Evaluation of Process of Accumulation Residual Deformations of Ring and Round Foundations by Method of Boundary Elements

Abstract

Construction of buildings is a labor-intensive process that requires well-balanced, well-calculated steps and solving complex mathematical problems. This is especially true for the setting of foundations — parts of the building that perceives the load and passes them to the ground. It is extremely important to provide stability and small shrinkage of the structure, thereby avoiding its possible uneven subsidence or destruction. This requires the implementation of forecasting and numerical calculations of structures. Therefore, the model of equilibrium of a foundation immersed in a soil environment satisfying the Laplace differential equation is developed in the article. And the integral equation obtained by K. Brebbia is the main calculation equation of the soil model.

The developed mathematical model provides the possibility of reliable prediction of the behavior of the foundation and deformation of the soil in a wide range of loads. The prognostication process is performed by sampling the boundary surface of the foundation and the soil active zone by the method of boundary elements. Nonlinear problem of the process of deformation of bases is solved using the step method of A.Iliushyn. The work of the soil was modeled by the theory of V. Nikolayevskyi and I. Boyko. Complete deformations, which consisted of increments of elastic and plastic deformations, were determined. Layout of the estimated influence matrix of MBE was performed on the basis of Mindlin's solutions.

The results of the forecasting by the method of boundary elements are presented on the loading and settling graphs of the ring and circular foundations. The fidelity to the choice of the settlement dilatation model is confirmed by the correspondence of numerical studies using the finite element method. Thus, the article is devoted to the study of the strained-deformed state of the boundary elements of ring and circular foundations and compares the results of the studies with their calculation by finite element method.