Engineering Hydrology (CE-802 (A)) - Unit 3 Short Notes

UNIT 3: FOUNDATION ENGINEERING

1.0 SUBSURFACE INVESTIGATION AND SOIL SAMPLING

1.1 Methods of Boring/Hole Advancement

• Percussion Boring (Shell & Auger): Impact-driven tool (shell) for cohesionless soils; auger for soft cohesive soils. Slow, disturbed samples.

• Rotary Drilling: Rotating core barrel with drilling fluid (bentonite mud/polymer) to cool bit, carry cuttings, stabilize borehole. Advantages: Fast, good for all soils/rock, undisturbed sampling possible.

• Other Methods:

  • Wash Boring: Jet of water loosens soil; unsuitable for sensitive soils.

  • Auger Boring: Hand/machine auger; shallow depths, disturbed samples.

  • Pressure Boring: (Percussion with water jet).

[!TIP] Exam Focus: Rotary drilling is most versatile. Know its tooling (core barrel, bits) and fluid functions.

1.2 Soil Sampling Techniques

• Disturbed vs. Undisturbed: Disturbed (structure altered) for classification; Undisturbed (preserved structure) for strength/compressibility.

• Sampling Tools:

  • Split Spoon (SPT): Disturbed, standard for SPT.

  • Shelby Tube: Thin-walled, pushed/rotated for undisturbed cohesive soils.

  • Piston Sampler: Advanced with piston for high-quality undisturbed samples.

• Key Parameters (for thin-walled tubes):

  • Inside Clearance (Ci): (Di - Dt) / Dt (1-3%). Allows sample expansion.

  • Outside Clearance (Co): (Dt - Do) / Do (<1%). Reduces friction.

  • Area Ratio (Ar): (Do² - Di²) / Di² * 100%. Should be < 10% for undisturbed.

  • Sample Quality: Assess by CNS (Clay, Non-plastic, Sand) layer at sample ends; disturbance reduces strength.

1.3 In-Situ Testing

• Standard Penetration Test (SPT):

  • Procedure: 30 cm blow count using 63.5 kg hammer, 75 cm drop, through split spoon.

  • N-value: Blows for last 30 cm penetration.

  • Corrections (Need: To compare results from different energies/overburdens):

    1. Overburden Pressure (K₀ or N₁): N₁ = N * (σ'ᵥ₀ / 0.1)^{0.5} (for sands).

    2. Dilatancy (N₂): For saturated fine sands/silts: N₂ = N * (15 / σ'ᵥ₀)^{0.5} (if N > 15).

    3. Energy Ratio (N₆₀): N₆₀ = N * (Eᵣ / 60%). Corrects to 60% theoretical energy.

  • Limitations: Disturbed sample, coarse gravel unreliable, operator dependent.

• Cone Penetration Test (CPT/SCPT):

  • Principle: Push 10-15 cm² cone at 20 mm/s. Measures qc (tip resistance), fs (sleeve friction), u (pore pressure).

  • Advantages over SPT: Continuous profile, quantitative, less disturbance, faster, detects thin layers.

  • Applications: Soil profiling, direct parameter estimation (e.g., qᵤ ≈ qc for clays, φ' from qc/fs ratio), liquefaction assessment.

• Other Tests:

  • Vane Shear Test: For soft clays (in-situ undrained shear strength cᵤ).

  • Pressuremeter Test: Measures soil modulus, limit pressure.

1.4 Geophysical Methods

• Seismic Refraction/Reflection: Measures seismic wave velocity → estimates depth to bedrock, soil stiffness.

• Electrical Resistivity: Measures soil resistivity → identifies strata, groundwater, contamination.

• Application: Rapid, economical for preliminary surveys; limited quantitative detail.

1.5 Bore-log Preparation and Reporting

• Components: Project info, method, depth, strata description (color, consistency, classification), sample data (type, depth, recovery), water table, test results (SPT N-value, lab tests).

• Graphical Representation: Stratum boundaries, sample depths, N-values, water table on a standardized log sheet.

1.6 Planning of Subsurface Exploration

• Depth: At least to bearing stratum or depth where σ'ᵥ₀ increase < 10% of applied stress. IS Criteria: Depth ≥ B (width) for isolated footing; ≥ 1.5B for rafts.

• Spacing: Grid pattern. IS Criteria: 1-2 per 400 m² for low-rise; 2-4 per 400 m² for high-rise. Closer near proposed foundation.

