Earthquake Resistant Design of Structures (CE-802 (D)) - Unit 4 Short Notes

Unit 4: Foundation Engineering (Based on Past Exam Analysis)

Note: These notes are synthesized exclusively from the provided "B FOUNDATION ENGINEERING" past question papers (May 2022 – Jun 2025). They do not cover topics from the official syllabus for CE-802(D) - Earthquake Resistant Design of Structures. Always cross-check with the university's prescribed syllabus.

A. Site Investigation & Soil Sampling

1. Subsurface Exploration Methods

• Boring Techniques:

  • Auger Boring: Hand/machine operated, suitable for soft soils, disturbed samples.

  • Shell & Auger Boring: For medium stiff soils, can retrieve undisturbed samples with Shelby tube.

  • Rotary Drilling: Uses rotary motion with drilling fluid (bentonite slurry). Most versatile for all soils/rocks, allows for undisturbed sampling. Advantage: Can drill through hard strata and boulders.

• Geophysical Methods:

  • Seismic Refraction: Measures velocity of seismic waves to infer stratum boundaries and bedrock depth.

  • Electrical Resistivity: Measures soil resistivity to detect changes in soil type, water table, and voids.

• Standard Penetration Test (SPT):

  • Procedure: Driving a split spoon sampler (50 mm ID) with a 63.5 kg hammer falling 760 mm. Record blows for 150 mm (pre-boring) and next 300 mm (N-value).

  • N-value: Number of blows for last 300 mm penetration.

  • Corrections to N-value:

    1. Overburden Pressure Correction (Kₙ or N₁₀):

$$N_{corrected} = N_{observed} \times K_n$$

where

$$K_n = \left( \frac{P_a}{\sigma'_{v0}} \right)^{0.5}$$

(for normally consolidated clays/sands, Pa = 100 kPa). Corrects for confining pressure effect.

    2.  **Dilatancy Correction (Nₘ):** For dense sands/gravels below water table, apply: 

$$N_{corrected} = N_{observed} - C_d$$

where

$$C_d = \left[ N_{observed} \times \left( \frac{\sigma'_{v0}}{P_a} \right)^{0.5} \right] \times 0.7 \times \log_{10} \left( \frac{\sigma'_{v0}}{P_a} \right)$$

. Corrects for false high N due to soil heave.

    3.  **Rod Length Correction:** For rod length < 6 m, energy ratio is low. Use correction charts (e.g., for 3 m rod length, multiply N by ~1.25).

*   **Significance:** Empirical index for relative density, shear strength, and bearing capacity. **Limitations:** Highly operator-dependent, poor sample quality, not suitable for very soft clays.

• Cone Penetration Test (CPT/SCPT):

  • Procedure: Pushing a 60° cone (10 cm² area) at 20 mm/s. Measures qc (tip resistance), fs (sleeve friction), u₂ (pore pressure).

  • Comparison with SPT: Continuous profile, more repeatable, provides quantitative soil parameters (e.g., friction ratio, pore pressure). SPT is discrete, gives N-value for empirical correlations.

2. Soil Sampling

• Disturbed vs. Undisturbed: Disturbed (structure altered) for classification, index properties. Undisturbed (structure preserved) for strength/consolidation tests.

• Sampling Tube Specifications:

  • Area Ratio (Ar):

$$A_r = \frac{(D_o^2 - D_i^2)}{D_i^2} \times 100\%$$

. Should be < 20% for good quality.

*   **Inside Clearance (Ci):** 

$$C_i = \frac{D_i - D_s}{D_s} \times 100\%$$

(Ds = sample diameter). Allows sample expansion.

*   **Outside Clearance (Co):** 

$$C_o = \frac{D_o - D_h}{D_h} \times 100\%$$

(Dh = hole diameter). Reduces friction.

• Sampling Techniques:

  • Open Drive Sampler (Split Spoon): For SPT, disturbed to slightly undisturbed.

  • Shelby Tube: Thin-walled, pushed/driven for undisturbed samples in soft clays.

  • Piston Sampler: Fixed piston prevents sample disturbance during driving.

• Quality Assessment: Low Ar, appropriate Ci/Co, minimal sample distortion.

