Geotechnical Engineering

DHARM

634 GEOTECHNICAL ENGINEERING

where qa = allowable soil pressure.

By taking moments about the property line or left edge, and on simplifying,

(^212)
12
BB
BB

• 
  


• =
  3 2
  L e^1
  PL
  PP
  i
  ei


• 
  

  ′

  
  


• 
  

  L
  N
  M
  O
  Q
  ()P ...(Eq. 15.19)
  L′ and e 1 are as indicated in Fig. 15.27.
  B 1 and B 2 may be solved from Eqs. 15.18 and 15.19 since the quantities on the right-
  hand sides are known.
  The solution leads to:
  B 1 =
  23
  1
  A
  L
  x
  L
  F −
  HG
  I
  KJ ...(Eq. 15.20)
  and B 2 =
  2 A
  L

  
  

• B 1 ...(Eq. 15.21)

The pressure intensities, q 1 and q 2 are calculated, once B 1 and B 2 are obtained:
q 1 = B 1. qa q 2 = B 2. qa ...(Eq. 15.22)
The bending moment and shear force diagrams can be easily sketched now, as shown in
Fig. 15.27. The maximum values are used for the purpose of design. From Eq. 15.20,

B 1 = 0 where x = L/3

For a rectangular shape,

x = L/2

Thus, a trapezoidal combined footing solution exists when x is such that:

L x L

32

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In tentative designs, whenever the distance x approaches L/3, or is less than L/3, the
length L should be increased by increasing the projection beyond the inner column.

15.7 Raft Foundations

A ‘raft’ or a ‘mat’ foundation is a combined footing which covers the entire area beneath of a
structure and supports all the walls and columns. This type of foundation is most appropriate
and suitable when the allowable soil pressure is low, or the loading heavy, and spread footings
would cover more than one half the plan area. Also, when the soil contains lenses of compress-
ible strata which are likely to cause considerable differential settlement, a raft foundation is
well-suited, since it would tend to bridge over the erratic spots, by virtue of its rigidity. On
occasions, the principle of floating foundation may be applied best in the case of raft founda-
tions, in order to minimise settlments.

15.7.1Common Types of Raft Foundations

Common types of raft foundations in use are illustrated in Fig. 15.28.

Fig. 15.28 (a) represents a true raft which is a flat concrete slab of uniform thickness
throughout the entire area; this is suitable for closely spaced columns, carrying small loads. (b)
represents a raft with a portion of the slab under the thickened column; this provides sufficient