Bridge Engineering (CE-802 (C)) - Unit 3 Short Notes

UNIT 3: FOUNDATION ENGINEERING (Bridge Engineering Context)

1.0 Subsurface Investigation and Soil Exploration

1.1 Soil Sampling Techniques

• Disturbed Sample: Soil structure altered during sampling. Used for classification, moisture content, compaction tests.

• Undisturbed Sample: Soil structure & moisture preserved. Essential for consolidation, permeability, shear strength tests.

• Sampling Tube Design:

  • Inside Clearance ($$\displaystyle C_i $$): Allows sample expansion during driving. $$\displaystyle C_i = \frac{D_i - D_c}{D_c} \times 100\% $$, where $$\displaystyle D_i $$ = inside dia. of tube, $$\displaystyle D_c $$ = outside dia. of cutting edge.

  • Outside Clearance ($$\displaystyle C_o $$): Reduces friction between sample & tube wall. $$\displaystyle C_o = \frac{D_o - D_t}{D_t} \times 100\% $$, where $$\displaystyle D_o $$ = outside dia. of tube, $$\displaystyle D_t $$ = inside dia. of tube.

  • Area Ratio ($$\displaystyle A_r $$): Indicates sample disturbance. $$\displaystyle A_r = \frac{(D_o^2 - D_i^2)}{D_i^2} \times 100\% $$. For good quality, $$\displaystyle A_r < 10\% $$ (clay), $$\displaystyle < 20\% $$ (sand).

• Sample Quality: Low $$\displaystyle A_r $$, adequate $$\displaystyle C_i $$ (1-2%), and $$\displaystyle C_o $$ (0-2%) give better undisturbed samples.

[!TIP] Common Pitfall: Confusing inside/outside clearance definitions. Remember: $$\displaystyle C_i $$ relates to cutting edge & tube ID; $$\displaystyle C_o $$ relates to tube OD & ID.

1.2 In-situ Testing Methods

• Standard Penetration Test (SPT):

  • Procedure: Drive split spoon sampler (50 mm ID) 450 mm into soil by 65 kg hammer falling 750 mm. Count blows for last 300 mm → N-value.

  • Corrections:

    1. Overburden Pressure ($$\displaystyle N_{corr} $$): $$\displaystyle N_{corr} = N \times \left( \frac{\bar{\sigma}_v'}{100} \right)^{0.5} $$ (for $$\displaystyle \phi \approx 0^\circ $$ clays).

    2. Dilatancy ($$\displaystyle N_{corr} $$): For dense sands ($$\displaystyle N > 15 $$), $$\displaystyle N_{corr} = N - 15 + \frac{15}{2} $$ (simplified).

    3. Rod Length ($$\displaystyle N_{corr} $$): Apply correction factor if rod length < 6 m.

  • Significance: Relative density, bearing capacity, settlement estimates. N-value is empirical; corrections essential for comparability.

• Cone Penetration Test (CPT):

  • Continuous pushing of 60° cone (10 cm² area) at 20 mm/s. Measures tip resistance ($$\displaystyle q_c $$) & sleeve friction ($$\displaystyle f_s $$).

  • SCPT: Adds pore pressure measurement ($$\displaystyle u_2 $$). Better for soil stratification & soft clays.

• Plate Load Test:

  • Setup: Load plate (0.3 m² typical) at foundation depth, apply load-settlement.

  • Interpretation: Ultimate load → bearing capacity. Settlement curve → modulus.

  • Settlement Prediction (for cohesive soils): $$\displaystyle S_{footing} = S_{plate} \times \frac{B_{footing}}{B_{plate}} $$ (for same pressure). For different pressures, use $$\displaystyle S \propto \frac{B}{1 + B} $$ or log-log extrapolation.

1.3 Boring and Drilling Methods

• Rotary Drilling: Rotates bit with circulating fluid (bentonite mud). Advantages: Fast, good for deep boreholes, minimal soil disturbance in clays, handles all soils/rocks. Primary method for bridge foundations.

• Auger Boring: Hand/machine-driven. Fast in cohesionless soils, but sample disturbance high, no water control.

• Wash Boring: Jet of water loosens soil; cuttings brought by slurry. Poor sample quality, used for quick stratification.

1.4 Geophysical Methods

• Principles: Measure physical properties (seismic velocity, electrical resistivity, gravity) to infer soil/rock layers.

