UNIT 3: FOUNDATION ENGINEERING - EXAM-FOCUSED NOTES

I. SUBSURFACE INVESTIGATION & SOIL SAMPLING

A. Soil Exploration Program

• Objective: To determine stratigraphy, soil properties, and groundwater level for safe, economical foundation design.

• IS Code Criteria (IS 1892, IS 6403) for depth & spacing of boreholes:

  • Depth: Boreholes should penetrate at least 3 m into rock or 1.5 times the width of the foundation into a competent stratum, whichever is deeper. For pile foundations, depth should be 1.5 to 2 times the pile length.

  • Spacing: Typically 10-30 m for regular sites; 5-10 m for heterogeneous or hilly terrain. For major structures, a grid pattern is used.

• Methods of Site Exploration:

  • Direct Methods: Test pits, trenches, borings (most common).

  • Indirect Methods (Geophysical): Seismic refraction, electrical resistivity, GPR (Ground Penetrating Radar). Used for rapid, large-area profiling.

[!TIP] Exam Focus: IS criteria for borehole depth is a recurring 7-mark question. Memorize the 1.5x width rule and the 3m into rock rule.

B. Boring / Drilling Methods

• Rotary Drilling Technique (Most Versatile & Frequent):

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

  • Advantages: Fast in hard soils/rock, produces large-diameter boreholes, excellent for obtaining undisturbed samples using Shelby tubes, suitable for all soil types.

  • Disadvantages: Expensive, requires skilled operation, mud management needed.

• Comparison of Boring Methods:

C. Standard Penetration Test (SPT)

• Definition: An in-situ test to provide a measure of soil density/consistency and estimate shear strength.

• Test Procedure:

  1. Borehole advanced to test depth.

  2. Standard split-spoon sampler (OD 50.8 mm, ID 35.1 mm) driven with a 65 kg hammer falling 750 mm.

  3. Number of blows for first 150 mm (seating drive) is ignored.

  4. N-value = Number of blows for next 300 mm penetration.

• Corrections to N-value (N₁₀₀):

  1. Overburden Pressure Correction (N₁): $$\displaystyle N_1 = N \times \left( \frac{\bar{\sigma}_v'}{100} \right)^{0.5} $$ (for $$\displaystyle \bar{\sigma}_v' $$ in kPa). Normalizes N to 100 kPa effective overburden.

  2. Dilatancy Correction (N₂): For dense sands/gravels below water table where pore pressure builds up. Applied if $$\displaystyle N > 15 $$ and $$\displaystyle \phi > 35^\circ $$. Uses $$\displaystyle N_2 = 15 + 0.5(N - 15) $$.

  3. Energy Correction (N₆₀): Corrects to 60% hammer energy (standard). $$\displaystyle N_{60} = N \times \frac{ER}{60} $$, where ER = actual hammer efficiency (%). IS 2131 uses 60% energy.

  • Corrected N-value (N_corr) is typically N₁ or N₁₀₀ (overburden corrected) used in correlations.

• Use: Empirical correlations for $\phi$, $$\displaystyle c_u $$, $$\displaystyle E_s $$, relative density, and bearing capacity.

[!TIP] Common Pitfall: Forgetting to apply all relevant corrections. Dilatancy correction is only for saturated, dense, coarse-grained soils. Always check water table and soil type.

D. Soil Sampling

• Disturbed Sample: Soil structure is disturbed. Obtained by auger, split-spoon (SPT), or grab sampler. Used for classification tests (sieve, hydrometer, Atterberg limits).

• Undisturbed Sample: Soil structure, moisture content, and strength are preserved. Obtained by thin-walled tube samplers (Shelby tube) in rotary drilling or piston samplers. Used for strength (UCS, triaxial) and consolidation tests.

• Sampling Tube Design & Quality Assessment:

  • Inside Clearance (Cᵢ): $$\displaystyle (D_i - D_s)/D_s \times 100\% $$. Allows sample to expand into tube, reducing friction. Typical: 1-2%.

  • Outside Clearance (Cₒ): $$\displaystyle (D_s - D_o)/D_o \times 100\% $$. Reduces wall friction during driving. Typical: 0-1%.

  • Area Ratio (Aᵣ): $$\displaystyle A_r = \frac{(D_o^2 - D_i^2)}{D_i^2} \times 100\% $$. Should be < 10% for undisturbed samples. Higher Aᵣ causes more disturbance.

