Foundation Engineering (CE-802 (B)) - Unit 5 Short Notes

1.0 SUBSURFACE INVESTIGATION & SAMPLING

1.1 Methods of Boring/Hole Advancement

• Percussion Boring: Repeated lifting and dropping of a heavy chisel to break rock/soil. Uses shell & auger to remove cuttings. Suitable for boulders/rock.

• Rotary Drilling: Most versatile & widely used. A rotating drill bit (diamond, tungsten carbide) cuts soil/rock. Circulates drilling fluid (bentonite mud) to cool bit, carry cuttings, and stabilize borehole walls.

  [!TIP] Advantages over percussion: Faster in soft soils & rock, produces undisturbed samples (with core barrel), better control in loose sands/water-bearing strata.

• Wash Boring: Jet of water softens soil; chopping bit breaks it; water carries cuttings to surface. Quick but highly disturbs granular soils.

• Auger Boring: Hand/machine-driven helical auger. Good for shallow depths in cohesive soils. Disturbed samples only.

1.2 In-Situ Testing

1.2.1 Standard Penetration Test (SPT)

• Procedure: Drive a split spoon sampler (50.8 mm ID, 63.5 mm OD) into soil at borehole bottom by a 63.5 kg hammer falling 760 mm. Record blows for each 150 mm penetration. N-value = blows for last 300 mm (discard first 150 mm as seating).

• Equipment: Donut hammer, tripod, drilling rig, sampler, liners.

• Corrections to N-value (Critical for Design):

  1. Overburden Pressure Correction (N₁): $$\displaystyle N_1 = N \times \frac{\bar{\sigma}_v'}{P_a} $$ where $$\displaystyle \bar{\sigma}_v' $$ = avg. effective overburden pressure (kPa) at test depth, $$\displaystyle P_a = 100 $$ kPa. For $$\displaystyle \phi > 5° $$, use $$\displaystyle N_2 = N_1 \times \left( \frac{P_a}{\bar{\sigma}_v'} \right)^{0.5} $$.

  2. Dilatancy Correction (N₂): For dense saturated fine sands/silts (N > 15). $$\displaystyle N_2 = N_1 \times \frac{2}{1 + \frac{N_1 \sigma'_v}{P_a}} $$.

  3. Energy Correction (N₆₀): Corrects to 60% standard energy. $$\displaystyle N_{60} = N_{obs} \times \frac{E_R}{60} $$ where $$\displaystyle E_R $$ = measured energy ratio (%). Standard is 60%.

  4. Rod Length Correction: For rod length < 6m, energy transfer reduces.

  [!TIP] Final Corrected N-value: Apply in order: Rod length → N₁ (overburden) → N₂ (dilatancy) → N₆₀ (energy). N₆₀ is most commonly used for liquefaction/empirical correlations.

• Significance: Index of relative density/consistency, estimate of φ, c, modulus, liquefaction potential.

• Limitations: Disturbs granular soils, not suitable for very soft clays, results variable.

1.2.2 Cone Penetration Test (CPT) & Seismic CPT (SCPT)

• Procedure: Push a standard cone (10 cm² area, 60° apex) into soil at 20 mm/s. Measure tip resistance (q_c) and sleeve friction (f_s) continuously. u₂ measures pore pressure.

• SCPT: Adds a seismic sensor to measure shear wave velocity (V_s) for small-strain stiffness.

• Comparison SPT vs. CPT:

  | Feature | SPT | CPT | |-------------------|----------------------------------|----------------------------------| | Disruption | High (chopping action) | Low (continuous push) | | Continuity | Discrete (every 1.5m) | Continuous profile | | Outputs | Single N-value | q_c, f_s, u₂, V_s (SCPT) | | In Sands | Better density estimate | Better friction estimate | | Soft Clays | Poor (sample disturbance) | Excellent |

1.2.3 Geophysical Methods

• Seismic Refraction: Measures travel time of compressional waves (P-waves) to determine layer thickness & depth to bedrock from velocity contrasts.

• Electrical Resistivity: Measures soil resistivity to detect stratification, groundwater, voids. Wenner & Schlumberger arrays common.

