Code of practice for determination of bearing capacity of shallow foundations

IS 6403: Scope - Key Formulas, Tables & Specifications

1. Scope Summary (Clause 2.0 & 3.1)

• Defines footing dimensions:
  • B = Width/side/diameter (cm)
  • L = Length of footing (cm)
• Soil parameters:
  • c = Cohesion (kgf/cm²)
  • ϕ = Angle of shearing resistance (°)
  • γ = Bulk unit weight (kgf/cm³)
• Load eccentricities: e, B', L' etc.

2. Shape Factors (Clause 5.1.2.1 & Table 2)

• Use B as diameter for circular footings in bearing capacity formulas.

3. Bearing Capacity Factors & Formula (from IS 6403 context)

• Corrected bearing capacity factors: N₀, Nq, Nγ, etc.
• Effective surcharge:
  [ q = \text{Effective surcharge at foundation base (kgf/cm}^2) ]
• Ultimate bearing capacity (general shear failure):
  [ q_a = c N_c + q N_q + 0.5 \gamma B N_\gamma ] where (N_c, N_q, N_\gamma) are bearing capacity factors depending on (\phi).

Summary Diagram of Shape Factors

graph LR
A[Continuous Strip] -->|A=1.00, sq=1.00, Y=1.00| B(Bearing Capacity)
C[Rectangle] -->|A=1+0.2 B/L,

IS 6403: Terms and Definitions (Clauses 2.0, 2.1, 3.1)

This section standardizes key terms and symbols used in bearing capacity analysis:

Key Symbols & Definitions

Important Notes:

• Bearing capacity factors (Nq, Nc, Ny) depend on soil friction angle φ and are calculated as per standard formulas.
• Effective dimensions (A', B', L') account for eccentric loading effects.
• Depth factors (de, da, dy) adjust bearing capacity for foundation depth.
• Inclination factors (io, iq, iy) modify capacity for inclined loads.

Example: Bearing Capacity

IS 6403: Key Symbols, Formulas & Shape Factors

1. Symbols & Notations (Clause 3.1)

2. Ultimate Bearing Capacity Formula (Clause 5.2.2.1)

[ 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 ]

• ( c ) = cohesion
• ( q ) = surcharge at foundation base
• ( \gamma ) = unit weight of soil
• ( N_c, N_q, N_\gamma ) = bearing capacity factors (from Table 1)
• ( S_c, S_q, S_\gamma ) = shape factors (see below)
• ( d_c, d_q, d_\gamma ) = depth factors
• ( i_c, i_q, i_\gamma ) = inclination factors

3. **Shape Factors (Table 2, Clause 5.1

IS 6403: Key Formulas, Tables & Specifications for Soil Sampling and Testing

1. Soil Sampling (Clause 4.1)

• Obtain undisturbed samples of diameter 40 to 100 mm or block samples.
• Samples used for:
  • Field density determination.
  • Shear strength & consolidation tests.
• Testing to follow IS 2720 series.

2. Shape Factors for Bearing Capacity (Clause 5.1.2.1, Table 2)

• Use B as diameter for circular footing in bearing capacity calculations.

3. General Notes

• Tests and parameters must comply with IS 2720.
• Use relative density formulas from Clause 5.2.1 for shear strength.
• Round off results as per IS 2-1960.

4. Typical Formula for Ultimate Bearing Capacity (Generalized)

[ q_u = c N_c s_c d_c + q N_q s_q d_q + 0.5 \gamma B N_\gamma s_\gamma d_\gamma ]

• (c) = cohesion
• (q) = surcharge
• (\gamma) = unit weight of soil
• (B) = width/diameter of footing
• (N_c, N_q, N_\gamma) = bearing capacity factors
• (s_c, s_q, s_\gamma) =

IS 6403: Ultimate Net Bearing Capacity Key Points

1. Ultimate Net Bearing Capacity Formula (Clause 5.2.2.1)

[ q_a = c N_c + q (N_a - 1) + 0.5 \gamma B N_y ]

• (c) = cohesion of soil
• (q) = effective overburden pressure at footing base
• (\gamma) = unit weight of soil
• (B) = width of footing
• (N_c, N_a, N_y) = bearing capacity factors from Table 1
• Correction factors (S_a, d_a, i_q, S_y, d_y, i_y, W_e) as per Clause 5.1

2. Bearing Capacity Factors (Table 1, Clause 5.1.1)

3. Notes:

• For (N_c', N_a', N_y'), calculate \

IS 6403: Allowable Bearing Capacity Summary

Key Definitions (Clause 2.1)

• Allowable Bearing Capacity: Net load intensity on soil causing settlement within permissible limits, ≤ net safe bearing capacity.

