Code of practice for calculation of settlements of foundations, Part 1: Shallow foundations subjected to symmetrical static vertical loads

IS 8009 Part 1 — Scope and Key Specifications

Scope

• Covers settlement analysis and design of foundations on cohesive soils.
• Applies to primary consolidation settlement and immediate settlement.
• Defines symbols, parameters, and procedures for evaluating soil compressibility and settlement.

Key Symbols (Clause 3.0)

Important Formula (Clause 9.2.2.1)

For certain cases (Fig. 2), settlement under concentrated load:

[ S_c = S_{oed} ]

Where:

• ( S_c ) = Settlement under concentrated load
• ( S_{oed} ) = Settlement corrected for foundation depth

Table 1: Factor ( \Lambda ) (related to pore pressure and loaded area)

(Exact values depend on footing shape and size; consult IS 8009 Table 1 for details)

Summary

• Use coefficients like ( C_v, m_v ) for consolidation parameters.
• Use influence factors ( I_B, I_H ) for stress distribution.
• Settlement calculation involves correcting for depth and load shape.

flowchart TD
    A[Foundation Load P] --> B[Stress Increase under footing]
    B --> C[Primary Consolidation Settlement \(S_c\)]
    B --> D[Immediate Settlement \(S_i\)]
    C --> E[Total Settlement \(S

IS 8009 (Part 1) - Key Definitions & Terminology (Clause 3.0)

This standard defines symbols commonly used in settlement calculations for shallow foundations:

Additional Notes

• Settlement Components:

  • Immediate settlement (Si)
  • Primary consolidation settlement (Sc)
  • Total settlement (St = Si + Sc + secondary settlements)

• Influence Factors:

  • Influence factor for immediate settlement (I)
  • Influence value for stress (IB)

• Pressure Parameters:

  • Effective pressure (p₀)
  • Pressure increment (Ap)

Typical Formula for Primary Consolidation Settlement (from IS 8009):

[ S_c = \frac{H}{1 + e_0} \times C_c \times \log \frac{p_0 + \Delta

IS 8009 Part 1: Assumptions in Settlement Analysis

Key Assumptions (Clause 4.1.2)

• Total soil stresses remain unchanged by settlement.
• Induced stresses from imposed loads can be estimated accurately.
• Loads transmitted to foundation are static and vertical.

Important Specifications for Settlement Calculation

• Boring and soil data quality (Clause 7.3):
  • 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).
  • At least one consolidation test per clay layer within the stress influence zone.
  • For thick clay layers, test samples at intervals ≤ 2 m.

Stress and Settlement Analysis (Clause 9.1)

• Settlement estimation methods depend on soil type:
  • Cohesionless soils: Settlement primarily elastic, estimated using SPT and empirical correlations.
  • Cohesive soils: Settlement from consolidation tests.

Typical Settlement Formula for Cohesive Soils (Consolidation Settlement):

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

Where:

• ( S_c ) = consolidation settlement
• ( H ) = thickness of compressible soil layer
• ( e_0 ) = initial void ratio
• ( \sigma'_0 ) = initial effective vertical stress
• ( \Delta \sigma ) = increase in effective stress due to load

Summary Diagram: Settlement Analysis Workflow

flowchart TD
    A[Site Investigation] --> B[Soil Sampling]
    B --> C{Soil Type?}
    C -->|Cohesive| D[Consolidation Tests]
    C -->|Cohesionless| E[SPT Tests]
    D --> F[Calculate Consolidation Settlement]
    E --> G[Estimate Elastic Settlement]
    F --> H[Settlement Estimation]
    G --> H

Use high-quality boring data and appropriate tests to ensure reliable settlement analysis per IS 8009 Part 1.

IS 8009 Part 1: Soil Profile Simplification & Layering

Key Points from Clauses:

• Clause 4.2.1:

  • Simplify soil profile into one or more layers based on uniformity.
  • Calculate average compressibility for each layer.
  • Total settlement = sum of settlements of all affected layers below the point of interest.

• Clause 9.2.2:

  • Differentiate settlement estimation methods for clay layers sandwiched between cohesionless soils or rock.
  • Immediate and consolidation settlements are treated differently per soil type.

