UNIT 1: FOUNDATION ENGINEERING (FOR BRIDGE APPLICATIONS)

I. SUBSURFACE EXPLORATION & SOIL INVESTIGATION

Significance & Planning

• Objective: To determine soil/rock profile, groundwater conditions, and obtain representative samples for lab testing to design safe, economical foundations.

• Significant Depth (IS Criteria): Exploration must reach a depth where the stress increase from foundation load is ≤ 10% of the effective overburden pressure at that depth. For bridge piers/abutments, depth should also consider scour depth and potential for differential settlement.

• Borehole Layout: For bridge substructures (piers, abutments), boreholes are typically placed at each proposed foundation location and intermediate points between them. Spacing depends on soil variability (closer for erratic strata).

Boring & Drilling Methods

Core Recovery & RQD:

• Core Recovery (%) = (Length of solid core recovered / Total length of core run) × 100

• Rock Quality Designation (RQD): RQD (%) = (Sum of lengths of core pieces > 100 mm / Total core run length) × 100. Used to assess rock mass quality.

Soil Sampling

• Disturbed Sample: Soil structure altered. Used for classification tests (sieve, hydrometer).

• Undisturbed Sample: Soil structure & moisture preserved. Used for strength (UCS, triaxial) and consolidation tests.

• Sampling Tube Parameters:

  • Inside Clearance (Ci): (Di - Do)/Do. Allows sample expansion. Typical: 0.5-1.5%.

  • Outside Clearance (Co): (Do - Dc)/Dc. Reduces friction. Typical: 0-0.5%.

  • Area Ratio (Ar): (Do² - Di²)/Di² × 100%. Should be < 10% for good recovery.

• CNS Layer Concept: A Constant Normal Stiffness layer simulates the restraint provided by surrounding soil during sampling, important for interpreting strength of soft clays.

In-Situ Testing

Standard Penetration Test (SPT)

• Procedure: Drive a split spoon sampler (50 mm ID) 450 mm into soil at bottom of borehole using a 65 kg hammer falling 750 mm. Record blows for each 150 mm penetration (N₁, N₂, N₃). Blow count (N-value) = blows for last 300 mm.

• Corrections:

  1. Overburden Pressure (N₁): N₁ = N × (σ'v₀ / 100 kPa)^0.5 (for σ'v₀ in kPa). Normalizes N to 100 kPa effective stress.

  2. Dilatancy (N₂): For dense sands/gravels below water table, N₂ = 15 + 0.5(N₁ - 15) if N₁ > 15. Corrects for pore pressure build-up.

  3. Energy (N₆₀): N₆₀ = N × (ER / 60%) where ER = actual hammer energy ratio. Most critical correction; all correlations use N₆₀.

• Limitations: Disturbed sample in granular soils; not reliable in very soft clays/gravels.

• Correlations: Relative density (Dr), friction angle (φ), undrained cohesion (cu).

Cone Penetration Test (CPT)

• Equipment: Continuous pushing of a 60° cone (10-15 cm² area) with friction sleeve at 20 mm/s. Measures tip resistance (qc) and sleeve friction (fs).

• Advantages over SPT: Continuous profile; quantitative, repeatable; provides friction ratio (Rf = fs/qc × 100%); detects thin layers; faster.

Plate Load Test

• Procedure: Load a rigid plate (typically 300-750 mm) at foundation depth, measure settlement.

• Settlement Prediction (Size Effect): For clay, settlement ∝ log(B). For sand, settlement ∝ 1/B.

  S₂ = S₁ × [log(B₂ / B₁)] (clay) or S₂ = S₁ × (B₁ / B₂) (sand).

• Ultimate Bearing Capacity (qu): From load-settlement curve (usually at settlement = 20% of plate width).

Bore-log Report

• Components: Project details, borehole location/depth, soil strata description (color, consistency, classification), water table depth, SPT N-values, lab test results, groundwater observations.

• Interpretation: Identify weak zones, depth to bearing stratum, estimate bearing capacity & settlement parameters for design.

II. SHALLOW FOUNDATIONS

Fundamental Concepts

Factors Affecting Capacity: Soil φ, c; footing size (B, L); depth (D_f); water table; load inclination; shape.

Bearing Capacity Theories

Terzaghi’s Theory (1943)

For strip, square, circular footings on general shear soil:

q_u = cN_c + qN_q + 0.5γBN_γ (strip)

q_u = 1.3cN_c + qN_q + 0.4γBN_γ (square)

q_u = 1.3cN_c + qN_q + 0.3γBN_γ (circular)

Where q = γD_f (effective surcharge).