1.3 Soil Sampling

1.3.1 Disturbed vs. Undisturbed Samples

• Disturbed: Structure altered. Used for classification tests (sieve, hydrometer, Atterberg limits, compaction).

• Undisturbed: Structure & moisture preserved. Used for strength & consolidation tests (triaxial, oedometer). Quality assessed by sample recovery ratio and visual inspection (no smearing, distortion).

1.3.2 Sampler Design Parameters

For a thin-wall tube sampler (diameter D, wall thickness t):

• Inside Clearance (C_i): $$\displaystyle (D_i - D_s)/D_s \times 100\% $$. Allows sample to expand into sampler (reduces friction). Optimal: 0.5-3%.

• Outside Clearance (C_o): $$\displaystyle (D_s - D_o)/D_o \times 100\% $$. Reduces drag on sample exterior. Optimal: 0-2%.

• Area Ratio (A_r): $$\displaystyle (D_s^2 - D_i^2)/(D_i^2) \times 100\% $$. Measures cutting edge sharpness. A_r < 10% for undisturbed.

  [!TIP] Sample Disturbance: High Area Ratio (>13%) causes significant disturbance. Low Inside Clearance (<0.5%) causes "suction" and sample expansion.

1.3.3 CNS Layer (Constant Normal Stress)

Concept in sampling: During driving, soil sample inside sampler experiences constant radial stress equal to in-situ lateral stress if C_i ≈ C_o. Minimizes disturbance.

1.4 Bore-log & Reporting

• Components: Borehole ID, location, depth, water table, soil description (USCS/IS classification), stratification (depth, thickness), sample type & depth, N-value, lab test results, groundwater level.

• IS Code Criteria (IS 1892:2016):

  • Depth: At least equal to width of foundation or 1.5 × width for clay, 2 × width for sand. Must penetrate weak layer to firm stratum.

  • Spacing: 15-30m for regular sites, closer for variable strata. Minimum 3 boreholes for small sites.

2.0 SHALLOW FOUNDATIONS - BEARING CAPACITY & SETTLEMENT

2.1 Fundamental Definitions

• Gross/Total Pressure (q): Load/area including weight of foundation & overburden.

• Net Pressure (q_net): $$\displaystyle q_{net} = q - \gamma D_f $$ (excludes overburden).

• Ultimate Bearing Capacity (q_u): Gross pressure causing shear failure.

• Net Ultimate Bearing Capacity (q_nu): $$\displaystyle q_{nu} = q_u - \gamma D_f $$.

• Net Safe Bearing Capacity (q_ns): $$\displaystyle q_{ns} = q_{nu} / FOS $$.

• Allowable Bearing Pressure (q_a): Pressure used for design (includes settlement criteria). Usually $$\displaystyle q_a \leq q_{ns} $$.

2.2 Bearing Capacity Theories

2.2.1 Terzaghi's Theory (1943)

• Assumptions: Strip footing, rough base, φ > 0°, failure surface as log spiral + linear rays, $c-\phi$ soil, $$\displaystyle D_f/B \leq B $$, ground surface horizontal.

• Equations:

  • Strip: $$\displaystyle q_u = c'N_c + q N_q + 0.5 \gamma B N_\gamma $$

  • Square: $$\displaystyle q_u = 1.3 c'N_c + q N_q + 0.4 \gamma B N_\gamma $$

  • Circular: $$\displaystyle q_u = 1.3 c'N_c + q N_q + 0.3 \gamma B N_\gamma $$

  • Where $$\displaystyle q = \gamma D_f $$, $$\displaystyle N_c, N_q, N_\gamma $$ = bearing capacity factors (function of φ').

2.2.2 IS Method (BIS Code 6403:1981)

• General Equation: $$\displaystyle q_u = c' N_c r_c + q N_q r_q + 0.5 \gamma B N_\gamma r_\gamma $$

• Correction Factors:

  • Shape Factors (r_c, r_q, r_γ): For rectangular footing: $$\displaystyle r_c = 1 + 0.2 \frac{B}{L} $$, $$\displaystyle r_q = 1 + 0.1 \frac{B}{L} $$, $$\displaystyle r_γ = 1 - 0.3 \frac{B}{L} $$.

