Engineering Hydrology (CE-802 (A)) - Unit 1 Short Notes

UNIT 1: FOUNDATION ENGINEERING (Based on Past Exam Analysis)

1.0 Subsurface Investigation and Soil Sampling

1.1 Significance and Planning of Site Exploration

• Objectives: Determine soil profile, groundwater level, obtain samples for lab tests, assess bearing capacity & settlement.

• IS Criteria for Depth & Spacing of Boreholes (IS 1892:2016):

  • Depth: Borehole depth should be until a competent stratum is reached or at least equal to width of foundation (B) for shallow foundations. For piles, depth should be at least 1.5–2 times pile length or until refusal.

  • Spacing: Grid pattern. For homogeneous sites: 30–50 m. For heterogeneous: 10–30 m. Closer spacing (5–10 m) for critical structures.

• Significant Depth of Exploration: Depth up to which stress increase due to foundation load is significant (typically where Δσ/σ'₀ ≤ 10%). Approx. $$\displaystyle D_s \approx B $$ for square footing.

• Components of Bore-Log Report:

  • Borehole number, location, elevation.

  • Soil description (color, consistency, stratification).

  • Depth of water table.

  • Sample type (disturbed/undisturbed) & recovery.

  • SPT N-value (blows/30 cm).

  • Laboratory test results (moisture, density, strength).

  • DiagramCANVAS: Vertical section showing borehole with soil layers, sample depths, water table, and SPT intervals

[!TIP] Exam Focus: IS 1892 criteria for depth/spacing are frequently asked. Remember: spacing reduces for variable soil.

1.2 Methods of Boring and Sampling

• Boring Methods:

  • Auger Boring: Manual/mechanical auger. Suitable for cohesive soils above water table. Samples disturbed. Fast, economical.

  • Wash Boring: Water jet through hollow boring rod. Suitable for granular soils. Caving possible. Samples disturbed.

  • Rotary Drilling: Rotating core barrel with diamond bit. Advantages: Fast, deep boring, can retrieve undisturbed samples in stiff soils/hard strata. Suitable for all soils & rock.

• Sampling Techniques:

  • Disturbed: Structure altered. Used for classification, moisture, density.

  • Undisturbed: Structure preserved. Used for strength, consolidation, permeability.

• Sampler Design & Quality Assessment:

  • Inside Clearance $$\displaystyle C_i = \frac{D_i - d_i}{d_i} \times 100\% $$ ($$\displaystyle D_i $$ = inside dia. of cutting edge, $$\displaystyle d_i $$ = inside dia. of tube). Should be 0–2% to minimize disturbance.

  • Outside Clearance $$\displaystyle C_o = \frac{D_o - d_o}{d_o} \times 100\% $$ ($$\displaystyle D_o $$ = outside dia. of cutting edge, $$\displaystyle d_o $$ = outside dia. of tube). Should be 0–2% for smooth entry.

  • Area Ratio $$\displaystyle A_r = \frac{(D_o^2 - d_i^2)}{d_i^2} \times 100\% $$. Should be < 10% for good sample quality.

  • Comment on Sample Quality: High $$\displaystyle A_r $$, $$\displaystyle C_i $$, $$\displaystyle C_o $$ → more disturbance. Low values → better quality.

• CNS Layer (Constant Normal Stiffness): Concept for sampling in stiff soils where sampler is designed to maintain constant normal stress on sample during driving to simulate in-situ stress path.

[!TIP] Common Pitfall: Confusing inside/outside clearance formulas. $$\displaystyle C_i $$ relates to tube ID, $$\displaystyle C_o $$ to tube OD.

1.3 In-Situ Testing

• Standard Penetration Test (SPT):

  • Procedure: Drive split spoon sampler (50 mm ID) 45 cm (or 30 cm) using 63.5 kg hammer falling 760 mm. Record blows for each 15 cm. N-value = blows for last 30 cm.

  • Corrections:

    1. Overburden Pressure Correction (K₀-correction): $$\displaystyle N_{60} = N_{field} \times C_N $$, where $$\displaystyle C_N = \sqrt{\frac{100}{\sigma'_{vo}}} $$ (σ' in kPa), limited to 2.0.

    2. Dilatancy Correction (for dense sands): If $$\displaystyle N_{60} > 15 $$, $$\displaystyle N_{corrected} = N_{60} \times C_d $$, where $$\displaystyle C_d = \frac{2}{1 + \frac{N_{60}}{15}} $$.

