Earthquake Resistant Design of Structures (CE-802 (D)) - Unit 3 Short Notes

UNIT 3: FOUNDATION ENGINEERING

1.0 SOIL EXPLORATION AND SITE INVESTIGATION

1.1 Methods of Boring/Hole Advancement

• Rotary Drilling:

  • Procedure: A rotating drill bit (diamond or tungsten carbide) attached to a drill string cuts the soil/rock. Circulation of drilling fluid (bentonite slurry or water) cools the bit, carries cuttings to the surface, and stabilizes the borehole.

  • Advantages over Percussion/Auger:

    • Produces continuous, undisturbed samples in cohesive soils and rock cores.

    • Faster in hard soils and rock.

    • Borehole is more stable due to fluid pressure.

    • Minimal disturbance to surrounding soil.

• Other Methods:

  • Percussion (Shell & Auger): Repeated lifting and dropping of a chisel or auger. Suitable for granular soils above water table. High disturbance.

  • Auger Boring: Hand/machine-driven helical auger. Fast, economical for shallow depths in soft soils. Disturbed samples only.

1.2 In-Situ Testing

• Standard Penetration Test (SPT):

  • Procedure: A split-spoon sampler (50.8 mm ID, 60.3 mm OD) is driven 450 mm into the bottom of a borehole using a 63.5 kg hammer dropped from 760 mm. The number of blows for the last 300 mm is the N-value (or N60).

  • Corrections to N-value & Need:

    [!TIP] Common Pitfall: Using raw N-value leads to erroneous density/strength estimation.

    • Overburden Pressure Correction (N₁): Normalizes N for different effective overburden stress ($$\displaystyle \sigma'_{vo} $$).

$$N_1 = N \times \left( \frac{100 \text{ kPa}}{\sigma'_{vo}} \right)^{0.5} \quad (\text{for } \sigma'_{vo} \text{ in kPa})$$

    *   **Dilatancy Correction (N₂):** For dense sands/gravels below water table, negative pore pressure increases N. Corrected value: $$\displaystyle N_2 = N_1 \times f $$ (where $$\displaystyle f < 1 $$ from charts).

    *   **Rod Length Correction:** Energy loss due to rod friction. Use correction factor based on rod length above the anvil.

    *   **Sampler Type Correction:** Different samplers (e.g., DSTM vs. standard) have different energy ratios.

*   **Final Corrected N:** $$\displaystyle N_{corr} = N_1 \times \text{(Dilatancy factor)} \times \text{(Rod factor)} $$.

• Cone Penetration Test (CPT):

  • A cone (10 cm² area, 60° apex) with friction sleeve is pushed into soil at 20 mm/s. Measures cone resistance ($$\displaystyle q_c $$) and sleeve friction ($$\displaystyle f_s $$) continuously.

  • Comparison with SPT (SCPT):

    | Feature | SPT | CPT | | :--- | :--- | :--- | | Sample | Disturbed | None (continuous profile) | | Discretization | Intermittent (every 1.5m) | Continuous | | Resolution | Low | High | | Data | Single N-value | $$\displaystyle q_c $$, $$\displaystyle f_s $$, pore pressure ($u$) | | Energy | Variable (~60% avg) | Constant, controlled |

• Plate Load Test:

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

  • Interpretation: Load-settlement curve gives ultimate bearing capacity ($$\displaystyle q_u $$) and modulus of subgrade reaction ($k$).

  • Settlement Prediction for Different Footing Sizes (Clay): For cohesive soils, immediate settlement scales with footing width.

$$\frac{S_{B}}{S_{plate}} = \frac{B}{B_{plate}} \quad \text{(for same pressure)}$$

For consolidation settlement, use $S \propto B$.

1.3 Soil Sampling

• Disturbed vs. Undisturbed:

  • Disturbed: Structure altered. Used for classification, water content, compaction tests.

  • Undisturbed: Structure preserved. Essential for consolidation, triaxial, permeability tests.

• Sampling Tube Parameters:

  • Inside Clearance (Cᵢ): $$\displaystyle (ID_{tube} - ID_{cutter}) / ID_{tube} $$. Allows sample expansion into tube. Typical: 0.5-1.5%.