IS Method (BIS: IS 6403)

General equation with shape (s_c, s_q, s_γ), depth (d_c, d_q, d_γ), and water table (W) factors:

q_u = cN_c s_c d_c W_c + q N_q s_q d_q W_q + 0.5γB N_γ s_γ d_γ W_γ

Bearing Capacity Factors (N_c, N_q, N_γ): Functions of φ (from tables/charts). For φ=0° (pure clay): N_c=5.7, N_q=1, N_γ=0.

Modes of Shear Failure

1. General Shear: Deep foundation, dense soil. Continuous failure surface to surface, distinct heave, sudden failure.

2. Local Shear: Medium dense soil. Failure surfaces develop only near footing, limited heave, gradual failure.

3. Punching Shear: Very shallow footing in loose soil. Soil punches into footing, no surface heave, gradual failure.

Settlement Analysis

Components:

1. Immediate (Elastic) Settlement (S_i): Immediate upon loading in cohesionless & saturated cohesive soils (undrained conditions).

2. Primary Consolidation (S_c): Gradual settlement due to pore water expulsion in saturated clays.

3. Secondary Compression (S_s): Post-consolidation settlement due to soil structure rearrangement.

Immediate Settlement in Cohesive Soils (Elastic theory, flexible footing):

S_i = (q B (1 - ν²) I_s) / E_s

Where:

• q = net pressure on footing

• B = footing width

• ν = Poisson’s ratio

• E_s = Modulus of elasticity of soil (from lab/empirical)

• I_s = Influence factor (from charts/tables based on L/B, D_f/B).

Footing Types & Design

• Isolated: Single column.

• Combined: Two or more columns.

• Strap: Connects isolated footings to distribute load.

• Raft (Floating): Covers entire area; used for low bearing capacity or heavy loads. Proportioning: Usually square; thickness ≥ 1/6 to 1/8 span; depth to width ratio ~ 0.5-0.75. Designed to reduce net pressure to ≤ allowable.

III. DEEP FOUNDATIONS (PILES & WELLS)

Pile Classification

• By Material: Concrete (precast/cast-in-situ), Steel (H-piles, pipe), Timber.

• By Function:

  • End-Bearing: Rest on hard stratum.

  • Friction (Floating): Shaft friction > toe resistance.

  • Combined: Both.

  • Tension (Uplift): Resist upward forces.

• By Installation:

  • Driven: Precast piles (displacement).

  • Bored/Cast-in-situ: Minimal displacement, suitable for sensitive sites.

  • Screw: Helical piles.

Pile Load Capacity

Static Formulas

• Clay (α-method): Q_u = α c_u A_s + q_b A_b

  • α = adhesion factor (0.5-1.0, decreases with depth/sensitivity)

  • c_u = undrained cohesion

  • A_s = shaft area

  • q_b = toe resistance = N_c c_u (for soft clay, N_c=9) or bearing capacity factor.

• Sand (β-method): Q_u = (σ'ₘ K tanδ) A_s + q_b A_b

  • σ'ₘ = avg effective vertical stress along shaft

  • K = earth pressure coefficient (0.5-1.0)

  • δ = friction angle (≈ φ - 5° to φ)

Dynamic Formulas (Hiley’s)

Q_u = (η W H) / (S + C/2)

Where:

• η = hammer efficiency

• W = hammer weight

• H = effective fall

• S = final settlement per blow

• C = total elastic compression (pile + cushion + soil)

• Allowable Load = Q_u / FOS

Pile Groups

• Group Efficiency (η_g): η_g = (Q_ug / n Q_u) where n = number of piles.

• Block Failure (cohesive soils): If spacing < ~3-4 diameters, group fails as a single block.

  Q_ug = c_u (B_g L_g) + γD_f (B_g L_g) N_c (for clay, ignoring shaft).

• Capacity Calculation (clay, no block failure): Q_ug = n Q_u + c_u (B_g L_g - n A_s) (accounting for overlap of stress bulbs).

• Example (3×3 group, square, spacing s):

  • Group width B_g = 2D + (n_row-1)s (for n_row=3: B_g = 2D + 2s)

  • Ultimate group capacity = n × Q_u (single) + c_u × (B_g² - n πD²/4) (if block failure not governing).