  • Depth Factor (r_q, r_γ): For $$\displaystyle D_f/B \leq 1 $$: $$\displaystyle r_q = 1 + 0.1 \frac{B}{L} \frac{D_f}{B} $$, $$\displaystyle r_γ = 1 - 0.3 \frac{B}{L} \frac{D_f}{B} $$.

  • Ground Water Table Factor (r_w): If water table at/base: $$\displaystyle r_w = 1 $$; if at surface: $$\displaystyle r_w = 0.5 $$; intermediate: linear interpolation based on submerged unit weight above WT.

2.3 Bearing Capacity Calculations

• For Cohesive Soils (φ=0°): $$\displaystyle N_c = 5.7 $$ (Terzaghi), $$\displaystyle N_q = 1 $$, $$\displaystyle N_γ = 0 $$. $$\displaystyle q_u = c_u N_c + \gamma D_f $$.

• For Cohesionless Soils (c=0°): $$\displaystyle q_u = q N_q + 0.5 \gamma B N_γ $$. Water table correction critical: Use submerged unit weight (γ') for layer below WT, apply $$\displaystyle r_w $$ factor.

• Factor of Safety: Applied to net ultimate capacity ($$\displaystyle q_{ns} = q_{nu}/FOS $$) for cohesive soils. For cohesionless, FOS on gross q_u is common due to settlement control.

• Water Table Cases:

  1. Far below base: Use γ (total).

  2. At ground level: Use γ' (submerged) + hydrostatic pressure (separate term).

  3. Intermediate: Calculate effective vertical stress at base level (γ' above WT, γ below).

2.4 Settlement of Shallow Foundations

2.4.1 Components of Total Settlement (S_total)

1. Immediate (Elastic) Settlement (S_i): Due to shear strain, occurs instantaneously in saturated clays (undrained) & granular soils.

2. Primary Consolidation Settlement (S_c): Due to expulsion of pore water from saturated clays, time-dependent.

3. Secondary Consolidation (S_s): Due to plastic adjustment of soil skeleton after primary consolidation, very slow.

2.4.2 Immediate Settlement Calculation

For cohesive soils (φ≈0°):

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

• $q$ = net pressure.

• $B$ = footing width.

• $\nu$ = Poisson's ratio (0.5 for undrained clay).

• $$\displaystyle E_s $$ = Secant modulus at relevant stress level (from lab oedometer/consolidated undrained triaxial).

• $$\displaystyle I_f $$ = Influence factor (from charts/tables, e.g., 1.06 for 1.6m×1.6m footing at 0.8m depth, ν=0.25).

[!TIP] Key: Use E_s at working stress, not E_50 or E_100. For sands, use E_s from correlation with N-value.

2.4.3 Plate Load Test & Scaling

• Test: Load a rigid plate (0.3m sq.) incrementally, measure settlement. Plot load-settlement curve.

• Ultimate Bearing Capacity (q_u,plate): From curve (e.g., settlement = 0.1B or plunging).

• Scaling to Footing (Terzaghi & Peck):

  • For Cohesive Soils: $$\displaystyle q_{u,footing} \approx q_{u,plate} $$ (size effect negligible).

  • For Cohesionless Soils: $$\displaystyle S_{footing} = S_{plate} \times \frac{B_{footing}}{B_{plate}} $$ (settlement proportional to width).

  • For Bearing Capacity: $$\displaystyle q_{u,footing} = q_{u,plate} \times \frac{B_{footing}}{B_{plate}} $$ (for sands, capacity ∝ B).

2.5 Types & Proportioning of Shallow Foundations

• Types: Isolated, Combined, Strap, Mat/Raft.

• Floating Foundation: Raft foundation where weight of structure + raft = weight of soil excavated. Net increase in vertical stress ≈ 0. Minimizes settlement.

• Raft Proportioning: Thickness ($t$) designed for shear & bending. For flat slab: $$\displaystyle t \geq \frac{B}{6} $$ (simplified). Must satisfy FOS > 1.5 against shear.

• Satisfactory Performance Criteria: Adequate bearing capacity, ** tolerable settlement** (uniform & total), stability (no tilting).

3.0 PILE FOUNDATIONS

3.1 Classification & Functions

• By Function: End-bearing, Friction, Combined.

