SETTLEMENT CALCULATIONS
The settlement of shallow foundations is divided into three segments—immediate or elastic settlement, primary consolidation settlement, and secondary consolidation settlement (creep). We have already considered elastic settlement (Chapter 7) and consolidation settlement. However, we have to make some modifi cations to the methods described in those chapters for calculating settlement of shallow foundations. These modifi cations are made to the method of calculating elastic and primary consolidation settlements.
Immediate Settlement:
We can use the theory of elasticity to determine the immediate or elastic settlement of shallow foundations. In the case of a uniform rectangular fl exible load, we can use Equations . However, the elastic equations do not account for the shape of the footing (not just L/B ratio) and the depth of embedment, which signifi cantly influence settlement. An embedded foundation has the following effects in comparison with a surface footing:
1. Soil stiffness generally increases with depth, so the footing loads will be transmitted to a stiffer soil than the surface soil. This can result in smaller settlements.
2. Normal stresses from the soil above the footing level have been shown (Eden, 1974; Gazetas and Stokoe, 1991) to reduce the settlement by providing increased confi nement on the deforming halfspace. This is called the trench effect or embedment effect.
3. Part of the load on the footing may also be transmitted through the side walls depending on the amount of shear resistance mobilized at the soil–wall interface. The accommodation of part of the load by side resistance reduces the vertical settlement. This has been called the side wall–soil contact effect. Gazetas et al. (1985) considered an arbitrarily shaped rigid footing embedded in a deep homogeneous soil (Figure ) and proposed the following equation for the elastic settlement:
where P is total vertical load, Eu is the undrained elastic modulus of the soil, L is one-half the length of a circumscribed rectangle, vu is Poisson’s ratio for the undrained condition, and ms, memb, and mwall are shape, embedment (trench), and side wall factors given as
Geometry to calculate
elastic settlement of shallow footings.
(On behalf of the Institution of Civil
Engineers.)
Ab is the actual area of the base of the foundation and Aw is the actual area of the wall in contact with the embedded portion of the footing. The length and width of the circumscribed rectangle are 2L and 2B, respectively. The dimensionless shape parameter, Ab/4L2, has the values for common footing geometry equations proposed by Gazetas et al. (1985) apply to a foundation of arbitrary shape on a deep homogeneous soil. There is no clear defi nition of what signifi es “deep.” The author suggests that the equations of Gazetas et al. can be used when the thickness of the soil layer is such that 90% of the applied stresses are distributed within it. For a rectangular area of actual width Br, the thickness of the soil layer should be at least 2Br. Equation (7.90) can be modifi ed to account for embedment as