Engineering Hydrology (CE-802 (A)) - Unit 5 Short Notes

UNIT 5: FOUNDATION ENGINEERING

I. SUBSURFACE INVESTIGATION AND SOIL SAMPLING

Methods of Boring/Hole Advancement

[!TIP] Exam Focus: Compare rotary vs. percussion methods. Rotary is preferred for deep, hard strata; percussion for shallow, cohesive soils with cobbles.

In-Situ Testing

Standard Penetration Test (SPT)

• Purpose: Measures relative density/consistency of cohesionless soils and undrained shear strength of cohesive soils.

• Equipment: Split spoon sampler, drop hammer (60 kg, 750 mm fall), drilling rig, tripod.

• Procedure:

  1. Drill hole to test depth, clean bottom.

  2. Drive sampler 450 mm (15") in three 150 mm (6") blows.

  3. Record blows for last 300 mm (12") as N-value (blows/30 cm).

• Corrections to N-value:

  • Overburden Pressure Correction (for cohesionless soils): $$\displaystyle N_{corr} = N \times \left( \frac{\bar{\sigma}_v'}{P_a} \right)^{0.5} $$ (for $$\displaystyle \bar{\sigma}_v' $$ in kPa, $$\displaystyle P_a $$ = 100 kPa). Normalizes N to standard effective overburden pressure.

  • Dilatancy Correction (for dense sands/overconsolidated clays): $$\displaystyle N_{corr} = N - f(N) $$ (using correction charts/graphs, e.g., Skempton's).

  • Energy Correction: $$\displaystyle N_{60} = N_{field} \times \frac{ER_{field}}{60\%} $$ (converts to standard 60% energy ratio).

  • Rod Length Correction: For rod length < 6m, energy transfer is less; correction factor applied.

• Significance: Quick, economical index property. Correlates with relative density, bearing capacity, settlement. Used for liquefaction assessment.

• Limitations: Sample disturbance, operator dependency, not suitable for very soft clays/gravels.

Cone Penetration Test (CPT/SCPT)

• Equipment: Cone penetrometer (standard cone: 10 cm² area, 60° apex angle) with friction sleeve and pore pressure transducer (SCPT).

• Parameters Measured:

  • $$\displaystyle q_c $$: Cone tip resistance (MPa)

  • $$\displaystyle f_s $$: Sleeve friction (MPa)

  • $u$: Pore water pressure (kPa) in SCPT.

• Advantages over SPT:

  • Continuous profile (no interruption for sampling).

  • More reliable, reproducible, less operator-dependent.

  • Provides detailed stratigraphy, soil type classification (e.g., $$\displaystyle q_c/f_s $$ ratio), and estimates of undrained shear strength ($$\displaystyle c_u = \frac{q_c - \sigma_v}{N_k} $$), relative density.

  • Direct measurement of pore pressure (SCPT) for consolidation/drainage characteristics.

• Interpretation: Used for soil profiling, bearing capacity, settlement, liquefaction potential, and pile design.

Soil Sampling

• Sampling Tube Design Parameters:

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

  • Outside Clearance: $$\displaystyle (OD_{cutter} - ID_{tube}) / ID_{tube} $$. Allows smooth penetration. Typical: 1-2%.

  • Area Ratio: $$\displaystyle A_r = \frac{(OD_{cutter}^2 - ID_{tube}^2)}{ID_{tube}^2} \times 100\% $$. Should be < 10-12% for undisturbed samples.

• Sample Quality Assessment:

  • Recovery Ratio (R): $$\displaystyle R = \frac{\text{Length of recovered sample}}{\text{Length of borehole advance}} \times 100\% $$. > 90% is good.

  • Visual inspection: Homogeneity, absence of voids, shear planes.

• CNS Layer: Confining Non-Sensitive layer. A layer of soil (often dense sand/soft rock) above the foundation level that provides confinement and reduces settlement. Important in bearing capacity calculations for stratified soils.