  • CNS Layer: The Constant Normal Stiffness layer is a theoretical concept where the sample experiences a constant confining pressure during sampling, simulating in-situ conditions. Important for understanding sample disturbance in sensitive clays.

• Types of Samplers:

  • Open Drive Sampler: Split-spoon (SPT), Shelby tube (thin-walled).

  • Piston Sampler: Maintains suction behind sample, excellent for soft clays.

  • Thin-Walled Tube Sampler: Key for undisturbed samples in cohesive soils.

II. SHALLOW FOUNDATIONS - BEARING CAPACITY & SETTLEMENT

A. Terminology & Definitions

B. Modes of Shear Failure

1. General Shear Failure (Dense sands, stiff clays): Continuous failure surface to surface, large settlements, well-defined peak in load-settlement curve. Most common for shallow foundations.

2. Local Shear Failure (Medium-dense sands, medium clays): Failure surfaces develop only near footing, moderate settlements, no distinct peak.

3. Punching Shear Failure (Very loose sands, soft clays): Failure zone is confined below footing, footing "punches" into soil, very large settlements, no peak.

• Factors: Soil density/strength ($\phi$, $c$), foundation depth/width ratio, stiffness.

C. Bearing Capacity Theories & Factors

• Terzaghi's Bearing Capacity Equation (1943):

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

*   For **strip footing**. Shape factors apply for square/circular.

*   **Assumptions**: Strip footing, $c-\phi$ soil, foundation depth $$\displaystyle D_f < B $$, rigid footing, $$\displaystyle z=0 $$ at base, no shear above base.

• IS Code (BIS) Method (IS 6403):

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

*   Includes **Shape (s)**, **Depth (d)**, and **Inclination (i)** factors. **Recurring calculation method.**

• Bearing Capacity Factors ($$\displaystyle N_c, N_q, N_\gamma $$):

  • Depend only on $\phi'$ (effective friction angle for long-term, $$\displaystyle \phi_u $$ for undrained).

  • Key Values:

    • $$\displaystyle \phi = 0^\circ $$ (Pure clay, undrained): $$\displaystyle N_c = 5.7 $$, $$\displaystyle N_q = 1 $$, $$\displaystyle N_\gamma = 0 $$.

    • $$\displaystyle \phi = 30^\circ $$: $$\displaystyle N_c \approx 37.2 $$, $$\displaystyle N_q \approx 18.4 $$, $$\displaystyle N_\gamma \approx 22.4 $$.

  • Formulas:

$$N_q = \frac{e^{\pi \tan \phi'} \tan^2(45^\circ + \phi'/2)}{ } \quad ; \quad N_c = (N_q - 1) \cot \phi' \quad ; \quad N_\gamma = 2(N_q + 1) \tan \phi'$$

• Factors Affecting Bearing Capacity:

  • Depth (d factors): $$\displaystyle D_f > 0 $$ increases capacity (especially $$\displaystyle N_q $$ term).

  • Width (B): $$\displaystyle N_\gamma $$ term proportional to $B$.

  • Water Table: Reduces effective unit weight ($\gamma'$) in $$\displaystyle N_\gamma $$ term and affects $$\displaystyle N_q $$ via $$\displaystyle \gamma D_f $$.

  • Load Inclination (i factors): Reduces capacity for eccentric or inclined loads.

  • Shape (s factors): Square/circular footings have higher $$\displaystyle N_c $$ than strip.

  • Ground Surface Inclination: Reduces capacity for sloping ground.

D. Water Table Correction

• Effect: Replaces $\gamma$ with submerged unit weight ($$\displaystyle \gamma' = \gamma_{sat} - \gamma_w $$) for soil below water table.

• Correction for $$\displaystyle N_q $$ term (if water table at $$\displaystyle D_w $$ from base):

  If $$\displaystyle D_w \leq D_f $$: Use $\gamma'$ for $$\displaystyle (D_f - D_w) $$ layer and $\gamma$ for $$\displaystyle D_w $$ layer in $$\displaystyle \gamma D_f N_q $$ term.

  If $$\displaystyle D_w > D_f $$: No correction needed for $$\displaystyle \gamma D_f N_q $$ term (all above WT).