  • Significance: Correlates with relative density, φ, bearing capacity, settlement. Corrected N used in design.

• Cone Penetration Test (CPT/SCPT): Continuous pushing of cone (10 cm² area) at 20 mm/s. Measures tip resistance ($$\displaystyle q_c $$) and sleeve friction ($$\displaystyle f_s $$). Provides detailed soil profiling, strength, and stratigraphy.

• Plate Load Test:

  • Setup: Load plate (0.3 m² typical) at foundation level, apply loads, measure settlements.

  • Settlement Interpretation: For cohesive soils, immediate settlement scales linearly with width:

$$S_B = S_b \times \frac{B}{b}$$

where $$\displaystyle S_b $$ = settlement of plate (size $b$), $$\displaystyle S_B $$ = settlement of footing (size $B$). For sandy soils, $$\displaystyle S_B \propto \sqrt{B/b} $$.

*   **Ultimate Bearing Capacity:** From load-settlement curve (e.g., settlement = 0.1B or tangent slope method).

*   **Water Table Influence:** If water table above plate base, use submerged unit weight for pressure calculations; plate settlement may be higher due to lower effective stress.

[!TIP] Exam Focus: SPT corrections and plate load test settlement scaling (especially for clay) are high-frequency. Always check water table position.

2.0 Bearing Capacity of Shallow Foundations

2.1 Fundamental Concepts & Definitions

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

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

• Net Safe Bearing Capacity ($$\displaystyle q_{ns} $$): $$\displaystyle q_{ns} = \frac{q_{nu}}{FOS} $$ (FOS = 2.5–3.0).

• Allowable Bearing Pressure: Pressure that can be applied at foundation base. Often $$\displaystyle q_{ns} + \gamma D_f $$ (gross) or $$\displaystyle q_{ns} $$ (net).

• Gross Pressure: Total vertical stress at foundation base including overburden.

2.2 Theories of Bearing Capacity

• Failure Modes:

  • General Shear: Continuous failure surface, large settlements, brittle soils.

  • Local Shear: Failure surface limited to footing width, moderate settlements.

  • Punching Shear: Like punching through weak layer, very large settlements.

• Terzaghi's Theory (1943):

  • Assumptions: Strip footing, rough base, φ>0, $$\displaystyle D_f $$=0, no shear above base, Rankine's active state in radial zones.

  • Bearing Capacity Factors: $$\displaystyle N_c $$, $$\displaystyle N_q $$, $$\displaystyle N_\gamma $$ (functions of φ).

  • Equation (Strip):

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

• IS Method (BIS Code IS 6403:1981):

  • General Equation:

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

    *   $$\displaystyle s_c $$, $$\displaystyle s_q $$, $$\displaystyle s_\gamma $$ = shape factors.

    *   $$\displaystyle d_c $$, $$\displaystyle d_q $$, $$\displaystyle d_\gamma $$ = depth factors.

*   **Shape Factors (for rectangular footing $B \times L$):**

    $$\displaystyle s_c = 1 + 0.2 \frac{B}{L} $$, $$\displaystyle s_q = 1 + 0.1 \frac{B}{L} $$, $$\displaystyle s_\gamma = 1 - 0.4 \frac{B}{L} $$.

• Factors Affecting Bearing Capacity:

  • Soil: $c$, $\phi$, $\gamma$, $$\displaystyle E_s $$, $\mu$.

  • Foundation: $B$, $L$, $$\displaystyle D_f $$.

  • Water table position.

  • Load inclination, surcharge, rate of loading.

2.3 Bearing Capacity Calculations

• Application for Footing Shapes:

  • Square: $$\displaystyle q_u = 1.3 c N_c + \gamma D_f N_q + 0.4 \gamma B N_\gamma $$ (Terzaghi).

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

  • Rectangular: Use IS shape factors.

• Water Table Correction:

  • If water table at depth $$\displaystyle D_w $$ below foundation base:

    • $$\displaystyle D_w < B $$: Use $\gamma'$ for portion below $$\displaystyle D_w $$, and apply correction factor $$\displaystyle r_d = 1 - 0.5 \frac{D_w}{B} $$ to $$\displaystyle N_\gamma $$ term.

    • $$\displaystyle D_w \geq B $$: No correction ($$\displaystyle r_d = 1 $$).