3. Borehole Logging & Reporting

• Components of Bore-log: Depth, soil description (color, consistency, structure), water table depth, SPT N-values, sampling details, lab test results.

• IS Criteria (IS 1892): Minimum boreholes = 1 per 400 m² for buildings, depth = at least up to competent stratum or 1.5-2× foundation width.

• Presentation: Graphical log with soil strata, standard symbols, and tabulated data.

[!TIP] Exam Focus: SPT corrections (overburden, dilatancy) and sampling tube geometry (Ar, Ci, Co) are very frequent. Be ready to compute these from given dimensions.

B. Shallow Foundations - Bearing Capacity & Settlement

1. Fundamental Definitions

2. Bearing Capacity Theories

• Terzaghi's Theory (1943): Assumptions: strip footing, rough base, φ>0, depth=width, no surcharge. Equation:

$$q_u = c N_c + q N_q + 0.5 γ B N_γ$$

For square/circular: modify shape factors.

• IS Code Method (IS 6403): Uses general equation with shape, depth, inclination, and ground water factors:

$$q_u = c N_c s_c d_c i_c + q N_q s_q d_q i_q + 0.5 γ B N_γ s_γ d_γ i_γ$$

*Factors (s, d, i) depend on foundation shape, depth, load inclination.*

• Bearing Capacity Factors (Nc, Nq, Nγ): Function of φ only. Use tables/charts (e.g., IS code, Vesic). For φ=0° (pure clay): Nc=5.7, Nq=1, Nγ=0.

• Water Table Correction (f_w): If water table is at/below foundation base:

  • For Nc & Nq: Use effective cohesion/φ and effective q.

  • For Nγ: Use f_w factor. If water table at base level, f_w = 0.5; if at surface, f_w = 0 (use submerged unit weight γ' for entire depth).

3. Settlement of Shallow Foundations

• Components:

  1. Immediate (Elastic) Settlement (S_i): Instantaneous, recoverable.

  2. Primary Consolidation Settlement (S_c): Due to pore water expulsion in cohesive soils.

  3. Secondary Compression (S_s): Post-primary consolidation due to soil structure adjustment.

• Immediate Settlement Calculation:

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

Where:

*   q = net pressure

*   B = footing width

*   ν = Poisson's ratio

*   E_s = Modulus of elasticity of soil (from lab/SPT correlations)

*   I_i = Influence factor (from charts, e.g., 1.06 for flexible square footing on clay).

*   \boxed{S_i = \frac{q B (1 - \nu^2)}{E_s} I_i}

• Consolidation Settlement (One-dimensional):

$$S_c = \frac{H}{1 + e_0} C_c \log_{10} \left( \frac{\sigma'_{mv} + \Delta \sigma}{\sigma'_{mv}} \right)$$

Where:

*   H = thickness of compressible layer

*   e₀ = initial void ratio

*   C_c = compression index

*   σ'ₘᵥ = initial effective vertical stress at mid-layer

*   Δσ = increase in vertical stress due to foundation load.

4. Types & Proportioning of Shallow Foundations

• Types: Isolated, Combined, Raft/Mat, Floating (excavated soil weight ≈ structure weight).

• Raft Foundation Proportioning: Depth chosen to reduce net pressure to ≤ allowable. Often used for weak soils or heavy loads.

• Basic Criteria: Adequate bearing capacity, tolerable settlement, and stability against sliding.

[!TIP] Exam Focus: Bearing capacity with water table correction (especially Nγ factor) and immediate settlement with given I_i are very common. Distinguish between gross/net pressures clearly.

C. Deep Foundations - Piles

1. Pile Classification & Functions

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

• By Action:

  • End-Bearing Pile: Rest on hard stratum.

  • Friction Pile: Resistance from skin friction.

  • Combined Pile: Both end-bearing and friction.

• By Installation: Driven (impact/vibratory), Bored (continuous/displacement), Screw, Under-reamed.

2. Pile Capacity Estimation Methods

• Static Formulae:

  • Clay (α-method):

$$Q_b = A_b \cdot N_c \cdot c$$

(base),

$$Q_s = \alpha \cdot \bar{c} \cdot A_s$$

(shaft). α = adhesion factor (0.6-1.0).