Special Piles

• Under-reamed Piles:

  • Components: Shaft + bulb(s) (under-ream) at one or more depths.

  • Suitability: Expansive/black cotton soils. Bulbs provide uplift resistance & anchorage against swelling.

  • Tensile Capacity: Q_t = n_b A_b c_u N_c + α c_u A_s (neglecting suction).

• Well Foundations (Caissons):

  • Components: Well curb (cutting edge), Steining (cylindrical wall), Well cap (top), Bottom plug, Sand filling.

  • Applications: Bridge piers in rivers/lakes (deep water, good scour resistance). Sunk by sinking/ excavation.

Negative Skin Friction (NSF)

• Causes: Loose fill, lowering water table, consolidation of surrounding soil causing downward drag on pile.

• Calculation (Single pile in clay):

  Q_nsf = α c_u A_s (for layer causing drag) or γ Δz K tanδ A_s (for granular drag layer).

  • Δz = depth of compressible layer.

  • Net Ultimate Capacity = Q_u (positive) - Q_nsf.

IV. EARTH RETAINING STRUCTURES

Lateral Earth Pressure Theories

Rankine’s Theory (1857)

• Assumptions: Semi-infinite soil, vertical wall, horizontal backfill, smooth wall (no friction), planar failure surface.

• Active Pressure (Cohesionless):

  σ_a = γz K_a - 2c √K_a (cohesive)

  K_a = tan²(45° - φ/2)

• Passive Pressure:

  σ_p = γz K_p + 2c √K_p

  K_p = tan²(45° + φ/2)

• At-Rest (Jakoby for cohesive):

  σ_0 = γz K_0 - 2c √K_0

  K_0 = 1 - sin φ (for cohesionless).

Coulomb’s Theory (1776)

• Assumptions: Planar failure surface, wall friction (δ) on failure plane, backfill inclined (β).

• Active Pressure Coefficient:

  K_a = [cos²(φ - δ)] / [cos²δ cos(δ+β) [1 + √(sin(φ+δ) sin(φ-β)/cos(δ+β))]²]

• Merits over Rankine: Considers wall friction (δ), inclined backfill (β), surcharge. More realistic for rough walls.

Graphical Methods

• Culmann’s Method: For active pressure with sloping, cohesionless backfill. Construct failure planes from wall toe at various angles; plot weight of wedge vs. pressure intercept. Envelope gives pressure diagram.

Retaining Wall Analysis

• Total Thrust (P_a): P_a = (1/2) K_a γ H² (level, cohesionless) + surcharge term.

• Point of Application: From base, H/3 (triangular), H/2 (uniform), varies for trapezoidal/with water.

• Distribution Diagrams:

  • Dry cohesionless: Triangular.

  • With water: Trapezoidal (submerged + buoyant unit weight above water table).

  • Stratified: Step diagram (different K_a, γ per layer).

• Example (Trapezoidal Masonry Wall): Calculate weight (W), moments about toe, check stability (FOS against overturning > 1.5, sliding > 1.5, bearing pressure < allowable).

Modes of Failure

1. Overturning: Wall rotates about toe.

2. Sliding: Horizontal thrust > friction resistance.

3. Bearing Capacity Failure: Excessive pressure on foundation soil.

4. Tension Cracks: At top of wall in cohesive backfill (active state).

Sheet Piles vs. Retaining Walls

V. SPECIAL SOILS & FOUNDATION PROBLEMS

Expansive Soils

• Characteristics: High montmorillonite clay content; high Liquid Limit (>50%), Plasticity Index; significant swell-shrink with moisture change.

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

• Preventive Measures:

  1. Under-reamed piles: Provide uplift resistance.

  2. Moisture Control: Impermeable barriers, landscaping, drainage.

  3. CNS Layer: Sand/gravel layer to maintain constant moisture.

  4. Lightweight structures, raft foundations.

Collapsible Soils

• Characteristics: Loose, metastable structure (often loess, windblown/water-laid); low density, high void ratio; susceptible to wetting-induced collapse.

• Problems: Sudden, large settlement upon wetting (e.g., from rain, broken pipes).

• Preventive Measures:

  1. Pre-wetting: Saturate before construction to induce collapse.

  2. Compaction: Dynamic compaction, heavy tamping.

  3. Replacement: Excavate and replace with good fill.

  4. Pile foundations to bypass collapsible zone.

VI. SOIL IMPROVEMENT TECHNIQUES

Soil Stabilization

• Mechanical: Compaction (increases density, reduces voids).