• Clause 6.2:

  • Consider drainage, flooding, and vegetation effects on soil behavior.

Typical Soil Layering & Settlement Calculation:

Settlement per layer (consolidation):
[ S = \frac{H}{1 + e_0} \times C_c \times \log \frac{\sigma'_0 + \Delta \sigma'}{\sigma'_0} ]

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

Simplification Steps:

1. Identify soil layers with uniform properties.
2. Calculate average properties (e.g., compressibility, void ratio) for each layer.
3. Estimate stress increase at midpoint of each layer.
4. Compute settlement layer-wise and sum up.

IS 8009 Part 1: Calculation of Vertical Stresses in Soil

Key Formulas & Concepts

1. Vertical Stress (σz) under Circular Load (Boussinesq solution):
   [ \sigma_z = q \times I_B ]

   • ( q ) = uniform load intensity
   • ( I_B ) = influence factor from charts or formula depending on ( R/z ) (radius to depth ratio)
   • Use Fig. 16 & 17 for graphical determination (Newmark’s influence chart).

2. Vertical Stress under Rectangular Load: [ \sigma_z = q \times I_B ]

   • ( I_B ) depends on ( L/z ) and ( B/z ) (length and width to depth ratios)
   • Use Fig. 18 for influence factors.

3. Influence Value:

   • Typical influence value ( I_B \approx 0.005 ) for Boussinesq solution (Fig. 20).

Procedure Using Influence Charts

• Draw the loaded area on the influence chart with the point of interest at the center.
• Scale depth ( z ) as unit length on the chart.
• Count the number of influence areas enclosed by the loaded area.
• Calculate vertical stress:
  [ \sigma_z = q \times I_B \times \text{(number of influence areas)} ]

Notes

• Elastic theory assumptions apply; soils are not perfectly elastic, so results are approximate.
• Charts (Figs. 15-20) are essential for practical estimation.
• For variable soil deposits or decreasing compressibility with depth, use Fig. 20.

flowchart TD
    A[Load q on Surface] --> B[Determine Depth z]
    B --> C{Load Shape?}
    C -->|Circular| D[Use Boussinesq Formula & Fig.17]
    C -->|Rectangular| E[Use Fig.18 Influence Chart]
    D --> F[Calculate Influence Value I_B]
    E --> F
    F --> G[Calculate σz = q × I_B]
    G --> H[Estimate Vertical Stress at Depth z]

Summary: Use IS 8009 Part 1 charts and formulas based on load geometry and depth to estimate vertical

Determination of Subsoil Profile (IS 8009 Part 1 - 1976)

Key Points from Clauses:

• Clause 6.2: Consider drainage, flooding, and presence of water-seeking trees as they affect soil settlement behavior.
• Clause 4.2: Soil profile must be identified accurately before foundation design.
• Clause 9.2.2.2: Provides formulas and tables for estimating settlement on cohesionless soils based on Standard Penetration Test (SPT) results.

Important Formula for Settlement (Clause 9.2.2.2):

For clayey soils without precompression (simple static or residual hydrostatic conditions):

[ S = H \cdot C_e \cdot \log \left(\frac{\sigma_0' + \Delta \sigma}{\sigma_0'}\right) ]

Where:

• (S) = Settlement
• (H) = Thickness of compressible soil layer
• (C_e) = Compression index (from soil tests)
• (\sigma_0') = Initial effective stress
• (\Delta \sigma) = Increase in effective stress due to foundation load

Table: Settlement per Unit Pressure from SPT (Fig. 9 Summary)

• Settlement decreases as SPT N-value increases.
• Use these values to estimate settlement for cohesionless soils.

Additional Notes:

• Perform Standard Penetration Test (SPT) to determine soil resistance.
• Check water table (WT) level as it influences effective stress.
• Use load tests for validation if possible.
• Consider drainage and environmental conditions as per Clause 6.2.

flowchart TD
    A[Site Investigation] --> B[Soil Profile Identification]
    B --> C[SPT & Load Tests]
    C --> D[Calculate Effective Stress Increase

IS 8009 Part 1: Preloading Pressure Conditions & Implications

Key Points from Clause 8.1.2 & Appendix A:

• Total vertical pressure (σv) at depth = Weight of overlying soil layers
  [ \sigma_v = \sum (\gamma_i \times h_i) ]
  where (\gamma_i) = unit weight of soil layer (i), (h_i) = thickness of layer (i).

