Methods of applied mathematics in solving the problem of the theory of consolidation of inhomogeneous hereditary-aging soils - Altynbekov, S. A.; Niyazymbetov, A. D. (Journal of Mathematics, Mechanics and Computer Science, 2020)
The issues of improving the existing methods of forecasting the precipitation of the foundations of structures, algorithmization of the solution of their problems have not yet been removed from the agenda of scientific research. This is confirmed by the annual international conferences, symposiums and congresses in the field of industrial, oil, civil and hydraulic engineering construction. The main goal of the study was to improve the existing methods of filtration theory of consolidation in relation to inhomogeneous soils and use it to solve the problem. A mathematical formulation of the spatial quasi-linear boundary value problem of consolidation of heterogeneous hereditary-aging soil is formulated. Here, the heterogeneity of the soil is due to changes in its deformation modulus, a measure of creep and lateral pressure coefficient during consolidation according to the exponential depth law. The quasilinearity boundary value problem is defined via the filtration coefficient. It is assumed that the filtration coefficient depends on the porosity coefficient. When taking into account the heterogeneity of the soil, it is not always possible to obtain analytical solutions to the problem. The application of the Fourier method leaves us on the way. To get out of this situation, the approximation function is proposed. Its error is investigated. For small values of inhomogeneity parameters, the approximation accuracy is high. To solve the problem, we used the iteration Method, the least squares method, the method of introducing a new unknown function, the method of converting inhomogeneous boundary conditions into homogeneous ones,the Fourier method, the approximation method, the method of introducing new variables, the method of decomposition by eigenfunctions, and the method of V. A. Florin for calculating the sedimentation of structures.