Determination of the initial stress tensor from deformation of underground opening in excavation process

Josef Malík; Alexej Kolcun

Applications of Mathematics (2022)

  • Volume: 67, Issue: 3, page 297-318
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Malík, Josef, and Kolcun, Alexej. "Determination of the initial stress tensor from deformation of underground opening in excavation process." Applications of Mathematics 67.3 (2022): 297-318. <http://eudml.org/doc/297929>.

@article{Malík2022,
abstract = {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.},
author = {Malík, Josef, Kolcun, Alexej},
journal = {Applications of Mathematics},
keywords = {initial stress tensor; first boundary value problem of the theory of elasticity; least square method; condition number of matrix; continuous dependence of eigenvalues on matrix elements},
language = {eng},
number = {3},
pages = {297-318},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Determination of the initial stress tensor from deformation of underground opening in excavation process},
url = {http://eudml.org/doc/297929},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Malík, Josef
AU - Kolcun, Alexej
TI - Determination of the initial stress tensor from deformation of underground opening in excavation process
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 297
EP - 318
AB - 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.
LA - eng
KW - initial stress tensor; first boundary value problem of the theory of elasticity; least square method; condition number of matrix; continuous dependence of eigenvalues on matrix elements
UR - http://eudml.org/doc/297929
ER -

References

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