• Effective stress (σ'):
  [ \sigma' = \sigma_v - u ]
  where (u) = pore water pressure (neutral pressure).

• Preloading conditions (Fig. 7):

  • Simple static
  • Residual hydrostatic
  • Artesian
  • Overconsolidated

• For clays, preloading condition identification relies on geological data and previous maximum intergranular pressure.

Settlement Calculation for Non-precompressed Clay (Clause 9.2.2.2):

[ S = H \times C_e \times \log \frac{\sigma'_0 + \Delta \sigma}{\sigma'_0} ]

• (S) = settlement
• (H) = thickness of compressible layer
• (C_e) = compression index (from consolidation tests)
• (\sigma'_0) = initial effective vertical stress
• (\Delta \sigma) = increase in effective stress due to loading

Table 9.1 (Summary):

Implications:

• Correct estimation of pore pressure and preloading condition is critical for accurate settlement prediction.
• Overconsolidated soils behave differently; settlements are generally smaller.
• Artesian and residual hydrostatic conditions affect pore pressure and hence effective stress.

flowchart TD
    A[Soil Layers] --> B[Calculate Total Vertical Pressure \(\sigma_v\

IS 8009 Part 1: Estimation of Pressure Increments Due to Loads

Key Clauses Summary:

• Clause 8.2.2: Pressure increment due to imposed loads is calculated as per Clause 8.3.
• Clause 8.3: Selection of stress distribution theories to compute pressure increments.
• Clause 8.3.6: Procedure and charts for pressure increment estimation are in Appendix B.
• Residual hydrostatic excess pressure is estimated by methods in Appendix A.
• Pressure changes from water table fluctuations are estimated via field data or anticipated changes.

Typical Procedure (from Appendix B):

1. Select Stress Distribution Theory:

   • Boussinesq’s theory for point loads or uniform loads.
   • Westergaard’s theory for layered soils or rigid inclusions.

2. Calculate Pressure Increment (Δp):

   • For uniform load ( q ) over area ( A ), pressure increment at depth ( z ) is:
     [ \Delta p = q \times I_z ]
   • ( I_z ) = influence factor from charts (Appendix B) based on load shape, size, and depth.

3. Use Charts/Tables:

   • Charts provide ( I_z ) values for rectangular/square loads.
   • Influence factor depends on depth-to-width ratio ( z/B ).

Typical Influence Factor Table (Example):

Notes:

• Pressure increments are additive to initial effective stresses.
• Use residual hydrostatic pressure from Appendix A for pore water pressure effects.
• Account for water table fluctuations separately.

flowchart TD
    A[Imposed Load q] --> B[Select Stress Distribution Theory]
    B --> C[Calculate Influence Factor I_z (Appendix B)]
    C --> D[Compute Pressure Increment Δp = q × I_z]
    D --> E[Add Residual Hydrostatic Pressure (Appendix A)]
    E --> F[Estimate Total Pressure Increment]

IS 8009 Part 1 (1976) – Settlement Computation Methods: Key Points

Settlement Computation Types (Clause 4.2.4)

• Cohesionless soils: Settlement computed differently than cohesive soils.
• Thin clay layer (Fig. 2): Settlement is one-dimensional (vertical compression).
• Thin clay layer (Fig. 3) or thick clay layer (Fig. 4): Settlement influenced by lateral deformation; requires 2D or 3D consideration.
• Multiple layers (Fig. 5 & 6): Settlement computed by summing contributions from independent soil layers.

General Approach for Settlement Computation

1. Identify soil type: Cohesive or cohesionless.
2. Determine soil layering: Thin/thick clay, sand layers, or mixed.
3. Apply appropriate formula based on soil type and layering.