• Chemical: Lime, cement, fly ash (reduces plasticity, increases strength).

• Electrical: Electro-osmosis (applies DC current to move water in fine-grained soils).

Geosynthetics

Functions:

• Separation: Prevent mixing of dissimilar soils.

• Reinforcement: Tensile strength to resist deformation.

• Filtration: Allow water flow, retain soil particles.

• Drainage: Convey water within plane.

• Erosion Control: Protect surface from water/wind.

Compaction

• Field Equipment:

  • Smooth Wheel: Granular soils, finishing.

  • Sheepsfoot/Padfoot: Cohesive soils, deep compaction.

  • Pneumatic (Tire): All soils, uniform pressure.

• Proctor Tests:

  | Feature | Standard (Light) | Modified (Heavy) | | :--- | :--- | :--- | | Compactive Effort | 600 kN-m/m³ | 2700 kN-m/m³ | | Hammer Wt./Fall | 2.5 kg / 305 mm | 4.5 kg / 457 mm | | Layers/Blows | 3 / 25 | 5 / 25 | | Optimum Moisture | Higher | Lower | | Max Dry Density | Lower | Higher |

  *Used for field control (relative compaction = field density / max density × 100%).

VII. THEORETICAL STRESS DISTRIBUTION

Boussinesq’s Theory (1885)

• Assumptions: Elastic, isotropic, homogeneous, semi-infinite half-space; point load applied vertically at surface.

• Vertical Stress (σ_z) at point (r, z):

  σ_z = (3P / 2π) × (z³ / (r² + z²)^(5/2))

• Influence Charts: Based on I_z = σ_z / P (influence factor). For rectangular footing, use 2:1 distribution or Newmark’s influence chart.

• Derivation Concept: From equilibrium equations and compatibility in cylindrical coordinates.

Westergaard’s Theory (1938)

• Assumptions: Material contains numerous closely spaced, vertical, incompressible sheets (like stratified rock/clay). Stress distribution is more uniform with depth compared to Boussinesq.

• Vertical Stress:

  σ_z = (P / πz) × [1 / (1 + 2(r/z)²)]^(3/2) (for point load).

• Difference: Westergaard gives lower stresses near load axis, higher stresses at large r/z compared to Boussinesq. More applicable to stratified soils (clay laminations).

Influence Factors & 2:1 Distribution

• 2:1 Distribution: Simplest approximation. Stress spreads at 2V:1H from loaded area. At depth z:

  σ_z = q × (B × L) / ((B + z) × (L + z))

• Elastic Settlement Influence Factor (I_s): From charts (e.g., Janbu, Steinbrenner) for rectangular footing on elastic half-space.

[!TIP] EXAM FOCUS - HIGH FREQUENCY TOPICS

1. SPT Corrections (N₁, N₂, N₆₀) – Derivation not needed, but know purpose & formula.

2. Bearing Capacity – Terzaghi vs. IS method; shape/depth/water table factors; circular footing with water table (common problem).

3. Pile Groups – Block failure vs. individual; 3×3 group calculation (see past papers).

4. Settlement – Immediate settlement formula with I_s; plate load test size effect (clay vs. sand).

5. Earth Pressure – Rankine vs. Coulomb; trapezoidal wall with stratified backfill (step-by-step thrust calculation).

6. Under-reamed Piles – Components, tensile capacity formula (ignore suction as per problem).

7. Geosynthetics – Types & functions table (3-4 mark questions).

8. Negative Skin Friction – Single pile calculation in cohesive layer.

9. Well Foundations – Components with sketch (curb, steining, cap).

10. Boussinesq vs. Westergaard – Key difference in stress distribution pattern.

[!CAUTION] COMMON PITFALLS

• Bearing Capacity: Using gross pressure (q) instead of net (q_net) in formula; forgetting water table correction factor (W).

• SPT: Applying corrections in wrong order; using uncorrected N for correlations.

• Settlement: Using E_s from lab (undrained) for immediate settlement in sand (should use modulus from pressuremeter/empirical).

• Pile Groups: Forgetting to check block failure separately; misapplying adhesion factor for group.

• Earth Pressure: Using Rankine for sloping backfill (use Culmann/Coulomb); ignoring surcharge/water.

• Units: Consistent units (kN, m, kPa) – convert cm to m, mm to m in calculations.