(SEM V) THEORY EXAMINATION 2024-25 GEOTECHNICAL ENGINEERING

Subject Code: BCE501
Maximum Marks: 70
Time: 3 Hours
Paper ID: 310116

Question Paper Overview

SECTION A (2 × 7 = 14 Marks)

(Short, conceptual questions — theory fundamentals and key terms)

a. List the three main phases of soil composition.
b. Define flocculated and dispersed soil structures.
c. State Darcy’s Law and explain the significance of hydraulic conductivity.
d. Write two measures to control seepage in earth dams.
e. State the assumptions of Terzaghi’s one-dimensional consolidation theory.
f. Differentiate between a direct shear test and a triaxial shear test.
g. State the difference between active and passive earth pressure.

SECTION B (Attempt any three × 7 = 21 Marks)

(Numerical and descriptive analytical questions)

a. Explain the significance of Atterberg limits (liquid, plastic, and shrinkage limits). Describe their determination and use in soil classification.
b. A partially saturated soil (Sr = 80%) has unit weights 18 kN/m³ (above water table) and 20 kN/m³ (below). Compute effective stress at 4 m depth with a water table at 2 m.
c. Explain the Proctor needle method and its significance in compaction quality control.
d. Describe the Mohr–Coulomb failure criterion in detail.
e. Discuss Coulomb’s theory of earth pressure and derive the active earth pressure expression considering wall friction. Compare with Rankine’s theory.

SECTION C (Attempt one part from each question × 7 = 35 Marks)

Q3
(a) Classify kaolinite, illite, and montmorillonite based on structural and engineering behaviour. Why is montmorillonite problematic in construction?
OR
(b) A soil has porosity = 40% and is fully saturated. If G = 2.65, calculate saturated and submerged unit weights.

Q4
(a) Explain total stress, effective stress, and neutral stress in soils, their interrelationships, and significance in design.
OR
(b) Derive the expression for critical hydraulic gradient and explain its physical meaning.

Q5
(a) A 6 m clay layer is loaded with 40 kPa, having Cv = 5×10⁻⁴ cm²/s, and drainage on both sides. Compute the time for 50% consolidation.
OR
(b) Differentiate between primary and secondary consolidation. Explain mechanisms and time scales.

Q6
(a) Examine liquefaction mechanisms and influencing factors.
OR
(b) Using Boussinesq’s equation, compute the vertical stress at depth z = 3 m and radial distance r = 4 m under a 200 kN point load.

Q7
(a) Derive Rankine’s active earth pressure for a c–ϕ soil (cohesive-frictional).
OR
(b) Illustrate Coulomb’s graphical method for earth pressure distribution in retaining walls.

Key Topics for Revision

1. Soil Composition and Structure

Phases of soil: Solids, water, air.

Soil structures:

Flocculated: Edge-to-face, common in clays (high shear strength, compressible).

Dispersed: Face-to-face, uniform, lower permeability.

2. Permeability and Seepage

Darcy’s Law:
q=k⋅i⋅Aq = k \cdot i \cdot Aq=k⋅i⋅A
where kkk = hydraulic conductivity.

Seepage Control:

Clay cores in dams

Grouting, cutoff walls, filters.

3. Soil Consistency Limits (Atterberg Limits)

Liquid limit (LL): Boundary between liquid and plastic state.

Plastic limit (PL): Boundary between plastic and semi-solid state.

Shrinkage limit (SL): Boundary between semi-solid and solid state.

Plasticity Index (PI) = LL − PL.

Used for soil classification and workability assessment.

4. Consolidation

Terzaghi’s 1D Consolidation Theory Assumptions:

Soil homogeneous, fully saturated.

Flow vertical only.

Darcy’s law valid.

Compression proportional to effective stress.

Primary consolidation: Expulsion of pore water.

Secondary consolidation: Creep and plastic readjustment over time.

5. Shear Strength

Mohr–Coulomb equation:
τ=c+σ′tan⁡ϕ\tau = c + \sigma' \tan \phiτ=c+σ′tanϕ
where ccc = cohesion, ϕ\phiϕ = angle of internal friction.

Tests:

Direct shear test: Simple, quick, plane of failure predefined.

Triaxial test: Versatile, allows drainage control and stress path analysis.

6. Effective Stress

Total stress (σ) = Effective stress (σ′) + Pore water pressure (u)
σ′=σ−u\sigma′ = \sigma - uσ′=σ−u

Controls strength, compressibility, and stability of soil structures.

7. Liquefaction

Occurs when saturated loose sand loses strength during earthquake shaking.

Influenced by: density, confining pressure, cyclic loading, grain size, water content.

Prevention: densification, drainage, soil improvement.

8. Earth Pressure Theories

Rankine’s Theory: Considers only soil parameters (no wall friction).

Coulomb’s Theory: Includes wall friction and wall inclination.

Active Pressure (Pa): Wall moves away → soil expands.

Passive Pressure (Pp): Wall moves toward soil → soil compresses.

9. Boussinesq’s Stress Distribution

For a point load Q on the surface:

σz=3Q2πz2⋅1(1+(r/z)2)5/2\sigma_z = \frac{3Q}{2\pi z^2} \cdot \frac{1}{(1 + (r/z)^2)^{5/2}}σz​=2πz23Q​⋅(1+(r/z)2)5/21​ 

10. Clay Minerals

11. Seepage & Critical Hydraulic Gradient

ic=G−11+ei_c = \frac{G - 1}{1 + e}ic​=1+eG−1​

Failure occurs when upward seepage equals submerged weight (quick sand condition).

12. Ground Improvement & Compaction

Proctor Test: Determines optimum moisture content (OMC) and maximum dry density (MDD).

Proctor Needle Method: Field control tool for checking compaction level.

Exam Tips

Draw clear diagrams for flow nets, Mohr circles, stress distribution, and earth pressure wedges.

Memorize key formulas with SI units.

Prepare numerical examples for consolidation, effective stress, and Boussinesq problems.

Revise assumptions and limitations of main theories (Terzaghi, Rankine, Coulomb).