Typical Settlement Formulas

• For cohesionless soils (elastic settlement):

[ S = \frac{q B (1 - \nu^2)}{E_s} I_p ]

Where:

• (S) = settlement,

• (q) = applied pressure,

• (B) = foundation width,

• (\nu) = Poisson’s ratio,

• (E_s) = soil modulus of elasticity,

• (I_p) = influence factor (from tables/graphs).

• For cohesive soils (consolidation settlement):

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

Where:

• (H) = thickness of compressible layer,
• (e_0) = initial void ratio,
• (\sigma'_0) = initial effective stress,
• (\Delta \sigma') = increase in effective stress.

Important Tables/Factors (from IS 8009 Part 1)

Consolidation Theory & Time-Dependent Settlements (IS 8009 Part 1)

Key Formulas

• Total settlement at time t:

[ S_t = S_i + U \times S_c ]

Where:

• ( S_t ) = settlement at time ( t )

• ( S_i ) = immediate settlement

• ( S_c ) = primary consolidation settlement

• ( U ) = degree of consolidation (function of time factor ( T ))

• Degree of consolidation:

[ U = F(T) ]

• Time factor:

[ T = \frac{C_v \times t}{H^2} ]

Where:

• ( C_v ) = coefficient of consolidation (m²/year) from oedometer test (IS 2720 Part XV)
• ( t ) = time in years
• ( H ) = drainage path length (m)

Important Notes

• Fig. 13 (IS 8009 Part 1) shows the relationship between ( U ) (percent consolidation) and ( T ) (time factor) for different drainage conditions:

  • One-way drainage (impermeable layer below)
  • Two-way drainage (permeable foundation assumed)

• Coefficient of consolidation ( C_v ) is obtained from laboratory consolidation tests using fitting methods.

• Appendix D provides procedures for evaluating time rate of settlement considering construction duration and loading history.

Graphical Interpretation (Simplified)

graph LR
A[Time Factor, T] --> B[Degree of Consolidation, U]
B --> C{Drainage Condition}
C --> D[One-way drainage curve]
C --> E[Two-way drainage curve]

Summary Table: Time Factor ( T ) vs Degree of Consolidation ( U ) (Approximate)

IS 8009 Part 1: Corrections for Foundation Depth and Rigidity (Clause 9.5)

1. Correction for Depth of Foundation (Clause 9.5.1)

• Settlement ( S ) calculated for surface foundations must be corrected for foundations at depth ( D ).
• Use Depth Factor from Fig. 12 (Fox's Correction Curves for flexible rectangular footings).
• Corrected Settlement formula:

[ S_{td} = S \times \text{Depth Factor} ]

Where:

• ( S ) = Settlement at surface
• ( S_{td} ) = Corrected settlement at depth ( D )

2. Correction for Rigidity of Foundation (Clause 9.5.2)

• For rigid foundations (e.g., heavy beam and slab rafts, massive piers), settlement at the center reduces.
• Use a Rigidity Factor to reduce the total settlement:

[ \text{Total settlement of rigid foundation} = \text{Rigidity factor} \times \text{Total settlement at center of flexible foundation} ]

3. Key Notes:

• Depth Factor depends on footing dimensions ( L \times B ) and depth ( D ).
• Rigidity Factor is less than 1, reflecting reduced settlement due to foundation stiffness.

4. Illustration (Mermaid.js):

flowchart TD
    A[Calculate Settlement at Surface (S)] --> B[Apply Depth Factor from Fig.12]
    B --> C[Corrected Settlement at Depth (S_td)]
    C --> D{Is Foundation Rigid?}
    D -- Yes --> E[Apply Rigidity Factor]
    D -- No --> F[Use S_td as Final Settlement]
    E --> G[Final Reduced Settlement]

For exact values of Depth Factor and Rigidity Factor, refer to Fig. 12 and relevant tables in IS 8009 Part 1.

IS 8009 Part 1: Special Cases and Limitations - Key Points

1. Complex Cases (Clause 3.6 & A-3.6)

   • Complex loading or boundary conditions are combinations of simple cases (A-3.2 to A-3.5).
   • These require individual analysis; the code does not provide direct formulas for them.