• Applications: Rapid site screening, locating bedrock depth, voids, weak zones. Complementary to boreholes, not replacement.

1.5 Planning of Exploration (IS Code Criteria)

• Depth: Boreholes must penetrate weak stratum and reach competent stratum (e.g., hard rock, dense sand). Minimum depth = width of foundation + 3 m (for bridges, often deeper).

• Spacing: For bridges, boreholes at each pier/abutment + intermediate points if length > 30 m. Grid spacing 30-50 m for approach fills.

• Bore-log: Graphical record of soil strata, water table, SPT N-values, lab test results. Interpretation: Identify weak zones, consistency, bearing capacity zones.

2.0 Shallow Foundations

2.1 Bearing Capacity

• Definitions:

  • Ultimate Bearing Capacity ($$\displaystyle q_u $$): Max pressure before shear failure.

  • Net Ultimate ($$\displaystyle q_{nu} $$): $$\displaystyle q_u - \gamma D_f $$, where $\gamma$ = unit weight, $$\displaystyle D_f $$ = foundation depth.

  • Safe/Allowable ($$\displaystyle q_{sa} $$): $$\displaystyle q_{nu} / \text{FOS} $$ (typically 2.5-3.0).

• Terzaghi's Theory (for strip footing, $$\displaystyle \phi > 0^\circ $$):

$$q_u = c N_c + \gamma D_f N_q + 0.5 \gamma B N_\gamma$$

• IS Code (BIS) Method (Generalized for shape, depth, load inclination):

$$q_u = c' N_c s_c d_c i_c + \gamma D_f N_q s_q d_q i_q + 0.5 \gamma B N_\gamma s_\gamma d_\gamma i_\gamma$$

• Shape factors ($s$), Depth factors ($d$), Inclination factors ($i$). For strip: $$\displaystyle s_c=1.3 $$, $$\displaystyle s_q=1.0 $$, $$\displaystyle s_\gamma=1.0 $$.

• Factors Affecting:

  • Water Table: Reduces effective stress. Correction: Use $\gamma'$ for submerged layers, adjust $$\displaystyle N_q $$ if water table at/above base.

  • Shape: Square/strip/circular have different $$\displaystyle N_c $$, $$\displaystyle N_q $$, $$\displaystyle N_\gamma $$ values.

• Bearing Capacity Factors ($$\displaystyle N_c, N_q, N_\gamma $$): Functions of $\phi'$. From tables or $$\displaystyle N_q = e^{\pi \tan \phi'} \tan^2(45^\circ + \phi'/2) $$.

[!TIP] Exam Focus: For circular footing, use $$\displaystyle N_c = 6.2 $$, $$\displaystyle N_q = 4.1 $$, $$\displaystyle N_\gamma = 3.7 $$ (approx) for $$\displaystyle \phi'=30^\circ $$. Always check water table position for correction.

2.2 Modes of Shear Failure

1. General Shear: Dense soils/cohesive. Sudden failure, well-defined failure wedge, large settlements.

2. Local Shear: Medium dense soils. Progressive failure, limited heave, moderate settlements.

3. Punching Shear: Very loose soils/soft clays. Foundation "punches" into soil without distinct failure surface, minimal heave.

2.3 Settlement Analysis

• Components:

  1. Immediate (Elastic): Instant upon loading, in cohesionless & saturated clays (undrained).

  2. Primary Consolidation: Due to pore water expulsion in saturated clays.

  3. Secondary Compression: Post-consolidation, due to soil structure rearrangement.

• Immediate Settlement (Cohesive soils):

$$S_i = \frac{q B (1 - \nu^2)}{E_s} I_f$$

where $$\displaystyle I_f $$ = influence factor (from charts, e.g., 1.06 for square footing on elastic half-space), $\nu$ = Poisson's ratio, $$\displaystyle E_s $$ = modulus of elasticity.

• Elastic Theories:

  • Boussinesq: Point load in elastic half-space. Assumes homogeneous, isotropic, weightless.

  • Westergaard: Assumes vertical cracks, incompressible material. More realistic for stratified soils.

• Plate Load Extrapolation: $$\displaystyle S_{footing} \approx S_{plate} \times \left( \frac{B_{footing}}{B_{plate}} \right) $$ for same pressure in clay.