  • If water table above foundation base, use $\gamma'$ for all $\gamma$ terms (overburden and $$\displaystyle N_\gamma $$ term).

• Layered Soils: If strong stratum at depth $$\displaystyle D < B $$ overlies weak stratum, failure may penetrate weak layer. Use weak layer parameters for depth of influence (approx. $B$ below strong stratum).

• Factor of Safety: Applied to $$\displaystyle q_{nu} $$ to get $$\displaystyle q_{ns} $$.

[!TIP] Common Pitfall: Forgetting to use effective unit weight ($\gamma'$) when water table is above foundation level. Always sketch water table position.

3.0 Settlement of Shallow Foundations

3.1 Components of Total Settlement

• Immediate (Elastic) Settlement ($$\displaystyle S_i $$): Occurs during/after construction in cohesive soils (undrained) and sandy soils (elastic). Recoverable partially.

• Primary Consolidation Settlement ($$\displaystyle S_c $$): Due to expulsion of water from saturated clays. Time-dependent, major component for clays.

• Secondary Consolidation Settlement ($$\displaystyle S_s $$): Creep after primary consolidation. Significant for organic clays.

3.2 Immediate Settlement

• Equation (Elastic Theory for Cohesive Soils):

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

*   $q$ = net pressure.

*   $B$ = footing width.

*   $\mu$ = Poisson's ratio.

*   $$\displaystyle E_s $$ = modulus of elasticity.

*   $$\displaystyle I_f $$ = influence factor (from charts, depends on $L/B$ and $\mu$).

• Calculation: Given $q$, $B$, $$\displaystyle E_s $$, $\mu$, $$\displaystyle I_f $$, compute $$\displaystyle S_i $$. For $$\displaystyle \phi = 0 $$ (clay), $$\displaystyle I_f $$ is often provided.

• Saturated Clay (Undrained): Use $$\displaystyle \mu = 0.5 $$ (incompressible), $$\displaystyle E_s = E_u $$ (undrained modulus).

[!TIP] Exam Focus: Immediate settlement formula is frequently tested. Remember $$\displaystyle I_f $$ is dimensionless and depends on footing shape.

4.0 Pile Foundations

4.1 Introduction & Classification

• Definition: Deep foundation transferring load to deeper, stronger strata.

• Classification:

  • Material: Concrete, steel, timber.

  • Action: End-bearing, friction, combined.

  • Installation: Driven (impact, vibration), bored (cast-in-place), screw, under-reamed.

4.2 Load Carrying Capacity of Single Pile

• Static Formulae:

  • Sandy Soils ($$\displaystyle c=0 $$):

$$Q_u = Q_{pb} + Q_{sf} = A_b \gamma' L N_q + \sum K \sigma'_{v} \tan \delta \Delta A_s$$

    Often simplified: $$\displaystyle Q_{sf} = \frac{1}{2} \gamma' L A_s K \tan \delta $$ (for uniform sand).

*   **Cohesive Soils ($$\displaystyle \phi=0 $$):**

$$Q_u = Q_{pb} + Q_{sf} = c_u N_c A_b + \alpha c_u A_s$$

    *   $$\displaystyle N_c = 9 $$ (deep foundation, Terzaghi).

    *   $\alpha$ = adhesion factor (0.6–0.9 for driven, 0.3–0.6 for bored).

• Dynamic Formulae (Drop Hammer):

  • Hiley's Formula (Energy Equation):

$$Q_d = \frac{W h}{s + e}$$

    $$\displaystyle Q_d $$ = dynamic load, $W$ = hammer weight, $h$ = fall, $s$ = observed settlement/blow, $e$ = elastic compression.

    **Allowable Load:** $$\displaystyle Q_a = \frac{Q_d}{FOS} $$.

• CPT/SPT Correlations: $N$-value → $\phi$, $$\displaystyle c_u $$; $$\displaystyle q_c $$ → $$\displaystyle q_u $$.

4.3 Pile Group Capacity & Negative Skin Friction

• Group Efficiency ($\eta$): $$\displaystyle \eta = \frac{Q_{ug}}{n Q_u} $$.

  • Cohesive Soils: If spacing $$\displaystyle s < 3D $$, block failure may occur: $$\displaystyle Q_{ug} = c_u A_g + \gamma' D_f A_g $$ (neglecting end bearing often). If $s \geq 3D$, $\eta \approx 1$, sum of individual capacities.

