Boussinesqlösningen

The Boussinesq solution refers to a fundamental concept in geomechanics and soil mechanics used to determine the stress distribution within an elastic half-space due to surface loads. It was developed by French mathematician Joseph Boussinesq in the late 19th century. The solution is an analytical approximation for how stress propagates downwards and outwards from a concentrated point load applied to the surface of a semi-infinite, homogeneous, and isotropic elastic material.

This solution is crucial for understanding the behavior of soils under various loading conditions, such as the foundations of buildings, bridges, and other structures. It allows engineers to estimate the increase in stress at any point within the soil mass. The Boussinesq solution forms the basis for more complex load distribution calculations and is widely used in geotechnical engineering practice.

The derivation involves applying principles of elasticity and integration to a specific loading scenario. The resulting equations provide stress components (vertical, horizontal, shear) as a function of the applied load, the depth below the surface, and the radial distance from the point of load application. While the Boussinesq solution assumes ideal elastic behavior, which soils only approximate, its widespread application and the availability of numerous extensions and empirical adjustments have made it a cornerstone for practical geotechnical analysis.