*   **Sand (β-method):** 

$$Q_s = \beta \cdot \bar{\sigma}'_v \cdot K \cdot \tan \delta \cdot A_s$$

. β = factor (0.2-0.4), K = lateral earth pressure coeff.

• Dynamic Formulae:

  • Engineering News Record (ENR):

$$Q_{safe} = \frac{W_1 h}{S + C} \times \frac{W_1}{W_1 + W_2} \times \frac{1}{FoS}$$

    *W1 = hammer weight, h = fall, S = final settlement per blow, C = constant (2.5 cm for drop hammer), W2 = pile weight.*

*   **Hiley's Formula (includes efficiency):** 

$$Q = \frac{\eta W H}{S + C/2}$$

where η = efficiency factor.

• Static Load Test: Direct measurement, most reliable. Ultimate load = load at settlement of 10% pile diameter (clay) or 5% (sand).

3. Negative Skin Friction (NSF)

• Definition: Downward drag force on pile due to relative downward movement of surrounding soil.

• Causes: Fill surcharge, lowering water table, consolidation of soft clay.

• Calculation for Single Pile:

$$Q_{nsf} = \gamma \cdot \Delta H \cdot K \cdot \tan \delta \cdot A_s$$

(for sand fill)

or 

$$Q_{nsf} = \bar{c}_u \cdot A_s$$

(for consolidating clay, use undrained cohesion).

*ΔH = thickness of compressible layer above neutral plane.*

• For Pile Group: Consider group perimeter in compressible layer.

4. Pile Group Capacity

• Group Efficiency (η): Ratio of group capacity to sum of individual capacities. η < 1.0 in cohesive soils due to overlapping stress bulbs.

• Ultimate Group Capacity:

  • Individual Failure: If piles far apart, Q_ug = η × Σ Q_ui.

  • Block Failure: If piles closely spaced, treat as single large foundation:

$$Q_{ug} = c \cdot (B_g \times L_g) + \gamma D_f \cdot (B_g \times L_g) \cdot N_q$$

(for clay)

    *B_g, L_g = group dimensions.*

• Spacing: Minimum 2-3× pile diameter to avoid group efficiency loss. Square/triangular arrangements.

5. Under-reamed Piles

• Concept: Single/multiple bulb(s) (under-ream) at base/shaft in expansive soils.

• Suitability: Expansive, collapsible, or loose soils. Provides uplift resistance.

• Ultimate Capacity (Tension/Compression):

$$Q_u = Q_{shaft} + Q_{bulb}$$

*Shaft:* α × c × A_s (clay) or β × K × σ'v × tanδ × A_s (sand).

*Bulb:* c × A_b (clay) or 0.5 × γ × B_b² × N_γ (sand).

*Where B_b = bulb diameter.*

6. Pile Design Problems

• Safe load = Ultimate capacity / FoS.

• Length determination: Solve for L in capacity equations considering layered soils.

• Bored vs. Driven: Driven piles have higher end-bearing and skin friction due to compaction; bored piles may have lower capacity in loose sands.

[!TIP] Exam Focus: Pile group capacity (individual vs. block failure) and negative skin friction calculations are extremely frequent. Under-reamed pile capacity is also common. Always check if end-bearing is neglected (as in many problems).

D. Earth Pressure & Retaining Structures

1. Types of Lateral Earth Pressure

• At-Rest (K₀): No lateral strain. Wall rigid, backfill undisturbed.

• Active (Kₐ): Wall moves away from soil, minimal lateral pressure.

• Passive (Kₚ): Wall pushed into soil, maximum lateral resistance.

• Condition: Active when wall tilts/separates; Passive when wall pushed.

2. Earth Pressure Theories

• Rankine's Theory (1875):

  • Assumptions: Smooth wall, horizontal/vertical backfill, no wall friction (δ=0), soil homogeneous, failure plane inclined at (45°+φ/2).

  • For Cohesionless Soil (c=0):

    • Active:

$$K_a = \tan^2 \left(45° - \frac{\phi}{2}\right)$$

    *   Passive: 

$$K_p = \tan^2 \left(45° + \frac{\phi}{2}\right)$$

*   **For Cohesive Soil (c>0):** Pressure at depth z: 

$$\sigma_h = \gamma z K_a - 2c \sqrt{K_a}$$

(active). Tension crack depth:

$$z_c = \frac{2c}{\gamma \sqrt{K_a}}$$

.

