pile group:
- A pile cap is embedded in the top layer, with its base (cutoff level) at a depth of 2 m below the ground level (indicated by a vertical dimension of 2 m).
- A column extends upwards from the pile cap above the ground level.
- Three piles of the group are shown in elevation, extending from the cutoff level (depth 2 m) to the base of the stiff clay layer (depth 17 m), giving a total embedded pile length of 15 m (1 m in Firm Clay, 9 m in Soft Clay, and 5 m in Stiff Clay).
- Labelled on the right as 'Pile group'.
What "Solve" is asking you to do
Choose the method, then carry it through to a final answer. Identifying what kind of problem this is and why that method applies is the first thing marked; a correct figure arrived at invisibly earns almost nothing.
Structure that answers it
Given data and what is required → method chosen, with the reason it applies → set-up (equation, circuit, free body, trial balance) → working, step by step → answer with units and any condition of validity
Where marks are lost
Doing the middle steps mentally and writing only the result. In mathematics papers, a further loss comes from giving a decimal where the exact value in surds or fractions was wanted, or from skipping the justification a part explicitly asks for.
How this answer will be evaluated
Approach
Framework: null. (a) calculate: given > formula > substitution > result with units > interpretation | (b) calculate: given > formula > substitution > result with units > interpretation | (c(i)) calculate: given > formula > substitution > result with units > interpretation | (c(ii)) calculate: given > formula > substitution > result with units > interpretation | (c(iii)) calculate: given > formula > substitution > result with units > interpretation Full marks: Complete working with all steps shown, correct units, proper assumptions stated, and final answers with appropriate significant figures.
Key points expected
- Compute initial effective stress at clay center
- Determine void ratio from water content and Gs
- Calculate compression index (Cc) from liquid limit
- Apply one-dimensional consolidation settlement formula
- Apply Terzaghi's general shear failure equation for strip footing
- Calculate net ultimate and net allowable bearing capacity
- Determine load per meter using factor of safety 2.5
- Calculate percent decrease in bearing capacity for flooding
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a) Average settlement of the clay layer due to applied net stress. 15 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Compute initial effective stress at clay center
- Determine void ratio from water content and Gs
- Calculate compression index (Cc) from liquid limit
- Apply one-dimensional consolidation settlement formula
Loses marks
- Using total stress instead of effective stress
- Incorrect conversion of water content to void ratio
- Omitting the initial effective stress term in settlement formula
Earns more
- Correct calculation of saturated unit weight of clay
- Explicit statement of normally consolidated assumption
- Clear separation of sand and clay stress contributions
Extra mark
- Sketch of soil profile with stress distribution
- Verification of Cc value against empirical range
- (b) Ultimate bearing capacity, net values, allowable pressure, and load/m for strip footing. 15 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Apply Terzaghi's general shear failure equation for strip footing
- Calculate net ultimate and net allowable bearing capacity
- Determine load per meter using factor of safety 2.5
- Calculate percent decrease in bearing capacity for flooding
Loses marks
- Using wrong bearing capacity factors for strip footing
- Ignoring water table effect on unit weight in Nγ term
- Incorrect calculation of net allowable bearing pressure
Earns more
- Correct adjustment of unit weight for water table position
- Clear distinction between gross and net bearing capacity
- Proper handling of water table rise in flooding scenario
Extra mark
- Sketch of footing with water table positions
- Reference to specific IS code clause for bearing capacity
- (c(i)) Velocities at sections ① and ② of the pipe-nozzle system.
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Apply continuity equation for incompressible flow
- Calculate velocity at section ① using given diameter
- Calculate velocity at section ② using nozzle diameter
- Maintain consistent units throughout calculation
Loses marks
- Using diameter instead of area in continuity equation
- Inconsistent unit conversion between cm and m
- Ignoring the incompressibility assumption for water
Earns more
- Clear statement of assumptions (steady, frictionless, 1D flow)
- Correct conversion of diameters to areas
- Proper application of mass conservation principle
Extra mark
- Sketch of flow system with labeled sections
- Verification of velocity values against expected ranges
- (c(ii)) Mass flow rate of water through the system.
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Calculate mass flow rate using density and velocity
- Use correct cross-sectional area for flow calculation
- Apply appropriate density value for water at 20°C
- Express result in standard SI units (kg/s)
Loses marks
- Using wrong density value for water
- Incorrect area calculation from given diameter
- Unit inconsistency in final mass flow rate
Earns more
- Clear identification of which section to use for calculation
- Consistent use of velocity from part (i)
- Proper handling of density units (kg/m³)
Extra mark
- Cross-check using both sections to verify consistency
- Statement of assumptions about flow conditions
- (c(iii)) Mercury manometer reading 'h' for the given system.
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Apply Bernoulli's equation between sections ① and ②
- Calculate pressure difference from velocity difference
- Relate pressure difference to manometer reading
- Use correct density ratio for mercury-water system
Loses marks
- Incorrect application of Bernoulli's equation
- Wrong density ratio in manometer calculation
- Ignoring elevation differences if present in system
Earns more
- Clear application of energy conservation principle
- Proper handling of pressure head conversion
- Correct use of manometer equation with density ratio
Extra mark
- Sketch of manometer with labeled heights
- Verification of pressure difference calculation
Model answer coming soon
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