Discontiuum mechanics of isotropic multilayered soils beneath a uniform vertical load

Calixtro Yanqui

In the proceedings of: GEO2011: 64th Canadian Geotechnical Conference, 14th Pan-American Conference on Soil Mechanics and Geotechnical Engineering, 5th Pan-American Conference on Teaching and Learning of Geotechnical Engineering

Session: Shallow Foundations

ABSTRACT: This paper deals with the basic principles of the deterministic discontinuum mechanics and its application to the simplification of the Burmister´s problem. For this purpose, the soil is modeled as a Bravais isometric lattice that is governed by the mean value principle, which is stated as the identity between a quantity at a homologous point and the mean value of the quantities at the neighboring nodes, located within the polyhedron of influence. Particularly, consistently with the result of the isotropic continuum mechanics, the biharmonic equation is obtained by averaging a stress function of the Kirchhoff´s kind. But the discrete nature of the discontinuous medium allows the simplification of the problem even more, by considering a partial or biased polyhedron. Taking advantage of this property, expressions for displacements, stresses and strains in a multilayer system, subjected to a uniformly distributed vertical load applied over the surface, are derived; which, compared to the Burmister´s results, are sufficiently rigorous, explicit, elementary, simple and accessible to the practical engineer.

RESUMEN: Este artículo trata de los principios básicos de la mecánica determinística del medio discontinuo y su aplicación a la simplificación del problema de Burmister. Con este propósito, el suelo es modelado como una red tridimensional isométrica de Bravais, que es gobernada por el principio del valor medio, el cual se define como la identidad entre una cantidad correspondiente a un punto homólogo y el promedio de las cantidades correspondientes a los nodos vecinos, localizados dentro del poliedro de influencia. Particularmente, en concordancia con el resultado de la mecánica del medio continuo isotrópico, la promediación de una función del esfuerzo del tipo de Kirchhoff conduce a la ecuación biharmónica. Pero la naturaleza discreta del medio discontinuo permite la simplificación del problema aún más, considerando un poliedro parcial o sesgado. Aprovechando esta propiedad, se derivan expresiones para los desplazamientos, esfuerzos y deformaciones en un sistema multicapa sometido a una carga vertical uniformemente distribuida sobre la superficie, las cuales, en comparación con los resultados de Burmister, son suficientemente rigurosas, explícitas, elementales, simples y accesibles al ingeniero práctico.

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