METHODS OF RAFT FOOTING DESIGN

According to IS – 2950:1965, the design criteria of raft footings are given below:

The maximum differential settlement in foundation on clayey soils and sandy soils should not exceed 40mm and 25 mm respectively. The maximum settlement should generally be limited to the following values:

Raft foundation on clay – 65 to 100 mm.

Raft foundation on sand – 40 to 65 mm.

Raft Foundation Design

There are two methods for the design of raft foundations. They are:

1) Conventional Method

2) Soil Line Method.

1. Conventional Method

Assumptions:

1. The soil pressure is assumed to be plane such that the centroid of the soil pressure coincides with the line of action of the resultant force of all the loads acting on the foundation.

2. The foundation is infinitely rigid and therefore, the actual deflection of the raft does not influence the pressure distribution below the raft.

In this method, allowable bearing pressure can be calculated by the following formulae:

Where clip_image007 and clip_image009 = allowable soil pressure under raft foundation in clip_image011 (use a factor of safety of three). The smaller values of clip_image007[1] and clip_image009[1]should be used for design.

clip_image013and clip_image015= reduction factor on account of subsoil water.

N = penetration resistance.

If the values of N is greater than 15 in saturated silts, the equivalent penetration resistance should be taken for the design. The equivalent penetration resistance can be determined by the formula:

The pressure distribution (q) under the raft should be calculated by the following formula:

Where Q = total vertical load on raft

x, y = co-ordinates of any given point on the raft with respect to the x and y axes passing through the centroid of the area of the raft.

A = total area of the raft.

clip_image021= eccentricities about the principal axis passing through the centroid of the section.

clip_image023 = moment of inertia about the principal axis through the centroid of the section.

clip_image021[1],clip_image023[1] can be calculated by the following equations:

clip_image025

clip_image027

clip_image029

clip_image031

Where clip_image033and clip_image035= eccentricities in x and y direction of the load from the centroid.

clip_image037and clip_image039= moment of inertia of the area of the raft respectively about the x and y axes through the centroid.

clip_image041 for the whole area about x and y axes through the centroid.

2) Soil line Method (Elastic Method)

A number of methods have been proposed based on primarily on two approaches of simplified and truly elastic foundations.

i. Simplified elastic foundation: The soil in this method is replaced by an infinite number of isolated springs.

ii. Truly elastic foundation: The soil is assumed to be continuous elastic medium obeying Hooke’s law.

In the case of foundation which is comparatively flexible and where loads tend to concentrate over small areas these methods are to be used. The method assumes in addition to other factors that the modulus of subgrade reaction, determined from tests is known. The modulus of subgrade reaction (clip_image043) as applicable to the case of load through a plate of size 30 cm x 30 cm or beams 20 cm wide on soil area is given in table-1 for cohesionless soils and table-2 for cohesive soils.

Table -1: Modulus of subgrade reaction clip_image043[1] for cohesionless soils

Soil Characteristics

clip_image002

Relative Density

Values of N

Dry or moist state

Submerged state

1. Loose

<10

1.5

0.9

1. Medium

10 to <30

4.7

2.9

3. Dense

30 and over

18

10.8

 

Table – 2: Modulus of subgrade reaction clip_image002 for cohesive soils

Soil Characteristics

clip_image004

Consistency

Unconfined compressive

 Strength (clip_image006)

 

1. Stiff

1 to <2

2.7

1. Very Stiff

2 to <4

5.4

3. Hard

4 and over

10.8

 

The above values of clip_image002[6] are corresponding to a square plate of size 30 cm x 30 cm. To find the values of K corresponding to different sizes and shapes, the following relationships to be used.

(a) Effect of size

clip_image004[3] for cohesionless soil

clip_image006[3] for cohesive soils.

Where, K = modulus of subgrade reaction for footing of width B cm

clip_image002[7] = modulus of subgrade reaction for a square plate of width 30cm x 30cm

K’ = modulus of subgrade reaction for footing of width clip_image008cm.

(b) Effect of shape

clip_image010 for cohesive soils

Where clip_image012= modulus of subgrade reaction for a rectangular footing having length L and width B.

clip_image014= modulus of subgrade reaction for square footing of side B.

The effect of shape is negligible in the case of footing on cohesionless soils.