• Significant Depth: Depth at which additional exploration doesn't change design. Often taken as depth where qᵤ from deeper stratum > qᵤ from shallower stratum × FOS.

2.0 BEARING CAPACITY OF SHALLOW FOUNDATIONS

2.1 Fundamental Definitions

• Ultimate Bearing Capacity (qᵤ): Max pressure before shear failure.

• Net Ultimate Bearing Capacity (qₙᵤ): qᵤ - γD (excludes overburden pressure at footing base).

• Net Safe Bearing Capacity (qₙₛ): qₙᵤ / FOS.

• Allowable Bearing Pressure (qₐ): qₙₛ + γD (gross pressure allowed).

• Gross vs. Net Pressure: Gross includes overburden; Net is net increase due to structure.

2.2 Theories of Bearing Capacity

• Terzaghi's Theory (1943): Assumptions: Strip footing, c-φ soil, rough base, φ > 0, D/B ≤ 1, γD/qₙᵤ ≤ 1.

  Equation (Strip): qᵤ = cNc + γD Nq + 0.5 γB Nγ

  Shape Factors (for sq/circ): Nc' = 1.3 Nc, Nq' = 1.2 Nq, Nγ' = 0.8 Nγ (approx).

• IS Code (BIS) Method (Generalized):

$$qᵤ = c' Nc sc dc ic + γ D Nq sq dq iq + 0.5 γ B Nγ sγ dγ iγ$$

Where `s` = shape, `d` = depth, `i` = load inclination factors (see 2.3).

• Hansen/Vesic Modifications: Include ground inclination (g), base inclination (b), load inclination (i). Vesic uses Nγ' = 2(Nq + 1) tanφ'.

2.3 Factors Influencing Bearing Capacity

• Soil: c, φ, γ.

• Geometry: B, D, shape (strip, sq, rect, circ), L/B ratio.

• Load: Inclination (reduces capacity), eccentricity (reduces effective area).

• Water Table: Correction factors for γ (use γ' if WT at/base), u (pore pressure).

• Rate of Loading: Undrained (φᵤ=0°, cᵤ) for rapid loading on clays; Drained (c', φ') for slow loading/sands.

2.4 Bearing Capacity Calculations for Specific Cases

• Purely Cohesive (φ=0°): Terzaghi: qᵤ = 5.14 c + γD (strip), qᵤ = 5.7 c + γD (square). Nγ=0.

• Purely Cohesionless (c=0): qᵤ = γD Nq + 0.5 γB Nγ. Nq, Nγ from φ.

• Stratified Soils: Weak layer at base → use c, φ of weak layer for Nc, Nq; γ of top layer for Nγ term. Check for punching shear.

• Water Table Positions:

  • Far below: Use γ for all.

  • At footing base: qᵤ = cNc + γ'D Nq + 0.5 γ'B Nγ (use γ' for all γ).

  • At ground level: qᵤ = cNc + γ'D Nq + 0.5 γB Nγ (only D term uses γ').

2.5 Modes of Shear Failure

• General Shear: Dense soils/rock. Continuous failure surface to surface. Sudden failure, large settlements.

• Local Shear: Medium-dense soils. Failure surfaces develop only near footing. Progressive failure.

• Punching Shear: Very soft soils, rigid footings. Soil pushed down like a punch. No distinct failure surface.

2.6 Factor of Safety (FOS)

• Typical Values: 2.5-3.0 for cohesive soils (uncertain c), 3.0-4.0 for cohesionless (variable φ).

• Considerations: Reliability of soil parameters, structure importance, permissible settlement, consequences of failure.

3.0 SETTLEMENT OF SHALLOW FOUNDATIONS

3.1 Components of Total Settlement (S)

• Immediate/Elastic (Sᵢ): Due to shear distortion, occurs instantly in cohesionless & saturated clays (undrained).

• Primary Consolidation (S𝚌): Due to pore water expulsion in saturated clays (drained). Time-dependent.

• Secondary Consolidation (Sₛ): Due to plastic adjustment of soil skeleton after primary consolidation. Very slow.

3.2 Immediate Settlement Calculation

• Elastic Theory (Boussinesq/Westergaard): 3D stress distribution.

• Equation:

$$Sᵢ = \frac{q B (1 - μ²)}{Eₛ} I_f$$

Where `q` = net pressure, `B` = width, `μ` = Poisson's ratio, `Eₛ` = modulus of elasticity, `I_f` = influence factor (from tables for shape, `D/B`, `μ`).