• By Material: Timber, Concrete, Steel, Composite.

• By Installation: Driven (displacement), Bored (non-displacement), Screw, Under-reamed.

3.2 Load Carrying Capacity of Single Pile

3.2.1 Static Formulas

• Cohesive Soils (α-method): $$\displaystyle Q_u = \alpha c_u A_s + q_b A_b $$

  • $\alpha$ = adhesion factor (0.5-1.0, decreases with L/D).

  • $$\displaystyle c_u $$ = average undrained cohesion along shaft.

  • $$\displaystyle A_s $$ = shaft area, $$\displaystyle A_b $$ = base area, $$\displaystyle q_b = N_c c_u $$ (usually $$\displaystyle N_c=9 $$).

• Cohesionless Soils (β/K_p method): $$\displaystyle Q_u = \gamma D_f A_s K_p \tan \delta + q_b A_b $$

  • $\beta$ or $$\displaystyle K_p \tan \delta $$ = friction factor (0.3-0.6 for sands).

  • $\delta$ = interface friction angle (≈ 0.75φ for concrete-sand).

  • $$\displaystyle q_b = \sigma'_{vb} N_q $$ (effective vertical stress at base × bearing capacity factor).

3.2.2 Dynamic Formulas

• ENR Formula (Drop Hammer):

$$Q_{all} = \frac{W h}{s + c} \times \frac{W + n W_p}{W + W_p} \times \frac{1}{FOS}$$

*   $W$ = hammer weight, $h$ = fall, $s$ = final set (penetration per blow, cm), $c$ = sum of elastic compressions (cm), $$\displaystyle W_p $$ = pile weight, $n$ = coefficient of restitution (0.3-0.5).

> [!TIP] **Elastic Compression (c):** $$\displaystyle c = \frac{P L}{A E} $$ (P = estimated load, L = length, A = area, E = modulus). **Iterative solution** often required.

3.2.3 SPT/CPT Correlations

• For Sands: $$\displaystyle q_b = 4 N_{60} \frac{B}{D} $$ (kPa) for driven piles (empirical).

• For Clays: $$\displaystyle Q_s = \alpha c_u A_s $$, where $\alpha$ correlated with $$\displaystyle c_u $$ or $$\displaystyle N_{60} $$.

3.3 Pile Groups

3.3.1 Group Efficiency & Failure Patterns

• Efficiency (η): $$\displaystyle η = \frac{Q_{ug}}{n Q_{us}} $$

  • Cohesive soils: η < 1 (block failure possible, group capacity < sum of individuals).

  • Cohesionless soils: η ≈ 1 (group capacity ≈ sum).

• Failure Patterns:

  • Individual Failure: Piles fail separately (large spacing, S > 6D).

  • Block Failure: Soil moves as a single block (small spacing, S < 3D in clays).

3.3.2 Capacity Calculation of Pile Groups

• For Cohesive Soils (Block Failure Possible):

$$Q_{ug} = \min \begin{cases} n \times Q_{us} \\ c' \times (B_g L_g) + \alpha \bar{c}_u \times (perimeter \times L) \end{cases}$$

*   $$\displaystyle B_g, L_g $$ = group footprint dimensions.

*   $$\displaystyle \bar{c}_u $$ = average cohesion along group perimeter.

*   **Adhesion factor (α) for group perimeter** often < 1.

• For Cohesionless Soils: $$\displaystyle Q_{ug} = n \times Q_{us} $$ (usually).

  [!TIP] Common Exam Problem: Given pile diameter, length, spacing, soil c, adhesion factor. Check block failure by calculating block area & perimeter capacity. Compare with n×Q_us.

3.3.3 Geometrical Properties

• Group Shape: Square, rectangular, circular.

• Arrangement: Square, triangular, rectangular.

• Spacing (S): Minimum 3D (clay) to 4-6D (sand) to avoid group capacity reduction.

3.4 Negative Skin Friction (NSF)

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

• Causes: Soft compressible soil (clay, fill), surcharge (new fill), lowering water table (causes consolidation).