*   **Water Table:** Use submerged unit weight γ' for soil below WT, add pore pressure.

• Coulomb's Theory (1776):

  • Assumptions: Wedge failure, wall friction δ (0<δ<φ), backfill inclined β.

  • Active Pressure Coefficient:

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

*   **Merits over Rankine:** Considers wall friction (δ), inclined backfill (β), more realistic for rough walls.

• Culmann's Graphical Method: For active pressure with irregular/stratified backfill and surcharge. Construct failure wedges from trial failure planes.

3. Earth Pressure Calculations

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

• Point of Application: From base, for triangular diagram: H/3; for trapezoidal: at (H/3)×(2a+b)/(a+b) from base.

• Water Table Effect: Use γ' for soil below WT, add pore pressure (u = γ_w × depth below WT) to total stress diagram.

• Surcharge (q): Add uniform pressure q × K_a to diagram.

• Stratified Backfill: Calculate K_a for each layer, draw separate diagrams, sum.

4. Retaining Walls

• Types: Gravity (massive), Cantilever (stem+base+heel), Counterfort (with vertical webs), Sheet Pile (flexible, for waterfronts).

• Sheet Pile vs. Retaining Wall:

  | Sheet Pile | Retaining Wall | | :--- | :--- | | Flexible, thin sections | Rigid, massive | | Used for temporary/waterfront | Permanent, land structures | | Design for bending moment | Design for stability (overturning, sliding) | | Anchored/braced often | Self-supporting |

• Modes of Failure:

  1. Overturning: Moment due to lateral earth pressure > resisting moment.

  2. Sliding: Horizontal thrust > frictional resistance (μ × normal force).

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

  4. Excessive Settlement/Differential Settlement.

• Stability Analysis:

  • FOS against Overturning: ≥ 1.5-2.0.

  • FOS against Sliding: ≥ 1.5 (with/without shear key).

  • Base Pressure Distribution: Check for uniform/trapezoidal. Max pressure < allowable bearing capacity.

[!TIP] Exam Focus: Rankine's active pressure for cohesive soils (with tension crack) and Coulomb's theory comparison are very frequent. Problems with stratified backfill and water table are common. Always compute both magnitude and point of application.

E. Special Soils & Soil Improvement

1. Expansive Soils

• Characteristics: High montmorillonite clay content, high shrinkage-swelling, low strength, high compressibility.

• Problems: Heave in wet season, shrinkage cracks in dry season, foundation movement, structural damage.

• Preventive Measures:

  • Moisture Control: Maintain constant moisture (wetting/drying).

  • Soil Replacement: Remove expansive soil, replace with granular fill.

  • Chemical Stabilization: Lime/cement treatment to reduce swell potential.

  • Deep Foundations: Under-reamed piles, friction piles to bypass active zone.

  • Raft Foundations: Spread load to reduce pressure.

2. Collapsible Soils

• Characteristics: Metastable structure (e.g., loess), low moisture, high void ratio, sudden collapse upon wetting.

• Problems: Sudden settlement upon saturation, differential settlement.

• Preventive Measures:

  • Pre-wetting: Saturate soil before construction.

  • Compaction: Dynamic compaction, heavy tamping.

  • Replacement: Remove collapsible layer.

  • Deep Foundations: Piles to reach stable stratum.

3. Soil Stabilization

• Need: Improve strength, reduce swell/shrink, increase durability.

• Methods:

  • Mechanical: Compaction (static, vibratory, kneading).

  • Chemical: Lime, cement, bitumen, fly ash.

  • Electrical: Electro-osmosis (for fine-grained soils, dewatering + consolidation).

4. Geosynthetics

• Types & Functions:

  | Type | Primary Functions | | :--- | :--- | | Geotextile (woven/non-woven) | Separation, Filtration, Reinforcement, Drainage | | Geogrid (uniaxial/biaxial) | Reinforcement (high tensile strength) | | Geomembrane (HDPE, LDPE) | Containment (liners for ponds, landfills) | | Geocomposite (geonet + geotextile) | Drainage (edge drains, blanket drains) |

• Uses in Foundation Engineering:

  • Separation: Over weak soils, between subgrade and ballast.