• General Rule: Calculate effective vertical stress at foundation base ($$\displaystyle \sigma'_v $$). If water table is within the failure zone, use $\gamma'$ for layers below WT.

E. Settlement of Shallow Foundations

• Components:

  1. Immediate (Elastic) Settlement ($$\displaystyle S_i $$): Occurs during/after construction in cohesive soils (undrained) and granular soils. Recoverable.

  2. Primary Consolidation Settlement ($$\displaystyle S_c $$): Due to expulsion of pore water from cohesive soils over time. Irrecoverable.

  3. Secondary Compression ($$\displaystyle S_s $$): Due to soil particle rearrangement after primary consolidation. Very slow.

• Immediate Settlement Calculation (Cohesive Soils):

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

*   $q$ = net pressure, $B$ = footing width, $\nu$ = Poisson's ratio, $$\displaystyle E_s $$ = **Secant modulus** (from lab test at relevant stress), $I$ = **Influence factor** (from **Steinbrenner's** or **Boussinesq** charts, depends on $L/B$ and $$\displaystyle D_f/B $$).

*   **For purely cohesive soil ($$\displaystyle \phi=0 $$)**: $I \approx 1.0 - 1.2$ for square footing.

• Consolidation Settlement:

$$S_c = \frac{H}{1 + e_0} C_c \log_{10} \frac{\sigma'_{vf}}{\sigma'_v}$$

*   $H$ = thickness of compressible layer, $$\displaystyle e_0 $$ = initial void ratio, $$\displaystyle C_c $$ = compression index, $$\displaystyle \sigma'_{vf} $$ = final effective vertical stress, $$\displaystyle \sigma'_v $$ = initial effective vertical stress.

• Plate Load Test & Extrapolation (Terzaghi & Peck):

  • Procedure: Load a rigid plate (usually 300-750 mm square) to failure, plot load-settlement curve.

  • Ultimate Bearing Capacity (q_u,plate): Determined from curve (e.g., settlement = 10% plate width).

  • Extrapolation to Footing:

    • For Cohesionless Soils (Sands/Gravels): $$\displaystyle q_{u,footing} = q_{u,plate} \times \frac{B_{footing}}{B_{plate}} $$ (for $$\displaystyle B_{footing} > B_{plate} $$).

    • For Cohesive Soils (Clays): $$\displaystyle q_{u,footing} \approx q_{u,plate} $$ (independent of width for $$\displaystyle \phi=0 $$).

  • Settlement Extrapolation: $$\displaystyle S_{footing} = S_{plate} \times \frac{B_{footing}}{B_{plate}} $$ (for sands). For clays, $S \propto \log B$.

[!TIP] Recurring Complex Question: "Calculate immediate settlement for c-φ soil." Use $$\displaystyle S_i = \frac{q B (1 - \nu^2)}{E_s} I $$ with given $I$. Do not use $$\displaystyle E_s $$ from Oedometer test; use $E$ from triaxial or $$\displaystyle E = 500-1000 \times q_u $$ for sands.

III. PILE FOUNDATIONS

A. Classification

B. Load Carrying Capacity of Single Pile

• Static Formulae (Sand & Clay):

$$Q_u = Q_b + Q_s$$

*   **End Bearing ($$\displaystyle Q_b $$)**: $$\displaystyle Q_b = A_p \times q_b $$

    *   $$\displaystyle A_p $$ = pile tip area, $$\displaystyle q_b $$ = bearing capacity at tip (often $$\displaystyle \approx 9c_u $$ for clays, or $$\displaystyle N_q \sigma'_v $$ for sands).

*   **Skin Friction ($$\displaystyle Q_s $$)**: $$\displaystyle Q_s = \sum (\pi D \Delta L \cdot f_s) $$

    *   $$\displaystyle f_s $$ = unit shaft friction.

    *   **For Clay**: $$\displaystyle f_s = \alpha \cdot c_u $$ (α = adhesion factor, 0.4-1.0).

    *   **For Sand**: $$\displaystyle f_s = K \sigma'_v \tan \delta $$ (K = earth pressure coeff, δ = friction angle).

