JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year SOIL MECHANICS Previous Question Paper (March - 2021 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Discuss the three phase diagram for soil and derive the expression,
Answer
A soil mass is a three-phase system consisting of soil solids, water, and air. The three-phase diagram represents these components by volume (Va, Vw, Vs) and weight (Wa, Ww, Ws). Since the weight of air is negligible (Wa = 0), the total weight W = Ws + Ww, and the total volume V = Va + Vw + Vs.
To derive the relationship e s = G w:
- By definition, void ratio e = Vv / Vs, where Vv = Va + Vw.
- Degree of saturation s = Vw / Vv, which implies Vw = s Vv = s e Vs.
- Water content w = Ww / Ws.
- Specific gravity of solids G = γs / γw = (Ws / Vs) / γw, which implies Vs = Ws / (G γw).
- Substituting Vw into the water content formula: w = Ww / Ws = (Vw γw) / Ws.
- Since Ws = G Vs γw, we have w = (s e Vs γw) / (G Vs γw).
- Canceling Vs and γw yields w = (s e) / G, which rearranges to e s = G w.
The dry unit weight of a sand sample in the loosest state is 13.50 kN/m3 and in the densest state, it is 21.25 kN/m3. Determine the density index of this sand when it has a porosity of 35%. Assume the grain specific gravity as 2.70.
Answer
Given: γd(min) = 13.50 kN/m3, γd(max) = 21.25 kN/m3, n = 35% (0.35), G = 2.70. Assume γw = 9.81 kN/m3.
- Calculate the void ratio at the current state (e): n = e / (1 + e) => 0.35 = e / (1 + e) => e = 0.35 / 0.65 = 0.5385.
- Calculate emax using γd(min): γd(min) = (G γw) / (1 + emax) => 13.50 = (2.70 * 9.81) / (1 + emax) => 1 + emax = 26.487 / 13.50 = 1.962 => emax = 0.962.
- Calculate emin using γd(max): γd(max) = (G γw) / (1 + emin) => 21.25 = 26.487 / (1 + emin) => 1 + emin = 26.487 / 21.25 = 1.246 => emin = 0.246.
- Density Index (ID) = (emax - e) / (emax - emin) = (0.962 - 0.5385) / (0.962 - 0.246) = 0.4235 / 0.716 = 0.5915.
The density index is 59.15%.
Define the following: Liquidity index, flow index and write their importance.
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A sample of saturated soil has a water content of 40%. The specific gravity of soil solids is 2.70. Determine its void ratio, porosity, saturated unit weight and dry unit weight.
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Define Darcy’s law and discuss the situations where it is valid.
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Determine the average horizontal and vertical permeability of a soil mass made up of three horizontal strata, each have thicknesses 1m, 1.5m and 2m respectively. The respective coefficient of permeability of these layers are
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Discuss the following: (i) quick sand condition (ii) piping phenomenon.
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For a homogeneous earth dam having water head 30m, a flow net was constructed with four flow channels. The number of potential drops was 16. The dam has a horizontal filter at the base near the toe. The coefficient of permeability of the soil was
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Discuss the merits of the following: a) Smooth wheel rollers, b) pneumatic tyred rollers and c) sheep foot rollers.
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Using Boussinesq’s expression, derive the expression for vertical stress at depth ‘z’ under the centre of a circular area of radius, ‘r’ loaded uniformly with a load ‘q’ at the surface of the mass of soil.
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A raft of the size 4m × 4m carries a uniform load of
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Define preconsolidation pressure and discuss the reasons for preconsolidation to occur in soils.
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A 20mm thick sample of clay was taken from field for predicting the times of settlement for a proposed building which exerts a uniform pressure of
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Discuss the benefits of conducting triaxial compression test.
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The following data relate to a triaxial compression tests performed on a soil sample. Determine the shear parameters such as cohesion and angle of internal friction from the above data using the relation of
| Test No. | Cell Pressure (σ3), kPa | Maximum Deviator Stress (σd), kPa |
|---|---|---|
| 1 | 80 | 175 |
| 2 | 150 | 240 |
| 3 | 210 | 300 |
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