Bridge Engineering (CE-802 (C)) - Unit 5 Short Notes

UNIT 5: FOUNDATION ENGINEERING FOR BRIDGE STRUCTURES

1.0 Site Investigation and Subsurface Exploration for Bridges

1.1 Objectives and Planning

• Primary Objective: To determine the strata sequence, engineering properties (strength, compressibility), and groundwater conditions to design safe, economical foundations.

• Planning: Based on bridge type, span, load magnitude, and site geology. Determines depth, spacing, and number of boreholes. For major bridges, boreholes at each pier/abutment location are mandatory.

1.2 Boring Methods

[!TIP] Exam Focus: Rotary drilling is most common for bridge projects due to depth and stability requirements. Auger boring is suitable only for shallow, dry, cohesive sites.

1.3 Sampling Techniques

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

• Undisturbed Sample: Soil structure preserved (as close to in-situ as possible). Used for strength (triaxial, direct shear) and consolidation tests.

• Sampling Tube Parameters:

  • Inside Clearance (Ci): (Di - Do)/Do. Allows sample expansion, reduces suction. Optimal: 0.5-1.5%.

  • Outside Clearance (Co): (Do - Dc)/Dc. Reduces friction during driving. Optimal: 0-2%.

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

  • Di = Inside diameter, Do = Outside diameter, Dc = Cutting edge diameter.

• Sample Quality: Assessed by length/diameter ratio (L/D > 2), visual examination, and laboratory recompression curve.

1.4 In-situ Tests

• Standard Penetration Test (SPT):

  • Procedure: Drive a split spoon sampler (50 mm ID) with a 65 kg hammer falling 750 mm. Count blows for first 150 mm (seating), next 300 mm (N-value).

  • N-value: Blows per 300 mm penetration. Raw indicator of relative density/consistency.

  • Corctions:

    1. Overburden Pressure Correction (N₁): N₁ = N × (σ'v₀ / 0.1 MPa)^0.5 (for cohesionless soils). Normalizes N to 1 atm overburden.

    2. Dilatancy Correction (N₂): For dense sands/gravels below water table. N₂ = 15 + (N₁ - 15)/2 if N₁ > 15.

  • Corrections are applied to make N-value comparable across different depths and soil types.

• Cone Penetration Test (CPT): Push a cone (10 cm², 60° apex) at 20 mm/s. Measures tip resistance (qc) and sleeve friction (fs) continuously. Provides excellent stratigraphy and strength profiles.

• Seismic CPT (SCPT): Adds downhole geophone to measure shear wave velocity (Vs) for small-strain stiffness.

• Plate Load Test:

  • Procedure: Load a rigid plate (0.3 m² typical) at foundation depth, measure settlement.

  • Interpretation:

    • Clay: Plot load-settlement, determine ultimate bearing capacity (qu) from curve or qu = P/A at large settlement. Settlement is primarily consolidation.

    • Sand: Settlement is primarily immediate (elastic). Use S = (qB/I)(1-ν²)/E_s with influence factor I from charts.

  • Settlement Prediction: For different size footing on clay, use square root scaling: (S₂/S₁) = √(B₂/B₁). For sand, use linear scaling: (S₂/S₁) = (B₂/B₁).

1.5 Borelog Preparation and IS Criteria

• Depth of Boreholes (IS 1892):

  • Should penetrate at least 3 m into bedrock or 2-3 pile lengths below anticipated foundation level.

  • Minimum depth = 1.5 to 2 times the width of the foundation.

  • Must penetrate below the zone of influence of the foundation (approx. 2B to 4B below base).

• Spacing: Based on soil variability. For uniform sites, spacing = 1.5 to 2 times foundation width. For variable sites, closer spacing.

• Borelog Report Components:

  1. Borehole location plan.

  2. Stratigraphic column with depth, description, sample type, SPT N-value, water table.

  3. Laboratory test results (moisture, density, strength, compressibility).

  4. Summary sheet with key parameters per layer.

  5. Recommendations for foundation type and capacity.

2.0 Soil Strength Parameters and Shear Failure

2.1 Shear Strength Envelope

• Mohr-Coulomb Failure Criterion: τ_f = c + σ' tan φ

  • τ_f = shear strength at failure

  • c = cohesion (intercept)

  • σ' = effective normal stress on failure plane

  • φ = angle of internal friction

2.2 Modes of Shear Failure

2.3 Factors Affecting Bearing Capacity

General equation: q_ult = c'N_c + qN_q + 0.5γBN_γ (Terzaghi for strip footing).

• Shape Factors: Increase N_c, N_q for square/rectangular; decrease N_γ.

