Piers transfer load from soft to strata. They derive resistance from shaft and base as in the case of piles.

Q_{ult} = Q_{b} + Q_{s}

= A_{b}q_{b} + A_{s}q_{s}

= ———- (1)

### Piers in Sands

In sands resistance in most cases is derived from base only. Shaft resistance is usually neglected due to following reasons.

- Depth being less than five times the width
- When there is possibility of scour especially in bridge foundations
- If there is Compressible fill
- If soil is liable to shrink

For sand c = 0, Hence, the bearing capacity is given by:

———- (2)

If depth is less than 5 times the width, piers at shallow depth and the soil is loose where Q_{b} is obtained from Terzaghi’s equation because the shear resistance in such situation above the base of the pier is negligible. On the other hand if the pier is embedded in hard strata at a depth greater than 5 times the width shear resistance at base is no longer negligible and Terzaghi’s equation can’t be used. The bearing capacity factors are obtained by Hansen equation.

In sands the bearing capacity in terms of shear criteria is usually very high unless the width of pier is small and located at shallow depth. Therefore, the carrying capacity of pier, in general, is governed by settlement criteria.

If depth is greater than 5 times the width, increase in bearing capacity with depth is no longer in accordance with the term Ïƒ_{v}(N_{q} – 1) in the Eq.(2) although the Eq.(2) shows linear variation of base resistance width depth. When, depth is greater than 15 times the width the base resistance is experimentally found to be independent of depth. Hence, influence of depth on settlement is relatively small, compared to the influence to the ultimate bearing capacity. This fact is illustrated by the following examples.

Load tests were made at the same depth on two circular bearing plates each covering an area of 1 ft^{2}. One plate was located on the bottom of a large open shaft, and the other on the bottom of a drill hole with the diameter of 1.15 ft. At a load of 2 tons/ft, the settlement of the plate in the shaft was 0.90 in, and that in the drill hole was 0.52 in.

Similar experiments were made in a shaft. The shaft was excavated to a depth of about 50 ft; a load test was made on a bearing plate of l ft square. The settlement under a load of 2 tons/ft was 0.25 in. A second bearing plate 3.3 by 3.3 ft was installed on the bottom of the shaft, and the narrow space between the edges of the plate and the sides of the shaft was filled with concrete to prevent the local heave of the loaded sand. The settlement of the plate at a load of 2 tons/ft was 0.47 in. By extrapolation, the settlement of a plate of the same size on the surface of a similar sand deposit with no confinement or surcharge would be 0.59 in (Terzaghi 1930).

These findings suggest that, for the same intensity of pressure and soil condition the settlement of a pier is equal to half of the settlement of a shallow foundation which means the allowable bearing capacity for the pier will be equal to two times the value for a shallow foundation. If the bearing capacity is computed using this approach the maximum settlement will not exceed over 25 mm and differential settlement between the piers will not exceed 12 mm if the piers have equal width. To compute bearing capacity using this approach the depth of pier must be embedded at least to a depth equal to 5 times the width. If this criteria is not fulfilled the bearing capacity of pier is taken equal to the bearing capacity of a shallow foundation.

**Piers in Clay**

**Bearing Capacity – **In Clay, Î´ = 0, N_{q }= 1 and N_{Î³} = 0. Hence, the bearing capacity equation becomes:

Q_{ult} = A_{b}s_{u}N_{c} + A_{s }Î± s_{u}‘

Q_{ult} = A_{b}s_{u}9 + A_{s }s_{u}‘

If depth is greater than 5 times the width the value of N_{c} becomes equal to 9 and the value of Î± is taken as 0.45. A Field test in California has shown that the value of Î± is found to vary from 0.49 to 0.52.

**Settlement –** Piers are not economical in normally consolidated clay because of the necessity of large area at base. There will be excessive settlement. Therefore, piers are not recommended for construction in normally consolidated clay. Generally, they are constructed in over consolidated clay. If the base width of the pier in over consolidated clay exceed 3 m it is necessary to calculate consolidation settlement as per the method suggested for other foundation. In clay the design load can be considerably increased for large piers if the piers are constructed hollows.

**Factor of Safety –** The factor of safety is taken as 3 for normal loads and 2 for maximum loads.