Code of practice for calculation of settlement of foundations, Part 2: Deep foundations subjected to symmetrical static vertical loading

Scope of IS 8009 Part 2 (1980) - Key Points & Symbols

• Purpose: Provides methods and symbols for settlement analysis of pile foundations in compressible soils.
• Applicable to: Pile groups, equivalent raft foundations, and consolidation settlement calculations.

Important Symbols (Clause 3.1)

Key Considerations (Clause 4.1)

• Settlement calculations assume soil consolidation behavior.
• Equivalent raft foundation concept is used for pile groups.
• Parameters like pile spacing ratio (s/d), compressible layer thickness, and foundation depth influence design.

Typical Formula for Primary Consolidation Settlement (Sc)

[ S_c = \frac{H}{1+e_0} \cdot C_c \cdot \log \frac{\sigma_0' + \Delta \sigma}{\sigma_0'} ]

Where:

• (H) = Thickness of compressible layer (cm)
• (e_0) = Initial void ratio
• (C_c) = Compression index
• (\sigma_0') = Initial effective stress (kg/cm²)
• (\Delta \sigma) = Increase in stress due to foundation load (kg/cm²)

Summary

IS 8009 Part 2 - Definitions and Symbols (Clause 3.1)

This clause defines key symbols used in pile foundation settlement calculations:

Notes:

• These symbols are essential for calculating immediate, primary consolidation, and final settlements of pile foundations.
• Refer to IS 8009 Part 2 for

IS 8009 Part 2 – General Considerations and Observations: Key Points

1. Symbols & Definitions (Clause 3.1)

• A = Cross-sectional area of pile (cm²)
• D = Depth of foundation (cm)
• Dp = Length of pile (cm)
• P = Average load per pile (kg)
• Pb = Average point resistance per pile (kg)
• Sg = Settlement of foundation structure (cm)
• Cv = Average coefficient of consolidation (m²/year)
• my = Coefficient of volume compressibility (cm²/kg)
• to = Thickness of compressible stratum (cm)
• σ'0 = Initial effective stress at mid-layer (kg/cm²)

2. General Observations on Settlement Computation (Clause 4.3)

• Settlement of deep foundations is complex; approximate methods are commonly used.
• Consider interaction between pile groups and soil layers.
• Use equivalent raft foundation concept for group piles.
• Settlement components include:
  • Immediate settlement (Si)
  • Primary consolidation settlement (Sc)
  • Secondary compression (if applicable)

3. Typical Formula for Primary Consolidation Settlement:

[ S_c = m_y \times H \times \Delta \sigma' ]

Where:

• (S_c) = Consolidation settlement (cm)
• (m_y) = Coefficient of volume compressibility (cm²/kg)
• (H) = Thickness of compressible layer (cm)
• (\Delta \sigma') = Increase in effective stress (kg/cm²)

4. Factors Affecting Settlement (from MI 130)

• Depth of equivalent raft foundation
• Thickness of compressible soil layer
• Length/width ratio of equivalent raft

5. Approximate Method Flow (Clause 8.3.3 & Fig.1)

flowchart TD
    A[Load on Pile Group] --> B[Calculate Equivalent Raft Pressure]
    B --> C[Determine Stress Increase in Soil Layers]
    C --> D[Estimate Immediate Settlement]
    C --> E[Estimate Primary Consolidation Settlement]
    D & E --> F[Sum Settlements for Total Settlement]

**

IS 8009 Part 2: Soil Profile & Properties — Key Points

1. Soil Profile Simplification (Clause 4.2 & 4.2.1)

• Soil is modeled as one or more layers based on uniformity.
• Total settlement = Sum of settlements of all affected layers.

2. Required Structural Details for Settlement Estimation (Clause 6.1)

• Site plan with location of proposed & neighboring structures.
• Building plan with layout of load-bearing walls/columns + dead/live loads.
• Structural rigidity information.
• Local settlement data from existing structures.