Bore-log and Reporting

• Components of Bore-log:

  1. Project details, borehole ID, coordinates, elevation.

  2. Drilling method, date, sampler type.

  3. Stratigraphic log: Depth, description (color, consistency, structure), SPT N-value, sample type & recovery.

  4. Groundwater level (static, during drilling).

  5. Laboratory test results (if any).

• IS Code Criteria (IS 1892:1979, IS 4464:1967):

  • Depth: Should penetrate to a stratum of adequate bearing capacity (usually 2-3B below expected foundation depth, or to rock).

  • Spacing: Grid pattern. For uniform soil: 30-50m; for variable soil: 10-30m; near existing structures: closer.

• Graphical Representation: Standardized symbols for soil types, boundaries, SPT N-values, water table.

Geophysical Methods

• Seismic Refraction: Measures velocity of seismic waves. Used to determine depth to bedrock, soil/rock layers, and approximate elastic moduli.

• Electrical Resistivity: Measures soil resistivity. Used to map soil strata, detect cavities, assess groundwater quality, and identify clay layers.

• Applications: Rapid, economical reconnaissance for large areas; supplement boring program; detect anomalies.

II. SHALLOW FOUNDATIONS

Types and Selection

• Types: Isolated, combined, strap, raft (spread over large area), floating (excavated soil mass = building weight, net load = 0).

• Basic Criteria: Adequate bearing capacity, tolerable settlement, structural integrity.

• Selection Factors: Soil bearing capacity & settlement potential, structural loads & arrangement, site constraints (space, adjacent structures), economics, construction feasibility.

Bearing Capacity

Key Definitions:

• Gross/Total Pressure ($q$): Load / area of footing.

• Net Pressure ($$\displaystyle q_{net} $$): $$\displaystyle q - \gamma D_f $$ ($\gamma$ = soil unit wt., $$\displaystyle D_f $$ = depth).

• Ultimate Bearing Capacity ($$\displaystyle q_u $$): Max pressure before 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 ($$\displaystyle q_a $$): $$\displaystyle q_{ns} $$ or based on settlement criteria.

Terzaghi’s Bearing Capacity Theory (1943)

• Assumptions: Strip footing, soil is homogeneous, isotropic, weightless ($$\displaystyle \gamma=0 $$) for $$\displaystyle N_c $$, $$\displaystyle N_q $$; $$\displaystyle N_\gamma $$ considers $\gamma$. Foundation is rigid, base rough. Shear failure along logarithmic spiral + radial + straight surfaces.

• Equation (General):

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

*   $c$ = cohesion, $$\displaystyle q = \gamma D_f $$ = effective overburden at base, $B$ = width, $\gamma$ = effective unit weight.

• Shape Factors (for non-strip footings):

  • Square: $$\displaystyle N_c' = 1.3 N_c $$, $$\displaystyle N_q' = 1.2 N_q $$, $$\displaystyle N_\gamma' = 0.4 N_\gamma $$

  • Circular: $$\displaystyle N_c' = 1.3 N_c $$, $$\displaystyle N_q' = 1.2 N_q $$, $$\displaystyle N_\gamma' = 0.3 N_\gamma $$

  • Rectangular: $$\displaystyle N_c' = (1 + 0.2 B/L) N_c $$, $$\displaystyle N_q' = (1 + 0.1 B/L) N_q $$, $$\displaystyle N_\gamma' = (1 - 0.3 B/L) N_\gamma $$

• Depth Factor: For $$\displaystyle D_f > B $$, $$\displaystyle N_q $$ increases (usually via $$\displaystyle N_q' = N_q (1 + 0.1 D_f/B) $$).

• Water Table Correction: If water table at depth $$\displaystyle d_w $$ from base:

  • For $$\displaystyle d_w > B $$: Use $\gamma'$ (buoyant unit wt.) in $\gamma B$ term.

  • For $$\displaystyle d_w < B $$: Use $\gamma'$ for $$\displaystyle (B - d_w) $$ depth, $\gamma$ for $$\displaystyle d_w $$ depth. Effectively, $$\displaystyle q_u $$ term uses $\gamma'$ if $$\displaystyle d_w $$ is shallow.

IS Method (BIS Code Approach - IS 6403:1981)

• Uses inclination factors ($$\displaystyle i_c $$, $$\displaystyle i_q $$, $$\displaystyle i_\gamma $$) for load inclination, base inclination, and backfill slope.

