Settlement of a Linearly Loaded Rectangular Area

The theoretical determination of the settlement of a linearly-loaded rectangular area at the surface of a semi-infinite mass of elastic, isotropic, homogeneous soil is presented. This linear stress distribution is commonly assumed in the design of foundations subject to an eccentric and inclined load in the case of dams, buildings, and retaining walls. The settlement coefficients have been calculated for several points of the loaded area by integration of the Boussinesq and Cerruti formulas for the settlement due to a single load, either normal or tangential. The numerical values of these coefficients have been listed in tables and plotted in charts as a function of the ratio of the sides of the rectangle. Practical examples are given. The main features of the theoretical analysis are given without going into the details of the calculations.