Studying Deformations of Rectangular Slabs on the Elastic Base upon Its Partial Weakening

Introduction. In today designing and construction, slabs laying on an elastic base are widely used as foundations of buildings and structures, road pavements, etc. Due to various impacts, the properties of a base can change over time, which inevitably affects the stress-strain state of a structure. Therefore, development of the analytical method for studying slab stress and deflection changes upon weakening a base the slab lays on is relevant.

Materials and Methods. The slabs on the elastic base were the objects of the research. The elasticity of a base was specified using the Pasternak model with two-bed coefficients. The derivation of the structure stress-strain state equations was presented taking into account the geometric nonlinearity. The system of differential equations was solved by the Bubnov-Galerkin method using approximative V.Z. Vlasov's beam functions. Such statement of a problem served to determine the stresses and deflections of a slab. The ratio determining the rate of fading of settlement deep inside a base was specified by a function enabling modeling various properties of a base beneath a slab.

Results. The results of deflection calculations obtained using the analytical formulas have been compared with the values obtained by means of software based on the finite element method. The possibility to model the decrease of base strength characteristics or base absence beneath a part of a slab has been shown. The values of deflections at various points of a slab in case of absence of the foundation beneath a part of a structure at the edge or in the centre have been investigated. Data obtained using the analytical formulas on the utmost values of a base beneath a part of a slab before its opposite edge begins to raise have been presented.

Discussion and Conclusion. The proposed statement of a problem can be used to investigate slab deflections and stresses occurring in its middle when the bearing capacity of a part of the subfoundation soil changes. The presented formula makes it possible to specify changes in the distribution of the bearing capacities of a base, it has several parameters offering wide opportunities for modeling the behaviour of a base. Graphs of deflection changes at different points of a slab are given, showing the possibilities to determine deflections of a slab on the elastic base upon base absence beneath a part of a slab at the edge (in the centre) or upon decrease in the strength of a base beneath a part of a slab. The size of the areas of base absence beneath a slab which keep the edge of a slab from raising is provided.

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