• General equation: $$\displaystyle q_u = c N_c s_c d_c i_c + q N_q s_q d_q i_q + 0.5 \gamma B N_\gamma s_\gamma d_\gamma i_\gamma $$

• Shape Factors ($s$): Similar to Terzaghi but slightly different values.

• Depth Factors ($d$): $$\displaystyle d_c = 1 + 0.2 \sqrt{N_c} \frac{D_f}{B} $$ (for $$\displaystyle D_f/B \leq 1 $$), $$\displaystyle d_q = d_\gamma = 1 + 0.1 \sqrt{N_q} \frac{D_f}{B} $$.

• Inclination Factors ($i$): For vertical load, $$\displaystyle i_c = i_q = i_\gamma = 1 $$.

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

• Depend only on $\phi$ (effective friction angle for drained conditions, undrained $$\displaystyle \phi_u=0 $$ for clays).

• Pure Clay ($$\displaystyle \phi=0 $$, $$\displaystyle c>0 $$): $$\displaystyle N_c = 5.7 $$, $$\displaystyle N_q = 1 $$, $$\displaystyle N_\gamma = 0 $$.

• Pure Sand ($$\displaystyle c=0 $$, $$\displaystyle \phi>0 $$): $$\displaystyle N_c = 0 $$, $$\displaystyle N_q $$ and $$\displaystyle N_\gamma $$ from tables/charts.

• c-$\phi$ soil: Use general equation with appropriate $N$ values.

Water Table Effect: Use effective unit weight ($\gamma'$) in the $$\displaystyle \gamma B N_\gamma $$ term and for $$\displaystyle q = \gamma' D_f $$ if water table is above foundation base.

Modes of Shear Failure

1. General Shear Failure: In dense sands/overconsolidated clays. Failure surfaces extend to surface. Sudden, large settlements, distinct failure wedge. Terzaghi’s theory applies.

2. Local Shear Failure: In medium-dense soils. Failure surfaces do not reach surface. Moderate settlements, gradual development. Bearing capacity factors are lower than general shear.

3. Punching Shear Failure: In very soft clays/sloose sands. Failure is like a "punch" through soil. Very small settlements, no distinct failure surface. Bearing capacity is governed by depth and base size; $$\displaystyle \gamma B N_\gamma $$ term negligible.

• Governing Factors: Soil density/strength ($\phi$, $c$), foundation depth-to-width ratio ($$\displaystyle D_f/B $$), relative stiffness of foundation vs. soil.

Settlement Analysis

• Components:

  1. Immediate (Elastic) Settlement ($$\displaystyle S_i $$): Due to elastic distortion at constant volume (undrained for clays, drained for sands). Occurs during/soon after loading.

  2. Primary Consolidation Settlement ($$\displaystyle S_c $$): Due to expulsion of pore water from saturated cohesive soils under increased effective stress. Time-dependent (months/years).

  3. Secondary Consolidation Settlement ($$\displaystyle S_s $$): Due to plastic rearrangement of soil skeleton after primary consolidation. Very slow.

• Immediate Settlement Calculation (Elastic Theory):

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

*   $q$ = net pressure, $B$ = width, $\nu$ = Poisson’s ratio, $$\displaystyle E_s $$ = **secant modulus** at stress level $q$.

*   $$\displaystyle I_z $$ = **influence factor** (from charts/tables, depends on $L/B$, $$\displaystyle D_f/B $$). For flexible footing on clay ($$\displaystyle \nu=0.5 $$), $$\displaystyle I_z \approx 1.0 $$ (for $L/B \geq 2$).

*   For **cohesive soils** ($$\displaystyle \phi=0 $$), $$\displaystyle S_i = q B (1 - \nu^2) / E_s $$ (since $$\displaystyle I_z = 1 $$ for $L/B \geq 2$).

• Factors Influencing $$\displaystyle S_i $$: $q$, $B$, $$\displaystyle E_s $$ (stress-dependent), $\nu$, $L/B$, $$\displaystyle D_f $$.

Plate Load Test

• Setup: Rigid plate (usually 300-750 mm square) at foundation depth, loaded incrementally. Settlements measured.

• Interpretation:

  • Ultimate Bearing Capacity ($$\displaystyle q_u $$): From load-settlement curve (e.g., where settlement = 20% plate thickness, or tangent intersection).