• Depth Factor: Increases capacity with depth (D > B/2 often negligible).

• Load Inclination: Reduces capacity for inclined/horizontal loads.

• Ground Surface Inclination: Reduces capacity for sloping ground.

• Water Table: Reduces effective unit weight (γ' = γ_sat - γ_w) and hence qN_q and 0.5γBN_γ terms. Correction factors R_w1, R_w2 applied.

3.0 Shallow Foundations for Bridge Components

3.1 Types

• Isolated Spread Footing: For individual bridge piers/columns.

• Combined Footing: For closely spaced columns.

• Raft/Mat Foundation: For abutments on weak soil or where settlement control is critical. Floating Foundation is a special raft where excavated soil weight equals superstructure weight, minimizing net increase in pressure.

3.2 Bearing Capacity Analysis

• Terzaghi's Theory (1943): Assumes general shear failure, depth/width ratio D/B ≤ 1, rigid footing. Provides N_c, N_q, N_γ for strip, square, circular footings.

• BIS Method (IS 6403): Based on Vesic (1975). More accurate for local shear. Uses shape, depth, load inclination, ground inclination factors.

  • Ultimate Capacity: q_ult = c'N_c d_c f_c + qN_q d_q f_q + 0.5γBN_γ d_γ f_γ

  • d_c, d_q, d_γ = depth factors

  • f_c, f_q, f_γ = shape factors

• Net vs. Gross:

  • Gross Ultimate (q_ult): Total pressure at failure.

  • Net Ultimate (q_nu): q_nu = q_ult - γD (excludes overburden pressure).

  • Net Safe Bearing Capacity (q_ns): q_ns = q_nu / FOS.

  • Allowable Bearing Pressure (q_a): q_a = q_ns + γD (includes overburden).

• Water Table Correction: If water table at depth Dw from base:

  • For Dw < B: R_w1 = 0.5 + 0.5 (Dw/B) (for γBN_γ term)

  • For Dw < D: R_w2 = 1 - 0.5 (Dw/D) (for qN_q term)

3.3 Settlement Analysis

• Components:

  1. Immediate (Elastic) Settlement (S_i): Due to shear distortion, occurs instantly. Calculated using elastic theory (Boussinesq) with influence factor (I).

     • S_i = (q B / E_s) (1 - ν²) I

     • I depends on footing shape and L/B ratio (from charts).

  2. Primary Consolidation Settlement (S_c): Due to expulsion of pore water from saturated cohesive soils. One-dimensional Terzaghi theory.

     • S_c = (C_c / (1 + e₀)) H log₁₀(σ'₀ + Δσ' / σ'₀)

  3. Secondary Consolidation (S_s): Post-primary, due to soil structure adjustment. Significant in organic clays.

  4. Total Settlement (S_total): S_i + S_c + S_s.

• Critical Neutral Surface (CNS) Layer: In layered clay, the layer where change in vertical stress (Δσ') is maximum relative to preconsolidation pressure (σ'_p). Settlement calculation often focuses on this layer.

• Allowable Settlement for Bridge Decks: Total ≤ 75 mm, Differential ≤ L/800 (where L = span). More stringent than buildings due to serviceability of deck.

3.4 Proportioning of Raft Foundations**

• Aim: To achieve uniform pressure distribution.

• Method: Assume linear stress distribution. Equate moment of loads about centerline to moment of soil pressure.

• Check: Eccentricity e = M/P must be < B/6 (for rectangular footing) to avoid tension. If e > B/6, pressure diagram is trapezoidal with zero at one edge.

4.0 Deep Foundations: Piles for Bridge Piers and Abutments

4.1 Classification

4.2 Single Pile Load Carrying Capacity (Q_u)

• Static Formulae (Based on Soil Parameters):

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

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

    • c_u = undrained cohesion (average along shaft)

    • A_p = base area, A_s = shaft area

  • Sand (β-method): Q_u = q N_q A_p + f_s A_s

    • f_s = K σ'₀ tan δ or f_s = β σ'₀ (β-method)

    • K = earth pressure coefficient, δ = friction angle (soil-pile)

  • λ-method (Broms): For clays, Q_u = (λ c_u) A_s + 9 c_u A_p (λ depends on pile type/installation).

• Dynamic Formulae (Based on Blow Counts):

  • Engineering News (EN) Formula: Q_safe = (W H e) / (s + C) / FOS

    • W = hammer weight, H = fall, e = efficiency (0.6-0.8), s = final settlement per blow, C = constant (25 mm for drop hammer).

  • Hiley's Formula: Q_safe = (η W H) / (s + 0.5C) / FOS (η accounts for pile/hammer/ram/cushion efficiency).

