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CE-802 (B) · Foundation Engineering/Quick Revision Short Notes

Foundation Engineering (CE-802 (B)) - Unit 4 Short Notes

UNIT 4: FOUNDATION ENGINEERING

I. SUBSURFACE INVESTIGATION & SOIL SAMPLING

A. Methods of Boring/Drilling

  • Rotary Drilling: Uses a rotating bit with circulating drilling fluid (mud) to cool bit, bring cuttings to surface, and stabilize borehole. Advantages: Fast in hard soils/rock, produces large undisturbed samples (with core barrel), suitable for all soils.

  • Percussion Drilling (Shell & Auger): Repeated dropping of a heavy chisel (shell) or rotation of auger flights. Advantages: Simple, cheap in soft soils. Disadvantages: Disturbs soil, slow in hard strata, cannot retrieve undisturbed samples.

  • Wash Boring: Jet of water loosens soil; cuttings brought by water. Fast but highly disturbed.

  • Auger Boring: Hand/machine auger. Used for shallow exploration in soft soils.

B. In-Situ Testing

  • Standard Penetration Test (SPT)

    • Procedure: Drive a split spoon sampler (50 mm ID) 450 mm into soil at bottom of borehole using a 63.5 kg hammer dropped 760 mm. Record blows for each 150 mm penetration. N-value = blows for last 300 mm (or total if < 300 mm driven).

    • Corrections:

      1. Overburden Pressure Correction (for cohesionless soils): $$\displaystyle N_{1} = N \cdot \left( \frac{\bar{\sigma}_v}{P_a} \right)^{0.5} $$ or $$\displaystyle N_{1} = N \cdot C_N $$ (where $$\displaystyle C_N $$ from IS code graph). Gives $$\displaystyle N_{1} $$ or $$\displaystyle N_{10} $$ (for 60% energy).

      2. Dilatancy Correction (for dense sands/gravels): $$\displaystyle N_{corr} = N_{1} \cdot C_D $$ (reduces N for very high $$\displaystyle N_{1} $$).

      3. Energy Ratio Correction: Convert field N to $$\displaystyle N_{60} $$ (standard 60% energy) using $$\displaystyle N_{60} = N_{field} \cdot \frac{ER_{field}}{60} $$.

    • Significance: Index of relative density/consistency, estimate of bearing capacity & settlement. Limitations: Not suitable for very soft clays, gravelly soils; disturbed sample; equipment/energy variations.

  • Cone Penetration Test (CPT / SCPT)

    • Procedure: Push a cone (10 cm² area, 60° apex) into soil at 20 mm/s. Measure cone resistance ($$\displaystyle q_c $$) and sleeve friction ($$\displaystyle f_s $$). Friction Ratio $$\displaystyle R_f = \frac{f_s}{q_c} \times 100\% $$.

    • Types: Mechanical (older, manual reading), Electrical (continuous digital recording).

    • Interpretation: $$\displaystyle q_c $$ correlates with soil strength/stiffness; $$\displaystyle R_f $$ helps classify soil (clay vs. sand).

    • Advantages over SPT: Continuous profile, faster, less disturbance, provides $$\displaystyle q_c $$ & $$\displaystyle f_s $$ simultaneously, good for soft soils.

C. Soil Sampling

  • Undisturbed Sample: Preserves in-situ structure & moisture. Used for strength & consolidation tests.

  • Disturbed Sample: Structure disturbed. Used for classification, water content, compaction.

  • Sampling Tube Parameters:

    • Inside Clearance ($$\displaystyle C_i = \frac{D_i - d}{d} \times 100\% $$): Allows sample to expand, reduces friction. Optimal: 0.5-3%.

    • Outside Clearance ($$\displaystyle C_o = \frac{D_o - D_i}{D_i} \times 100\% $$): Reduces friction on tube exterior. Optimal: 0-2%.

    • Area Ratio ($$\displaystyle A_r = \frac{(D_o^2 - d^2)}{d^2} \times 100\% $$): Measure of sharpness. For undisturbed: $$\displaystyle A_r < 20\% $$ (preferably < 13%).

    • Effect: High $$\displaystyle A_r $$, low $$\displaystyle C_i $$ → severe disturbance, sample shrinkage.

  • Techniques: Open tube (soft clays), Piston sampler (prevents suction, better for soft sensitive clays).

D. Planning & Execution of Exploration

  • Depth: At least up to depth where vertical stress increase from foundation ≤ 10-20% of effective overburden stress. For piles, depth to firm stratum or at least 1.5-2× pile length.

