Calculation of foundation mesh slabs on an elastic layer

Abstract

In this work, the authors have developed the procedure for calculation of mesh slabs on an elastic base modeled by an elastic homogeneous isotropic layer affected by the external load. The history of development of calculations of structures on an elastic basis demonstrates that, due to the scientific and technical progress, methods for calculation of aforementioned structures were improved and refined. This can be traced on various models of the elastic foundation that were used to simulate real soils in their natural occurrence or in an artificial base when setting up fundamentally new problems of structural analysis. Variety of practical tasks results in ambiguous modelling of the elastic base. The authors refer to the works of Tarasevich A. N., Kozunova O. V. and Semenyuk S. D. that provide extensive systematic review of elastic base models for calculation of foundation beams, beam and foundation slabs, as well as for calculation of cross tapes for shallow foundations. The relevance and timeliness of the proposed work is due to the fact that the issues of calculation of mesh slabs and the system of cross tapes on an elastic base have not yet been fully studied. The authors are familiar with the works of M. I. Gorbunov-Posadov, I. A. Simvulidi, G. Ya. Popov, S. D. Semenyuk, S. N. Klepikov, where various approaches are used to conduct the researches in calculation of mesh slabs and spatial monolithic foundations as the system of cross tapes on an elastic base. The procedure proposed is based on the Ritz variational method and the mixed method of structural mechanics using the Zhemochkin influence functions. To calculate the coefficients of canonical equations and the absolute terms for the mixed method of structural mechanics by way of the Zhemochkin method, the ratios of deflections with the normal restrained in the center of the slab are used in the calculation. The numerical implementation of the new general-purpose approach is carried out, as an example, for the rectangular foundation slab with holes, symmetrically loaded by the uniformly distributed load, on the elastic uniform isotropic layer. Graphical results of calculations are given, describing the settlements of the foundation mesh slab and the distribution of contact stresses under the slab.