*   **Adhesion Factor (α)**: $$\displaystyle \alpha = 0.5 \phi_u $$ (for $$\displaystyle \phi_u < 20^\circ $$), or $$\displaystyle \alpha = 1.0 $$ for very soft clays. **Decreases with pile roughness and time.**

• Dynamic Methods:

  • Engineering News Record (ENR) Formula:

$$Q_{all} = \frac{W h}{s + C} \times \frac{W + n W_e}{W + W_e}$$

    *   $W$ = hammer weight, $h$ = fall, $s$ = final set (penetration per blow), $C$ = constant (2.5 cm for drop hammer, 1.2 cm for steam hammer), $$\displaystyle W_e $$ = pile weight, $n$ = **coefficient of restitution** (0.25-0.4 for wood, 0.5-0.7 for steel).

    *   **Q_all** is allowable load (with FOS). **Recurring calculation.**

*   **Wave Equation Analysis**: Sophisticated, uses computer to model stress wave propagation. Determines pile capacity and driving stresses.

• In-situ Methods: Static Load Test (Maintained load or Cyclic load) is most reliable. Pile is loaded to failure.

C. Pile Group & Group Efficiency

• Group Capacity vs. Sum of Individual Capacities:

  • Cohesive Soils (Clay): Group capacity < sum of individuals due to overlapping stress zones. Block failure may occur if spacing is small (<3-4D). Ultimate group capacity may be calculated as a single large footing at depth of pile tip.

  • Cohesionless Soils (Sand): Group capacity ≈ sum of individuals if spacing >3D. Efficiency η ≈ 1.0.

• Geometrical Properties Affecting Spacing:

  • Pile Diameter (D): Spacing typically 3D to 6D center-to-center.

  • Pile Length (L): Influences zone of influence.

  • Group Shape: Square, rectangular, circular. Affects block failure zone.

  • Arrangement: Square, triangular, rectangular.

• Calculation of Pile Group Capacity (Clay, Neglecting End Bearing):

$$Q_{ug} = \sum Q_s \text{ (individual)} \times \eta$$

*   For **closely spaced piles** (block failure): $$\displaystyle Q_{ug} = c_u \cdot A_{block} + \sum Q_s $$ (often $$\displaystyle \sum Q_s $$ is small and neglected).

    *   $$\displaystyle A_{block} = (n_s \cdot s) \times (n_r \cdot s) - n \cdot A_p $$ (for square group), where $s$ = spacing, $n$ = total piles.

*   **Recurring Calculation:** Given $$\displaystyle c_u $$, $D$, $L$, spacing, adhesion factor α. Compute individual $$\displaystyle Q_s $$, then group capacity considering spacing effect.

D. Negative Skin Friction (NSF)

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

• Causes: Placement of fill, lowering water table, consolidation of soft clay.

• Calculation for Single Pile:

$$Q_{nsf} = \pi D \cdot L_{nsf} \cdot f_{nsf}$$

*   $$\displaystyle L_{nsf} $$ = length of pile in compressible layer.

*   $$\displaystyle f_{nsf} $$ = **unit negative skin friction**.

    *   For fill/loose sand: $$\displaystyle f_{nsf} = K \cdot \bar{\sigma}_v' \cdot \tan \delta $$ (often taken as **$$\displaystyle \bar{\sigma}_v' $$** or **$$\displaystyle 0.5 \bar{\sigma}_v' $$** if no data).

    *   For consolidating clay: $$\displaystyle f_{nsf} = \sigma'_v \cdot \tan \phi' $$ or **$$\displaystyle c_u $$** (undrained).

• Effect: Reduces net pile capacity: $$\displaystyle Q_{net} = Q_{ult} - Q_{nsf} $$. Must be considered in design.

E. Special Pile Types - Under-reamed Piles

• Concept: Single or multiple bulbs (under-reams) of larger diameter (2-3x shaft) at the base and/or intermediate depths. Acts as anchor in expansive soils.

• Components: Shaft, bulb (reversed cone), collar (transition).

• Ultimate Tensile Capacity (Uplift):

$$Q_{tu} = Q_{bu} + Q_{su}$$

*   $$\displaystyle Q_{bu} $$ = bulb resistance (end bearing in uplift) = $$\displaystyle A_b \cdot q_b $$ (use $$\displaystyle c_u $$ or $$\displaystyle N_q \sigma'_v $$).

*   $$\displaystyle Q_{su} $$ = shaft adhesion above bulb = $$\displaystyle \alpha \cdot c_u \cdot A_s $$.