  • Spacing (IS Criteria): For uniform soil: 25-30 m. For variable soil/important structure: 10-15 m. For preliminary: 50-100 m.

  • Bore-log: Graphical record of soil strata, sample depths, SPT N-values, water table, lab test results. Standard format (IS 1892).

  • Water Table: Critical for effective stress calculation, bearing capacity, and construction dewatering.

E. Geophysical Methods (Brief)

  • Seismic Refraction: Measures velocity of seismic waves → delineates strata boundaries, rock depth.

  • Electrical Resistivity: Measures soil resistivity → correlates with soil type, compaction, water content.

  • Application: Rapid, economical for preliminary site investigation over large areas.

II. SHALLOW FOUNDATIONS: BEARING CAPACITY & SETTLEMENT

A. Fundamental Concepts

  • Gross Pressure ($q$): Total pressure at foundation base = $$\displaystyle \frac{Q}{A} + \gamma D_f $$.

  • Net Pressure ($$\displaystyle q_{net} $$): Pressure in excess of initial effective overburden = $$\displaystyle q - \gamma D_f $$.

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

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

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

  • Allowable Bearing Pressure ($$\displaystyle q_a $$): Net pressure ensuring tolerable settlement + FS against shear.

  • Factors Affecting BC: Soil strength ($c, \phi$), foundation size/shape/depth, water table, loading rate.

B. Theories of Bearing Capacity

  • Terzaghi's Theory (1943): Assumes general shear failure, $c-\phi$ soil, depth/width ratio $$\displaystyle D_f/B \leq 1 $$, rigid footing.

    • Strip: $$\displaystyle q_u = cN_c + qN_q + 0.5\gamma BN_\gamma $$

    • Square: $$\displaystyle q_u = 1.3cN_c + qN_q + 0.4\gamma BN_\gamma $$

    • Circular: $$\displaystyle q_u = 1.3cN_c + qN_q + 0.3\gamma BN_\gamma $$

  • IS Code Method (IS 6403): Uses Terzaghi factors with shape, depth, inclination factors. General:

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

where $$\displaystyle B' = B $$ for strip, $$\displaystyle B' = B \cos\lambda $$ for inclined load.

  • Water Table Correction:

    • If water table above base: Use submerged unit weight ($\gamma'$) for $\gamma$ term, and pore water pressure ($$\displaystyle u = \gamma_w (D_f + B) $$) subtract from $$\displaystyle q_u $$.

    • Factors: $\gamma$ term uses $\gamma'$ if WT between $$\displaystyle D_f $$ and $B$; $q$ term uses $$\displaystyle \gamma D_f $$ (effective) if WT above $$\displaystyle D_f $$.

C. Bearing Capacity Calculations

  • Pure Clay ($$\displaystyle \phi=0° $$): $$\displaystyle N_c = 5.7 $$, $$\displaystyle N_q = 1 $$, $$\displaystyle N_\gamma = 0 $$. → $$\displaystyle q_u = cN_c + \gamma D_f $$.

  • Sandy Soil ($$\displaystyle c'=0 $$): $$\displaystyle q_u = q N_q + 0.5\gamma BN_\gamma $$.

  • c-φ Soil (General): Use given $$\displaystyle N_c, N_q, N_\gamma $$ (from tables for $\phi$). Apply shape/depth factors per IS/Terzaghi.

D. Settlement of Foundations

  • Components:

    1. Immediate (Elastic) Settlement ($$\displaystyle S_i $$): Instantaneous, recoverable. For clays: $$\displaystyle S_i = \frac{q B (1 - \mu^2)}{E_s} I_s I_p $$

      • $$\displaystyle I_s $$: Influence factor (from table/fig, depends on $B/L$).

      • $$\displaystyle I_p $$: Depth factor ($\approx 1$ for $$\displaystyle D_f/B \leq 1 $$).

    2. Primary Consolidation Settlement ($$\displaystyle S_c $$): Time-dependent, due to pore water expulsion in clays.

    3. Secondary Compression ($$\displaystyle S_s $$): Post-consolidation, due to soil structure adjustment.

  • Plate Load Test:

    • Procedure: Load plate (0.3-0.5 m²) at ground level or in pit, measure settlement vs. load.

    • Interpretation: Ultimate load from plot (log-log or tangent). Settlement Prediction for different footing size:

$$S_{footing} = S_{plate} \cdot \frac{B_{footing}}{B_{plate}} \cdot \frac{B_{plate} + 0.5}{B_{footing} + 0.5}$$

    (for sandy soils, $S \propto B$; for clays, $S \propto B$ if $q$ same).

