UNIT 5: FOUNDATION ENGINEERING (AS APPLIED TO EARTHQUAKE-RESISTANT DESIGN)

I. SOIL EXPLORATION & SITE CHARACTERIZATION

Subsurface Investigation Program

• Significant depth: Depth where vertical stress increase due to foundation ≤ 10% of initial effective stress. For isolated footing, ≈ 2B to 4B (IS 1892).

• Boring methods:

  • Rotary drilling: Most versatile; uses rotary motion with drilling fluid (bentonite). Advantages: Fast, good for all soils, undisturbed sampling possible. Disadvantages: Costly, fluid management needed.

  • Others: Auger boring (soft soils), wash boring (coarse soils), percussion drilling (hard strata).

• Bore-log report: Standardized presentation (IS 1892) including soil profile, sample description, lab test results, groundwater level.

Soil Sampling

• Disturbed vs undisturbed: Disturbed for classification; undisturbed for strength/consolidation tests.

• Sampling tube design:

  • Inside clearance: $$\displaystyle \frac{ID_{cutting} - ID_{tube}}{ID_{tube}} \times 100\% $$ (typical 1–2%).

  • Outside clearance: $$\displaystyle \frac{OD_{tube} - OD_{cutting}}{OD_{tube}} \times 100\% $$ (typical 0–2%).

  • Area ratio: $$\displaystyle \frac{OD_{tube}^2 - ID_{tube}^2}{ID_{tube}^2} \times 100\% $$ (< 10% for undisturbed).

• CNS layer: Constant Normal Stiffness layer—soil layer that maintains constant stiffness during sampling to minimize disturbance.

In-situ Testing (Very High Frequency)

• Standard Penetration Test (SPT):

  • Procedure: Drive split-spoon sampler (OD 50.8 mm) with 65 kg hammer falling 750 mm. Count blows for last 300 mm after seating 150 mm.

  • N-value: Blows for final 300 mm penetration.

  • Corrections:

    | Correction | Need | Formula/Note | |------------|------|--------------| | Overburden | N increases with $$\displaystyle \sigma'_v $$ | $$\displaystyle N_{corr} = N_{obs} \times \frac{100}{\sigma'_v\ (kPa)} $$ (or $$\displaystyle \frac{70}{\sigma'_v\ (t/m^2)} $$) | | Dilatancy | Dense sands show artificially high N | $$\displaystyle N_{corr} = N_{obs} - 15 $$ (for $$\displaystyle N_{obs} > 15 $$ in dense sands) | | Rod length | Energy loss with long rods | Apply correction factor based on rod length |

    [!TIP] Apply corrections sequentially: overburden first, then dilatancy if applicable.

  • Significance: Empirical correlations for relative density, friction angle, liquefaction potential.

• Cone Penetration Test (CPT):

  • Procedure: Push 10 cm² cone (60° apex) at 20 mm/s; measure tip resistance ($$\displaystyle q_c $$) and sleeve friction ($$\displaystyle f_s $$).

  • Advantages over SPT: Continuous profile, faster, quantitative, less disturbance, no borehole.

• Plate Load Test:

  • Procedure: Load rigid plate (0.3–0.5 m²) incrementally; measure settlement.

  • Ultimate load: From load-settlement curve (failure at large settlement).

  • Settlement scaling:

    • Clay: $$\displaystyle S_{footing} \approx S_{plate} \times \frac{B_{footing}}{B_{plate}} $$.

    • Sand: $$\displaystyle S_{footing} \approx S_{plate} \times \left(\frac{B_{footing}}{B_{plate}}\right)^{0.5} $$.

• Geophysical methods:

  • Seismic refraction: Determine layer boundaries and velocities.

  • Resistivity: Identify soil types, groundwater.

II. BEARING CAPACITY OF SHALLOW FOUNDATIONS

Fundamental Concepts & Definitions

Modes of Shear Failure

1. General shear: Continuous failure surface to surface; large settlements; dense soils.

2. Local shear: Failure surface limited to soil immediately under footing; medium settlements; medium-dense soils.

3. Punching shear: Soil punches into footing; no surface failure; loose soils.

Theoretical Approaches & Equations

• Terzaghi’s theory (strip footing, rough base, φ > 0):

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

$$\displaystyle N_c, N_q, N_\gamma $$: bearing capacity factors (function of φ).