2.4 Types and Design of Shallow Foundations

• Types: Isolated, combined, strip, raft (floating).

• Raft Proportioning: Used when $$\displaystyle q_{allow} < \text{weight of structure}/\text{area} $$. Aim for uniform pressure distribution. Thickness based on shear & bending.

• Performance Criteria:

  1. Bearing Capacity ≥ applied pressure.

  2. Settlement ≤ allowable (often 25-50 mm for bridges).

  3. Differential Settlement < span/400.

  4. Stability against sliding, overturning.

3.0 Pile Foundations

3.1 Classification and Functions

• Based on Material: Concrete, steel, timber, composite.

• Based on Shape: Solid, hollow, H-section.

• Based on Construction: Driven, bored, screw, under-reamed.

• Based on Action:

  • End-bearing: Transfer load to hard stratum.

  • Friction (Skin Friction): Load via shaft adhesion.

  • Combined: Both mechanisms.

• Bridge Use: For deep soft soils, scour protection, lateral load resistance, uplift.

3.2 Load Carrying Capacity of Single Pile

• Static Formulas:

  • End Bearing: $$\displaystyle Q_b = A_p \cdot q_b $$, where $$\displaystyle q_b = 9c $$ (clay) or $$\displaystyle N_q \sigma'_v $$ (sand).

  • Shaft Friction:

    • Clay: $$\displaystyle Q_s = \Sigma (\alpha \cdot c \cdot A_s) $$, $\alpha$ = adhesion factor (0.5-1.0).

    • Sand: $$\displaystyle Q_s = \Sigma (\beta \cdot \sigma'_v \cdot A_s) $$, $\beta$ = friction factor (~0.5 $\tan \phi$).

• Dynamic Formulas (Driven piles):

  • Drop Hammer (Engineering News): $$\displaystyle Q_{safe} = \frac{W h}{S + e} \cdot \frac{W + n P}{W} \cdot \frac{1}{FOS} $$, where $W$=hammer wt., $h$=fall, $S$=set, $e$=elastic compression, $n$=coefficient (0.1-0.2), $P$=pile wt.

• From SPT/CPT:

  • Sand: $$\displaystyle Q_b = A_p \cdot (N_q \sigma'_v) $$, $$\displaystyle Q_s = f_s \cdot A_s $$.

  • Clay: $$\displaystyle Q_s = \alpha \cdot c_u \cdot A_s $$, $$\displaystyle Q_b = 9 c_u A_p $$.

3.3 Pile Groups

• Group Efficiency ($\eta$): $$\displaystyle \eta = \frac{Q_{ug}}{n Q_{up}} $$, where $$\displaystyle Q_{ug} $$ = group capacity, $$\displaystyle Q_{up} $$ = single pile capacity.

• Block Failure (cohesive soils, close spacing): Entire soil block between piles fails.

$$Q_{ug} = c (B_g L_g) + \gamma D_f (B_g L_g) \quad \text{(for square group, ignoring base)}$$

where $$\displaystyle B_g $$, $$\displaystyle L_g $$ = group dimensions.

• Spacing: Typically $3D$ to $4D$ (center-to-center) to avoid group efficiency < 1.0.

[!TIP] Common Error: Using single pile formula for group without checking spacing. For $$\displaystyle s < 4D $$, group efficiency may drop due to overlapping stress zones.

3.4 Negative Skin Friction (NSF)

• Causes: Downward movement of soil relative to pile (e.g., fill consolidation, lowering water table, collapsible soils).

• Effect: Increases load on pile, reduces capacity.

• Calculation:

  • Single Pile: $$\displaystyle Q_{nsf} = \gamma \cdot K \cdot \sigma'_v \cdot A_s $$ (sand) or $$\displaystyle \alpha \cdot \bar{c} \cdot A_s $$ (clay) for dragged length.

  • Group: Consider group action for NSF zone.

• Mitigation: Use neutral plane concept, sleeves, or load calculation with NSF.

3.5 Special Pile Types

• Under-reamed Piles:

  • Components: Shaft + bulbs (under-reams) at intervals (typically 2-3 m). Bulb dia. = 2-3× shaft dia.

  • Tensile Capacity: $$\displaystyle Q_t = \Sigma (A_b \cdot q_b)_b + \Sigma (\alpha \cdot c \cdot A_s)_s $$, where $$\displaystyle A_b $$ = bulb area.

