STRESSES IN SOIL FROM SURFACE LOADS
The distribution of stresses within a soil from applied surface loads or stresses is determined by assuming that the soil is a semi-infi nite, homogeneous, linear, isotropic, elastic material. A semi-infi nite mass is bounded on one side and extends infi nitely in all other directions; this is also called an “elastic halfspace.” For soils, the horizontal surface is the bounding side. Because of the assumption of a linear elastic soil mass, we can use the principle of superposition. That is, the stress increase at a given point in a soil mass in a certain direction from different loads can be added together. Surface loads are divided into two general classes, fi nite and infi nite.
However, these are qualitative classes and are subject to interpretation. Examples of fi nite loads are point loads, circular loads, and rectangular loads. Examples of infi nite loads are fi lls and surcharges. The relative rigidity of the foundation (a system that transfers the load to the soil) to the soil mass infl uences the stress distribution within the soil. The elastic solutions presented are for fl exible loads and do not account for the relative rigidity of the soil foundation system. If the foundation is rigid, the stress increases are generally lower (15% to 30% less for clays and 20% to 30% less for sands) than those calculated from the elastic solutions presented in this section. Traditionally, the stress increases from the elastic solutions are not adjusted because soil behavior is nonlinear and it is better to err on the conservative side.
The increases in soil stresses from surface loads are total stresses. These increases in stresses are resisted initially by both the porewater and the soil particles. Equations and charts for several types of fl exible surface loads based on the above assumptions are presented. Most soils exist in layers with fi nite thicknesses. The solution based on a semi-infi nite soil mass will not be accurate for these layered soils. In Appendix C, you will fi nd selected graphs and tables for vertical stress increases in one-layer and two-layer soils. A comprehensive set of equations for a variety of loading situations is available in Poulos and Davis (1974).
Boussinesq (1885) presented a solution for the distribution of stresses for a point load applied on the soil surface. An example of a point load is the vertical load transferred to the soil from an electric power line pole.
The increases in stresses on a soil element located at point A (Figure ) due to a point load, Q, are
Point load and vertical stress distribution with
depth and radial distance.
where n is Poisson’s ratio. Most often, the increase in vertical stress is needed in practice. Equation can be written as
where I is an infl uence factor, and
The distributions of the increase in vertical stress from Equationsreveal that the increase in vertical stress decreases with depth (Figure ) and radial distance (Figure ). The vertical displacement is
and the radial displacement is
where E is Young’s modulus.