1.6 LIMITATIONS OF BOUSSINESQ’S SOLUTION
1. The solution was initially obtained for determination of stresses in elastic solids. Its application to soils may be questioned, as the soils are far from purely elastic solids. However, experience indicates that the results obtained are satisfactory.
2. The application of Boussinesq’s solution can be justified when the stress changes are such that only a stress increase occurs in the soil. The real requirement for use of the solution is not that the soil be elastic (i.e., fully recoverable), but it should have a constant ratio between stress and strain. When the stress decrease occurs, the relation between stress and strain is not linear and therefore, the Boussinesq’s solution is not strictly applicable. If the stresses induced in the soil are small in comparison with the shear strength of the soil, the soil behaves somewhat elastically and the Boussinesq’s solution can be used.
3. For practical cases, the Boussinesq’s solution can be safely used for homogeneous deposits of clay, man- made fills and for limited thickness of uniform sand deposits. In deep sand deposits, the modulus of elasticity increases with an increase in depth and therefore, the Boussinesq’s solution will not give satisfactory results. In this case, the assumption of proportionality between stress and strain can not be justified. For such a case, non-linear elastic solutions or elastic-plastic solutions are required.
4. The point load applied below ground surface cause somewhat smaller stresses than are caused by surface loads, and therefore, the Boussinesq’s solution is not strictly applicable. However, the solution is frequently used for shallow footings, in which z is measured below the base of the footing.
|Fig. 1.4: Contour of vertical stress|
beneath uniformly loaded circular area
|Fig. 1.5: Pressure Bulb for square and long footings|