• BIS (IS 6403) method (general):

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

• Shape factors ($s$): strip=1, square=1.3, circular=1.3, rectangular: $$\displaystyle s_c = 1 + 0.2B/L $$, etc.

• Depth factors ($d$): for $$\displaystyle D_f/B \leq 1 $$, $$\displaystyle d_c = 1 + 0.2\sqrt{D_f/B} $$, $$\displaystyle d_q = 1 + 0.1\sqrt{D_f/B} $$, $$\displaystyle d_\gamma = 1 - 0.4\sqrt{D_f/B} $$.

• Inclination factors ($i$): for load inclination θ, $$\displaystyle i_c = (1 - \theta/90°)^2 $$, etc.

• Water table correction:

  • If water table above base: use buoyant unit weight ($\gamma'$) for γ term; effective surcharge ($$\displaystyle q = \gamma D_f $$) for q term.

  • Correction factors: $$\displaystyle q_\gamma = 0.5 $$ if water table at base; $$\displaystyle q_q = 1 $$ if below base.

  [!TIP] For water table at ground level: use γ' for all terms, q = 0.

Numerical Problem Solving

• Pure clay (φ = 0°): $$\displaystyle q_u = c N_c + \gamma D_f $$ ($$\displaystyle N_\gamma = 0 $$). $$\displaystyle N_c $$: strip=5.7, square=6.2, circular=6.3.

• Sand (c = 0): $$\displaystyle q_u = q N_q + 0.5 \gamma B N_\gamma $$.

• With water table: Apply buoyant unit weight and correction factors as above.

III. SHALLOW FOUNDATION DESIGN & SETTLEMENT

Types of Shallow Foundations

• Isolated, combined, raft, floating.

• Proportioning criteria: Raft for weak soils/high loads; isolated for good soil/light loads.

Settlement Components

1. Immediate (elastic) settlement:

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

$$\displaystyle I_z $$: influence factor (from charts), $$\displaystyle E_s $$: modulus of elasticity.

2. Primary consolidation (clay):

$$S_c = \frac{C_c}{1+e_0} H \log \frac{\sigma'_0 + \Delta\sigma}{\sigma'_0}$$

3. Secondary compression (creep):

$$S_s = \frac{C_\alpha}{1+e_0} H \log \frac{t_2}{t_1}$$

Settlement Calculation Problems

• Immediate: Use $$\displaystyle I_z $$ from elastic theory charts (for clay/sand).

• Consolidation: Compute $\Delta\sigma$ via 2:1 distribution or influence factor.

• Plate load test scaling:

  • Clay: $$\displaystyle S_{footing} = S_{plate} \times \frac{B_{footing}}{B_{plate}} $$.

  • Sand: $$\displaystyle S_{footing} = S_{plate} \times \left(\frac{B_{footing}}{B_{plate}}\right)^{0.5} $$.

Performance Criteria

• Total settlement: < 25–40 mm (typical).

• Differential settlement: < span/500.

IV. DEEP FOUNDATIONS: PILES

Pile Classification

Load Carrying Capacity: Approaches

• Static formulae:

  • α-method (clay, undrained): $$\displaystyle f = \alpha c_u $$, $$\displaystyle Q_s = \alpha c_u A_s $$, $$\displaystyle Q_b = A_b c_u N_c $$ (often neglected for soft clay).

  • β-method (sand, effective stress): $$\displaystyle f = \beta \sigma'_v $$, $$\displaystyle \beta = K \tan\delta $$, $$\displaystyle Q_s = \beta \sigma'_v A_s $$, $$\displaystyle Q_b = A_b \sigma'_{vb} N_q $$.

• Dynamic formulae:

  • Drop hammer (Hiley’s formula):

$$Q = \frac{W h (1-\alpha)}{s + 0.5e}$$

$W$: hammer weight, $h$: fall, $\alpha$: coefficient of restitution, $s$: permanent set, $e$: elastic compression.