  • Granular Soils: Usually $\eta \approx 1$, sum of individual capacities.

• Negative Skin Friction (NSF):

  • Causes: Soft compressible soil around pile, lowering water table, fill placement.

  • Calculation (Single Pile in Cohesive Soil):

$$Q_{nsf} = \bar{c}_a \cdot \pi D \cdot L_{nsf}$$

    $$\displaystyle \bar{c}_a $$ = average adhesion (≈ $$\displaystyle 0.5 c_u $$ to $$\displaystyle c_u $$), $$\displaystyle L_{nsf} $$ = depth of compressible layer.

    Or for granular: $$\displaystyle Q_{nsf} = \sum \gamma \Delta z K \tan \delta \pi D $$.

*   **Effect:** Reduces net allowable load: $$\displaystyle Q_{net,allow} = Q_{allow} - Q_{nsf} $$.

4.4 Special Pile Types & Problems

• Under-reamed Piles:

  • Concept: Pile with enlarged bulbs (under-reams) at intervals. Suitable for expansive soils to resist uplift.

  • Ultimate Tensile Capacity:

$$Q_t = Q_{bulb} + Q_{shaft}$$

    $$\displaystyle Q_{bulb} = c_u \cdot A_b \cdot N_c $$ ($$\displaystyle N_c $$ given, e.g., 9), $$\displaystyle Q_{shaft} = \alpha \cdot c_u \cdot A_s $$ (shaft adhesion only, bulbs not included in shaft adhesion).

• Problems & Preventive Measures: Bearing capacity failure, settlement, pile breakage, ground heave. Preventive: proper design, pre-drilling, control of hammer energy.

[!TIP] Exam Focus: Pile group capacity in clay (block vs sum) and NSF calculation are critical. Under-reamed pile tensile capacity formula is specific.

5.0 Earth Pressure and Retaining Structures

5.1 Types of Lateral Earth Pressure

• At-rest ($$\displaystyle K_0 $$): No lateral strain.

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

• Passive ($$\displaystyle K_p $$): Wall moves toward, maximum pressure.

5.2 Classical Theories

• Rankine's Theory (1875):

  • Assumptions: Smooth wall, horizontal backfill, no wall friction ($$\displaystyle \delta = 0 $$), soil surface horizontal.

  • Derivation: From stress conditions at failure (Mohr-Coulomb).

  • For Cohesionless Soil:

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

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

    Active: $$\displaystyle \sigma_a = \gamma z K_a - 2c \sqrt{K_a} $$ (tension crack if $$\displaystyle c>0 $$).

    Passive: $$\displaystyle \sigma_p = \gamma z K_p + 2c \sqrt{K_p} $$.

*   **Tension Crack Depth:** $$\displaystyle z_c = \frac{2c}{\gamma \sqrt{K_a}} $$.

• Coulomb's Theory (1776):

  • Assumptions: Wall friction ($$\displaystyle \delta > 0 $$), inclined backfill ($\beta$), planar failure surface.

  • Merits over Rankine: Considers wall friction, inclined backfill → more realistic for rough walls.

  • $$\displaystyle K_a $$ Expression (conceptual): Minimization of $$\displaystyle P_a $$ w.r.t. failure plane angle $\theta$.

• Comparison:

  | Aspect | Rankine | Coulomb | |---------------------|--------------------------------------|--------------------------------------| | Wall friction | Neglected ($$\displaystyle \delta=0 $$) | Considered ($$\displaystyle \delta > 0 $$) | | Backfill | Horizontal only | Inclined allowed | | Failure surface | Curved (log-spiral) | Planar | | Simplicity | Simple | More complex | | Accuracy | Less for rough walls | Better for rough walls |

5.3 Earth Pressure Calculations

• Active/Passive Intensity:

  • Cohesionless: $$\displaystyle \sigma = \gamma z K $$ ($$\displaystyle K = K_a $$ or $$\displaystyle K_p $$).

  • Cohesive: $$\displaystyle \sigma_a = \gamma z K_a - 2c \sqrt{K_a} $$, $$\displaystyle \sigma_p = \gamma z K_p + 2c \sqrt{K_p} $$.

• Effect of Water Table:

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

  • Add pore water pressure separately for total stress analysis.