• Calculation for Single Pile:

$$Q_{nsf} = \alpha \cdot \bar{\sigma}_v' \cdot A_s \quad \text{or} \quad Q_{nsf} = \gamma \cdot \Delta H \cdot A_s$$

*   $\alpha$ = adhesion factor for soft clay (0.3-0.5).

*   $$\displaystyle \bar{\sigma}_v' $$ = **effective vertical stress** at mid-depth of compressible layer.

*   $\Delta H$ = settlement of soil layer (from consolidation).

> [!TIP] **NSF acts as additional load** on pile. **Net capacity = Q_u - Q_nsf**.

3.5 Under-reamed Piles

• Concept: Single/double under-reamed bulbs (enlarged base) on a bored pile. Provides tensile & uplift resistance.

• Construction: Bored manually/machine, under-reamed using special tool, cast in-situ.

• Suitability: Expansive soils (counteract swelling pressure), lifting forces (towers, bridges), collapsible soils.

• Ultimate Tensile Capacity (Neglecting suction & adhesion):

$$Q_{tu} = q_b \times A_b + \alpha \bar{c}_u \times (shaft area below bulb)$$

*   $$\displaystyle q_b = 9 c_u $$ (for bulb in stiff clay).

*   **Bulb diameter** typically 2.5-3× shaft diameter.

*   **Adhesion on shaft below bulb** may be neglected if smooth.

4.0 EARTH PRESSURE & RETAINING STRUCTURES

4.1 Types of Lateral Earth Pressure

• At Rest (K₀): Wall immovable, soil never yielded. $$\displaystyle K_0 = 1 - \sin \phi' $$ (for normally consolidated clays).

• Active (Kₐ): Wall moves away from soil, soil expands, minimum pressure. $$\displaystyle \sigma_h = K_a \sigma_v' - 2c' \sqrt{K_a} $$.

• Passive (Kₚ): Wall moves into soil, soil compressed, maximum pressure. $$\displaystyle \sigma_h = K_p \sigma_v' + 2c' \sqrt{K_p} $$.

4.2 Earth Pressure Theories

4.2.1 Rankine's Theory (1875)

• Assumptions: Semi-infinite soil mass, wall friction δ=0, horizontal backfill, vertical wall, cohesionless or cohesive with vertical rupture plane.

• For Cohesionless (c'=0): $$\displaystyle K_a = \tan^2(45° - \phi'/2) $$, $$\displaystyle K_p = \tan^2(45° + \phi'/2) $$.

• For Cohesive (c'>0): $$\displaystyle \sigma_a = K_a \sigma_v' - 2c' \sqrt{K_a} $$ (tension crack depth $$\displaystyle z_c = \frac{2c'}{\gamma \sqrt{K_a}} $$).

• With Water Table: Use submerged unit weight below WT, add hydrostatic pressure separately.

4.2.2 Coulomb's Theory (1776)

• Assumptions: Plane rupture surface, wall friction δ considered, inclined backfill β possible.

• Wedge Analysis: Consider limiting equilibrium of soil wedge sliding on plane at angle α.

• Expression for Kₐ (simplified, δ=0): Same as Rankine. With δ>0, $$\displaystyle K_a $$ increases.

• Effect of Wall Friction (δ): $$\displaystyle K_a $$ reduces as δ increases (for given φ'). Actual δ depends on wall material (smooth concrete: δ≈φ/2, rough: δ≈2φ/3).

4.2.3 Comparison: Rankine vs. Coulomb

4.2.4 Culmann's Graphical Method

• Used for active pressure with sloping, broken, or surcharged backfill.

• Construction:

  1. Plot weight triangle OW (soil wedge weights for various α).

  2. From W, draw friction lines at angle δ to radial lines.

  3. From O, draw pressure lines parallel to wall.

  4. Envelope of intersection points gives active pressure diagram.

  5. Resultant (Pₐ) = max ordinate on envelope, acts at centroid of pressure diagram.

4.3 Earth Pressure Calculations (Problem-Based)

• Dry Cohesionless: $$\displaystyle \sigma_a = K_a \gamma z $$.

• Submerged/Saturated: Use γ' below WT, add u = γ_w (z - z_w) separately. Total = $$\displaystyle K_a \gamma' z + \gamma_w (z - z_w) $$.