Allowable load = $Q / \text{FOS}$.

• CPT-based methods: Correlations between $$\displaystyle q_c $$ and pile resistance.

Single Pile Capacity Calculations

• In sand:

  • $$\displaystyle Q_b = A_b \cdot q_b $$, $$\displaystyle q_b = \sigma'_{vb} N_q $$.

  • $$\displaystyle Q_s = \sum f_i \cdot A_{s,i} $$, $$\displaystyle f_i = \beta \sigma'_{vi} $$.

• In clay:

  • Undrained: $$\displaystyle Q_s = \alpha c_u A_s $$, $$\displaystyle Q_b $$ often neglected.

  • Drained: $$\displaystyle Q_s = \beta \sigma'_{vi} \tan\delta \cdot A_s $$, $$\displaystyle Q_b = A_b \sigma'_{vb} N_q $$.

• Water table effects: Use effective stress parameters below water table.

Pile Groups

• Group efficiency: $$\displaystyle \eta = \frac{Q_{ug}}{n Q_u} $$.

• Block failure (cohesive soils):

$$Q_{ug} = \min\left(\sum Q_u,\ Q_{block}\right)$$

$$\displaystyle Q_{block} = c_u N_c A_g + \gamma D A_g N_q $$ ($$\displaystyle N_q = 1 $$ for φ=0).

• Spacing: Typically ≥ 2.5D (friction piles), ≥ 2D (end-bearing).

• Group settlement: > single pile due to overlapping stress zones.

Special Pile Types & Phenomena

• Under-reamed piles:

  • Concept: Enlarged base for uplift resistance in expansive soils.

  • Ultimate tensile capacity (neglecting suction):

$$Q_t = \alpha c_u A_s + A_u c_u N_c$$

• Suitability: Expansive soils, soft clay with high swell potential.

• Negative skin friction:

  • Causes: Fill, lowering water table, consolidation.

  • Calculation: $$\displaystyle Q_{nsf} = \sum \sigma'_{v} \tan\delta \cdot \Delta A_s $$ (downward force).

  • For groups, consider group effect.

• Pile load tests: Routine test (proof load), maintained load test (ultimate capacity).

V. EARTH PRESSURE & RETAINING STRUCTURES

Types of Earth Pressure

• At rest ($$\displaystyle K_0 $$): No lateral strain.

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

• Passive ($$\displaystyle K_p $$): Wall moves toward → maximum pressure.

Classical Earth Pressure Theories

• Rankine’s theory:

  • Assumptions: Wall frictionless, horizontal backfill, cohesionless (or with c).

  • Active: $$\displaystyle K_a = \tan^2(45^\circ - \phi/2) $$.

  • Passive: $$\displaystyle K_p = \tan^2(45^\circ + \phi/2) $$.

  • For cohesive soil: $$\displaystyle p_a = \gamma z K_a - 2c \sqrt{K_a} $$ (tension crack if $$\displaystyle p_a < 0 $$).

• Coulomb’s theory:

  • Assumptions: Wall friction (δ), inclined backfill (β), planar failure wedge.

  • Active coefficient:

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

• Merits: Accounts for wall friction and backfill slope.

• Culmann’s graphical method:

  • For non-horizontal backfill, stratified soils, surcharge.

  • Procedure: Draw failure wedges, plot weight, locate critical wedge.

Earth Pressure Calculation Problems

• Dry/moist/submerged: Use appropriate unit weight.

• With surcharge: Add $$\displaystyle q K_a $$ uniformly.

• Distribution diagrams:

  • Rankine/Coulomb: Linear for cohesionless, parabolic for cohesive.

  • Tension crack depth: $$\displaystyle z_{tc} = \frac{2c}{\gamma \sqrt{K_a}} $$.

• Resultant thrust: Magnitude = area of pressure diagram; point of application = centroid.

