Inverse Problem of Determining the Strength Characteristics of Multi-Story Buildings on Piles

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 202 - 213
• Main Authors: Favorskaya, A. V., Petrov, I. B.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Elastic properties; Geometry; Inverse problems; Iterative solution; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Multistory buildings; Pile foundations; Probability Theory and Stochastic Processes; Subsidence; Wall thickness; Weather; buildings at Far North; direct problems; 2010 Mathematics Subject Classification: 65M06, 65M25, 35Q74, 35L05, 35R30; inverse problems; piles; seismic stability; grid-characteristic method; multi-story buildings
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608555

Weather conditions in the Far North require the use of pile foundations for multi-story buildings. Unlike mid- and equatorial latitudes, it is impossible to strengthen the soil between the piles; on the contrary, the properties and geometry of the subsidence of this soil depend on weather conditions. In this paper, the grid-characteristic method on systems of individual pairwise non-conformal curvilinear and Cartesian grids is used to solve inverse problems of determining the strength properties of piles and foundations of buildings operated in the Far North. To solve the inverse problem, a software package has been developed that uses an iterative solution of direct problems. The method allows one to vary such values as pile length, wavelength, number of piles per room, pile thickness, soil subsidence and its shape, elastic properties of the surrounding geological environment, number of floors, ceiling height, wall thickness, etc. In order to demonstrate the capabilities of the proposed method, a number of dependencies of strength characteristics on variable parameters were obtained.