Code of practice for design and construction of raft foundations, Part 1: Design

IS 2950 Part 1: Scope & Key Specifications

This standard deals with the design of raft foundations considering soil-structure interaction using modulus of subgrade reaction (k).

Key Definitions:

• Terms as per IS 2809-1972 apply.
• Modulus of subgrade reaction (k) represents soil stiffness under footing load.

Modulus of Subgrade Reaction (k) for Design:

• Values apply for 30 cm x 30 cm square plate or 30 cm wide beams.
• Used for raft foundation design where soil behavior is isotropic under footing width.

Tables for Modulus of Subgrade Reaction (k):

Usage Notes:

• Use these k-values unless specific site tests (plate load) are available.
• Superimpose moments and shears for columns/walls for total design forces.

Summary Diagram:

flowchart TD
    A[Soil Type] --> B[Cohesionless]
    A --> C[Cohesive]
    B --> D{Relative Density / SPT N}
    D -->|Loose (N

IS 2950 Part 1 - Definitions & Key Specifications

1. Definitions

• As per Clause 2.1, definitions follow IS 2809-1972 (Terms related to soil and foundation engineering).

2. Modulus of Subgrade Reaction (k)

• Used for design of raft foundations, representing soil stiffness under footing.
• Applies to 30 x 30 cm plates or beams 30 cm wide (Clause 2.9).

3. Key Tables for Modulus of Subgrade Reaction (k) (kg/cm³)

Notes:

• Use these values unless specific site tests are available.
• Modulus k reflects soil reaction under footing load, crucial for elastic foundation analysis (Clause 5.2.1.1).

flowchart TD
    A[Soil Type] --> B[Cohesionless]
    A --> C[Cohesive]
    B --> D[Relative Density / SPT]
    D --> E[Loose, Medium, Dense]
    C --> F[Unconfined Compressive Strength]
    F --> G[Stiff,

IS 2950 Part 1: Necessary Information for Raft Foundation Design

Key Specifications & Tables

1. Modulus of Subgrade Reaction (k)

• Used for soil-structure interaction, based on plate load tests (30x30 cm plate or 30 cm wide beams).

Table 1: For Cohesionless Soils

Table 2: For Cohesive Soils

2. Necessary Design Information (Clause 3.1)

• Site Plan: Location of proposed & neighboring structures.
• Building Plan & Sections: Floor levels, openings, load-bearing elements.
• Loading Conditions: Schematic load combinations.
• Environmental Factors: Seismicity, groundwater, flooding, erosion.
• Geotechnical Data: Soil profile, stratification, shear parameters, compressibility, swelling, field tests (SPT, pressure meter).
• Modulus of Elasticity (E) & Poisson’s Ratio (ν): Per Appendix A.
• Allowable Angular Distortion & Differential Settlement: Per IS 1904-1978.
• Performance Review: Similar local structures.
• Impact on Neighboring Structures.
• Proximity to Mines/Reservoirs.

Notes:

• Use these k-values

IS 2950 Part 1: Design Considerations - Key Formulas & Tables

1. Modulus of Subgrade Reaction (k)

• Used for soil-structure interaction, typically for raft foundations.
• Based on plate load tests (30 cm x 30 cm plate or 30 cm wide beams).
• Values depend on soil type, moisture, and density.

2. Foundation Rigidity Criterion

• For k > 0.5 kg/cm³, foundation may be assumed rigid (Clause 2.1.1).

3. Design Approach

• Foundation analyzed as inverted beam or slab.
• Loads, shrinkage, creep, temperature effects, reinforcement per IS 456-1978 (Plain & Reinforced Concrete).

4. Parameters for Analysis

• Average soil parameters from limited test points (Clause 3.2).
• Accuracy in averaging critical for reliable design.

5. Modulus of Elasticity (E) and Poisson’s Ratio (ν)

• Determined as per Appendix A (Clause 3.1(f)) for soil and foundation materials.

flowchart LR
    A[Soil Parameters] --> B[Determine k from Table 1]
    B --> C{Is k > 0.5?}
    C -- Yes --> D[Assume Rigid Foundation]
    C -- No --> E[Flexible Foundation Analysis]
    D & E --> F[Design as Inverted Beam/Slab per IS 456]
    F --> G[Check Loads, Shrinkage, Creep, Temp Effects]

Summary: Use Table 1 for modulus of subgrade reaction based on soil type and moisture. For

IS 2950 Part 1: Design Methods for Rigid and Flexible Foundations

1. Rigid Foundation (Clause 5.1)

• Assumes linear distribution of contact pressure.
• Foundation is rigid relative to soil; compressible soil layer is shallow.
• Contact pressure varies planarly, centroid aligns with resultant load.

2. Flexible Foundation (Clause 5.2.1.1 and Appendix F)

• Based on Elastic Plate Theory on Winkler foundation.
• Considers deflection restraint due to foundation continuity.
• Total effect at a point found by superposition of column loads within two adjoining bays.
• Numerical methods like Finite Difference or Finite Element can be used for accuracy.

