GATE — Agricultural Engineering (AG) · India · IITs and IISc on rotation (2026: IIT Guwahati)
Original practice questions written to the published syllabus · not past papersSoil as an engineering material: its phases, flow of water through it, compaction, consolidation, shear strength and stability.
In the exams: GATE AG Section 4 (soil mechanics asked in 6 of 8 papers 2019–26); ICAR AIEEA-PG Unit IV; NCEES PE soils and foundations
GATE — Agricultural Engineering (AG), Section 4 Soil and Water Conservation Engineering
Numerical-answer and MCQ items: phase relations (e, n, S, γd from given masses and volumes), Atterberg indices, constant- and falling-head permeability, equivalent permeability of layered soils, seepage from flow nets and critical gradient, effective stress with a water table, Rankine active thrust with surcharge or water table, and the factor of safety of an infinite slope with and without seepage. Almost all require careful arithmetic and units.
How our questions for GATE spread across the units of Soil Mechanics. Difficulty: 34 easy, 42 medium, 24 hard.
| Terzaghi one-dimensional consolidation | 12 | |
| Permeability | 10 | |
| Shear strength and the Mohr-Coulomb criterion | 10 | |
| Earth pressure: active and passive (Rankine) | 10 | |
| Phase relations | 9 | |
| Slope stability, including infinite slopes | 9 | |
| Bearing capacity basics | 9 | |
| Index properties and soil classification | 8 | |
| Effective stress | 8 | |
| Compaction and the Proctor test | 8 | |
| Seepage and flow nets | 7 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A soil has a bulk unit weight of 19.0 kN/m³, a water content of 12% and G = 2.65. Taking γw = 9.81 kN/m³, what is its degree of saturation?
B. 0.597
γd = γ/(1 + w) = 19.0/1.12 = 16.96 kN/m³. e = Gγw/γd − 1 = 2.65 × 9.81/16.96 − 1 = 0.532. S = wG/e = 0.12 × 2.65/0.532 = 0.597. Using the bulk instead of the dry unit weight to find e gives e = 0.368 and S = 0.864; 0.318 is just wG with no division by e.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
A sand deposit has an in-situ void ratio of 0.62. Laboratory tests give a maximum void ratio of 0.85 and a minimum void ratio of 0.45. What is its relative density?
D. 57.5%
Dr = (emax − e)/(emax − emin) = (0.85 − 0.62)/(0.85 − 0.45) = 0.23/0.40 = 57.5%, a medium-dense sand. 42.5% comes from putting emin in the numerator, which measures looseness instead of density. 27.1% divides by emax alone (0.23/0.85), and 72.9% is e/emax (0.62/0.85).
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
In a hydrometer analysis, how long does a spherical particle of diameter 0.01 mm and specific gravity 2.65 take to settle 100 mm in water of viscosity 1.0 × 10⁻³ Pa·s (γw = 9.81 kN/m³)?
B. 18.5 min
Stokes' law: v = (γs − γw)D²/(18μ) = (2.65 − 1) × 9810 × (1.0 × 10⁻⁵)²/(18 × 10⁻³) = 8.993e-05 m/s. Time = 0.1/v = 1112 s = 18.5 min. Using γs instead of (γs − γw) ignores buoyancy and gives 11.5 min; the other options are factor-of-ten unit slips.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
In a falling-head test, the standpipe area is 1.0 cm², the specimen is 10 cm long with an area of 50 cm², and the head falls from 100 cm to 50 cm in 600 s. What is k?
D. 2.31e-04 cm/s
k = (aL/(At))·ln(h1/h2) = (1.0 × 10)/(50 × 600) × ln 2 = 3.333e-04 × 0.693 = 2.31e-04 cm/s. Using log10 without the 2.303 factor gives 1.00e-04; swapping the standpipe and specimen areas gives an absurdly high 5.78e-01.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
If the compactive effort applied to a soil is increased, how do its maximum dry density and optimum moisture content change?
D. Maximum dry density rises; optimum moisture content falls
More energy packs the grains more closely with less water needed for lubrication, so the curve moves up and to the left. This is why the modified Proctor test gives a higher maximum dry density at a lower optimum than the standard test.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
A soil (G = 2.70) has a standard Proctor maximum dry unit weight of 17.5 kN/m³ at an optimum moisture content of 16%. With γw = 9.81 kN/m³, what is the percentage air voids at optimum?
C. 5.4%
e = Gγw/γd − 1 = 2.70 × 9.81/17.5 − 1 = 0.5135. S = wG/e = 0.16 × 2.70/0.5135 = 0.841. n = e/(1 + e) = 0.3393. na = n(1 − S) = 5.4%, within the few-per-cent range typical at optimum. 15.9% is air content (fraction of voids), not air voids (fraction of total volume). 8.2% uses e instead of n (0.5135 × 0.159); 84.1% is the degree of saturation.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
Which assumption underlies Rankine's earth pressure theory?
D. The back of the wall is vertical and perfectly smooth
Rankine assumed a smooth vertical wall so that the stresses in a semi-infinite soil mass in plastic equilibrium apply directly. Wall friction is included in Coulomb's wedge theory; the log-spiral surface is used in more refined passive calculations.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
What is the steepest slope angle for a long, dry cohesionless embankment face (φ′ = 35°) if a factor of safety of 1.5 is required?
C. 25.0°
F = tanφ′/tanβ, so tanβ = tan35°/1.5 = 0.4668 and β = 25.0°. Dividing the angle directly (35/1.5 = 23.3°) is not the same because tan is not linear. 35° gives F = 1. 46.4° multiplies tanφ′ by 1.5 instead of dividing.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
A plate load test with a 0.3 m square plate on a deep, uniform dense sand gives an ultimate bearing pressure of 400 kPa. By the usual plate-load relation for sand, what is the ultimate bearing capacity of a 1.5 m square footing at the same level?
A. 2000 kPa
For sand the ultimate capacity from the γBNγ term is proportional to width: qf = qp × Bf/Bp = 400 × 1.5/0.3 = 2000 kPa. 400 kPa (no scaling) applies to clays, where capacity does not depend on width. The test reflects only soil within about twice the plate width, so deeper weak layers must be checked separately. 80 kPa inverts the width ratio (400 × 0.3/1.5), and 10000 kPa squares it (400 × 25).
Further reading: IS 1888; Punmia, Jain and Jain, Soil Mechanics and Foundations
How does compaction differ from consolidation?
D. Compaction expels air quickly by mechanical energy; consolidation slowly expels water from saturated soil under sustained load
Compaction is a rapid densification of partly saturated soil by rolling, tamping or vibration that reduces air voids. Consolidation is the gradual volume decrease of a saturated soil as pore water drains under a sustained load, governed by permeability.
Further reading: Das and Sobhan, Principles of Geotechnical Engineering
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