• CPT-based Correlations: Directly use q_c and f_s from CPT to estimate q_p and f_s for pile.

4.3 Pile Groups

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

  • Clay: η_g ≈ 1.0 for spaced groups (s/B ≥ 3). Block Failure occurs for close spacing (s/B < 3), where group capacity < sum of individuals.

  • Sand: η_g < 1.0 (typically 0.6-0.8) due to overlapping stress bulbs.

• Settlement of Pile Groups: Often governs design, not capacity. Settlement of group > settlement of single pile at same load. Must be analyzed as a raft on piles or using equivalent pier method.

• Spacing: Minimum 3d (clay) to 4d (sand) center-to-center to minimize interaction. Pile cap dimensions extend beyond outer piles by ≥ 150 mm or ≥ 0.5d.

• Design: Group capacity = min(η_g × n × Q_u, Block Failure Capacity).

4.4 Negative Skin Friction (NSF)

• Causes: Downward movement of soil relative to pile.

  1. Fill/Embankment Loading: New fill compresses, dragging soil down.

  2. Groundwater Drawdown: Lowers phreatic surface, increases effective stress, causes consolidation.

  3. Liquefaction: Loose saturated sand loses strength, settles.

• Calculation:

  • NSF Force (per unit area): f_ns = K σ'₀ tan δ or f_ns = β σ'₀ (similar to positive skin friction).

  • Depth of NSF Zone: From new ground surface down to neutral plane where soil settlement equals pile settlement.

  • Total NSF (single pile): Q_ns = Σ (f_ns × π d × Δz) over critical layer(s).

  • Pile Group: Add group effect (overlapping zones). Often conservatively taken as full perimeter of group block.

• Mitigation: Use smooth pile surfaces (bitumen coating), pre-bore oversized hole and fill with sand/bentonite, use lightweight fill, preload site before piling.

4.5 Under-reamed Piles

• Concept: Single or multi-bulbed enlarged bases (under-reams) on a bored pile shaft. Acts as anchor in expansive soils.

• Components: Shaft, under-ream bulbs (diameter 2-3× shaft), neck (between bulbs), pilot hole.

• Suitability for Expansive Soils: Bulbs provide tensile resistance against swelling pressure and uplift capacity.

• Ultimate Tensile Capacity (T_u): (Neglecting suction/adhesion)

  • T_u = (π d_l L_l c_u α) + Σ (π D_b²/4 × c_u × N_c)

  • d_l = shaft diameter in active zone, L_l = length in active zone, α = adhesion factor.

  • D_b = bulb diameter, N_c = bearing capacity factor (≈ 9 for clay).

4.6 Design Examples (Layered Soils)

• Step 1: Identify soil layers and properties (c_u, φ, γ).

• Step 2: Assume pile length L and penetration into bearing stratum.

• Step 3: Calculate shaft friction in each layer:

  • Clay: Q_s = α_i c_ui × π d × Δz_i

  • Sand: Q_s = β_i σ'₀i tan δ × π d × Δz_i

• Step 4: Calculate end bearing:

  • Clay: Q_b = N_c c_ub A_p (use c_u at pile tip)

  • Sand: Q_b = q N_q A_p (use q = γ' D or γ D if dry)

• Step 5: Q_u = Q_s + Q_b. Apply FOS (3 for static, 2.5 for dynamic) to get safe load.

• Step 6: Check tension (if applicable) and lateral capacity.

5.0 Earth Pressure and Retaining Structures for Bridges

5.1 Types of Earth Pressure

• At-rest (K₀): Wall does not move. K₀ = 1 - sin φ' (for cohesionless, normally consolidated).

• Active (Ka): Wall moves away from soil. Minimum pressure. K_a = tan²(45° - φ'/2) (Rankine, for cohesionless).

• Passive (Kp): Wall moves into soil. Maximum pressure. K_p = tan²(45° + φ'/2) (Rankine).

5.2 Earth Pressure Theories

[!TIP] Exam Focus: For bridge abutments with sloping backfill or rough walls, Coulomb's theory is more realistic. Rankine is simpler for level, smooth backfills.

5.3 Earth Pressure Calculations

• With Surcharge (q): Add q K_a (uniform) or γ_z K_a (strip surcharge) to pressure diagram.

• With Water Table:

  • Submerged: Use submerged unit weight (γ') and water pressure separately. Total pressure = submerged earth pressure + pore water pressure.

  • Seepage (downward): Increases effective stress, hence pressure. σ' = γ' z + i γ_w z (where i = hydraulic gradient).

• Stratified Backfills: Calculate pressure at layer interfaces. Use weighted average K_a or Culmann's method for accuracy.