3. Key Formulas (Appendix F, Clause 1.1)

For a flexible raft foundation under column load ( P ):

[ M_r, M_t, w = \text{Radial moment, Tangential moment, Deflection at radius } r ]

where:

• ( r ) = distance from column load,
• ( L = \sqrt[4]{\frac{D}{k}} ) = radius of effective stiffness,
• ( D = \frac{E t^3}{12(1-\nu^2)} ) = flexural rigidity,
• ( k ) = modulus of subgrade reaction,
• ( t ) = raft thickness,
• ( E ) = modulus of elasticity,
• ( \nu ) = Poisson's ratio.

Deflection and moments are functions of ( r, L, P ), and dimensionless functions ( Z_0, Z_1, Z_2 ) (refer Fig.4 in IS 2950).

4. Parameters Summary

IS 2950 Part 1 - Structural Design Key Points

1. Applicability (Clause 5.1.1)

• Use method if:
  • Relative stiffness factor, K > 0.5 (Appendix C for K evaluation)
  • Column spacing < 1.75 √A (A = area, see Appendix C)

2. Design Basis (Clause 6.1)

• Loads, shrinkage, creep, temperature, reinforcement & detailing per IS 456:1978.
• Foundation treated as inverted beam or slab.

3. Modulus of Elasticity (E) & Poisson’s Ratio (Appendix A)

• E and Poisson's ratio (#) determined as per Appendix A.
• Use E for soil-structure interaction and foundation design.

4. Modulus of Subgrade Reaction (k) for Raft Foundations (Clause 1.1 & Table 1)

5. Superposition of Moments and Shears (Clause 1.5)

• Calculate moments and shears for each column/wall.
• Superimpose to get total values.

Summary Diagram: Design Flow

flowchart TD
    A[Check Stiffness Factor K > 0.5 or Column Spacing < 1.75√A] --> B{Condition Met?}
    B -- Yes --> C[Use IS 2950 Part 1 Method]
    B -- No --> D[Use Alternative Methods]
    C --> E[Design Loads & Reinforcement per IS 456]
    E --> F[Calculate E, Poisson's Ratio]
    F --> G[Determine Modulus of Subgrade Reaction (k)]
    G --> H[Calculate Moments & Shears

Determination of Modulus of Elasticity (E) and Poisson's Ratio (ν) — IS 2950 Part 1

1. Modulus of Elasticity (E)

• E depends on soil type, void ratio, stress history, moisture, and depth.
• Laboratory determination is difficult due to sampling disturbance.
• Recommended: Use field tests (e.g., triaxial tests, static cone penetration).
• Clause A-3.3:

  E is taken as the tangent modulus at half the maximum deviator stress during the second loading cycle.

2. Poisson's Ratio (ν)

• Typically determined from triaxial tests measuring lateral and axial strains.
• No explicit formula in IS 2950; use lateral strain / axial strain ratio in elastic range.

3. Modulus of Subgrade Reaction (Eₛ)

• From plate load test (IS 1888-1982):

  [ E_s = \frac{4B(1 - \nu^2)}{\pi I} \times \frac{q}{s} ]

  Where:

  • ( q ) = contact pressure intensity
  • ( B ) = least lateral dimension of plate
  • ( s ) = settlement
  • ( \nu ) = Poisson's ratio
  • ( I = 0.82 ) (influence factor for square plate)

Summary Table

flowchart TD
    A[Soil Sample] --> B{Test Type}
    B -->|Lab Triaxial| C[Measure Stress-Strain]
    B -->|Field Test| D[Plate Load Test]
    C --> E[Calculate E at 0.5 max deviator stress]
    C --> F[Calculate

Modulus of Subgrade Reaction (k) - IS 2950 Part 1 Summary

1. Definition:

• ( k ) is the modulus of subgrade reaction in kg/cm³ for a 30 x 30 cm square plate or beams 30 cm wide.

2. Values for Cohesive Soils (Table 2):

3. Values for Cohesionless Soils (Table 1):

4. Calculation Notes:

• ( E_s ) (tangent modulus) is taken at half the max deviator stress during the 2nd loading cycle.
• Use Appendix A for estimating ( E_s ) and ( \nu ) if lab data unavailable.
• Plate load test or static cone penetration test recommended for field determination.

5. Practical Use:

• Use these values for raft foundation design where soil is isotropic up to footing width.
• Adjust ( k ) for different plate sizes using empirical correlations if needed.

flowchart LR
    A[Soil Type] --> B[Cohesive Soil]
    A --> C[Cohesionless Soil]
    B --> D[Use Table 2]
    C --> E[Use Table 1]
   

Evaluation of Relative Stiffness Factor (K) - IS 2950 Part 1

1. Definition of Relative Stiffness Factor (K)

The relative stiffness factor ( K ) expresses the ratio of structural stiffness to foundation soil stiffness, determining whether a structure behaves rigidly or flexibly.