• Limitations: Assumes linear elasticity, homogeneous soil. Applicable to sands & stiff clays; for soft clays, use Eₛ from undrained triaxial test (Eᵤ = 3cᵤ approx.).

3.3 Consolidation Settlement (Brief)

• One-Dimensional Theory (Terzaghi): Assumes drainage only vertically.

• Calculation (Void Ratio Method):

$$S_c = \frac{H}{1 + e₀} C_c \log_{10} \frac{σ'_f}{σ'_0}$$

Where `H` = thickness, `e₀` = initial void ratio, `C_c` = compression index, `σ'_0` = initial effective stress, `σ'_f` = final effective stress.

• Key: Determine C_c from oedometer test, find preconsolidation pressure (σ'_p).

3.4 Field Evaluation: Plate Load Test

• Setup: Steel plate (0.3-0.6 m²) at footing level, loaded incrementally, settlement measured.

• Interpretation: Load-settlement curve → ultimate bearing capacity (qᵤ(plate)).

• Scaling to Footing:

  • Bearing Capacity: qᵤ(footing) ≈ qᵤ(plate) for cohesive soils; qᵤ(footing) > qᵤ(plate) for cohesionless (size effect).

  • Settlement: For cohesive soils, S(footing) ≈ S(plate) (similar stress increase). For sands, S ∝ 1/B.

• Limitations: Size effect (plate smaller than footing), depth effect (test at surface vs. footing at depth), limited depth of influence.

4.0 PILE FOUNDATIONS

4.1 Introduction and Classification

• Need: Weak/compressible surface soils, high loads, scour, uplift.

• Classification:

  • Material: Concrete, steel, timber, composite.

  • Function: End bearing, friction, combined.

  • Installation: Driven (impact/vibratory), bored (cast-in-situ), drilled, screw.

4.2 Static Load Carrying Capacity of Single Pile (Qᵤ)

• General Expression: Qᵤ = Qₚ + Qₛ (End bearing + Shaft friction).

• End Bearing (Qₚ):

  • Cohesive: Qₚ = Aₚ * qᵤ (use qᵤ of bearing stratum).

  • Cohesionless: Qₚ = Aₚ * qᵤ (use qᵤ from bearing capacity theory).

• Shaft Friction (Qₛ):

  • α-method (Cohesive): Qₛ = α * cᵤ * (π d L)

    α = adhesion factor (0.5-1.0, decreases with cᵤ).

  • β-method (Cohesionless): Qₛ = β * σ'ᵥ₀ * K * tanδ * (π d L)

    β = factor (≈1), K = lateral earth pressure coefficient, δ = friction angle (≈φ).

• Negative Skin Friction (NSF):

  • Definition/Causes: Downward drag on pile due to settlement of surrounding soil (loose fill, lowering WT, soft compressible layer).

  • Calculation (Single Pile):

    NSF = (π d L) * γ * Δσ' * f

    Where f = adhesion factor (0.3-0.7 for clays, tanφ for sands), Δσ' = effective stress increase in compressible layer.

4.3 Dynamic Load Carrying Capacity

• Drop Hammer (Engineering News Formula):

  Qᵤ = \frac{W h}{s + 0.1} * \frac{W + n P}{W}

  W= hammer weight, h= fall, s= final set (cm/blow), P= pile weight, n= coefficient (1 for piles > 15m).

• Hiley's Formula (Better):

  Qᵤ = \frac{η W h}{s + 0.5 C}

  η = efficiency (hammer-pile-system), C = total elastic compression (pile+soil).

• Limitations: Empirical, needs calibration with static load test.

4.4 Pile Group Capacity

• Group Efficiency (η_g): η_g = Qᵤ(group) / (n * Qᵤ(single)).

• Block Failure (Closely spaced in clay):

  Qᵤ(group) = c * (B_g * L_g) + γ D * (B_g * L_g)

  Treats group as single large footing.

• Individual Pile Summation (Wide spaced): Qᵤ(group) = n * Qᵤ(single).

• Spacing: Typically 3d to 4d center-to-center. Affects group efficiency and settlement.

4.5 Settlement of Pile Groups

• Components: Settlement of individual pile (shaft + tip) + settlement of underlying soil mass (group action).

• Group Settlement: Often > n * S(single) due to overlapping stress bulbs.

4.6 Special Pile Types

• Under-reamed Piles:

  • Components: Shaft, under-reams (bulbs), top/bottom plugs.

