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Saratov State Technical University, Russia
Championship participant: the National Research Analytics Championship - "Russia";
the Open European-Asian Research Analytics Championship;
In this paper we study the deformation and durability cylindrical shell on the basis of the underlying. For a basisof model buildingwe takethe modelof elastic foundationVlasov-Leont'ev. To account for thedeformationof the rheologicalbaseused bythe integratedform of the lawof viscoelastic deformation.The resultingresolving equationsare presentedin incrementsaccording to the methodof successiveperturbationparametersV.V.Petrov.
Keywords: basic problems, calculation, viscoelastic, deformation,durability,construction.
The social and economic changes in Russia have affected all aspects of society life including the construction industry. All participants in construction process became the quite real entities. The modern project is based on three managers: architect, designer and geotechnician. Еarlier understanding of this fact by a project manager will provide the more perfect geotechnical component of a design solution, the more reliable a projecting building, the safer technologies of its construction for surrounding buildings. The list of basic problems for modern city construction includes tight construction deadlines, aspiration to arrange an underground space under construction spot and yard space, increase of loads onto base.
Their successful solution can only be ensured by use of the modern geo-technologies adapted to the engineering-geological conditions of city, as well as by use of the latest tools for calculation the "building-foundation-base"system. The geotechnical norms TCN 50-302-96 directly require to consider the joint work of constructions' bearing structures with their base and correctly to model their joint work.
This paper presents a variant of techniques to solve this problem of the joint calculation for base and elements. Boundary conditions - the simple support. Equation of state in increments:
In tackling theusedmathematical modeling ofstaticviscoelasticstructural elements.You must havethe equilibrium equations, boundary conditions, andequation of staterelations for theequation of stateparameter changeson the parameters ofthe external process.
The approach is based on an extensive literature review of current damage concepts included in current mechanistic-based design procedures, soil permanent deformation laboratory data. Design outputs are compared in terms of reliability and thickness using these design procedures. It is shown that the provides higher reliability values compared to the probabilistic procedure. All the existing subgrades fail distress reliability such as rutting and top down cracking reliabilities. Currently uses a single load P value to deal with variability associated with subgrade strength design. Is used to generate full scale subgrades response and performance data for development and verification of subgrades design criteria. The physical properties of subgrades structures significantly influence both the response of the subgrades to applied loads and the long-term performance.It is, therefore, of the utmost importance that full scale test subgrades be constructed with uniformity in material properties, layer thicknesses, and other considerations for which non-uniformity might result in nonrepresentative and nontypical behavior and failures. Current mechanistic-based design methods for the design of subgradesuse vertical strain criteria to consider foundationrutting.
A considerable number of measurements of the physical properties test basis were made at all stages of construction and after construction was completed. The measurements were made for three purposes: construction quality control, construction acceptance, and material characterization. The material characterization tests were performed to provide information for theoretical modeling and were not related to construction and contractual requirements. The material characterization tests were performed to provide information for theoretical modeling and were not related to construction and contractual requirements.Tests were conducted on the subgrade materials, base subbase, and surface layers. For a basisof model buildingwe takethe modelof elastic foundation, Vlasov- Leont'ev  (Fig.1).
Fig. 1 Modelof elastic foundation.
Here: u(x,y,z)=0; v(x,y,z)=0;
Increments of displacements of points:
The unknown functions ΔUi, ΔWk; and - dimensionless φi(z), ψk(z).
The resolving equations:
Elastic modulus - E,
D*, E*- Volterra integral operators.
The theory of hereditary creep includes all the theories based on rheological models. Condition of reliabilityε ≤ εdestructiv., (ε – deformation). To solve this problem apply the variational method of Bubnov-Galerkin, the calculation is performed onsmall intervalsof time.
L =length ofcasing5 m,the wall thicknessh = 0,4m,the shell radiusR =3m, Poisson's ratio ν = 0,35.Displacementgraphics element (curve 1), 2 - the base layer are shown in Fig. 2.
Fig. 2 Displacementcurves
Plots of thestresses and strains ofthe middle surface ofthe shellare shown in fig. 3.Taking into account nonlinearproperties (curve 1) significantlyaffect the results ofthe numerical calculation [3, p.4].
Fig. 3 Stresses and strains