  • Outside Clearance (Cₒ): $$\displaystyle (OD_{cutter} - ID_{tube}) / ID_{tube} $$. Reduces friction during driving. Typical: 0-2%.

  • Area Ratio (Aᵣ): $$\displaystyle (OD_{cutter}^2 - ID_{tube}^2) / ID_{tube}^2 $$. Should be < 20% for good quality.

• Sample Quality: Assessed by recovery ratio, visual examination (disturbance, layering), and laboratory tests (e.g., consolidation).

1.4 Subsurface Investigation Planning

• Depth of Boreholes (IS Criteria):

  • Minimum depth = width of foundation ($B$).

  • Must penetrate weak stratum (e.g., clay) to at least 2B or to a firm stratum.

  • In compressible soils, depth should reach non-compressible stratum or where $$\displaystyle \Delta\sigma / \sigma'_{vo} < 10\% $$.

  • For piles, depth = pile length + 3-5 m.

• Bore-log Report: Graphical/ tabular record of soil strata, depth, description, SPT N-values, water table, lab test results.

• Geophysical Methods: Seismic refraction, electrical resistivity, GPR. Used for rapid profiling, depth to bedrock, groundwater, detecting anomalies.

2.0 BEARING CAPACITY OF SHALLOW FOUNDATIONS

2.1 Fundamental Definitions

2.2 Factors Affecting Bearing Capacity

• Soil: $c$, $\phi$, $\gamma$, stratification, water table.

• Foundation: Dimensions ($B$, $L$), depth ($$\displaystyle D_f $$), shape, load inclination.

• Construction: Rate of loading, drainage conditions.

2.3 Theories and Methods

• Terzaghi’s Bearing Capacity Theory (1943):

  • Assumes general shear failure, strip footing, base horizontal, soil above base is weightless.

  • Equation (Strip Footing):

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

*   **Shape Factors:**

    *   Square: $$\displaystyle q_u = 1.3c N_c + \gamma D_f N_q + 0.4 \gamma B N_\gamma $$

    *   Circular: $$\displaystyle q_u = 1.3c N_c + \gamma D_f N_q + 0.3 \gamma B N_\gamma $$

    *   Rectangular: $$\displaystyle q_u = \left(1 + 0.2\frac{B}{L}\right) c N_c + \gamma D_f N_q + \left(1 - 0.4\frac{B}{L}\right) 0.5 \gamma B N_\gamma $$

*   **Bearing Capacity Factors ($$\displaystyle N_c, N_q, N_\gamma $$):** Functions of $\phi$. For $$\displaystyle \phi = 0^\circ $$: $$\displaystyle N_c = 5.7 $$, $$\displaystyle N_q = 1 $$, $$\displaystyle N_\gamma = 0 $$.

• IS Code Method (IS: 6403): Uses Terzaghi’s equation with depth factors and inclination factors.

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

Where $s$, $d$, $i$ are shape, depth, and load inclination factors.

2.4 Failure Modes

2.5 Special Cases

• Water Table Effect:

  • If water table above base: Use submerged unit weight ($\gamma'$) for $\gamma$ terms and effective cohesion ($c'$). Apply water table correction factor ($$\displaystyle r_w $$).

  • Correction Factor (r_w):

$$r_w = 0.5 \left(1 - \frac{D_w}{B}\right) \quad \text{for } N_\gamma \text{ term}$$

    Where $$\displaystyle D_w $$ = depth of water table below base. If $$\displaystyle D_w \geq B $$, $$\displaystyle r_w = 1 $$.

• c-φ Soils (Immediate vs. Long-term):

  • Immediate (Short-term): Use undrained parameters ($$\displaystyle c_u $$, $$\displaystyle \phi_u = 0^\circ $$). $$\displaystyle N_c = 5.14 $$ (for $$\displaystyle \phi=0 $$).

  • Long-term (Drained): Use effective parameters ($c'$, $\phi'$).

• Stratified Soils: Use weighted average of $c$, $\phi$ for critical layer or apply Hansen’s correction factors for strength discontinuity.

3.0 SETTLEMENT OF FOUNDATIONS

3.1 Components of Settlement

1. Immediate (Elastic) Settlement ($$\displaystyle S_i $$): Occurs during/soon after construction in cohesive soils (undrained) and cohesionless soils (due to shear distortion).