3. Types of Soil Formations (Clause 4.2.2)

Settlement Calculation (General Formula)

[ S = \sum_{i=1}^{n} \Delta H_i = \sum_{i=1}^{n} \frac{q_i H_i}{E_i} ]

Where:

• ( S ) = total settlement
• ( \Delta H_i ) = settlement of layer (i)
• ( q_i ) = stress increment in layer (i)
• ( H_i ) = thickness of layer (i)
• ( E_i ) = modulus of elasticity of soil layer (i)

flowchart TD
    A[Soil Profile] --> B{Uniformity?}
    B -->|Yes| C[Single Layer Model]
    B -->|No| D[Multiple Layers Model]
    D --> E[Calculate Settlement per Layer]
    E --> F[Sum Settlements]
    F --> G[Total Settlement]

Summary:

• Model soil in layers based on uniformity.
• Use structural & site data for accurate load and settlement estimation.
• Identify soil type for appropriate settlement calculation.

Assumptions in Settlement Analysis (IS 8009 Part 2)

• Clause 4.1.2 Assumptions:

  • Total soil stresses from construction remain unchanged by settlement.
  • Induced stresses due to loads can be estimated.
  • Load on foundation is static and vertical.

• Settlement Estimation (Clause 4.3.2):

  • Settlement is theoretically the integral of vertical strain through soil depth.
  • Practical methods simplify this due to complexity.

• Settlement Computation Steps (Clause 10.1):

  • Based on Terzaghi’s 1D consolidation theory:

    [ S_t = S_f + U S_c ]

    where:

    • (S_t) = total settlement at time (t)
    • (S_f) = final settlement after full consolidation
    • (U) = degree of consolidation (function of time factor (T))

  • Degree of consolidation (U = F(T)) depends on drainage and pressure distribution (see Fig. 13, Part I).

  • Coefficient of consolidation (C_v) is obtained from 1D consolidation tests per IS 2720 (Part XV).

Summary Table: Key Parameters for Settlement Analysis

flowchart TD
    A[Load applied on soil] --> B[Induced vertical stress]
    B --> C[Vertical strain in soil layers]
    C --> D[Settlement calculation by integration]
    D --> E[Apply Terzaghi's consolidation theory]
    E --> F[Calculate degree of consolidation (U)]
    F --> G[Estimate settlement at time t: S_t = S_f + U S_c]

IS 8009 Part 2 on deep foundations under symmetrical static vertical loading focuses on settlement calculation, with key points on load transfer as follows:

Key Concepts for Load Transfer in Deep Foundations

• Load Transfer Mechanism: Load is transferred from the superstructure to the pile through:

  • Base resistance (Q_b) at the pile tip.
  • Shaft (skin) friction (Q_s) along the pile length.

• Total Load on Pile (Q): [ Q = Q_b + Q_s ]

• Settlement Computation (Clause 4.3):

  • Settlement is due to compression of soil layers around and beneath the pile.
  • Settlement is calculated by summing settlements due to base and shaft separately.

Typical Formulas

Typical Tables (from IS 8009 Part 2)

Summary

• Calculate shaft friction and base resistance separately.
• Use soil parameters from site investigation.
• Settlement is additive from shaft and base components.
• Ensure symmetrical vertical loading for validity.

flowchart TD
    Load --> Pile
    Pile --> ShaftFriction[Load Transfer via Shaft Friction]
    Pile --> BaseResistance[Load Transfer via Base Resistance]
    ShaftFriction --> Soil[Soil Layers Along Pile]
   

IS 8009 Part 2: Immediate Settlement Calculation

Key Formula (Clause 9.4.3.2 & 9.1.4.1)

[ S_i = \frac{q \cdot H}{E} \cdot I ]

Where:

• (S_i) = Immediate settlement
• (q) = Applied stress at foundation base
• (H) = Thickness of clay stratum
• (E) = Modulus of elasticity from triaxial consolidated undrained test (at effective stress)
• (I) = Influence factor (depends on clay thickness and boundary conditions)

Determination of Parameters

• (E): Obtained from the stress-strain curve of triaxial consolidated undrained test, with consolidation pressure = effective pressure at sample depth.
• (I):
  • For finite thickness clay stratum: Use Fig. 11, Part I (where Hur = Ht)
  • For semi-infinite clay stratum: Use Table 2, Part I

Notes

• The method assumes elastic compression behavior under immediate loading.
• Applicable for deep foundations under symmetrical static vertical loads.
• Time-dependent settlements (primary consolidation) are treated separately.