  • Suitability: Expansive soils (swell-shrink), uplift loads, soft clays. Bulbs provide anchorage against heave.

• Other Types:

  • Bored Piles: Low noise/vibration, good for sensitive areas.

  • Screw Piles: Helical plates, for light loads in granular soils.

4.0 Well Foundations (Caissons)

4.1 Components and Construction

• Components (with sketch):

  1. Well Curb: Bottom cutting edge (steel/iron), conical.

  2. Well Steining: Vertical wall above curb (brick/masonry), tapers outward.

  3. Well Cap: Top slab for load transmission.

  4. Shoring: Horizontal timbers inside well for sinking.

  5. Muck: Excavated material.

• Sinking Process: Excavate inside, self-weight or kentledge sinks well. Trim bottom, maintain verticality. Sand filling may be used for stability.

4.2 Design Considerations

• Bearing Capacity: Base on soil below curb (end-bearing + skin friction if any).

• Settlement: Elastic + consolidation of soil below.

• Stability During Sinking:

  • Uplift: Check buoyancy (well empty vs full).

  • Buckling: Wall thickness & shoring design.

  • Tilting: Control by uneven excavation or loading.

• Bridge Suitability: Deep water/scour zones, massive loads, good for abutments & piers in rivers.

5.0 Earth Retaining Structures

5.1 Earth Pressure Theories

• Types:

  • At Rest ($$\displaystyle K_0 $$): No lateral strain. $$\displaystyle K_0 = 1 - \sin \phi' $$ (Jaky's formula).

  • Active ($$\displaystyle K_a $$): Wall moves away, minimum pressure.

  • Passive ($$\displaystyle K_p $$): Wall moves into soil, maximum pressure.

• Rankine's Theory:

  • Assumptions: Wall frictionless, vertical, horizontal backfill, cohesionless/cohesive.

  • Cohesionless: $$\displaystyle K_a = \tan^2(45^\circ - \phi'/2) $$, $$\displaystyle K_p = \tan^2(45^\circ + \phi'/2) $$.

  • Cohesive: $$\displaystyle P_a = \frac{1}{2} \gamma H^2 K_a + 2c \sqrt{K_a} $$ (with tension crack at top).

• Coulomb's Theory:

  • Considers wall friction ($\delta$), inclined backfill. Planar failure surface.

  • $$\displaystyle K_a = \frac{\cos^2(\phi' - \delta)}{\cos^2 \delta \cos(\delta + \beta) \left[1 + \sqrt{\frac{\sin(\phi' + \delta) \sin(\phi' - \beta)}{\cos(\delta + \beta)}} \right]^2} $$.

  • Comparison: Coulomb < Rankine for $$\displaystyle K_a $$ (more realistic). Rankine simpler for $$\displaystyle \delta=0 $$.

5.2 Earth Pressure Calculation

• Conditions:

  • Dry: Use $\gamma$ above water table.

  • Submerged: Use $\gamma'$ below water table, plus water pressure.

  • Seepage: Add seepage force (flow net analysis).

• Effect of Surcharge: Add uniform pressure $q$ → increase pressure by $$\displaystyle q K_a $$ at all depths.

• Distribution: Linear for cohesionless, parabolic for cohesive (with tension crack).

5.3 Retaining Wall Design

• Stability Checks:

  1. Overturning: $$\displaystyle \frac{\Sigma M_{resisting}}{\Sigma M_{overturning}} \geq 1.5 $$.

  2. Sliding: $$\displaystyle \frac{\Sigma F_{resisting}}{\Sigma F_{driving}} \geq 1.5 $$. Resisting = $\mu \Sigma W$ (friction) + cohesion if base.

  3. Bearing Capacity: Check eccentricity $e \leq B/6$; pressure $$\displaystyle q_{max} \leq q_{allow} $$.

• Pressure Distribution: Linear if $e \leq B/6$; trapezoidal/triangular if $$\displaystyle e > B/6 $$.

• Total Thrust ($$\displaystyle P_a $$): Magnitude from theory, point of application at $H/3$ from base for triangular distribution.

5.4 Failure Modes of Retaining Walls

• Structural: Wall cracking, sliding on base, overturning.

• Global Stability: Deep-seated failure, bearing capacity failure, slope failure in backfill.