E. Types & Proportioning of Shallow Foundations

  • Types: Isolated, Combined, Strip, Raft/Mat, Floating (basement).

  • Raft Foundation Proportioning:

    • Purpose: Reduce differential settlement, increase bearing capacity.

    • Criteria: Net pressure ≤ allowable BC; total settlement ≤ permissible; shear stress at base ≤ soil shear strength.

    • Common Shapes: Square (for columns), Rectangular (for walls), Combined.

  • Basic Performance Criteria: Adequate bearing capacity, tolerable total/differential settlement, sufficient structural strength.

III. DEEP FOUNDATIONS: PILES

A. Pile Classification & Functions

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

  • By Action:

    • End Bearing: Rest on hard stratum (rock/dense sand).

    • Friction/Skin Friction: Resistance from shaft adhesion.

    • Combined: Most piles.

  • By Installation: Driven, Bored, Driven & Bored, Screwed, Under-reamed.

  • Functions: Carry vertical loads, resist uplift, lateral loads, absorb vibrations.

B. Pile Load Capacity

  • Static Formulae (Based on soil parameters):

    • Sand: $$\displaystyle Q_u = A_b q_{ub} + A_s f_s $$, where $$\displaystyle q_{ub} = \gamma D_f N_q $$ (for deep), $$\displaystyle f_s = K \sigma'_{vm} \tan\delta $$.

    • Clay (undrained): $$\displaystyle Q_u = A_b N_c c_u + A_s \alpha c_u $$.

  • Dynamic Formulae (Based on hammer blow):

    • Engineering News Formula: $$\displaystyle Q_{all} = \frac{W h}{S + 0.1} \cdot \frac{W + n W_p}{W} $$ (FS=6-8).

    • Hiley's Formula (incorporates efficiency, restitution): $$\displaystyle Q_{all} = \frac{\eta W h}{S + 0.5} \cdot \frac{W + n W_p}{W} $$ (FS=2.5-3.5).

  • Load Testing: Static load test (main method for verification), dynamic test (predictive).

C. Pile Capacity in Cohesive Soils (Clay)

  • Undrained Analysis ($$\displaystyle \phi_u=0 $$): $$\displaystyle Q_u = A_b N_c c_u + A_s \alpha c_u $$.

    • $\alpha$ = adhesion factor (decreases with $$\displaystyle c_u $$, pile material). From $$\displaystyle c_u $$ (IS 2911): $$\displaystyle \alpha = 0.7 $$ for $$\displaystyle c_u \leq 25 $$ kPa, $$\displaystyle \alpha = 0.7 - 0.007(c_u - 25) $$ for $$\displaystyle 25 < c_u \leq 75 $$, $$\displaystyle \alpha = 0.5 $$ for $$\displaystyle c_u > 75 $$ kPa.

    • From UCS ($$\displaystyle q_u $$): $$\displaystyle c_u = q_u/2 $$ for undrained triaxial.

  • Drained Analysis (effective stress): Use $c'$, $\phi'$, $\delta$ (≈ $\phi'$ for concrete).

D. Pile Capacity in Cohesionless Soils (Sand)

  • Use $$\displaystyle N_q $$ from SPT or bearing capacity theory: $$\displaystyle Q_u = A_b \gamma D_f N_q + A_s K \sigma'_{vm} \tan\delta $$.

  • Effect of Installation:

    • Driven Piles: Increase density → higher $$\displaystyle N_q $$, $$\displaystyle f_s $$ (due to compaction & negative skin friction initially).

    • Bored Piles: Looser → lower $$\displaystyle f_s $$, no initial NSF.

E. Pile Groups

  • Group Efficiency ($$\displaystyle \eta_g $$): $$\displaystyle \eta_g = \frac{Q_{ug}}{n Q_{us}} $$. For clays: $$\displaystyle \eta_g \approx 1 $$ if spacing $$\displaystyle > 3-4d $$. For sands: $$\displaystyle \eta_g < 1 $$ due to overlap of stress bulbs.

  • Block Failure Concept (for closely spaced groups in clay): Treat as single large foundation. $$\displaystyle Q_{ug} = A_b N_c c_u + A_s \alpha c_u $$ (with $$\displaystyle A_b $$, $$\displaystyle A_s $$ of block).

  • Spacing: Minimum $2d$ (clay), $3d$ (sand) to avoid group action. Governed by pile diameter, arrangement (square/triangular).

F. Negative Skin Friction (NSF)

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

  • Causes: Fill over natural ground, lower water table, consolidation of soft clay.