• Cohesive Backfill (c'>0): $$\displaystyle \sigma_a = K_a \gamma z - 2c' \sqrt{K_a} $$ (until tension crack depth). Beyond that, $$\displaystyle \sigma_a = K_a \gamma z $$.

• With Surcharge (q): Add $$\displaystyle K_a q $$ uniformly to pressure diagram.

• Stratified Backfill: Calculate Kₐ for each layer using its φ'. Pressure at interface = pressure from top layer + $$\displaystyle K_a \gamma_{layer} \times thickness $$. Diagram piecewise linear.

4.4 Retaining Wall Design & Analysis

• Total Active Thrust (Pₐ):

  • Simple case (c=0, horizontal backfill): $$\displaystyle P_a = \frac{1}{2} K_a \gamma H^2 $$ (per unit length).

  • Point of Application: From base, H/3 for triangular diagram.

• Pressure Distribution at Base:

  • Active case: Linear (c=0) or non-linear (c>0, with tension crack).

  • With water: Add hydrostatic wedge.

• Modes of Failure:

  1. Overturning: Moment due to lateral thrust > resisting moment (due to weight). FOS = Resisting Moment / Overturning Moment ≥ 1.5.

  2. Sliding: $$\displaystyle P_a > \mu W $$ (μ = coefficient of friction, often 0.5-0.7). FOS = (μW + P_p) / P_a ≥ 1.5 (include passive if key).

  3. Bearing Capacity Failure: Eccentric loading on base. Check e ≤ B/6 for uniform pressure. Max pressure $$\displaystyle q_{max} = \frac{W}{B} \left(1 + \frac{6e}{B}\right) \leq q_{allow} $$.

• Design Checks: All three FOS must satisfy code limits.

4.5 Sheet Piles

• Differentiation: Sheet piles are interlocking vertical elements (steel, wood, concrete) driven to form continuous wall for cofferdams, bulkheads, excavation support. Retaining walls are massive, free-standing structures (gravity, cantilever).

• Uses: Temporary/permanent ** excavation support**, seawalls, riverbank protection, containment.

5.0 SOIL IMPROVEMENT & PROBLEMATIC SOILS

5.1 Geosynthetics

5.1.1 Types & Functions

5.1.2 Uses in Foundation Engineering

• Reinforcement: Over soft soil, increase bearing capacity, reduce settlement (geogrids/geocells).

• Separation: Prevent mixing of dissimilar soils (e.g., subgrade and ballast).

• Filtration: Allow water flow but retain soil particles (non-woven geotextile).

• Drainage: Transmit water (geocomposites,geonets).

5.2 Soil Stabilization

5.2.1 Need & Situations

• Improve strength & stiffness, reduce compressibility & permeability, control shrink-swell.

• Situations: Weak subgrade, expansive soils, road construction, embankments on soft ground.

5.2.2 Methods

• Mechanical: Compaction (increase density, reduce voids). Proctor tests determine optimum moisture.

• Chemical:

  • Lime: Best for high-plasticity clays. Reduces plasticity, increases strength via pozzolanic reactions.

  • Cement: For sands & gravels, low-plasticity silts. Binds particles.

  • Bitumen: For waterproofing & binding (road bases).

• Electrical (Electro-osmosis):

  • Principle: Apply DC current between electrodes in saturated clay. Water moves from anode (+) to cathode (-).

  • Use: Dewatering & consolidation of saturated clays (e.g., for slope stability, foundation preloading). Can combine with chemical injection (electro-chemical).

5.3 Problematic Soils

5.3.1 Expansive Soils

• Characteristics: High shrink-swell potential due to montmorillonite clay minerals. Indicators: Liquid limit > 50%, Plasticity index > 25%, Activity > 1.5.

• Problems: Heave during wetting (swelling pressure up to 200+ kPa), cracks in dry season, differential movement causing structural damage.

• Preventive Measures:

  1. Moisture Control: Maintain constant moisture (impermeable barriers, landscaping).

  2. Replacement: Remove & replace with non-expansive fill.

  3. Under-reamed Piles: Transfer load to stable strata below active zone.

  4. Chemical Stabilization: Lime/cement treatment.

  5. Saturated & Stiffened Soil: Pre-wet & compact to create stable crust.

5.3.2 Collapsible Soils

• Characteristics: Loose, metastable structure (often loess, wind-blown or alluvial). Sudden collapse upon wetting or loading. Low moisture content, high void ratio.