5.5 Sheet Piles

• Comparison: Flexible, thin sections (vs rigid walls). Used for temporary/permanent excavation support, cofferdams.

• Uses: River walls, trench sheeting, bulkheads. Anchored or cantilever.

6.0 Problematic Soils and Soil Improvement

6.1 Expansive Soils

• Characteristics: High montmorillonite content, swell-shrink with moisture change. High liquid limit (>50%), plasticity index (>30%).

• Problems: Heave/frost damage, differential settlement, cracking.

• Preventive Measures:

  • Moisture control: Impermeable barriers, drainage.

  • Chemical stabilization: Lime, cement.

  • Under-reamed piles: Transfer load below active zone.

  • Lightweight fills: Reduce surcharge.

6.2 Collapsible Soils

• Characteristics: Metastable structure (loess, wind-blown), sudden settlement upon wetting. Low density, high void ratio.

• Problems: Post-construction collapse, uneven settlement.

• Mitigation: Pre-wetting, compaction, replacement, piles to bypass layer.

6.3 Soil Stabilization Techniques

• Mechanical: Compaction (static, dynamic), preloading/surcharging.

• Chemical: Lime (clays), cement (sands/clays), bitumen (waterproofing).

• Electrical: Electro-osmosis (consolidate clays by applying DC current).

6.4 Geosynthetics

• Types & Functions:

  | Type | Primary Function | Bridge Application | |------|------------------|-------------------| | Geotextile | Separation, filtration | Under embankments, drainage | | Geogrid | Reinforcement | Retaining walls, slopes | | Geomembrane | Impermeability | Lining, seepage control | | Geocell | Confinement | Slope protection, load distribution |

• Uses: Separation (prevent mixing), reinforcement (increase shear strength), filtration (allow flow, retain soil), drainage (convey water), protection (against puncture).

7.0 Additional Topics

7.1 Factors Affecting Foundation Type Selection

• Soil conditions: Bearing capacity, settlement potential, depth to bedrock.

• Loads: Magnitude, type (axial, lateral, moment), importance (bridge vs building).

• Constructability: Access, equipment, vibration/noise constraints, water table.

• Cost: Initial vs lifetime cost.

• Durability: Corrosion, scour, environmental effects.

• Bridge Specific: Scour depth, lateral loads (wind, seismic), fatigue.

7.2 CNS Layer in Sampling

• Cavity, No-Seal (CNS) Layer: Zone of disturbed soil at bottom of borehole due to drilling. Affects SPT N-value (too low). Correction: Use energy corrections and interpret N-values cautiously in disturbed zone.

7.3 Light vs Heavy Proctor Tests

• | Light (Standard) | Heavy (Modified) | |----------------------|----------------------| | Hammer: 2.5 kg, 300 mm drop | 4.5 kg, 450 mm drop | | Layers: 3, 25 blows/layer | 5, 25 blows/layer | | Mold: 944 cm³ | 944 cm³ | | Max dry density: Lower | Higher (~5-10% more) | | Optimum moisture: Higher | Lower | | Use: Embankments, subgrades (low traffic) | Use: Airfields, highways, heavy fills |

7.4 Influence Factors in Settlement Calculations

• Immediate Settlement: $$\displaystyle I_f $$ from Boussinesq charts (shape & depth dependent). For flexible square footing: $$\displaystyle I_f \approx 1.06 $$ at $$\displaystyle z/B=0 $$, decreases with depth.

• Consolidation Settlement: $I$ from Terzaghi's 1D consolidation (assumes uniform load). For flexible footing, $I \approx 1.0$ at center.

• Key: Influence factors account for load distribution and soil layer geometry.

Final Exam Strategy:

1. Derivations: Know Terzaghi's $$\displaystyle q_u $$, Boussinesq stress, Rankine $$\displaystyle K_a $$.

2. Numericals: Practice SPT corrections, bearing capacity with water table, pile group capacity, plate load extrapolation, earth pressure for stratified backfill.

3. Diagrams: Sketch failure zones, earth pressure diagrams, pile group layouts, well components.

4. IS Codes: Refer IS 1892 (exploration), IS 6403 (bearing capacity), IS 2911 (piles), IS 1904 (retaining walls).

5. Bridge Context: Always link foundation choice to scour, lateral loads, and durability.