  • Calculation for Single Pile:

$$Q_{nsf} = \Sigma (\gamma \Delta z \cdot K \cdot \tan\delta) \cdot \pi d \cdot \Delta z$$

or $$\displaystyle Q_{nsf} = \pi d \cdot L_{critical} \cdot f_{nsf} $$.

*   $$\displaystyle f_{nsf} = \gamma' z K \tan\delta $$ (if submerged), or $\gamma z K \tan\delta$.

*   $K$: Earth pressure coefficient (0.3-0.5 for fill, 1.0 for consolidating clay).

*   $\delta$: Interface friction angle (≈ $\phi$ for sand, $$\displaystyle \phi_u $$ for clay).

*   $$\displaystyle L_{critical} $$: Depth from where NSF acts (usually from fill top to neutral plane).
  • Effect: Reduces net pile capacity: $$\displaystyle Q_{net} = Q_{up} - Q_{nsf} $$.

G. Special Pile Types

  • Under-reamed Piles

    • Concept: Single/multiple bulb(s) (under-ream) on shaft in expansive soils. Bulbs provide uplift resistance & bearing.

    • Components: Shaft, under-ream bulb(s), top cap.

    • Suitability: Expansive, collapsible, loose sands, soft clays with low bearing capacity.

    • Ultimate Capacity (tension): $$\displaystyle Q_u = A_b N_q \gamma' D_f + A_s \alpha c_u + \text{bulb resistance} $$. Bulb resistance = $$\displaystyle \pi (D_b^2 - d^2)/4 \cdot N_q \gamma' D_f $$ (end bearing) + skin below bulb.

  • Well Foundations (Caissons)

    • Components:

      1. Well curb (bottom cutting edge, concrete).

      2. Well steining (masonry/concrete above curb, provides weight).

      3. Cutting edge (steel angle).

      4. Lining (curbs/steining, provides support).

      5. Bottom plug (concrete, seals bottom).

      6. Top plug (concrete, distributes load from pier).

    • Sinking Process: Excavate inside, gravity/ballast/water jetting, trim soil, lower. Problems: Tilt, shift, bottom heave, sand boiling, air pressure.

IV. EARTH PRESSURE & RETAINING STRUCTURES

A. Types of Lateral Earth Pressure

  • At Rest ($$\displaystyle K_0 $$): No lateral strain. $$\displaystyle K_0 = 1 - \sin\phi' $$ (for normally consolidated clays/sands).

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

  • Passive ($$\displaystyle K_p $$): Wall pushed into soil → maximum pressure.

B. Earth Pressure Theories

  • Rankine's Theory (1875): Assumes wall smooth, backfill horizontal, cohesionless/c-cohesive with vertical wall.

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

    • Cohesive ($$\displaystyle c>0 $$): $$\displaystyle P_a = \frac{1}{2} \gamma H^2 K_a + 2c \sqrt{K_a} $$ (at depth $H$).

    • With Surcharge $q$: $$\displaystyle P_a = q H K_a + \frac{1}{2} \gamma H^2 K_a $$.

  • Coulomb's Theory (1776): Considers wall friction $\delta$, wall inclination $\beta$, backfill inclination $\alpha$.

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

    • Merits over Rankine: More realistic (includes $\delta$, $\alpha$, $\beta$). Demerits: Complex, trial wedge.

C. Calculation of Earth Pressure

  • Dry/Moist: Use total unit weight $\gamma$.

  • Submerged: Use $\gamma'$ for soil, plus water pressure on wall.

  • Water Table: Calculate pore pressure at depth, subtract from total stress to get effective stress pressure. Total pressure = effective + pore water.

  • Culmann's Graphical Method: For irregular backfill profiles, multiple wedges. Construct log-spiral failure surfaces graphically to find maximum active pressure and its location.

D. Retaining Wall Design & Analysis

  • Types:

    • Gravity: Mass masonry/concrete, relies on weight.

    • Cantilever: Base slab + stem + heel/toe, economical up to ~6 m.

    • Counterfort: For tall walls (>6 m), reduces bending in slab.

    • Sheet Pile: Flexible, thin sections (wood/steel), used for temporary/permanent retaining (cofferdams, quay walls). Differentiation: Sheet piles are flexible (deflect, earth pressure varies with depth), designed for bending; Retaining walls are rigid (earth pressure distribution known, designed for stability & base pressure).