  • Settlement Prediction: For cohesive soils, settlement of full-size footing ($$\displaystyle S_f $$) from plate settlement ($$\displaystyle S_p $$) at same $q$:

$$S_f = S_p \left( \frac{B_f}{B_p} \right) \left( \frac{2 B_p}{B_f + B_p} \right)^2$$

(for flexible footing, $$\displaystyle B_f > B_p $$).

*   For **cohesionless soils**, settlement is proportional to $B$ (not $$\displaystyle B^2 $$).

• Limitations: Small plate size may not represent full-scale behavior (scale effect). Test depth limited. Expensive and time-consuming. Not suitable for very stiff soils or rocks.

III. DEEP FOUNDATIONS (PILES)

Classification and Types

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

• By Function:

  • End-Bearing Pile: Rest on hard stratum; capacity from tip.

  • Friction Pile: Capacity mainly from skin friction along shaft.

  • Combined Pile: Both end-bearing and friction.

• By Installation:

  • Driven Piles: Precast, driven by hammer (displacement, noise, soil heave).

  • Bored Piles: Cast-in-situ, minimal disturbance (non-displacement).

  • Screw Piles: Helical plates, used for light loads.

• Under-reamed Piles:

  • Components: Shaft, under-reams (bulbs, 2-3m dia) at intervals (2-3m) in expansive/weak soils.

  • Suitability: Expansive soils (black cotton soil), loose sands, collapsible soils. Provide uplift resistance & bearing capacity by creating anchorage against swelling/shrinkage.

Pile Load Capacity

Ultimate Static Capacity: $$\displaystyle Q_u = Q_b + Q_s $$

• End Bearing ($$\displaystyle Q_b $$): $$\displaystyle Q_b = A_b \cdot q_b $$

  • $$\displaystyle A_b $$ = base area (for bored piles, may be reduced due to necking).

  • $$\displaystyle q_b $$ = bearing pressure at base. For clay: $$\displaystyle q_b = N_c c_u $$ (usually $$\displaystyle N_c=9 $$). For sand: $$\displaystyle q_b = q \cdot N_q $$ (effective stress).

• Skin Friction ($$\displaystyle Q_s $$): $$\displaystyle Q_s = \sum (f_s \cdot A_s) $$

  • α-method (Clay): $$\displaystyle f_s = \alpha \cdot c_u $$ (α = adhesion factor, 0.5-1.0, decreases with depth/softness).

  • β-method (Sand): $$\displaystyle f_s = \beta \cdot \sigma_v' $$ (β = friction factor, $\tan \delta$, $\delta$ = interface friction angle, ~0.5-0.7 $\phi$).

Dynamic Methods (Drop Hammer Formula - Engineering News Formula)

• Formula: $$\displaystyle Q_{ dyn} = \frac{W h}{s + 0.5} \cdot \frac{W + n w}{W + w} $$

  • $W$ = hammer weight, $h$ = fall height, $s$ = final settlement per blow, $w$ = pile weight, $n$ = coefficient of restitution (0.25-0.4 for wood, 0.5-0.7 for steel/concrete).

• Allowable Load: $$\displaystyle Q_a = \frac{Q_{ dyn}}{FOS} $$ (FOS typically 3-6).

Pile Groups

• Group Efficiency ($\eta$): $$\displaystyle \eta = \frac{Q_{ug}}{n Q_u} $$ (n = number of piles). $$\displaystyle \eta < 1 $$ due to overlap of stress zones.

• Block Failure Concept: For closely spaced piles ($$\displaystyle s < 6d $$), group fails as a single block with dimensions $(n \times s) \times (m \times s)$. Capacity = $$\displaystyle A_{block} \cdot q_u + \text{shaft friction on block perimeter} $$.

• Spacing Criteria: Minimum center-to-center spacing = 2.5-3 times pile diameter for bored piles, 3-4 times for driven piles (to avoid stress overlap & damage).

• Group Capacity Calculation:

  • If $$\displaystyle s > 6d $$: $$\displaystyle Q_{ug} = n Q_u $$ (no group effect).

  • If $$\displaystyle s < 6d $$: Use group efficiency or block failure (whichever gives lower value).

