Geodesic
Determination of the initial stress tensor from deformation of underground opening in excavation process
Applications of Mathematics, Tome 67 (2022) no. 3, pp. 297-318.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2021.0266-20
Classification : 65N30, 74-xx, 74A10, 93E24
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 
@article{10_21136_AM_2021_0266_20,
     author = {Mal{\'\i}k, Josef and Kolcun, Alexej},
     title = {Determination of the initial stress tensor from deformation of underground opening in excavation process},
     journal = {Applications of Mathematics},
     pages = {297--318},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2022},
     doi = {10.21136/AM.2021.0266-20},
     mrnumber = {4409308},
     zbl = {07547197},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0266-20/}
}
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
SP  - 297
EP  - 318
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0266-20/
DO  - 10.21136/AM.2021.0266-20
LA  - en
ID  - 10_21136_AM_2021_0266_20
ER  - 
%0 Journal Article
%A Malík, Josef
%A Kolcun, Alexej
%T Determination of the initial stress tensor from deformation of underground opening in excavation process
%J Applications of Mathematics
%D 2022
%P 297-318
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0266-20/
%R 10.21136/AM.2021.0266-20
%G en
%F 10_21136_AM_2021_0266_20
Malík, Josef; Kolcun, Alexej. Determination of the initial stress tensor from deformation of underground opening in excavation process. Applications of Mathematics, Tome 67 (2022) no. 3, pp. 297-318. doi : 10.21136/AM.2021.0266-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0266-20/

Cité par Sources :