  • Reinforcement: In retaining walls, slopes, embankments.

  • Drainage: Horizontal/vertical drainage paths.

  • Protection: Over geomembranes/waterproofing.

[!TIP] Exam Focus: Characteristics and preventive measures for expansive and collapsible soils are highly recurrent. Geosynthetics types and functions are also frequent (short notes).

F. Settlement & Related Calculations

1. Immediate Settlement (Reiterated)

• Theory: Elastic half-space (Boussinesq). Influence factor Iᵢ depends on foundation shape, rigidity, and soil Poisson's ratio.

• Estimation of Eₛ: From lab tests or correlations:

  • For sand:

$$E_s = 500 \text{ to } 1000 \times N$$

(in t/m²).

*   For clay: 

$$E_s = 500 \text{ to } 1000 \times c_u$$

(in t/m²).

• Problem Type: Given q, B, ν, Eₛ, Iᵢ → compute Sᵢ.

2. Consolidation Settlement (Core Concept)

• One-Dimensional Consolidation (Terzaghi):

$$S_c = \frac{H}{1 + e_0} C_c \log_{10} \left( \frac{\sigma'_{mv} + \Delta \sigma}{\sigma'_{mv}} \right)$$

*For overconsolidated clay (OCR > 1), use recompression index C_r for Δσ < σ'_p:*

$$S_c = \frac{H}{1 + e_0} \left[ C_c \log_{10} \frac{\sigma'_{mv} + \Delta \sigma}{\sigma'_p} + C_r \log_{10} \frac{\sigma'_p}{\sigma'_{mv}} \right]$$

• Key Parameters: e₀ (from undisturbed sample), C_c (from oedometer test), σ'ₘᵥ (initial effective stress), σ'_p (preconsolidation pressure), OCR = σ'_p / σ'ₘᵥ.

3. Plate Load Test

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

• Interpretation: Plot load-settlement curve. Ultimate load = load at rapid settlement increase.

• Extrapolation to Field Footing:

  • For Cohesive Soils (clay): Ultimate bearing capacity independent of size (Terzaghi). So, qₐ (footing) = qₐ (plate).

  • For Cohesionless Soils (sand): Ultimate bearing capacity ∝ B. So,

$$q_{footing} = q_{plate} \times \frac{B_{footing}}{B_{plate}}$$

.

*   **Settlement Extrapolation:** For similar soil and pressure level, settlement ∝ log(B). Use: 

$$S_{footing} = S_{plate} \times \frac{\log(B_{footing}/B_{plate})}{\log(B_{plate}/B_{plate})}$$

? Actually, common approximation: For same Δσ, S ∝ B. But more accurately, from elastic theory, S ∝ B. So if pressures are same, S_footing ≈ S_plate × (B_footing / B_plate). Check exam question context.

*   **Typical Problem:** "Plate 0.3 m square settles 4 mm at load q. Find settlement of 2 m square footing at same q." → For clay, same q → same settlement? Not exactly, but often assumed same for ultimate capacity. For settlement, if soil is cohesionless, S ∝ B, so S_footing = 4 × (2/0.3) ≈ 26.7 mm. **But careful:** In clay, immediate settlement Sᵢ ∝ B, consolidation settlement S_c ∝ log(B). So depends on dominant component. Past question (Jun 2025) gave influence factor and asked for immediate settlement directly, not extrapolation. May 2024 asked: "Plate ultimate load 180 kPa, find ultimate capacity of 2m footing?" → For clay, same = 180 kPa; for sand, q ∝ B → 180 × (2/0.3) = 1200 kPa. **Answer depends on soil type.**

[!TIP] Exam Focus: Plate load test extrapolation depends critically on soil type. For clay, q_u is size-independent; for sand, q_u ∝ B. Settlement extrapolation is less common but know the principle. Consolidation settlement formula is essential.

Final Reminder: These notes are tailored to the Foundation Engineering questions provided. For the actual Earthquake Resistant Design of Structures (CE-802(D)), refer to the official syllabus covering IS 1893, 13920, seismic analysis methods, ductility, etc.