Solution of the Boussinesq Problem in a Depth‐Dependent Nonhomogeneous Half‐Space

ABSTRACT In this study, the Boussinesq problem is modeled using the half‐space model of the soil foundation to determine the collapse of the ground surface under a point load applied to the surface when the elastic modulus of the ground changes as a continuous function of depth. Analytical solutions are developed for the cases where the elastic modulus increases depending on the depth coordinate. The solutions are presented as the product of the classical Boussinesq solution and a dimensionless function that considers the heterogeneity with depth. Finally, a comparative analysis of the subsidence at dimensionless distances from the point load for different heterogeneity functions is performed compared to the classical solution.

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