Ultimate Net Bearing Capacity (Clause 5.2.2.1)

[ q_u = c N_c + q (N_q - 1) + 0.5 \gamma B N_\gamma ] Where:

• (c) = soil cohesion
• (q) = effective overburden pressure at footing base
• (\gamma) = unit weight of soil
• (B) = width of footing
• (N_c, N_q, N_\gamma) = bearing capacity factors (from Table 1)

Bearing Capacity Factors (Table 1, Clause 5.1.1)

Notes:

• For (N_c', N_q', N_\gamma'), use (\phi' = \phi

Effect of Water Table on Bearing Capacity (IS 6403: Clause 5.1.2.4)

• Let:
  • D = Depth of footing base from ground surface
  • B = Width of footing
  • D_w = Depth of water table from ground surface
  • W' = Reduction factor for unit weight of soil above water table

Key Provisions:

Linear Interpolation Formula:

[ W' = 0.5 + 0.5 \times \frac{D_w - D}{B} \quad \text{for } D < D_w < (D + B) ]

Effective Surcharge (Clause 2.2.2):

[ q' = \gamma \times D_w + \gamma_{submerged} \times (D - D_w) ]

• (\gamma) = Total unit weight of soil above water table
• (\gamma_{submerged} = \gamma - \gamma_w) (submerged unit weight)
• (\gamma_w) = Unit weight of water (≈ 9.81 kN/m³)

Method of Analysis Based on Relative Density (Clause 5.2.1.1, Table 3):

flowchart TD
    A[Water Table Depth (D_w)] --> B{Position wrt footing base (D) and width (B)}
    B -->|D_w ≤ D| C

Here are the key formulas, tables, and specifications from IS 6403 for Shape, Depth, and Load Inclination Factors:

1. Shape Factors (Table 2, Clause 5.1.2.1)

• B = width, L = length of footing.

2. Depth Factors (Clause 5.1.2.2)

[ d_e = 1 + 0.2 \frac{D_f}{B} \quad \text{for all soils} ]

[ d_a = d_y = \begin{cases} 1 & \phi < 10^\circ \ 1 + 0.1 \frac{D_f}{B} N_o & \phi > 10^\circ \end{cases} ]

• (D_f) = depth of footing, (B) = width of footing, (N_o) = bearing capacity factor.

3. Bearing Capacity Factors (Table 1, Clause 5.1.1)

Methods Based on Shear Strength Parameters (IS 6403)

1. Ultimate Net Bearing Capacity for Strip Footings (Clause 5.1.1):

• General Shear Failure:

[ q_a = c N_c + q (N_q - 1) + 0.5 \gamma B N_\gamma ]

• Local Shear Failure:

[ q'_a = c N'_c + q (N'q - 1) + 0.5 \gamma B N'\gamma ]

where:

• (c) = cohesion
• (q) = effective overburden pressure at foundation base
• (\gamma) = unit weight of soil
• (B) = width of footing
• (N_c, N_q, N_\gamma) = bearing capacity factors (from Table 1)
• (N'_c, N'q, N'\gamma) = modified bearing capacity factors

2. Bearing Capacity Factors (Table 1, Clause 5.1.1):

Note: For (N'_

IS 6403: Methods Based on Standard Penetration Test (SPT)

Key Specifications:

• SPT Resistance (N): Number of blows per 30 cm penetration, measured as per IS 2131-1981.
• Sampling Interval: At intervals of 75 cm vertically or at strata changes.
• Averaging N: Average N between footing base and depth = 1.5 to 2 × foundation width; discard values >50% above average except loose seams.

Ultimate Bearing Capacity Formula (Clause 5.3.1.1):

For fairly saturated homogeneous cohesive soils:

[ q_a = \text{(formula context missing in snippet, typically)} \quad q_a = N_q c + \gamma D_f N_\gamma + 0.5 \gamma B N_q ]

Where:

• (q_a) = ultimate bearing capacity
• (c) = cohesion
• (\gamma) = unit weight of soil
• (D_f) = depth of foundation
• (B) = width of foundation
• (N_q, N_\gamma) = bearing capacity factors (depend on (\phi))

Relationship between SPT N and Internal Friction Angle (\phi) (Fig. 1):

Notes:

• Use IS 6403 formulas in conjunction with shear strength parameters.
• For static cone penetration test, refer Fig. 2 chart in IS 6403.
• Round off values as per IS 2-1960.

flowchart TD
    A[Perform SPT] --> B[Record N values]
    B --> C[Average N over depth 1.5-2B]
    C --> D[Determine \phi from N (Fig.1)]
    D --> E[Calculate ultimate bearing capacity qa]
    E --> F[Design

IS 6403: Methods Based on Static Cone Penetration Test (CPT)

Key Formulas & Specifications

1. Ultimate Bearing Capacity on Saturated Cohesive Soils (Clause 5.3.1.1):

[ q_a = c N_c + q N_q + 0.5 \gamma B N_\gamma ]

• (c): cohesion (from unconfined compressive strength or CPT)
• (q = \gamma D_f): effective overburden pressure
• (B): footing width
• (N_c, N_q, N_\gamma): bearing capacity factors (from soil friction angle (\phi))

2. Cohesion from Static Cone Point Resistance (q_c) (Clause 5.3.1.2):

3. Static Cone Point Resistance Measurement (Clause 5.2.3):

• Measure (q_c) at 10-15 cm intervals.
• Correct for dead weight of rods.
• Average (q_c) over depth = base of footing to (1-2 \times B).
• Use minimum average (q_c) for design.