Negative Skin Friction (NSF)

• Cause: Downward movement of soil relative to pile (e.g., due to new fill, consolidation, lowering water table).

• Effect: Increases load on pile (down-drag force), reduces net capacity.

• Calculation for Single Pile:

  • NSF Force ($$\displaystyle F_{nsf} $$): $$\displaystyle F_{nsf} = \sum (f_{nsf} \cdot A_s) $$ over critical depth.

  • $$\displaystyle f_{nsf} = K \cdot \sigma_v' \cdot \tan \delta $$ (for sand) or $$\displaystyle f_{nsf} = \gamma \cdot z \cdot \tan \phi $$ (for fill overlying clay).

  • Net Ultimate Capacity: $$\displaystyle Q_{u,net} = Q_u - F_{nsf} $$.

• NSF in Groups: More severe due to group effect; critical depth may be larger.

Special Piles

• Well Foundations (Caissons):

  • Components: Well curb (bottom cutting edge), well steining (masonry/concrete rings), well cap (top), sand filling inside, pneumatic/air lock (for deep wells).

  • Uses: Bridge piers, abutments in sandy/cohesive soils, deep water foundations.

• Under-reamed Pile Capacity:

  • Compressive: $$\displaystyle Q_u = Q_b (\text{shaft tip}) + Q_s (\text{shaft}) + Q_{ur} (\text{under-ream bulbs}) $$.

  • Tensile: $$\displaystyle Q_t = Q_{ur} (\text{bulbs in tension}) + Q_s (\text{uplift on shaft above bulbs}) $$. Adhesion factor for uplift is lower.

IV. EARTH PRESSURE AND RETAINING STRUCTURES

Types of Lateral Earth Pressure

• Active ($$\displaystyle \sigma_a $$): Wall moves away from soil. Minimum pressure. $$\displaystyle \sigma_a = K_a \sigma_v - 2c \sqrt{K_a} $$ (for cohesive soil).

• Passive ($$\displaystyle \sigma_p $$): Wall moves into soil. Maximum pressure. $$\displaystyle \sigma_p = K_p \sigma_v + 2c \sqrt{K_p} $$.

• Earth Pressure at Rest ($$\displaystyle \sigma_0 $$): Wall rigid, no movement. $$\displaystyle \sigma_0 = K_0 \sigma_v $$.

  • Jaky’s Formula (for sand): $$\displaystyle K_0 = 1 - \sin \phi' $$.

Earth Pressure Theories

Rankine’s Theory (1875)

• Assumptions: Wall frictionless ($$\displaystyle \delta=0 $$), soil cohesionless or homogeneous cohesive, vertical wall, horizontal backfill, failure plane through toe.

• Active (Cohesionless): $$\displaystyle K_a = \tan^2(45^\circ - \phi'/2) = \frac{1 - \sin \phi'}{1 + \sin \phi'} $$.

• Passive (Cohesionless): $$\displaystyle K_p = \tan^2(45^\circ + \phi'/2) = \frac{1 + \sin \phi'}{1 - \sin \phi'} $$.

• For Cohesive Soil: $$\displaystyle \sigma_a = \gamma z K_a - 2c \sqrt{K_a} $$ (tension zone at top). $$\displaystyle \sigma_p = \gamma z K_p + 2c \sqrt{K_p} $$.

• Limitation: Assumes $$\displaystyle \delta=0 $$, not realistic for rough walls.

Coulomb’s Theory (1776)

• Assumptions: Wall friction ($\delta$) considered, backfill dry/cohesionless, planar failure surface at angle $\theta$ to horizontal.

• Procedure: Consider a wedge of soil. Equilibrium of forces (weight $W$, $$\displaystyle P_a $$, reaction $R$ on failure plane). $$\displaystyle P_a $$ is resolved parallel to wall.

• Active Pressure: $$\displaystyle P_a = \frac{1}{2} \gamma H^2 \frac{\cos^2(\phi' - \beta)}{\cos^2 \beta \cos(\delta + \beta) \left[1 + \sqrt{\frac{\sin(\phi' + \delta) \sin(\phi' - \beta)}{\cos(\delta + \beta) \cos(\beta - \alpha)}} \right]^2} $$

  • $\beta$ = backfill slope angle, $\alpha$ = wall inclination (from vertical), $\delta$ = wall friction angle.

