The Terzaghi’s Equations will be used in the analysis of the ultimate bearing capacity of the soils. However, the analysis is based on the fact that a shallow foundation is defined as one whose depth is lesser or equal to the width.
The data for the shallow foundation
Taking a shallow foundation width is depth of 50m and the width 50m,
The unit weight of the soil is given (zone A):55kN/m2 to 80kN/m2
The unit surcharge imposed by the soil above the footing= 50*60=3000kN/m taking the unit weight as 60kN/m (on the assumption that it is in between 55 and 70 that is given). Taking the soil fiction angle as 0 and determining the coefficients of  cohesion, surcharge and  unit weight from the bearing capacity tables.
(Kumbhojkar, 1993)
Depending on the type of footing to be used, Terzaghi suggested the following formulas to be used:
For the square and circular footing respectively. In this analysis, the footing will be assumed to be square.
The above formulas will need to be modified, as per terzaghi requirements with the eventual local shear formulas being:
This is the case for undrained soils and therefore, working on the firm spoil layer of the zone A site where Cu=55-70kN/m2
Strip footing:
Qu=5.7Cu+q which, assuming a Cu of 60 gives Qu=342kN/m2+q and calculating q
q Is given as .however, considering that we are working on stiff clay the table given by IS1904 (1978) indicate all the bearing capacities of some soils, but on a presumptive basis. The bearing capacity of the stiff clay soil can be taken as 100kN/m2.
Therefore: q=50*100=5000kN/m2
Therefore, the total general shear will be initiated when the total load exceeds 5000+234=5234Nm2 (strip footing)
On the other hand the ultimate load bearing capacity of the soil for local shear can be calculated-from the local shear formulas-as:
C’ is the contribution of cohesion’
The contribution factor for cohesion c= (Bowles, 1997)
According to the field tests, the results indicate that N values were greater than 50.We may take 50 as the N value which means that the contribution of cohesion =300
All the coefficients have been determined while the breadth of the footing has been assumed to be 50m, therefore, the local shear that may be experienced for a square footing=2223+0+8000=10223
The analysis indicates that bearing capacity for the ultimate shear is less than the bearing capacity for the local shear.
Calculating for zones 2 and 3
The development of the area 3 considers wall loads of between 35KN/m per meter run and 45kN/m per meter run.
The analysis will consider a shallow foundation whose depth will be about 1.0 to 7.10m.
Working on the same parameters as zone 1;
(Kumbhojkar, 1993)
Soft clay has a bearing capacity of 100kN/m2 (IS1904, 1978)
However, the undrained bearing capacity of the soil is taken between 30kN/m2 to 35kN/m2.
Working on the average of these extremes, the assumption may work on Cu=33kN/m2.
Which is later on used to determine the bearing capacity of the strip foundation under general shear
Which translates to 5188.1kN/m2, significantly lower.
On the other hand, the ultimate bearing capacity under local shear can be calculated from the modified formulas:
The contribution of cohesion factor can be taken as 300, the same as in the first calculation.
Therefore, the bearing capacity of the shallow foundation can be taken as: 2223+0+660=2883
Comparing the two spoils, the soft clay has a lower bearing capacity than the firm clay.
Zone C
Zone C is to be used for the development of commercial development with the main concern the bearing capacity of about 8000kN to be attained.
The analysis will be based on the bearing capacity of the very stiff clay.
The data provided for the stiff clay: Cu=150kN/m2to 225kN/m2.We can assume the Cu to be 200kN/m2.
The bearing capacity of the stiff clay is 100kN/m2 which gives q as 5000kN/m2
However, the ultimate bearing capacity can be calculated through:
Which gives 1140+5000=6140kN/m2 much more than that of the stiff and soft clay. This is the ultimate bearing capacity of the soil under general stress.
The local bearing capacity of the soil can be calculated from:
In all the above analyses, the bearing capacity of the soil can be estimated from the following equations is used to measure the load capacity of the pile at the tip:
On the other hand, the following equation is used to determine the fractional resistance of the soil and pile interface.
The two equations are combined to determine the bearing capacity of the soil under deep foundation.
In this analysis, the consideration is steel piles which have a friction angle of 20 degrees. Considering piles of 10m diameter.
Zone 1
Area of circular pile=78.53m2
Cu=assuming 175kN/m2 (stiff to very stiff clay)
This is just an indication of the bearing capacity of the soil when a pile is used as the foundation on very stiff clay. Shortage of data on for analysis indicates that the load capacity of the soil is very high.
A high bearing capacity of the soil is one of the most fundamental and important aspects that is considered during the design and construction of the foundation. An increase in the bearing strength of the soil means that the ground can accommodate a heavier load and stresses such as those associated with settlement are not highly pronounced. An increase in the strength of the soil results into economies when designing the foundation mainly due to the sizing as well as the depth. On the other hand, soils with lower bearing capacities require huge investment s and more to this may be subjected to higher degrees of settlement and stresses. These soils usually require humongous investment either because of the extensive area that has to be covered by a shallow foundation or the increase in depth when the foundation is a deep one.
Geotechnical investigations such as the standard penetration test are the basic building blocks of geotechnical engineering. These investigations are used to determine the properties of the soil and therefore ensure that the right foundation is designed and constructed. However, designing a foundation on the basics of soil properties as well as the loading may not be sufficient. Some areas are subjected to seismic activities which means that there is a change in the arrangement of the soil particles.