• Effect of Surcharge ($q$): Uniform surcharge adds $$\displaystyle q K_a $$ (active) or $$\displaystyle q K_p $$ (passive) uniformly with depth.

• Stratified Backfill: Calculate pressure layer by layer using respective $\gamma$, $c$, $\phi$. Sum contributions.

5.4 Graphical Methods

• Culmann's Graphical Method:

  • For inclined, broken-back, or surcharged backfills.

  • Steps: Draw backfill surface, trial failure planes, compute weight of wedge ($W$), calculate $$\displaystyle P_a = \frac{W \sin(\phi + \delta)}{\cos(\delta - \theta)} $$, plot envelope.

  • DiagramCANVAS: Culmann's construction showing backfill, trial wedges, and pressure envelope

5.5 Retaining Wall Design & Failure

• Types:

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

  • Cantilever: Base and stem, economical for height > 3 m.

  • Sheet Pile: Flexible, interlocked, used for cofferdams, temporary works.

• Total Thrust:

  • Active: $$\displaystyle P_a = \frac{1}{2} \gamma H^2 K_a $$ (horizontal, no surcharge, c=0). Point of application: $H/3$ from base.

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

• Modes of Failure:

  1. Overturning: Moment about toe > resisting moment.

  2. Sliding: $$\displaystyle P_a > \mu (W + P_v) $$ (base friction).

  3. Bearing Capacity Failure: Excessive pressure under toe.

• Earth Pressure on Walls: For given geometry (e.g., trapezoidal wall with varying unit weight), compute pressure at base considering all layers, then total thrust and point of application.

[!TIP] Exam Focus: Active pressure with water table, surcharge, and stratification is recurrent. Always check for tension cracks in cohesive soils.

6.0 Special Topics and Soil Improvement

6.1 Problematic Soils

• Expansive Soils:

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

  • Problems: Heave of foundations, cracks in structures, differential movement.

• Collapsible Soils:

  • Characteristics: Loess, metastable structure (bonded particles), low moisture content, sudden collapse upon wetting.

  • Problems: Sudden settlement, damage to foundations.

• Comparison:

  | Feature | Expansive Soils | Collapsible Soils | |----------------------|--------------------------------------|-------------------------------------| | Primary Issue | Swell with water increase | Collapse with water increase | | Mechanism | Clay mineral expansion | Bond breakdown | | Dry Condition | Shrink, crack | Stable, high strength | | Preventive | Moisture control, deep foundations | Pre-wetting, compaction |

6.2 Ground Improvement & Geosynthetics

• Soil Stabilization:

  • Need: Improve strength, reduce swell/shrink, increase bearing capacity.

  • Electrical Stabilization: Apply DC current through soil (electro-osmosis) to dewater and consolidate cohesive soils.

• Geosynthetics:

  • Types: Geotextiles (woven/non-woven), geomembranes (HDPE, PVC), geogrids (uniaxial/biaxial), geocells, geocomposites.

  • Functions:

    | Function | Description | |----------------|------------------------------------------------------| | Separation | Prevent mixing of dissimilar soils | | Reinforcement | Tensile strength to soil (e.g., in slopes) | | Filtration | Allow flow but retain fine particles | | Drainage | Convey water (geocomposites,geonets) | | Protection | Protect geomembranes from puncture | | Barrier | Impermeable layer (geomembranes) |

  • Uses: Reinforced soil walls, slope stabilization, drainage layers, liners for landfills, separation in roads.

6.3 Other Foundation Types

• Well Foundations (Caissons):

  • Components with Sketch:

    DiagramCANVAS: Cross-section of well foundation showing well curb (bottom), well steining (tapered section), cutting edge, well apron (top), lining, and sand filling

  • Used for bridges, deep water structures.

• Raft Foundations:

  • Floating Foundation Concept: Weight of structure + raft = weight of soil displaced → reduce net pressure.

  • Proportioning: Length/width ratios (1.5–2.5), thickness based on shear and moment, often with stiffening beams.

• Sheet Piles:

  • Differentiation from Retaining Walls: Sheet piles are flexible, interlocked, thin sections; retaining walls are rigid, massive (gravity/cantilever).

  • Uses: Cofferdams, quay walls, excavation support, temporary shoring.

[!TIP] Exam Focus: Expansive vs collapsible soils comparison and geosynthetics functions are frequently asked. Sketch of well components is essential.