New Formulations of Boussinesq Solution for Vertical and Lateral Stresses in Soil

Calculation of stresses within a soil body due to surface loading is a required step when designing buried commodities and subgrade wall structures. The Boussinesq equation is commonly used for determining stresses in soil due to surface loading, with examples for use found industrywide. However, the available formulations have limitations, or they only cover simple cases. The purpose of this work is to review the derivation of the Boussinesq equation for vertical and lateral stresses in a soil body and to present several new, closed-form solutions for various surface load cases, including finite line and finite area loads. The formulations are presented as Cartesian coordinate functions such that the stress at any point in the subsurface plane of interest can be found, not just the peak stress or the stress contour at a specific line. This is particularly useful when considering load distribution at a lateral extent from a finite loading, which may be significantly lower than the peak loading.