*   **Suitability Criteria for Expansive Soils**:

    1.  Depth of **active zone** (seasonal moisture variation) must be known.

    2.  Bulb placed **below active zone** in stable stratum.

    3.  Provides **uplift resistance** against swelling pressure.

    4.  Can also take **compressive load**.

*   **Advantages**: Economical in expansive soils, good uplift capacity, minimal excavation.

IV. LATERAL EARTH PRESSURE & RETAINING STRUCTURES

A. Types of Lateral Earth Pressure

B. Classical Theories

• Rankine's Theory (1875):

  • Assumptions: Wall is smooth & vertical, backfill is horizontal, cohesionless or cohesive with vertical rupture plane, $c-\phi$ soil.

  • For Cohesionless ($$\displaystyle c=0 $$):

$$K_a = \tan^2(45^\circ - \phi/2) \quad ; \quad K_p = \tan^2(45^\circ + \phi/2)$$

*   **For Cohesive ($$\displaystyle c>0 $$)**:

$$\sigma_a = K_a \gamma z - 2c \sqrt{K_a} \quad (\text{intercept at } z = \frac{2c}{\gamma \sqrt{K_a}})$$

    *   **Tension crack depth** ($$\displaystyle z_{tc} $$) in active state: $$\displaystyle z_{tc} = \frac{2c}{\gamma \sqrt{K_a}} $$ (if $$\displaystyle c>0 $$).

*   **Earth Pressure at Rest ($$\displaystyle K_0 $$)**: Jaky's formula for normally consolidated clays/sands: $$\displaystyle K_0 = 1 - \sin \phi' $$.

• Coulomb's Wedge Theory (1776):

  • Assumptions: Wall is rough (friction angle $\delta$), backfill is inclined ($\beta$), planar failure surface, $c-\phi$ soil.

  • General Expression (for active):

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

*   **Culmann's Graphical Method**: Used for **non-horizontal, non-uniform backfill** with **cohesion**. Steps:

    1.  Draw backfill surface to scale.

    2.  From trial failure point $A$, draw $AC$ at angle $\phi'$ to horizontal.

    3.  From $A$, draw $AD$ at angle $\delta$ to wall.

    4.  Weight of wedge $ABC$ = $W$. Draw $W$ parallel to $AC$.

    5.  From $C$, draw $CE$ parallel to $AD$ (cohesion vector $$\displaystyle = c \cdot AC $$).

    6.  Complete parallelogram $WCEF$. $EF$ gives **lateral thrust** on wall for that failure plane.

    7.  Repeat for multiple $A$ points. **Maximum $EF$ = $$\displaystyle P_a $$**.

*   **Merits over Rankine**:

    1.  Considers **wall friction ($\delta$)**.

    2.  Applicable for **inclined backfill ($\beta$)**.

    3.  More **realistic** for rough walls.

    4.  Can handle **stratified backfill** graphically (Culmann).

C. Earth Pressure Calculations for Retaining Walls

• Total Thrust ($$\displaystyle P_a $$):

  • For homogeneous cohesionless backfill:

$$P_a = \frac{1}{2} K_a \gamma H^2 \quad \text{(acts at } H/3 \text{ from base)}$$

*   **For cohesive backfill with surcharge ($q$)**:

$$P_a = \frac{1}{2} K_a \gamma H^2 + K_a q H + 2c \sqrt{K_a} H$$

    *   Acts at: $$\displaystyle \bar{z} = \frac{H}{3} \left( \frac{2K_a \gamma H + 3K_a q}{K_a \gamma H + 2K_a q + 6c\sqrt{K_a}} \right) $$ from base.

*   **With Water Table**: Use **submerged unit weight ($\gamma'$)** for soil below WT. Add **hydrostatic pressure** ($$\displaystyle \gamma_w H_w $$) as separate triangular distribution.

*   **Stratified Backfill**: Calculate thrust for each layer separately, sum vectorially. Point of application found by taking moment of each layer's thrust about base.

• Effect of Tension Cracks: In active state for cohesive soils, tension crack reduces effective height. Depth $$\displaystyle z_{tc} = \frac{2c}{\gamma \sqrt{K_a}} $$. Thrust calculated only for depth $$\displaystyle (H - z_{tc}) $$.