• Distribution Diagrams:

  • Cohesionless: Linear with depth (from γ z K_a).

  • Cohesive: Parabolic (from 2c√K_a at top, linear γ z K_a added).

  • With Water: Hydrostatic (triangular) added.

5.4 Retaining Walls for Bridge Abutments and Wing Walls

• Types:

  • Gravity: Mass (masonry/concrete) resists overturning. Thick base.

  • Cantilever: Stem and base slab; economical up to 8-10 m.

  • Counterfort: Stem supported by transverse counterforts; for heights > 10 m.

• Stability Checks (per meter length):

  1. Overturning: Σ M_resisting / Σ M_overturning ≥ 1.5 (typical FOS).

  2. Sliding: Σ F_resisting / Σ F_driving ≥ 1.5. F_resisting = (W + V) tan δ + B q (base friction + cohesion).

  3. Bearing Capacity: Net pressure q_net = (W ± M_e/B) / B must be < q_all. Check eccentricity e = M/W < B/6.

• Tension Cracks: In cohesive backfills with Ka, tension can develop at top. Depth of crack (z_c): z_c = 2c / (γ √K_a).

• Design: Proportion dimensions (base width B, stem thickness) to satisfy all three checks simultaneously.

5.5 Modes of Failure of Retaining Walls**

1. Overturning about toe.

2. Sliding on base.

3. Bearing capacity failure (excessive pressure on toe).

4. Global slope failure (deep-seated).

5. Excessive settlement (differential).

5.6 Sheet Piles vs. Retaining Walls

6.0 Special Soils and Ground Improvement in Bridge Construction

6.1 Expansive Soils

• Characteristics: High shrink-swell potential due to montmorillonite clay minerals; low strength when wet, hard when dry; volume change with moisture.

• Problems for Bridge Foundations: Heave during wetting (uplift), subsidence during drying (differential settlement), leading to cracks in piers/abutments and deck distortion.

• Preventive Measures:

  1. Moisture Control: Impermeable liners, drainage, landscaping to maintain constant moisture.

  2. Under-reamed Piles: Provide tensile capacity to resist heave.

  3. Flexible Foundations: Rafts or deep foundations that span potential zones of differential movement.

  4. Soil Replacement/Stabilization: Replace with non-expansive fill or stabilize with lime/cement.

6.2 Collapsible Soils

• Characteristics: Metastable structure (e.g., loess). Low density, high void ratio, cemented by soluble salts. Sudden collapse upon wetting or loading.

• Problems: Sudden, large settlements under bridge loads, especially after rains or if groundwater rises.

• Treatment:

  1. Pre-wetting (Pre-soaking): Saturate soil before construction to induce collapse.

  2. Compaction: Dynamic compaction, heavy tamping to densify.

  3. Stabilization: Lime/cement to bind particles.

  4. Pile Foundations: Transfer load through collapsible zone to stable stratum.

6.3 Soil Stabilization Techniques

6.4 Geosynthetics

• Types & Functions:

  | Type | Primary Functions | Bridge Applications | | :--- | :--- | :--- | | Geotextiles (woven/non-woven) | Separation, Filtration, Reinforcement, Drainage, Protection | Separate subgrade from ballast; reinforce approach fills; filter behind abutments. | | Geogrids (uniaxial/biaxial) | Reinforcement (high tensile strength) | Reinforce soil layers in embankments, approach slabs, reduce differential settlement. | | Geomats/Mats | Erosion Control, Protection | Protect slopes, prevent soil erosion near abutments. | | Geocells | Confinement, Reinforcement | Stabilize soft subgrades under approach fills or working platforms. | | Geocomposites (geodrains, etc.) | Drainage (geocomposite drains) | Accelerate consolidation in soft soils under embankments. |

• Key Uses in Bridge Works: Reinforcement of approach embankments (most critical to prevent "bump at the bridge"), separation/filtration in poor soils, erosion control on slopes, drainage systems.

7.0 Advanced Analysis and Bridge-Specific Foundations

7.1 Stress Distribution in Soils

• Boussinesq (1885): Assumes homogeneous, isotropic, elastic half-space, point load at surface. 3D problem.

  • Vertical Stress: σ_z = (3Q/2π) × (z³ / (r² + z²)^(5/2))

  • Assumptions: Linear elastic, Poisson's ratio ν appears in horizontal/lateral stress formulas but not in σ_z formula above.

• Westergaard (1938): Assumes vertical, incompressible columns (like rock with joints). More appropriate for stratified or highly fissured soils.

  • Vertical Stress: σ_z = (Q/π) × (1/(z² + r²))^(3/2) × (1/(1+2√(m))) where m = (1-ν²)/(1-2ν).