If needed, I can help summarize Fig. 11 or Table 2 from Part I for specific values of (I).

Calculation of Consolidation Settlement (IS 8009 Part 2)

Key Formulas:

1. Primary Consolidation Settlement:

[ S_c = A \times S_{oed} \quad \text{(Eq. 11)} ]

• ( S_c ) = Consolidation settlement
• ( A ) = Factor related to pore pressure parameter and geometry (from Fig. 10, Part I)
• ( S_{oed} ) = Oedometric settlement

If ( A ) is unknown, use values from Table 1, Part I.

2. Settlement at any time ( t ):

[ S_t = S_c + U S_c \quad \text{(Eq. 15)} ]

• ( S_t ) = Settlement at time ( t )
• ( U ) = Degree of consolidation (function of time factor ( T ))
• ( U = F(T) ) (see Fig. 13, Part I)

3. Degree of Consolidation ( U ) and Time Factor ( T ):

• ( U ) depends on drainage conditions and pressure distribution.
• Use Tarzaghi’s 1D consolidation theory.
• ( T = \frac{C_v t}{H^2} ), where:
  • ( C_v ) = Coefficient of consolidation (from IS 2720 Part XV)
  • ( t ) = Time
  • ( H ) = Drainage path length

Notes:

• Foundation concrete can be assumed permeable for drainage.
• ( C_v ) should be determined from lab consolidation tests.
• Use simplified methods provided in IS 8009 Part II for deep foundations under vertical loads.

Summary Table (Conceptual):

Settlement Computation for Different Pile Types
(IS 8009 Part 2 key points)

1. General Approach (Clause 4.3)

• Settlement of deep foundations depends on soil strata, pile type, and load transfer mechanism.
• Consider immediate, consolidation, and creep settlements.
• Pile group effects and interaction with soil must be accounted.

2. Settlement Formulae (Clause 9.6.3)

Two empirical formulae by Skempton and Mayerhoff for pile group settlement:

[ S_t = S_1 \left[ 4B + 2.712 \right] ]

• S_t = Settlement of pile group
• S_1 = Settlement of single pile
• B = Width of pile group (or pile diameter depending on context)

Note: Pile load tests after driving all piles (IS 2911 Part IV) provide S_1.

3. Settlement in Soft Clay (Clause 9.5.1)

• When soft clay underlies bearing stratum, settlement includes consolidation settlement of soft clay.
• Use consolidation theory or empirical correlations for clay settlement.
• Total settlement = immediate settlement + consolidation settlement.

4. Additional Notes

• Settlement from pile load test is most reliable.
• For friction piles, settlement depends on skin friction mobilization.
• For end-bearing piles, settlement mainly from bearing stratum compression.

Summary Table

flowchart TD
    A[Load on Pile Group] --> B[Single Pile Settlement (S1)]
    B --> C[Apply Group Factor: 4B + 2.712]
    C --> D[Group Settlement (St)]
    A --> E[Soil Type Check]
    E -->|Soft Clay| F[Calculate Consolidation Settlement]
    F --> G[Add to Total Settlement]

References:

• IS 8009 Part 2: Clauses

Estimation of Time Rate of Settlement as per IS 8009 Part 2

Key Formulas:

• Total settlement at time t: [ S_t = S_f + U S_c \quad \text{(Eq. 15)} ] Where,

  • ( S_t ) = settlement at time ( t )
  • ( S_f ) = immediate settlement (instantaneous)
  • ( S_c ) = consolidation settlement (final)
  • ( U ) = degree of consolidation at time ( t )

• Degree of consolidation: [ U = F(T) \quad \text{(Eq. 16)} ] Where,

  • ( T ) = time factor, related to time ( t ), drainage path length ( H ), and coefficient of consolidation ( C_v ): [ T = \frac{C_v t}{H^2} ]

Notes:

• ( U ) vs. ( T ) relationship is graphically shown in Fig. 13, Part I of IS 8009.
• For clay layers, the foundation concrete can be assumed permeable for drainage.
• ( C_v ) (coefficient of consolidation) is obtained from 1D consolidation tests per IS 2720 (Part XV)-1965.
• Settlement integration involves vertical strain over depth (Clause 4.3.2), but simplified methods are often used.