2. Formulas for ( K )

3. Flexural Rigidity ( EI ) of Structure (Clause 1.1)

[ EI = E_w I_w b + \frac{E_f}{8} \left[ I_u + I_l + I_b \right] b^2 (l_u + l_l + l_b) ]

• (E_w, I_w): Modulus & moment of inertia of infilling (wall)
• (E_f, I_u, I_l, I_b): Modulus & moments of inertia of frame members (upper/lower columns, foundation beam)
• (b): Length in bending direction (cm)
• (l_u, l_l, l_b): Lengths of columns and beams (cm)

Summation over all storeys including foundation.

4. Modulus of Subgrade Reaction ( k ) for Cohesive Soils (Table 2)

| Soil Consistency | Unconfined Compressive

Pressure Distribution Under Raft (IS 2950 Part 1)

Key Formula (Clause 1.1: D-1.1)

[ q = \frac{Q}{A'} \pm \frac{6 M_x e_x}{I_x b} \pm \frac{6 M_y e_y}{I_y a} ]

Where:

• ( q ) = pressure at any point on raft
• ( Q ) = total vertical load on raft
• ( A' = a \times b ) = total raft area (a, b = raft dimensions)
• ( M_x, M_y ) = moments about x and y axes
• ( I_x, I_y ) = moments of inertia of raft area about x and y axes
• ( e_x, e_y ) = eccentricities of load from centroid
• ( x, y ) = coordinates of point considered on raft

Simplified for rectangular raft:

[ q = \frac{Q}{a b} \pm \frac{6 M_x y}{b^3} \pm \frac{6 M_y x}{a^3} ]

Important Notes:

• Negative ( q ) means partial soil contact; recalculate ( I_x, I_y, e_x, e_y ) for the effective contact area.
• Soil type affects pressure distribution (Clause 4.5.3): cohesive soils increase edge pressure; granular soils reduce it.
• Consider consolidation effects for long-term pressure changes.
• For uniform column loads/spacings (variation < 20%), analyze raft as independent strips (Clause 5.1.3).

Moments of Inertia for Rectangular Raft:

[ I_x = \frac{b a^3}{12}, \quad I_y = \frac{a b^3}{12} ]

Summary Diagram:

flowchart LR
    Q[Total Load Q]
    A[Raft Area A' = a×b]
    Mx[Moment Mx]
    My[Moment My]
    Ix[Moment of Inertia Ix]
    Iy[Moment of Inertia Iy]
    ex[Eccentricity ex]
    ey[Eccentricity ey]
    q[Pressure q at (x,y)]

    Q --> q
    A --> q
    Mx --> q

IS 2950 Part 1 - Contact Pressure & Moments Below Flexible Foundation

1. Contact Pressure Distribution (Clause 5.2.1, Appendix E & F)

• Flexible Foundation modeled as an elastic plate on Winkler foundation.
• Governing differential equation solution gives:
  • Radial moment ( M_r )
  • Tangential moment ( M_t )
  • Deflection ( w )

2. Key Parameters & Formulas (Clause F-1.1)

[ \begin{aligned} & M_r, M_t, w \text{ at any radius } r \text{ from column load } P \ & L = \sqrt[4]{\frac{D}{k}} \quad \text{(Radius of effective stiffness)} \ & D = \frac{E t^3}{12(1-\nu^2)} \quad \text{(Flexural rigidity)} \ & k = \text{modulus of subgrade reaction} \ & t = \text{raft thickness}, \quad E = \text{modulus of elasticity}, \quad \nu = \text{Poisson's ratio} \ \end{aligned} ]

• ( Z_0, Z_1, Z_2 ) are functions related to shear, moment, and deflection (refer Fig.4 in IS 2950).

3. Rigid Foundation Contact Pressure (Clause 5.1)

• Assumed linear (planar) distribution of contact pressure.
• Foundation considered rigid relative to soil.
• Centroid of pressure coincides with resultant load line of action.

Summary Table

IS 2950 Part 1: Analysis of Flexible Raft Foundations Using Plate Theory

Key Concepts:

• Raft modeled as a plate on Winkler elastic foundation.
• Governing differential equation relates radial moment (M_r), tangential moment (M_t), and deflection (w).
• Superposition principle used for multiple column loads within the zone of influence (typically two adjoining bays).

Important Parameters:

Governing Equation (simplified form):

[ M_r, M_t, w \quad \text{are functions of} \quad P, r, L, k, D, E, t, \nu ]

• Deflection and moments are obtained by solving the plate differential equation on Winkler foundation.
• Functions (Z_1, Z_2, Z_3) (see Fig. 4 in IS 2950) represent shear, moment, and deflection shapes.

Procedure Summary (Clause 5.2.1.1 & Appendix F):

1. Model raft as elastic plate on Winkler foundation.
2. Calculate deflection and contact pressure for each column load individually.
3. Superimpose effects of all columns within zone of influence (2 adjoining bays).
4. Use contact pressure distribution to compute bending moments and shears.

Flexural Rigidity Formula:

[ D = \frac{E t^3}{12(1 - \nu^2)} ]

Design Notes:

• For **non-uniform column spacing