Additional Notes

• Use Fig. 2 (IS 6403) to relate static cone resistance to ultimate bearing capacity for cohesionless soils.
• Shear strength variation within (0.5B) depth should not exceed ±50% for averaging.
• Round off values per IS:2-1960 rules.

flowchart TD
    A[Static Cone Penetration Test] --> B[Measure \(q_c\) at intervals]
    B --> C[Correct \(q_c\) for rod weight]
    C --> D[Average \(q_c\) over depth (base to 1

IS 6403: Considerations for Layered and Desiccated Soils

1. Desiccated Cohesive Soil (Clause 5.3.3)

• Undrained cohesion c decreases with depth, stabilizing around 3.5 m below ground.
• Use Fig. 4 (bearing capacity factors) and Table 4 for ultimate net bearing capacity ( q_d ) when the pressure bulb lies within desiccated soil.
• Trial and error method: For footing width ( B ), estimate ( q_a ) by matching with ( 90.8 \times B \times c_1 ) where ( c_1 ) is cohesion from borehole data.

2. Ultimate Net Bearing Capacity (Table 4 Excerpt)

(Use values as per detailed table for design)

3. Method of Analysis Based on Relative Density (Table 3, Clause 5.2.1.1)

4. Shape Factors for Footings (Table 2, Clause 5.1.2.1)

| Footing Shape | Shape Factor (A) | Shape Factor (S_e) | Shape Factor (S_q) | Shape Factor (S_y) | |-------------------|--------------------

Eccentricity Effects on Foundations (IS 6403)

1. Effective Dimensions with Eccentricity (Clause 5.0.1)

• Single Eccentricity (along one direction):
  [ \text{Effective dimension} = \text{Original dimension} - 2e ] Use this reduced dimension in bearing capacity and footing area calculations.

• Double Eccentricity (along length (L) and width (B)):
  [ L' = L - 2e_L, \quad B' = B - 2e_B ] [ A' = L' \times B' ] Use (L', B', A') for bearing capacity and load resistance.

2. Shape Factors (Table 2, Clause 5.1.2.1)

Use (B) as diameter for circular footings.

3. Key Symbols (Clause 3.1)

• (A) = Area of footing
• (A') = Effective area (after eccentricity)
• (B, L) = Width and length of footing
• (e, e_B, e_L) = Eccentricities
• (c) = Cohesion
• (\phi) = Angle of shearing resistance
• (q) = Effective surcharge
• (N_o, N_q, N_\gamma) = Bearing capacity factors
• (S_e, S_q, S_\gamma) = Shape factors

4. Ultimate Bearing Capacity (Clause

IS 6403: Key Formulas, Tables & Guidelines for Bearing Capacity Calculation

1. Ultimate Net Bearing Capacity (Clause 5.2.2.1)

[ q_u = cN_c s_c d_c i_c + \sigma N_q s_q d_q i_q + 0.5 \gamma B N_{\gamma} s_{\gamma} d_{\gamma} i_{\gamma} ]

• (c) = cohesion
• (\sigma) = effective overburden pressure
• (\gamma) = unit weight of soil
• (B) = width of footing
• (N_c, N_q, N_{\gamma}) = bearing capacity factors (from Table 1)
• (s_c, s_q, s_{\gamma}) = shape factors (Table 2)
• (d_c, d_q, d_{\gamma}) = depth factors
• (i_c, i_q, i_{\gamma}) = inclination factors

2. Shape Factors (Table 2, Clause 5.1.2.1)

Use (B) as diameter for circles.

3. Method of Analysis Based on Relative Density (Table 3, Clause 5.2.1.1)

IS 6403: References and Related Standards - Key Points

Relevant IS Codes & Standards:

• IS 6403 (1981): Code for Determination of Bearing Capacity of Shallow Foundations.
• IS 2-1960: Rules for rounding off numerical values.
• Related standards align terminology and procedures for soil bearing capacity and foundation design.

Key Symbols & Parameters (Clause 3.1)

Important Formulas

• Bearing Capacity Factors:

[ N_c = \frac{N_q - 1}{\tan \phi} ]

[ N_q = e^{\pi \tan \phi} \tan^2 \left( 45^\circ + \frac{\phi}{2} \right) ]

• Net Ultimate Bearing Capacity (General Shear Failure):

[ q_a = c N_c + q N_q + 0.5 \gamma B N_\gamma ]

• Correction for Water Table:

[ W' = \text{Correction factor depending on depth to water table} ]

Notes:

• Use relative density (R) and corrected SPT value (N) for soil characterization.
• Apply shape factors (Se, Sa, sY) and inclination factors (io, iq, iy) for load eccentricity.
• Round off as per IS 2-1960 for compliance.

flowchart LR
    A[Soil Parameters] --> B[Calculate Bearing Capacity Factors (Nc, Nq, Nγ)]
    B --> C[Apply Shape & Inclination Factors]
    C --> D[Calculate Net Ultimate Bearing Capacity