Summary Table:

graph TD
A[Time t

Correction Factors and Depth Effects
(as per IS 8009 Part 2 and references to Part 1)

1. Correction for Depth of Foundation Settlement

The corrected settlement ( S_c ) is given by:

[ \boxed{ S_c = S_i \times \text{Depth Factor} } ]

• ( S_i ) = Calculated settlement (without depth correction)
• Depth Factor = Read from Fig. 12, Part 1 of IS 8009 (varies with depth and soil conditions)

2. Depth Factor

• The depth factor accounts for the increase in soil stiffness and confinement effects with foundation depth.
• It is a dimensionless multiplier less than or equal to 1, reducing settlement estimates for deeper foundations.
• Typically depends on:
  • Depth of foundation ( D ) (cm)
  • Thickness of compressible layer ( t_0 ) (cm)
  • Soil properties and loading conditions

3. Relevant Symbols from Clause 3.1

4. Additional Notes

• Depth correction is essential for pile foundations and equivalent raft foundations.
• Applicable for both primary consolidation settlement and immediate settlement.
• Use Fig. 12 (Part 1) for accurate depth factor values; if unavailable, approximate from empirical charts or literature.

Summary Diagram of Correction Process

flowchart LR
    A[Calculate Settlement \(S_i\)] --> B[Read Depth Factor from Fig. 12]
    B --> C[Calculate Corrected Settlement \(S_c = S_i \times \text{Depth Factor}\)]
    C --> D[Use \(S_c\) for design and analysis]

References:

• IS 8009 Part 1, Fig. 12 (Depth Factor chart)
• IS 8009 Part 2, Clauses 9.1

IS 8009 Part 2 - Testing Methods for Settlement Evaluation: Key Points

1. Data Requirements (Clause 7.3)

• Cohesionless soils: Use Standard Penetration Test (SPT) results per IS:2131-1963.
• Cohesive soils: Use consolidation test results on undisturbed samples as per IS:2720 (Part XV)-1965.
• Number of tests depends on soil uniformity and structure importance.
• For clay layers, test at least one sample per clay layer within stress influence zone.
• For thick clay layers, samples at ≤ 2 m intervals.

2. Stress Analysis (Clause 8 & 1.1)

• Methods estimate:
  • Elastic compression
  • Immediate settlement
  • Primary consolidation settlement
• Time rate of settlement can be computed.

3. Typical Formula for Primary Consolidation Settlement (from IS 8009 Part 2 & IS 2720 Part XV):

[ S_c = \frac{H}{1+e_0} \cdot C_c \cdot \log \left(\frac{\sigma'_0 + \Delta \sigma}{\sigma'_0}\right) ]

Where:

• (S_c) = Consolidation settlement
• (H) = Thickness of compressible layer
• (e_0) = Initial void ratio
• (C_c) = Compression index (from consolidation test)
• (\sigma'_0) = Initial effective stress
• (\Delta \sigma) = Increase in effective stress due to loading

Summary Table: Test Type vs Soil Type

flowchart TD
    A[Soil Type] -->|Cohesionless| B[SPT Test (IS:2131)]
    A -->|Cohesive| C[Consolidation Test (IS:2720 Pt XV)]
    B --> D[Settlement Calculation]
    C -->

Settlement of Pile Groups (IS 8009 Part 2)

Key Points & Formulas:

• Clause 9.6.3:
  Settlement of pile group, ( S_t ), can be estimated from test pile settlement ( S_1 ) using Skempton and Mayerhoff formulae:
  [ S_t = S_1 \left( 4B + 2.712 \right) ]
  where B = width of the equivalent footing representing the pile group.

• Clause 9.6.2:
  For friction pile groups in cohesionless soils:

  • Group settlement ≤ settlement of a single test pile (due to soil compaction between piles).
  • Group settlement ≈ settlement of an equivalent well foundation with dimensions equal to pile group size (refer Eq. 8 and Fig. 2 in IS 8009 Part 2).

