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Title: Determination of the initial stress tensor from deformation of underground opening in excavation process (English)
Author: Malík, Josef
Author: Kolcun, Alexej
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 67
Issue: 3
Year: 2022
Pages: 297-318
Summary lang: English
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Category: math
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Summary: A method for the detection of the initial stress tensor is proposed. The method is based on measuring distances between pairs of points located on the wall of underground opening in the excavation process. This methods is based on solving twelve auxiliary problems in the theory of elasticity with force boundary conditions, which is done using the least squares method. The optimal location of the pairs of points on the wall of underground openings is studied. The pairs must be located so that the condition number of the least square matrix has the minimal value, which guarantees a reliable estimation of initial stress tensor. (English)
Keyword: initial stress tensor
Keyword: first boundary value problem of the theory of elasticity
Keyword: least square method
Keyword: condition number of matrix
Keyword: continuous dependence of eigenvalues on matrix elements
MSC: 65N30
MSC: 74-xx
MSC: 74A10
MSC: 93E24
idZBL: Zbl 07547197
idMR: MR4409308
DOI: 10.21136/AM.2021.0266-20
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Date available: 2022-04-14T13:35:50Z
Last updated: 2024-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/150317
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