Engineering and Construction

In order to assess the distribution of pressure under a foundation it is necessary to make a reasonable estimate of the weight of the foundation. In addition to distrib- uting the forces to the ground the foundation block is also required to provide stability in cases where overturning moments are present.
 
Referring to Fig. 27.2, loads P, H and M are factored as appropriate while W, the foundation mass, is factored by 1.0, being a restoring moment. Moments about A give



From this a minimum value of W for stability is produced.

The minimum value for D  for a mass concrete foundation is established by 45° dispersal from the edge of the baseplate shown in Fig. 27.3. Shallower foundations can be used if they are suitably reinforced.

The distribution of pressure under the foundation is then assessed as follows.

Fig. 27.2 Stability of foundation

Fig. 27.3 Thickness of foundation

Case 1
See Fig. 27.4(a):

It is necessary for fgmax to be less than the stipulated ground bearing capacity for the foundation to be satisfactory.

For fgmin to be zero (Fig. 27.4(b)):


Replacing the forces by the resultant acting at eccentricity x:


This is the limiting condition for the application of Case 1.

Fig. 27.4 Ground pressure – Case 1

Case 2
This occurs when  fgmin is negative. As no tension can exist between the soil and  the underside of the concrete base a compressive stress wedge is formed at the  compression side of the foundation. The summation of the stress under the block must equal the resultant of the applied loads. When  x > L/6, the length of the  triangular stress wedge is three times the edge distance (L/2  - x) in order that  the resultant acts at the centroid of the wedge. The theory proposes that  3(L/2 - x) is the length of surface contact between the foundation and the ground (Fig. 27.5).


When  fgmax exceeds the stipulated ground bearing pressure, dimensions B or L or both may be increased within the limits of economy, after which piling or ground mprovement techniques can be investigated.

Fig. 27.5 Ground pressure – Case 2