  • Key Difference: Westergaard gives higher vertical stress near axis (r=0) and lower at large r compared to Boussinesq.

• Influence Charts: Graphical solutions (e.g., Newmark's chart) for Boussinesq σ_z under uniformly loaded areas. Based on influence factor I.

7.2 Well Foundations (Caissons)

• Components:

  • Well curb: Bottom cutting edge (usually steel).

  • Well steining: Concrete ring above curb (provides weight for sinking).

  • Skin plates: Steel plates lining the well.

  • Bottom plug: Concrete plug at bottom (after reaching final depth).

  • Top plug: Concrete fill above bottom plug.

  • Cofferdam: When well is used to enclose area for dry construction.

• Suitability for Major Bridge Piers: Ideal for deep water or very soft soils (like clay/kutch). Can be sunk to great depths. Provides large base area and deep penetration.

• Construction Stages:

  1. Sinking: Excavate inside, well sinks under its weight (may add ballast). Use water jetting or air pressure in hard strata.

  2. Sealing: Plug bottom with concrete under water.

  3. Pumping: Dewater, construct pier foundation/pier inside.

7.3 Sheet Piles in Bridge Works

• Uses:

  • Cofferdams: To create dry work area for pier construction in rivers/lakes.

  • Temporary Shoring: Support excavations for abutments or wing walls.

  • Permanent: In marine environments for erosion protection or as part of quay walls.

• Types:

  • Cantilever: For depths up to 4-5 m in granular soils.

  • Anchored: For greater depths; uses tie rods/anchors to reduce bending moment.

7.4 Settlement Criteria for Bridge Decks**

• Total Settlement: Should not exceed 75 mm (IRCA, AASHTO often suggest 25-50 mm). More stringent for high-speed rail.

• Differential Settlement: ΔS / L ≤ 1/800 (where L = span between supports). Critical to prevent deck tilting, bearing misalignment, and joint damage.

• Long-term Consolidation vs. Immediate: In cohesive soils, consolidation settlement governs long-term performance. Immediate settlement is more critical in granular soils. Both must be predicted and controlled.

8.0 Design Examples and IS Codes

8.1 Step-by-Step Solutions for Typical Problems

General Approach for Bearing Capacity & Settlement:

1. Determine soil profile and parameters (c, φ, γ, E_s, ν, e₀, C_c).

2. Check water table position, apply corrections.

3. Calculate q_ult using BIS (Vesic) method with shape/depth factors.

4. Compute q_ns = (q_ult - γD)/FOS. Compare with applied pressure.

5. For settlement: Calculate S_i using I factor and S_c using C_c method.

6. Check S_total < S_allow and ΔS < L/800.

General Approach for Pile Groups:

1. Determine Q_u for single pile (static/CPT).

2. Check spacing (s ≥ 3d). If s < 3d, calculate block failure capacity (Q_block = c N_c A_block + ...).

3. Group capacity = min(η_g × n × Q_u, Q_block).

4. Check settlement of group (often governs).

5. For negative skin friction, calculate f_ns in compressible layers above neutral plane, sum over group perimeter if needed.

General Approach for Retaining Walls:

1. Calculate K_a (Rankine/Coulomb) based on backfill φ and wall friction δ.

2. Compute active thrust (P_a): P_a = (1/2) γ H² K_a (for level, cohesionless) + surcharge + cohesion component.

3. Determine point of application (from base): H/3 for triangular, H/2 for uniform (cohesion).

4. Check stability: Overturning (ΣM_R/ΣM_O ≥ 1.5), Sliding (ΣF_R/ΣF_D ≥ 1.5), Bearing (q_max, q_min within limits).

5. Design dimensions (base width B, stem thickness) iteratively.

8.2 Relevant IS Codes and Standards

• IS 6403 (1981, reaffirmed 2016): Code for ultimate bearing capacity of shallow foundations.

• IS 2911 (Parts 1-4, 1979, reaffirmed 2019): Code for design and construction of pile foundations. Part 1: Concrete piles; Part 2: Steel piles; Part 3: Under-reamed piles; Part 4: Load testing.

• IS 1892 (1979, reaffirmed 2016): Code for subsurface exploration for foundations. Covers depth/spacing of boreholes, sampling, SPT.

• IS 800 (2007): Code for general construction in steel (includes earth-retaining structures).

• IS 10262 (2019): For concrete mix design (relevant for pile/raft concrete).

• IS 456 (2000): Plain and reinforced concrete code (for footing design).

• IRC 6 (2022): Standard specifications and code of practice for road bridges (loads, loads combinations).