2. Primary Consolidation Settlement ($$\displaystyle S_c $$): Due to expulsion of pore water from cohesive soils under sustained load. Time-dependent.

3. Secondary Compression Settlement ($$\displaystyle S_s $$): Due to plastic adjustment of soil skeleton after primary consolidation. Long-term.

3.2 Immediate Settlement Calculation

• Equation (Elastic Theory for Cohesive Soils):

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

Where:

*   $q$ = net pressure

*   $B$ = footing width

*   $\nu$ = Poisson’s ratio

*   $$\displaystyle E_s $$ = **Secant modulus** at stress level $q$

*   $$\displaystyle I_f $$ = **Influence factor** (from charts/tables). For rectangular footing on elastic half-space, $$\displaystyle I_f \approx 1.06 $$ for $L/B \geq 2$.

• Key: Use $$\displaystyle E_s $$ corresponding to stress increase due to applied load, not in-situ stress.

3.3 Settlement Prediction from Plate Load Test

• Method 1 (Bearing Capacity Analogy): For cohesive soils, ultimate bearing capacity $$\displaystyle q_u \propto B^0 $$ (Terzaghi). Hence, settlement at same net pressure:

$$S_{B} = S_{plate} \times \frac{B}{B_{plate}}$$

• Method 2 (Settlement Curves): Plot $S$ vs. $p$ for plate and footing. Read settlement for footing at pressure $p$ from plate curve using influence factor ratio.

4.0 EARTH PRESSURE AND RETAINING STRUCTURES

4.1 Types of Earth Pressure

• At Rest ($$\displaystyle K_0 $$): Wall does not move. $$\displaystyle K_0 = 1 - \sin\phi' $$ (for normally consolidated clays/sands).

• Active ($$\displaystyle K_a $$): Wall moves away from backfill. Minimum pressure.

• Passive ($$\displaystyle K_p $$): Wall moves into backfill. Maximum pressure.

$$K_a = \tan^2\left(45^\circ - \frac{\phi}{2}\right), \quad K_p = \tan^2\left(45^\circ + \frac{\phi}{2}\right)$$

4.2 Classical Theories

4.3 Active Earth Pressure Calculation

• Homogeneous Soil (Dry): $$\displaystyle P_a = \frac{1}{2} \gamma H^2 K_a $$ (per unit length). Acts at $H/3$ from base.

• Stratified Backfill: Replace top layer by equivalent surcharge ($$\displaystyle q = \gamma_1 h_1 $$) on lower layer. Calculate $$\displaystyle P_a $$ for each layer and sum.

• With Water Table & Seepage: Use submerged unit weight ($\gamma'$) below water table. Add hydrostatic pressure ($$\displaystyle \gamma_w h $$) to total pressure diagram.

• Tension Crack Depth (Cohesive Soil, Rankine):

$$z_t = \frac{2c}{\gamma \sqrt{K_a}} \quad \text{(Depth from surface)}$$

4.4 Passive Earth Pressure

• Used for stability (e.g., counterforts, anchor blocks). Magnitude: $$\displaystyle P_p = \frac{1}{2} \gamma H^2 K_p $$ (cohesionless). Design rarely uses full $$\displaystyle K_p $$ due to wall movement requirements.

4.5 Retaining Wall Design & Analysis

• Total Thrust: Vector sum of all pressures (earth, water, surcharge).

• Point of Application: For triangular distribution, at $H/3$ from base. For complex distributions, take moment about base.

• Modes of Failure:

  1. Overturning

  2. Sliding (along base or weak plane)

  3. Excessive bearing pressure (uneven distribution)

  4. Deep-seated failure (global stability)

4.6 Sheet Piles vs. Retaining Walls

5.0 PILE FOUNDATIONS

5.1 Types and Functions

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

• By Function: End-bearing (hard stratum), Friction (shaft resistance), Combined.

• By Installation: Driven (displacement), Bored (non-displacement), Under-reamed (tension/expansive soils).