  • Stability Checks:

    1. Overturning: $$\displaystyle \frac{M_{resisting}}{M_{overturning}} \geq 1.5 $$ (usually).

    2. Sliding: $$\displaystyle F_{resisting} = \mu \Sigma W + P_p $$ (passive at toe), $$\displaystyle F_{overturning} = P_a $$. $FS \geq 1.5$.

    3. Bearing Capacity: Net pressure at toe/heel < allowable.

  • Earth Pressure Distribution: For Rankine active on vertical wall with horizontal backfill: Triangular, zero at top, $$\displaystyle K_a \gamma H $$ at base. Point of application: $H/3$ from base.

  • Total Thrust & Point of Application: Integrate pressure diagram. For triangular: $$\displaystyle P_a = \frac{1}{2} K_a \gamma H^2 $$ (plus surcharge term), acts at $H/3$ from base.

E. Modes of Shear Failure of Retaining Walls (with sketches)

  1. Overturning: Wall rotates about toe.

  2. Sliding: Wall slides horizontally along base.

  3. Excessive Bearing Pressure: Pressure at toe exceeds soil BC.

  4. Deep Shear Failure: Failure surface extends deep into soil (for weak soils).

V. SPECIAL TOPICS: PROBLEMATIC SOILS & IMPROVEMENT

A. Expansive Soils

  • Characteristics: High montmorillonite content, high shrink-swell potential with moisture change, low strength when wet, high when dry, cracks in dry season.

  • Problems in Foundations: Heave in wet season, settlement in dry season, differential movement, cracking of structures.

  • Preventive Measures:

    • Moisture Control: Impermeable barriers, landscaping, drainage.

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

    • Chemical Stabilization: Lime, cement, fly ash.

    • Deep Foundations: Piles/under-reamed piles to bypass active zone.

    • Floating Raft: To counteract heave.

B. Collapsible Soils

  • Characteristics: Loose, metastable structure (often loess), high void ratio, low saturation, sudden collapse upon wetting or loading.

  • Problems: Sudden, large settlement upon wetting (e.g., from rain, pipe leak).

  • Preventive Measures:

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

    • Compaction: Dynamic/static to densify.

    • Chemical Stabilization: Lime, cement.

    • Deep Foundations: Piles to reach stable strata.

C. Geosynthetics

  • Types & Functions:

    | Type | Primary Function(s) | Use in Foundation Engg. | |---------------|----------------------------------------------|------------------------------------------------| | Geotextile| Separation, Filtration, Reinforcement, Drainage, Erosion Control | Separation between subgrade & embankment, reinforcement in slopes/retaining walls, drainage layers. | | Geogrid | Reinforcement (tensile strength) | Reinforcement in retaining walls, slopes, embankments on weak soils. | | Geomembrane| Sealing, Containment | Liners for ponds, landfills, seepage control. | | Geocell | Confinement, Reinforcement | Confinement of granular fills, erosion control, load distribution. |

  • Various Uses: Separation (prevent mixing), Reinforcement (increase shear strength), Filtration (allow flow, retain soil), Drainage (collect/transmit water), Erosion control.

D. Soil Stabilization

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

  • Methods:

    1. Mechanical: Compaction (increases density, reduces voids).

    2. Chemical: Lime (for clay), Cement (for sand/clay), Bitumen (for waterproofing, base courses).

    3. Electrical: Electro-osmosis (for fine saturated clays, dewatering & consolidation using DC current).

[!TIP] Exam Focus from Past Papers:

  • SPT Corrections: Always mention Energy Ratio Correction (to $$\displaystyle N_{60} $$) as primary step. Dilatancy correction for dense sands ($$\displaystyle N_{corr} < N_{1} $$).
  • Pile Group Capacity: For soft clay with no end bearing, $$\displaystyle Q_{ug} = \eta_g \cdot n \cdot A_s \cdot \alpha c_u $$. For square group with spacing $s$, block area = $$\displaystyle (n_p d + (n-1)s)^2 $$.
  • Plate Load Test Settlement: Use $$\displaystyle S_{footing} = S_{plate} \cdot \frac{B_f}{B_p} \cdot \frac{B_p + 0.5}{B_f + 0.5} $$ (for sandy soils, simpler $S \propto B$ may be accepted).
  • Rankine vs Coulomb: Coulomb is more general (includes $\delta, \alpha, \beta$). Rankine assumes smooth wall, horizontal backfill. Coulomb gives lower $$\displaystyle K_a $$ for $$\displaystyle \delta > 0 $$.
  • Under-reamed Piles: Mention bulb diameter (2-3× shaft), spacing (1.5-2× bulb dia), suitability for expansive soils (provides uplift resistance).
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