• Problems: Sudden settlement (can be several % of layer thickness) causing severe damage.

• Preventive Measures:

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

  2. Compaction: Dynamic compaction, compaction grouting.

  3. Replacement: Excavate and replace with engineered fill.

  4. Chemical Stabilization: Lime/cement to bind particles.

  5. Deep Foundations: Piles to bypass collapsible zone.

6.0 SPECIAL FOUNDATIONS & MISCELLANEOUS

6.1 Well Foundations (Caissons)

• Components with Sketch:

  
  Top Plug (concrete)
  
  Well Cap (RCC)
  
  Well Steining (brick/masonry)
  
  Well Curb (bottom cutting edge)
  
  Diaphragm Wall (temporary partition)
  
  Bottom Plug (concrete)
  
  Cutting Edge (steel)
  
  

  • Well Curb: Bottom-most reinforced concrete part with cutting edge.

  • Well Steining: Tapered walls (1:10 to 1:12) to reduce skin friction during sinking.

  • Diaphragm Wall: Internal partition for large wells.

  • Bottom/Top Plug: Seal bottom after sinking, provide base for well cap.

• Suitability: Deep water foundations (bridges, docks), scour zones, hard strata at depth.

• Sinking Process: Excavate inside, self-weight + surcharge causes sinking. Trim bottom, grout outside if needed.

6.2 Stress Distribution in Soils

6.2.1 Boussinesq's Theory (1885)

• Assumptions: Homogeneous, isotropic, elastic half-space, point load on surface, no shear strength (only elastic).

• Vertical Stress under Point Load (P):

$$\Delta \sigma_z = \frac{3P}{2\pi z^2} \cdot \frac{1}{\left[1 + \left(\frac{r}{z}\right)^2\right]^{5/2}}$$

*   $z$ = depth, $r$ = radial distance.

• Isobars: Lines of equal $$\displaystyle \Delta \sigma_z $$. 2:1 Distribution: Simplified method: stress spreads at 2V:1H from loaded area.

• Influence Charts (e.g., Newmark's): For uniformly loaded areas.

6.2.2 Westergaard's Theory (1938)

• Assumptions: Soil is incompressible in vertical direction (layered, with rigid horizontal layers), point load.

• Key Difference: Accounts for stratification. Vertical stress does not spread laterally as much as Boussinesq. More conservative (higher stress) near loaded area.

• Equation (for point load on surface):

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

*   For $$\displaystyle r=0 $$, $$\displaystyle \Delta \sigma_z = \frac{P}{\pi z^2} $$ (vs. Boussinesq's $$\displaystyle \frac{0.318P}{z^2} $$).

6.3 Modes of Shear Failure in Soils

• General Shear Failure: Dense sands / stiff clays. Continuous failure surface to surface. Sudden failure, well-defined peak, large settlements. q-settle curve: distinct peak.

• Local Shear Failure: Medium-dense sands / medium-stiff clays. Failure surface develops only near footing. Progressive failure, no clear peak, moderate settlements.

• Punching Shear Failure: Very loose sands / soft clays. Failure resembles punching through soil. No distinct failure surface. q-settle curve: no peak, gradual failure. Compression dominates under footing.

  [!TIP] Curve Interpretation: General → peak & sudden drop; Local → slight peak; Punching → no peak.

6.4 Factors Affecting Selection of Foundation Type

• Soil Conditions: Depth to firm stratum, bearing capacity, settlement potential, water table.

• Structural Loads: Magnitude, type (axial, moment), distribution.

• Adjacent Structures: Need to limit vibration, settlement, excavation effects.

• Cost & Constructability: Shallow vs. deep cost, equipment availability, time.

• Durability & Maintenance: Corrosion, scour, access.

• Environmental: Noise, vibration, disposal of spoils.

END OF UNIT 5 NOTES
Aligned with RGPV CE-802(B) past papers (2022-2025). Focus on problem-solving for bearing capacity, settlement, pile groups, earth pressure, and SPT corrections.