5.2 Pile Capacity Estimation

• Static Methods:

  • α-method (Cohesive soils): Ultimate shaft friction $$\displaystyle f_s = \alpha c_u $$. End bearing $$\displaystyle q_b = N_c c_u $$ (usually $$\displaystyle N_c = 9 $$).

$$Q_u = \sum (f_s \cdot A_s) + q_b \cdot A_b$$

*   **β-method (Cohesionless soils):** $$\displaystyle f_s = \beta \sigma'_{vo} $$ (where $$\displaystyle \beta = K \tan\delta $$). $$\displaystyle q_b = N_q \sigma'_{vo} $$.

• Dynamic Methods (Drop Hammer):

  • Formula (Engineering News Record):

$$Q_{allow} = \frac{W_1 h}{s + 0.1} \times \frac{W_1}{W_1 + W_2} \times \frac{1}{FOS}$$

    Where $$\displaystyle W_1 $$ = hammer weight, $h$ = fall, $s$ = final settlement per blow, $$\displaystyle W_2 $$ = pile weight.

*   **Including Elastic Compression & Restitution:** More complex forms account for pile set and coefficient of restitution ($e$).

5.3 Pile Groups

• Group Efficiency ($\eta$): $$\displaystyle \eta = \frac{Q_{ug}}{n Q_{us}} $$. Usually < 1 due to overlapping stress zones.

• Spacing Factors: Minimum center-to-center spacing = 3D (driven) or 2D (bored) to avoid group effect.

• Group Capacity:

  • Block Failure (Clays): Treat as single large pile of dimensions $$\displaystyle (n_1 B) \times (n_2 B) $$. $$\displaystyle Q_{ug} = c_u \cdot A_{block} + \text{shaft of block} $$.

  • Individual Failure (Sands): $$\displaystyle Q_{ug} \approx n \cdot Q_{us} $$ (if spacing adequate).

  • Practical: $$\displaystyle Q_{ug} = \eta \cdot n \cdot Q_{us} $$.

5.4 Negative Skin Friction (NSF)

• Cause: Downward movement of soil relative to pile (e.g., fill placement, consolidation, soft soil settlement).

• Effect: Increases load on pile, reduces capacity.

• Calculation (Single Pile):

$$Q_{nsf} = \alpha \cdot c_u \cdot A_s \quad \text{(cohesive)} \quad \text{or} \quad Q_{nsf} = \beta \cdot \gamma \cdot z \cdot A_s \quad \text{(cohesionless)}$$

Where $z$ = depth of compressible layer.

• For Group: Consider envelope area of group.

5.5 Special Pile Types

• Under-reamed Piles:

  • Concept: Single/multiple bulbs (under-reams) at intervals along shaft. Provides tensile and compressive capacity.

  • Suitability: Expansive soils, loose sands, zones with swelling pressure.

  • Components: Shaft, bulb (diameter 2-3× shaft), neck.

  • Capacity (Tension): $$\displaystyle Q_t = \sum (A_b \cdot q_b) + \alpha \cdot \sum (A_s \cdot c_u) $$ (neglect adhesion in bulb zone).

• Bored Piles in Layered Soils:

  • Length Determination: For given load $Q$, find $L$ such that $$\displaystyle Q_u \geq Q \times FOS $$. Sum capacities from each layer:

$$Q_u = \sum (\alpha_i c_{ui} \cdot \pi D L_i) + q_{b} \cdot \frac{\pi D^2}{4}$$

    Where $$\displaystyle q_b $$ from bottom layer.

5.6 Design Parameters

• Adhesion Factor (α): $$\displaystyle \alpha = 0.7 $$ for soft clays, $0.5-0.6$ for stiff clays. Reduces $$\displaystyle c_u $$ for shaft friction.

• Water Table: Use effective stress parameters below WT. For shaft friction in saturated clay, use undrained $$\displaystyle c_u $$ (total stress method).

• Stratification: Use minimum $$\displaystyle c_u $$ or $\phi$ along shaft for conservative design.

6.0 SPECIAL SOILS AND GROUND IMPROVEMENT

6.1 Expansive Soils

• Characteristics: High montmorillonite content, high LL (>50%), high shrink-swell potential, low strength when wet, cracks on drying.

• Problems: Differential heave/shrinkage, cracking of foundations/structures, tilting.

• Preventive Measures:

  • Moisture Control: Maintain constant moisture (impermeable layer, landscaping).

  • Chemical Stabilization: Lime, cement.