D. Retaining Walls

• Types:

  • Gravity: Mass of masonry/concrete provides stability (e.g., dry stone wall).

  • Cantilever: Reinforced concrete with heel and toe slabs (most common).

  • Counterfort: Vertical webs (counterforts) reduce bending in slab for tall walls.

  • Sheet Pile: Interlocking steel sheets driven into ground. Used for temporary/permanent walls in soft soils/water.

• Differentiation: Sheet Pile vs. Retaining Wall:

• Modes of Failure (for gravity/cantilever walls):

  1. Overturning: Moment about toe > resisting moment. FS > 1.5.

  2. Sliding: Horizontal thrust > frictional resistance ($\mu \cdot W$). FS > 1.5.

  3. Bearing Capacity Failure: Excessive pressure on soil. Max pressure $$\displaystyle q_{max} < q_{all} $$.

  4. Excessive Settlement: Differential settlement causes cracking.

• Stability Analysis: Check FS against overturning, sliding, and bearing capacity. Ensure no tension at heel.

E. Well Foundations

• Components (with neat sketch):

  1. Well Curb: Bottom-most, sloped cutting edge.

  2. Well Steining: Curved masonry above curb (tapers to reduce skin friction).

  3. Cutting Edge: Steel angle at curb bottom for sinking.

  4. Apron: Platform around top to prevent soil collapse.

  5. Well Shaft: Main cylindrical body.

  6. Well Cap: Top concrete beam to distribute load.

  7. Plug: Bottom concrete plug after reaching final depth.

• Sinking Process: Excavation inside, gravity/ballast/water jetting causes sinking. Problems: Tilt, shift, sand boil, bottom heave.

[!TIP] Recurring Sketch Question: Draw and label all 7 components of a well foundation. Be precise with cutting edge, steining taper, and apron.

V. SPECIAL SOILS & SOIL IMPROVEMENT

A. Problematic Soils

• Expansive Soils (Black Cotton Soils):

  • Characteristics: High montmorillonite clay content, high shrink-swell potential, low strength when wet, high CEC.

  • Problems: Seasonal heave/shrinkage causing differential settlement, cracking in foundations/floors/slabs, loss of strength.

  • Preventive Measures:

    1. Moisture Control: Maintain constant moisture (landscaping, waterproofing, drainage).

    2. Lightweight Structures: Reduce imposed load.

    3. Deep Foundations: Piles to transfer load below active zone.

    4. Under-reamed Piles: Provide uplift resistance.

    5. Chemical Stabilization: Lime, cement treatment.

    6. Soil Replacement: Remove and replace with non-expansive fill.

• Collapsible Soils:

  • Characteristics: Loose, dry, cemented (e.g., loess, gypsum). Stable when dry, collapse suddenly upon wetting.

  • Problems: Sudden, excessive settlement upon saturation (rainfall, leakage).

  • Preventive Measures:

    1. Pre-wetting before construction.

    2. Deep foundations to bypass collapsible zone.

    3. Soil stabilization (lime, cement).

    4. Compaction to increase density.

    5. Drainage control to prevent wetting.

B. Soil Stabilization & Improvement

• Need: To improve strength, reduce compressibility, control swell/shrink, increase durability.

• Methods:

  • Mechanical: Compaction (in-situ densification).

  • Chemical: Lime (for clays), Cement (for sands/clays), Bitumen (for waterproofing, base courses).

  • Electrical: Electro-osmosis (for fine-grained, saturated soils). Applies DC current to move water toward anode, dewatering and consolidation.

  • Physical: Geosynthetics (reinforcement, separation), Vibro-compaction, Stone columns.

C. Geosynthetics

• Types & Primary Functions:

• Uses in Foundation Engineering:

  1. Reinforcement: In reinforced soil foundations and mechanically stabilized earth (MSE) walls.

  2. Separation: Between soft subgrade and granular fill to prevent mixing.

  3. Filtration: Allow water flow but retain soil particles (e.g., behind sheet piles).

  4. Drainage: Collect and convey seepage water (geocomposite drains).

  5. Containment: For contaminated sites or water barriers.

VI. SETTLEMENT OF FOUNDATIONS (Advanced & Integrated)

A. Elastic Settlement of Shallow Foundations on Cohesive Soils

• Equation (Steinbrenner's Approximation):

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

*   $q$ = net pressure, $B$ = footing width, $\nu$ = Poisson's ratio, $$\displaystyle E_s $$ = **Secant modulus** (from triaxial test at $$\displaystyle \sigma'_3 = \sigma'_v $$), $I$ = **influence factor**.