• Merits over Rankine:

  • Accounts for wall friction ($\delta$) and sloping backfill ($\beta$).

  • More realistic for rough walls and inclined backfills.

  • Can handle cohesion (with modifications).

• Limitation: Assumes planar failure surface (not always true for cohesive soils).

Culmann’s Graphical Method

• Used for active pressure with sloping, cohesionless backfill and wall friction.

• Procedure:

  1. Plot backfill surface to scale.

  2. Draw $$\displaystyle K_a $$ lines (at angle $\phi'$ to horizontal) from trial points on backfill.

  3. From each trial point, draw line parallel to wall face (at angle $\delta$ to normal).

  4. Intersection of $$\displaystyle K_a $$ line and wall-parallel line gives point on pressure line.

  5. Draw envelope (Culmann line) from these points. Perpendicular from any point on backfill to this envelope gives active pressure magnitude.

• Result: Gives total active thrust ($$\displaystyle P_a $$) and its point of application.

Earth Pressure Calculations

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

• Point of Application: For triangular diagram (cohesionless, horizontal surface), at $H/3$ from base. For trapezoidal (with cohesion), at $H/2 - \Delta$ (where $\Delta$ is shift due to cohesion).

• Effect of Water Table: Use submerged unit weight ($\gamma'$) below water table. Add hydrostatic pressure separately.

• Tension Cracks in Cohesive Backfill: Depth of tension crack $$\displaystyle z_{tc} = \frac{2c \sqrt{K_a}}{\gamma \sqrt{K_a}} $$. Active pressure diagram triangular from $$\displaystyle z_{tc} $$ to $H$.

Retaining Wall Design & Stability Checks

Modes of Failure:

1. Overturning: Wall rotates about toe. Check Factor of Safety (FOS) against overturning: $$\displaystyle FOS_{OT} = \frac{\sum \text{Resisting Moments (MR)}}{\sum \text{Overturning Moments (MO)}} \geq 1.5 $$.

2. Sliding: Wall slides along base. $$\displaystyle FOS_{Sliding} = \frac{\mu \sum V + P_p}{\sum H} \geq 1.5 $$ ($\mu$ = friction coeff., $$\displaystyle P_p $$ = passive pressure at toe).

3. Bearing Capacity Failure: Excessive pressure on toe/heel. Check net pressure distribution (usually trapezoidal) against allowable bearing capacity.

• Pressure Distribution: For rigid wall on elastic foundation, pressure is linear (trapezoidal/triangular). Max pressure at toe: $$\displaystyle q_{max} = \frac{P}{B} \left(1 + \frac{6e}{B}\right) $$, min at heel: $$\displaystyle q_{min} = \frac{P}{B} \left(1 - \frac{6e}{B}\right) $$ ($e$ = eccentricity of resultant from center).

Sheet Piles

• Differentiation: Sheet piles are interlocking vertical elements (steel, vinyl, wood) driven to form a continuous wall for temporary/permanent earth retention (cofferdams, excavation support). Retaining walls are independent, massive structures (gravity, cantilever, anchored) designed for permanent support.

• Uses: Cofferdams, excavation support, waterfront structures, erosion control, temporary shoring.

V. SOIL PROPERTIES, IMPROVEMENT, AND SPECIAL FOUNDATIONS

Problematic Soils

Expansive Soils (Black Cotton Soils):

• Characteristics: High montmorillonite clay content, high swell-shrink potential, low strength when wet, hard when dry, high liquid limit (>50%), high plasticity index.

• Foundation Problems: Differential heave/shrinkage causing cracks, loss of bearing capacity during wetting, cyclic damage.

• Preventive Measures:

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

  • Replacement: Remove & replace with granular fill.

  • Stabilization: Lime/cement treatment.

  • Under-reamed Piles: Provide anchorage against heave.

  • Raft Foundations: Spread load to reduce pressure fluctuations.

Collapsible Soils (Loess, Metastable):

• Characteristics: Porous, loose, cemented by soluble salts/calcium carbonate, stable when dry but collapse upon wetting.