Retaining Walls

• Types:

  | Type | Description | |------|-------------| | Gravity | Mass concrete, relies on weight | | Cantilever | Stem, base slab, heel, toe | | Sheet pile | Interlocking sheets, flexible |

• Differences: Sheet pile vs retaining wall:

  | Aspect | Sheet Pile | Retaining Wall | |--------|------------|---------------| | Material | Steel, vinyl, wood | Concrete, masonry | | Flexibility | Flexible | Rigid | | Depth | Deep excavations | Shallow to moderate | | Construction | Driven/bored | Cast-in-situ | | Uses | Cofferdams, temporary | Permanent structures |

• Modes of failure:

  1. Sliding: Along base, $$\displaystyle \text{FOS} = \frac{\mu \Sigma W}{\Sigma P_a} $$.

  2. Overturning: $$\displaystyle \text{FOS} = \frac{\Sigma M_{resisting}}{\Sigma M_{overturning}} > 1.5 $$.

  3. Bearing capacity: Eccentric load, check pressure distribution.

• Design:

  • Total active thrust from earth pressure.

  • Base pressure (rectangular base):

$$q_{max/min} = \frac{\Sigma W}{A} \pm \frac{6M}{B^2}$$

• Ensure $$\displaystyle q_{max} \leq q_{allow} $$, $e \leq B/6$.

VI. SPECIAL SOILS & GROUND IMPROVEMENT

Expansive Soils

• Characteristics: Montmorillonite clay, high swell-shrink, low strength wet/high dry.

• Problems: Heave, foundation damage, seasonal movement.

• Preventive measures:

  • Moisture control: Wetting, barriers.

  • Under-reamed piles: Uplift resistance.

  • Chemical stabilization: Lime, cement.

  • Geosynthetics: Reinforcement.

  • Deep foundations: Transfer load to stable stratum.

Collapsible Soils

• Characteristics: Loose, metastable, sudden collapse upon wetting.

• Problems: Sudden settlement.

• Preventive measures: Pre-wetting, compaction, reinforcement, replacement.

Soil Stabilization Techniques

• Mechanical: Compaction (smooth wheel, sheepsfoot, pneumatic). Proctor tests: Light (285 kN/m³) vs Heavy (600 kN/m³).

• Chemical: Lime (clay), cement (sand-clay), fly ash. Mechanisms: cation exchange, pozzolanic.

• Electrical: Electro-osmosis—DC current moves water toward anode for clay dewatering.

Geosynthetics (Recurring Topic)

• Applications:

  • Embankments: Reinforcement, separation.

  • Slopes: Reinforcement, erosion control.

  • Retaining walls: Reinforcement (MSE walls).

  • Pavements: Separation, reinforcement.

  • Erosion control: Mats, blankets.

VII. OTHER FOUNDATION SYSTEMS & MISCELLANEOUS TOPICS

Well Foundations

• Components (with sketch):

  • Well curb: Bottom frame.

  • Well steining: Enlarged top for stability.

  • Cutting edge: Chisel-shaped for sinking.

  • Apron: Protects base from scouring.

  • Well socket: Socket into rock.

  • Sand filling: Inside well for stability.

  [!TIP] Sketch: Circular well with labeled components.

  DiagramCANVAS: Well foundation components: curb, steining, cutting edge, apron, sand filling

Sheet Piles

• Uses: Cofferdams, retaining walls, erosion control, shoring.

Modes of Shear Failure in Soils

• General, local, punching shear (see II.A.2).

Floating Foundations

• Raft foundation designed so net bearing pressure ≈ 0 (weight of excavated soil = weight of structure). Used in very weak soils.

EXAM FOCUS SUMMARY

• Highest Frequency: SPT (procedure & corrections), Bearing Capacity calculations (Terzaghi/BIS), Pile Capacity (single & group), Earth Pressure (Rankine/Coulomb), Immediate Settlement, Expansive Soils, Geosynthetics.

• Recurring Numerical: Pile group capacity, bearing capacity with water table, active earth pressure, immediate settlement, plate load test scaling.

• Theoretical Emphasis: Definitions (bearing capacity terms, earth pressure types), Failure modes, Soil exploration methods, Stabilization techniques.

[!TIP] For numerical problems:

1. State all assumptions.

2. Use consistent units (kN, m).

3. Box final answers.

4. For SPT corrections, apply overburden first, then dilatancy if dense sand.

5. For pile groups in clay, check both ΣQᵤ and block failure.