  • Under-reamed Piles: Transfer load to stable stratum.

  • Raft Foundations: Spread load.

  • Soil Replacement: Remove & replace with non-expansive fill.

6.2 Collapsible Soils

• Characteristics: Loess deposits, low moisture, metastable (cemented by salts/calcium), high porosity, sudden collapse upon wetting.

• Problems: Sudden settlement on wetting (e.g., due to rain, pipe leak).

• Preventive Measures:

  • Pre-wetting: Saturate soil before construction to induce collapse.

  • Compaction: Dynamic compaction, heavy tamping.

  • Pile Foundations: Transfer load through collapsible zone.

  • Chemical Stabilization: Lime, cement.

6.3 Geosynthetics

6.4 Soil Stabilization Techniques

• Mechanical: Compaction (increases density, reduces voids), blending with good soil.

• Chemical: Lime (reduces plasticity, strength gain in clays), Cement (granular soils, low plasticity), Bitumen (waterproofing, binding).

• Electrical: Electro-osmosis or Electro-kinetic consolidation.

  • Process: Apply DC current between electrodes inserted in soil.

  • Effect: Pore water moves from anode (+) to cathode (-). Consolidation occurs.

  • Applications: Accelerate consolidation in very low permeability clays, dewatering, soil stabilization.

7.0 SHALLOW FOUNDATIONS: TYPES AND DESIGN ASPECTS

7.1 Types of Footings

• Isolated: Under single column.

• Combined: Under two or more columns.

• Strip: Under continuous wall.

• Raft (Mat): Covers entire area. Used when:

  • Soil low bearing capacity.

  • Close column spacing.

  • Basement needed.

• Floating: Raft designed such that load removed from soil = weight of soil excavated. Net pressure ≈ 0.

7.2 Floating/Raft Foundations

• Concept: Excavate soil, construct raft, so that total load (structure + raft) = weight of displaced soil.

• Proportioning: Depth chosen to balance loads. Often used in soft clays.

• Bearing Capacity: Check using net pressure (which is small/zero).

7.3 Well Foundations

• Components (with Sketch):

  
  Well Cap
  
    |
  
  Well Steining (masonry above curb)
  
    |
  
  Well Curb (bottom cutting edge, concrete)
  
    |
  
  Well Lining (temporary, inside)
  
    |
  
  Bottom Plug (concrete)
  
  

  • Cutting Edge: Lower edge of well curb (steel angle).

  • Well Steining: Masonry above curb, provides weight for sinking.

  • Well Cap: RCC beam on top to distribute column load.

• Uses/Advantages: Deep foundations for bridges, harbors, river structures. Can be sunk to great depth, inspect bottom, provide large base.

8.0 STRESS DISTRIBUTION IN SOILS (MISCELLANEOUS)

8.1 Boussinesq’s Theory

• Assumptions: Homogeneous, isotropic, elastic, semi-infinite half-space. Point load applied vertically.

• Vertical Stress ($$\displaystyle \sigma_z $$) at Point (r, z):

$$\sigma_z = \frac{3P}{2\pi} \cdot \frac{z^3}{(r^2 + z^2)^{5/2}}$$

• Influence Charts: Based on this equation (e.g., Newmark’s chart).

8.2 Westergaard’s Theory

• Assumptions: Soil contains vertical, infinitely long, incompressible sheets (cracks). Load carried only by vertical columns of soil between sheets. No lateral strain.

• Vertical Stress:

$$\sigma_z = \frac{P}{\pi z^2} \cdot \frac{1}{(1 + 2(r/z)^2)^{3/2}}$$

• Essential Difference: Westergaard gives higher stress near axis and faster decay with $r$ compared to Boussinesq. More realistic for stratified or fissured clays.

9.0 COMPACTION AND FIELD COMPACTION

9.1 Compaction Equipment

• Rollers: Smooth-wheeled (granular), Padfoot (cohesive), Pneumatic-tired (flexible).

• Rammers: Small, for confined areas.

• Vibratory Plates/ Rollers: For granular soils, deep compaction.

9.2 Laboratory Compaction Tests

[!TIP] Exam Tip: Modified Proctor gives higher MDD & lower OMC due to higher compaction energy. Always specify which test is used for field specification.