Foundation calculation for buildings and structures with two elastic characteristics of the foundation using features of Fourier transformsfor finite functions

Vestnik MGSU 1/2014
  • Kurbatskiy Evgeniy Nikolaevich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sci- ences, Professor, head, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Mai Duc Minh. - Moscow State University of Railway Engineering (MIIT) postgraduate student, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 41-51

The problem of a beam resting on elastic foundation often occurs in the analysis of building, geotechnical, highway, and railroad structures. Its solution demands modeling of the mechanical behavior of the beam, the mechanical behavior of the soil as elastic subgrade and the form of interaction between the beam and the soil. The oldest, most fa- mous and most frequently used mechanical model is the one devised by Winkler (1867), in which the beam-supporting soil is modeled as a series of closely spaced, mutually independent, linear elastic vertical springs, which, evidently, provide resistance in direct proportion to the deflection of the beam.The solution is presented for the problem of an Euler–Bernoulli beam supported by an infinite two-parameter Pasternak foundation. The beam is subjected to arbitrarily distributed or concentrated vertical loading along its length. Static response of a beam on an elastic foundation characterized by two parameters is investigated assuming, that the beam is subjected to external loads and two concentrated edge load. The governing equations of the problem are obtained and solved by pointing out that there is a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact in the foundation reactions of the two-parameter foundation model. The proposed method is based on the properties of Fourier transforms of the finite functions. Particular attention is paid to the problem, taking into account the deformation of soil areas outside the beam. The beam model with two foundation coefficients more realistically describes the behavior of strip footings under loading.

DOI: 10.22227/1997-0935.2014.1.41-51

References
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  3. Pasternak P.L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshchi dvukh koeffitsientov posteli [Fundamentals of a New Method of Elastic Foundation Analysis by Means of Two-constants]. Moscow, 1954, 55 p.
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Method of calculating pilestrip foundations in case of karst hole formation

Vestnik MGSU 2/2014
  • Gotman Al'fred Leonidovich - Institute “BashNIIstroy” Doctor of Technical Sciences, Professor, Deputy Director in Science, Scientific-Research Institute “BashNIIstroy”, Institute “BashNIIstroy”, 3 Konstitutsii st., Ufa, 450064, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Magzumov Rail' Nailovich - Institute “BashNIIstroy” junior research worker, Institute “BashNIIstroy”, 3 Konstitutsii st., Ufa, 450064, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 74-83

The paper presents pile strip foundations in the areas with karst risk. The analysis of karst hole formation mechanism shows the lateral soil pressure on the piles caused by the downfallen soil on the hole rims, which transfers around the hole edges during karst hole formation. In this case, the horizontal pressure of the pile reactive force in the area of the pile connection with the raft is transferred to the raft. Pile failure at the hole boundaries will lead to the increase of the raft bearing distance above the karst hole. The inadequate raft bearing capacity can provoke the emergency situation. The existing Codes on karst protective foundations design do not contain the analysis of pile and raft horizontal pressure under the downfallen soil.The goal of this work is to develop the method of pile strip foundations analysis in the areas with karst risk in case of karst hole formation. The analysis of stress-strain state of the system “foundation soil — pile foundation” was carried out using numerical modeling in geotechnical program MIDAS GTS. As a result of numerical investigations, the diagrams of lateral soil pressure onto the piles and the raft are plotted. The pile pressure is approximated with the linear or bilinear function in dependence on geometrical dimensions of the karst hole and strength characteristics of soil that generates the horizontal pressure.In the Codes, the analysis of a pile under lateral soil pressure is given for a pile with the free end. In the problem examined, the pile head has the hinged bearing in place of the connection with the raft. In view of the given boundary data, the pile design scheme is plotted. The inner forces and displacements of the pile are determined by integrating the differential equation of a pile bending. The consistent integrations are evaluated out of the boundary conditions. The boundary values of inner forces and displacements are evaluated from the equality conditions of displacements and inner forces in the pile at the level of the hole bottom that are evaluated in turn for the upward and downward pile section. The method of pile analysis is developed in case of lateral soil pressure approximation with the linear function.The method worked out allows recalculating a pile being at the edge of the karst hole and accepting the lateral pressure of the downfallen soil on the hole edges.

DOI: 10.22227/1997-0935.2014.2.74-83

References
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