*   **Influence Factor ($I$)**: Depends on **$L/B$** and **$$\displaystyle D_f/B $$**. Tabulated values (e.g., from **Steinbrenner 1934**). For square footing ($$\displaystyle L/B=1 $$) at surface ($$\displaystyle D_f/B=0 $$), $I \approx 1.06$ to $1.12$.

*   **Calculation Steps**:

    1.  Determine $q$, $B$, $\nu$, $$\displaystyle E_s $$ (from lab at relevant stress).

    2.  Find $I$ from table for given $L/B$ and $$\displaystyle D_f/B $$.

    3.  Compute $$\displaystyle S_i $$.

• Note: For sands, $$\displaystyle E_s $$ is stress-dependent; use $$\displaystyle E_s = K \cdot \sigma_v^{0.5} $$.

B. Consolidation Settlement

• One-Dimensional Theory:

$$\boxed{S_c = \frac{H}{1 + e_0} C_c \log_{10} \frac{\sigma'_{vf}}{\sigma'_v}}$$

*   $H$ = initial thickness of compressible layer.

*   $$\displaystyle e_0 $$ = initial void ratio.

*   $$\displaystyle C_c $$ = compression index (from oedometer test).

*   $$\displaystyle \sigma'_v $$ = initial effective vertical stress at mid-layer.

*   $$\displaystyle \sigma'_{vf} $$ = final effective vertical stress after construction (including stress from foundation).

• Primary vs. Secondary: Primary is due to water expulsion; Secondary (creep) occurs after primary consolidation, calculated using $$\displaystyle C_\alpha $$.

C. Total Settlement

• Total Settlement ($$\displaystyle S_{total} $$):

$$S_{total} = S_i + S_c + S_s$$

• Allowable Settlement Criteria:

  • Total: < 25-50 mm for ordinary structures.

  • Differential: < L/400 for flexible structures, L/1000 for rigid.

  • Rapid vs. Slow: Immediate ($$\displaystyle S_i $$) is critical for sandy soils; consolidation ($$\displaystyle S_c $$) for clays.

VII. FIELD COMPACTION & CONTROL

A. Compaction Equipment

• Smooth-wheel Rollers: For granular soils, base courses.

• Sheepsfoot Rollers: For cohesive soils, deep compaction.

• Pneumatic-tired Rollers: For granular and slightly cohesive soils, uniform pressure.

• Vibratory Rollers: For granular soils, high compaction.

• Hand-operated: Plate compactors, rammers for confined areas.

B. Compaction Tests

• Standard Proctor (IS 2720 Part. VII):

  • Mold: 1000 cm³, Hammer: 2.5 kg, Drop: 310 mm, Layers: 3, Blows: 25/layer.

  • $$\displaystyle \gamma_{d,max} $$ lower, OMC higher than Modified.

• Modified Proctor (IS 2720 Part. VIII):

  • Mold: 944 cm³, Hammer: 4.9 kg, Drop: 450 mm, Layers: 5, Blows: 25/layer.

  • $$\displaystyle \gamma_{d,max} $$ higher, OMC lower. Used for heavy compaction (highways, dams).

• Differentiation:

[!TIP] Memory Aid: "Modified = More effort" → Higher dry density, lower optimum moisture content. Always use Modified Proctor for important earthworks.

Final Exam Strategy:

1. Prioritize Numerical Problems: Pile groups, bearing capacity (water table), earth pressure (total thrust), settlement (immediate), SPT corrections.

2. Master IS Code Formulas: Bearing capacity (IS 6403), borehole depth (IS 1892).

3. Draw Neat Sketches: SPT, CPT, pile types, well components, earth pressure diagrams (Rankine/Coulomb), failure modes.

4. Compare & Contrast: Rankine vs. Coulomb, SPT vs. CPT, Standard vs. Modified Proctor, Sheet pile vs. Retaining wall, Disturbed vs. Undisturbed.

5. Understand Concepts: CNS layer, group efficiency, negative skin friction, expansive soil behavior.