  • Suitability: Expansive soils (counteract uplift), loose soils (increase tension capacity), soft rocks.

  • Ultimate Capacity (Tension/Compression):

    Qᵤ = Qₛ + Qᵤ(under-ream)

    Qₛ = α * cᵤ * (π d L) (shaft adhesion).

    Qᵤ(under-ream) = Aᵤ * qᵤ (base area of bulb × bearing capacity of soil at bulb level).

    Often neglect adhesion on under-ream bulb for tension.

• Micropiles: Small diameter (≤ 300 mm), high capacity, used in restricted access.

• Composite Piles: Combination (e.g., concrete filled steel tube).

5.0 LATERAL EARTH PRESSURE AND RETAINING STRUCTURES

5.1 Types of Lateral Earth Pressure

• At-rest (K₀): No lateral strain. K₀ = 1 - sinφ' (for normally consolidated clays/sands).

• Active (Kₐ): Wall moves away from soil → minimum pressure.

• Passive (Kₚ): Wall pushed into soil → maximum pressure. Kₚ = tan²(45° + φ'/2) (Rankine).

5.2 Classical Theories

• Rankine's Theory (1875):

  • Assumptions: Smooth wall, semi-infinite soil, horizontal backfill, φ > 0.

  • Cohesionless Active: σₕ = γ z Kₐ, Kₐ = tan²(45° - φ'/2).

  • Cohesive Active: σₕ = γ z Kₐ - 2c √Kₐ (tension crack if σₕ < 0).

  • Water Table: Use submerged unit weight γ' below WT, add pore pressure u to total stress.

• Coulomb's Theory (1776):

  • Assumptions: Wedge failure, planar surface, wall friction δ (≤ φ/2 to 2φ/3).

  • Derivation: Force equilibrium of wedge. Kₐ and Kₚ are functions of φ, δ, β (backfill slope).

  • Comparison: Coulomb more general (accounts for δ, sloping backfill). Rankine is special case (δ=0, β=0). Coulomb gives higher Kₐ (more realistic).

5.3 Graphical Methods

• Culmann's Graphical Construction: For irregular backfill profiles, surcharges, multiple strata. Construct failure wedges graphically to find maximum active pressure.

5.4 Earth Pressure on Retaining Walls

• Distribution:

  • Cohesionless: Linear from zero at top to γH Kₐ at base.

  • Cohesive: Parabolic (due to -2c√Kₐ term).

• Total Thrust (Pₐ): Area under pressure diagram.

  • Cohesionless: Pₐ = 0.5 γ H² Kₐ (acts at H/3 from base).

  • Cohesive: Pₐ = 0.5 γ H² Kₐ - 2c H √Kₐ (acts at H/3 from base for linear part; parabolic part centroid at H/6 from base).

• Surcharge: Add uniform pressure q → Pₐ(q) = q H Kₐ (acts at H/2).

• Stratified Backfill: Calculate pressure at stratum interfaces, draw diagram piecewise.

• Water Table with Seepage: Use γ' for soil below WT, pore pressure u = γ_w (z - z_w); total pressure = effective + pore pressure.

5.5 Design and Failure of Retaining Walls

• Modes of Failure:

  1. Overturning: Moment about toe > resisting moment. Check FOS ≥ 1.5.

  2. Sliding: Horizontal force > friction + cohesion. Check FOS ≥ 1.5.

  3. Bearing Capacity Failure: Excessive pressure on soil. Check q_max ≤ qₐ.

  4. Excessive Settlement/Differential Settlement.

• Tension Cracks (Cohesive Backfill): Depth zₜ where σₕ = 0:

  zₜ = 2c / (γ √Kₐ) (if zₜ < H). Cracks reduce pressure above zₜ.

5.6 Sheet Piles

• Definition: Interlocking vertical elements (steel, vinyl) driven into ground, supported by anchors/struts.

• Differentiation: Retaining walls are freestanding structures with base; sheet piles are flexible, rely on embedment and supports.

• Uses: Cofferdams, excavation support, waterfront bulkheads, slope stabilization.

6.0 SPECIAL FOUNDATIONS AND GROUND IMPROVEMENT TECHNIQUES

6.1 Raft (Mat) Foundations

• Need: Low bearing capacity, high loads, unequal settlement prevention (esp. on soft clays/expansive soils).

• Floating Foundation Concept: Excavated soil weight ≈ weight of structure → net increase in vertical stress ≈ zero.

• Proportioning: Thickness based on shear and punching shear; rigidity to distribute loads.