• Clause 9.7.1:

  • Replace pile group by an equivalent footing (Fig. 1A/1B).
  • Compute settlement as for shallow foundations (Clause 9.4.3), ignoring depth correction.

• Clause 9.3.1:
  Settlement through compressible strata + settlement in sand; depends on point resistance to total load ratio.

Summary Table:

Conceptual Diagram:

flowchart TD
    A[Pile Group] --> B[Equivalent Footing]
    B --> C[Calculate Settlement using shallow foundation methods]
    A --> D[Single Pile Load Test]
    D --> E[Obtain \(S_1\)]
    E --> F[Compute \(S_t = S_1 (4B + 

Settlement in Special Soil Conditions (IS 8009 Part 2 - Key Points)

• Data Requirements:

  • For cohesionless soils: Use Standard Penetration Test (SPT) results (IS 2131-1963).
  • For cohesive soils: Use consolidation test results on undisturbed samples (IS 2720 Part 15-1965).

• Sampling Frequency:

  • At least one consolidation test per clay layer within the stress influence zone.
  • For thick clay layers, samples at intervals ≤ 2 m.

• Settlement Calculation:

  • Requires adequate boring data and judicious interpretation.
  • Accuracy improves with the number of consolidation tests.

Typical Settlement Calculation Formula for Cohesive Soils:

[ S = \frac{H}{1+e_0} \cdot C_c \cdot \log \frac{\sigma'_0 + \Delta \sigma}{\sigma'_0} ]

Where:

• (S) = settlement
• (H) = thickness of compressible layer
• (e_0) = initial void ratio
• (C_c) = compression index
• (\sigma'_0) = initial effective stress
• (\Delta \sigma) = increase in effective stress due to foundation load

Summary Table for Sampling and Testing:

flowchart TD
    A[Start: Soil Investigation] --> B{Soil Type?}
    B -->|Cohesionless| C[Conduct SPT (IS 2131)]
    B -->|Cohesive| D[Collect Undisturbed Samples]
    D --> E[Perform Consolidation Tests (IS 2720 Pt 15)]
    C & E --> F[Interpret Data & Calculate Settlement]

IS 8009 Part 2 — Limitations & Recommendations (Clauses 3.1, 4.1, 8.3.3)

Key Symbols & Parameters (Clause 3.1)

• A = Cross-sectional area of pile (cm²)
• D = Depth of foundation (cm)
• Dp = Length of pile (cm)
• Ev = Modulus of elasticity vertical (kg/cm²)
• P = Average load per pile (kg)
• Sc = Primary consolidation settlement (cm)
• Soed = Settlement from 1D consolidation test (m)
• $ = Ratio of pile spacing to diameter

Limitations (Clause 4.1)

• Assumptions include uniform soil layers, pile group behavior approximated by equivalent raft.
• Valid for compressible soil layers with known consolidation parameters.
• Approximate methods recommended for complex soil strata (Clause 8.3.3).

Recommendations

• Use equivalent raft concept for pile groups to estimate foundation pressure (Pb).
• Refer to Fig. 1 and Fig. 2B for deformation modulus curves and settlement approximations.
• Follow updated test standards:
  • IS 2720 Part 15 (1986) for consolidation properties.
  • IS 8009 Part 4 for load tests on piles.

Typical Formula for Primary Consolidation Settlement (Sc):

[ S_c = \frac{H_0}{1+e_0} \cdot C_c \cdot \log \frac{\sigma_0' + \Delta \sigma}{\sigma_0'} ]

Where:

• (H_0) = Thickness of compressible soil (cm)
• (e_0) = Initial void ratio
• (C_c) = Compression index
• (\sigma_0') = Initial effective stress
• (\Delta \sigma) = Increase in stress due to foundation load

flowchart LR
    A[Load on Pile Group] --> B[Equivalent Raft Pressure]
    B --> C[Increase in Effective Stress]
    C --> D[Primary Consolidation Settlement (Sc)]
    D --> E[Total Settlement Estimation]

Summary: Use updated IS test methods, apply equivalent