2. Stress Distribution Theories (Appendix B, Clause 8.3.6)

   • Selection depends on assumptions about soil homogeneity and elasticity.
   • Common theories: Boussinesq, Westergaard, and Elastic Half-Space.
   • Use the theory best matching the soil and loading conditions.

3. Assumptions for Variable Deposits (Clause 5.1, B-5.1)

   • Treat variable deposits as homogeneous, isotropic, elastic for vertical stress computations.

4. Limitations (Clause 9.2.2.1)

   • For certain cases (Fig. 2), vertical stress increment:
     [ S_c = S_{oed} ]
   • Where ( S_c ) = computed stress increment, ( S_{oed} ) = observed or oedometric stress.

Summary Table: Stress Distribution Theories

flowchart LR
    A[Simple Cases (A-3.2 to A-3.5)] --> B[Complex Cases (3.6)]
    B --> C[Individual Analysis Required]
    D[Variable Deposits (B-5.1)] --> E[Assume Homogeneous, Isotropic, Elastic]
    F[Stress Distribution Theories] --> G[Boussinesq]
    F --> H[Westergaard]
    F --> I[Elastic Half-Space]

Note: For complex cases, use finite element or numerical methods beyond IS 8009 scope.

Determination of Preloading Pressure Conditions
As per IS 8009 (Part 1) - 1976, Clauses 8.1.2, A-1, A-3.1, 9.2.2.2

Key Concepts

• Total vertical pressure (σv) at depth = weight of overlying soil layers
  [ \sigma_v = \sum (\gamma_i \times h_i) ]
  where (\gamma_i) = unit weight of ith soil layer, (h_i) = thickness.

• Pore water pressure (u):

  • For pervious layers: estimated from groundwater level.
  • For clays: depends on preloading condition type (simple static, residual hydrostatic, artesian, overconsolidated).

• Effective stress (σ'):
  [ \sigma' = \sigma_v - u ]

Preloading Conditions (Fig. 7 in IS 8009)

Settlement Estimation for Clay (Clause 9.2.2.2)

For non-precompressed clay (simple static, residual hydrostatic, artesian):

[ S = H \times C_e \times \log \frac{\sigma'_f}{\sigma'_i} ]

• (S) = settlement
• (H) = thickness of compressible layer
• (C_e) = compression index
• (\sigma'_f) = final effective stress after loading
• (\sigma'_i) = initial effective stress (depends on preloading condition)

Reference Table: Settlement per Unit Pressure from SPT (Fig. 9)

Use SPT N-values and footing width to estimate settlement.

IS 8009 Part 1: Selection of Stress Distribution Theories (Clause 8.3 & Appendix B)

Key Points:

• Purpose: To estimate pressure increments in soil due to imposed loads using appropriate stress distribution theories.
• Applicability: Elastic theory solutions (e.g., Boussinesq) are exact only for elastic, isotropic materials; soils are often non-elastic, so results are approximate.
• Guidelines:
  • For normally consolidated clays (effectively isotropic), use Boussinesq solution.
  • For complex load cases, individual treatment is required (Clause 3.6).

Important Formulas and Tables:

1. Boussinesq Vertical Stress Increment (σz):

[ \sigma_z = \frac{3P}{2\pi z^2} \cdot \frac{1}{\left[1 + \left(\frac{r}{z}\right)^2\right]^{5/2}} ]

• (P) = point load on surface
• (z) = depth below surface
• (r) = radial distance from load axis

2. Influence Charts:

• Fig. 18: Rectangular area uniformly loaded — use influence values to compute stress increment.
• Fig. 20: Influence chart for vertical stress with Fröhlich concentration factor (m' = 4).

3. Influence Value (Example):

Practical Notes:

• Use Boussinesq theory for normally consolidated clays (Clause B-2.1).
• For precompressed clays, other specialized methods may be required (Clause B-3).
• The accuracy is limited by soil non-elasticity; treat results as approximate.

flowchart TD
    A[Surface Load] --> B{Soil Type}
    B -->|Normally Consolidated Clay| C[Boussinesq Solution]
    B -->|Precompressed Clay| D[Specialized Method]
    B -->|Complex Case| E[Individual Treatment]
    C --> F[Use Influence Charts]
    F --> G[Calculate Stress Increment]

**