6.2 Well (Caisson) Foundations

• Components (Sketch):

  • Well curb: Bottom cutting edge.

  • Well steining: Masonry/concrete above curb, provides weight for sinking.

  • Cutting edge: Chisel-shaped steel.

  • Bottom plug: Seals bottom after reaching depth.

  • Top plug: Supports well cap.

  • Well cap: Distributes load from pier to well.

• Construction Stages: Sinking (dredging inside), sealing (bottom plug), dewatering, concreting.

• Types: Open (air chamber), Pneumatic (compressed air for working in dry bottom).

6.3 Geosynthetics

• Types & Functions:

  | Type | Function(s) | |----------------|--------------------------------------------------| | Geotextiles | Separation, Filtration, Reinforcement, Drainage | | Geogrids | Reinforcement (high tensile strength) | | Geomembranes | Containment (liners, covers) | | Geocomposites | Drainage (geonets, geocomposite drains) |

• Uses in Foundation Engineering: Reinforcement in weak soils (roadways, slopes), separation between dissimilar materials, drainage layers, protection for liners.

6.4 Soil Stabilization

• Objectives: Increase strength, reduce swell/shrinkage, reduce permeability, improve workability.

• Mechanical: Compaction, densification (vibro-compaction, dynamic compaction).

• Chemical: Lime, cement, fly ash (additives to alter soil chemistry).

• Electrical: Electro-osmosis (apply DC current to dewater/consolidate fine clays).

6.5 Field Compaction

• Equipment:

  • Smooth-wheeled: Sands, gravels.

  • Sheepsfoot: Cohesive soils (kneading action).

  • Pneumatic-tired: Medium soils, flexible layers.

  • Vibratory: Cohesionless soils (granular).

• Compaction Control:

  • Light Proctor (Standard): 2.5 kg hammer, 305 mm drop, 3 layers, 25 blows/layer. Energy ≈ 600 kN-m/m³.

  • Heavy Proctor (Modified): 4.9 kg hammer, 457 mm drop, 5 layers, 25 blows/layer. Energy ≈ 2700 kN-m/m³.

  • Comparison: Modified gives higher MDD, lower OMC. Used for field control (specify % of Modified MDD).

7.0 PROBLEMATIC SOILS AND FOUNDATIONS

7.1 Expansive Soils

• Characteristics: High clay content (montmorillonite), high shrink-swell potential, low strength when wet, high in dry season.

• Problems: Heave (wet), shrinkage cracks (dry), differential movement → structural damage (cracks, tilting).

• Preventive Measures:

  • Moisture control (maintain constant WT, wetting/drying barriers).

  • Under-reamed piles (best for heavy structures).

  • Raft foundations (spread load, bridge cracks).

  • Soil replacement/stabilization (lime/cement).

  • Deep foundations (piles) below active zone (typically 2-3 m).

7.2 Collapsible Soils

• Characteristics: Loose, dry, low-density deposits (loess, wind-blown silt), metastable structure (cemented bonds), sudden collapse upon wetting/loading.

• Problems: Sudden, non-uniform settlement → severe damage.

• Preventive Measures:

  • Pre-wetting: Saturate soil before construction to induce collapse.

  • Compaction (dynamic/static) to densify.

  • Pile foundations (transfer load through collapsible zone).

  • Chemical stabilization (lime, cement).

7.3 Other Problematic Soils (Brief)

• Loess: Wind-deposited silt, collapsible upon wetting. Similar measures as collapsible soils.

• Organic Soils (Peat): Very high compressibility, low strength, long-term settlement. Avoid if possible; use deep foundations or pre-consolidation.

> [!TIP] Exam-Winning Strategy:

1. Draw Neat Sketches for SPT, CPT, bearing capacity failure modes, Culmann's method, well components, under-reamed pile.

2. Memorize Key Formulas: Bearing capacity (Terzaghi/IS), pile capacity (α, β, NSF), immediate settlement, earth pressure (Rankine active).

3. Practice Numerical Types: From past papers: SPT corrections, bearing capacity with water table, pile group (block vs. individual), plate load test scaling, earth pressure on stratified backfill, under-reamed pile tension capacity.

4. Differentiate Clearly: SPT vs. CPT, Rankine vs. Coulomb, raft vs. well foundation, disturbed vs. undisturbed.

5. IS Code References: Mention IS 1892 (exploration), IS 6403 (boring/sampling), IS 8009 (bearing capacity), IS 2911 (piles) where relevant.