• Foundation Problems: Sudden, large settlements upon wetting (from rain, leakage, groundwater rise).

• Preventive Measures:

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

  • Compaction: Heavy compaction to break bonds.

  • Replacement: Remove collapsible layer.

  • Pile Foundations: Transfer load to stable stratum.

  • Chemical Stabilization: Lime/cement to increase strength.

Soil Stabilization

• Mechanical: Compaction (increases density, reduces voids), Reinforcement (geosynthetics, fibers).

• Chemical: Lime (reduces plasticity, strength gain in clays), Cement (binds particles, good for sands/clays), Fly Ash (pozzolanic reaction, fills voids).

• Electrical: Electro-osmosis/Electrokinetics: Apply DC current to move water/fine particles. Used for dewatering soft clays and stabilization.

Geosynthetics

Uses in Foundation Engineering:

• Reinforcement: In retaining walls, slopes, embankments, raft foundations.

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

• Filtration: Replace graded filter blankets in drainage.

• Drainage: Edge drains, blanket drains.

• Protection: Protect geomembranes/liners from puncture.

Field Compaction

• Equipment:

  • Rollers: Smooth-wheel (static/vibratory), padfoot (for cohesive soils), pneumatic (rubber-tired, uniform pressure).

  • Rammers: Jumping/impact (for cohesive soils, trenches).

  • Vibratory Plates: For granular soils, tight areas.

• Light vs. Heavy Proctor Test:

  | Feature | Light Proctor (ASTM D698) | Heavy Proctor (ASTM D1557) | | :--- | :--- | :--- | | Compaction Energy | 600 kN-m/m³ | 2700 kN-m/m³ | | Mold Volume | 944 cm³ | 944 cm³ (Mod.) or 2124 cm³ | | Hammer Weight | 2.5 kg | 4.5 kg | | Drop Height | 305 mm | 457 mm | | Layers | 3 | 5 | | Blows per Layer | 25 | 25 | | Result | Lower MDD, higher OMC | Higher MDD, lower OMC |

Special Foundations

• Floating Foundations: Excavated soil mass = weight of structure. Net increase in vertical stress = 0. Used for very soft clays (e.g., Rotterdam). Proportioning: Depth of excavation $$\displaystyle D_f $$ such that $$\displaystyle \gamma_{soil} \cdot D_f = \gamma_{concrete} \cdot D_f + \text{structure load} $$. Often combined with raft.

• Raft Foundations: Thick reinforced concrete slab covering entire footprint. Used when:

  • Soil bearing capacity low.

  • Loads heavy/unequal.

  • Settlement control critical.

  • Design Consideration: Thickness based on shear & punching shear; reinforcement for flexure; check for differential settlement.

VI. STRESS DISTRIBUTION IN SOILS

Boussinesq’s Theory (1885)

• Assumptions: Homogeneous, isotropic, elastic (Hooke’s law), semi-infinite half-space, weightless ($$\displaystyle \gamma=0 $$), point load applied at surface.

• Vertical Stress under Point Load ($Q$) at depth $z$, radial distance $r$:

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

• Below Center of Load ($$\displaystyle r=0 $$): $$\displaystyle \sigma_z = \frac{3Q}{2\pi z^2} = \frac{0.4775 Q}{z^2} $$.

• Influence Charts: Based on theory for rectangular/square loads (e.g., Newmark’s chart).

Westergaard’s Theory (1938)

• Assumptions: Material has vertical, incompressible sheets/joints (like clay laminations). Poisson’s ratio $$\displaystyle \nu = 0 $$ for vertical deformation.

• Vertical Stress under Point Load:

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

• Below Center ($$\displaystyle r=0 $$): $$\displaystyle \sigma_z = \frac{Q}{\pi z^2} $$.

• Applicability: More appropriate for stratified soils (e.g., clays with laminations) and rapid loading (undrained conditions, $$\displaystyle \nu=0.5 $$ approx.).

Comparison

[!TIP] Exam Focus: Westergaard gives lower vertical stress than Boussinesq for same $Q$, $z$. Use Westergaard for saturated clays (undrained, $\nu \approx 0.5$) and laminated soils. Boussinesq for sands/drained clays.