Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
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
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
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.
References:
[1] Bhatia, R.: Matrix Analysis. Graduate Texts in Mathematics 169. Springer, New York (1997). DOI 10.1007/978-1-4612-0653-8 | MR 1477662 | Zbl 0863.15001
[2] Blaheta, R., Jakl, O., Kohut, R., Starý, J.: GEM -- a platform for advanced mathematical geosimulations. Parallel Processing and Applied Mathematics. Part 1 Lecture Notes in Computer Science 6067. Springer, Berlin (2010), 266-275. DOI 10.1007/978-3-642-14390-8_28
[3] Haimson, B. C., Cornet, F. H.: ISRM suggested methods for rock stress estimation---Part 3: Hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). Int. J. Rock Mech. Min. Sci. 40 (2003), 1011-1020. DOI 10.1016/j.ijrmms.2003.08.002
[4] Halmos, P. R.: Measure Theory. Graduate Texts in Mathematics 18. Springer, Berlin (1974). DOI 10.1007/978-1-4684-9440-2 | MR 0033869 | Zbl 0283.28001
[5] Hudson, J. A., Cornet, F. H., Christiansson, R.: ISRM suggested methods for rock stress estimation---Part 1: Strategy for rock stress estimation. Int. J. Rock Mech. Min. Sci. 40 (2003), 991-998. DOI 10.1016/j.ijrmms.2003.07.011
[6] Lax, P. D.: Linear Algebra and Its Applications. Pure and Applied Mathematics. Wiley, New York (2007). MR 2356919 | Zbl 1152.15001
[7] Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Studies in Applied Mechanics 3. Elsevier, Amsterdam (1981). DOI 10.1016/c2009-0-12554-0 | MR 0600655 | Zbl 0448.73009
[8] Sjöberg, J., Christiansson, R., Hudson, J. A.: ISRM suggested methods for rock stress estimation---Part 2: Overcoring methods. Int. J. Rock Mech. Min. Sci. 40 (2003), 999-1010. DOI 10.1016/j.ijrmms.2003.07.012
[9] al., K. Souček et: Comprehensive Geological Characterization of URF Bukov---Part II. Geotechnical Characterization. Final report no. 221/2018/ENG. Ostrava, SÚRAO (2017).
[10] Sugawara, K., Obara, Y.: Draft ISRM suggested method for in situ stress measurement using the compact conical-ended borehole overcoring (CCBO) technique. Int. J. Rock Mech. Min. Sci. 36 (1999), 307-322. DOI 10.1016/S0148-9062(99)00004-2
[11] Wiles, T. D., Kaiser, P. K.: {\it In situ} stress determination using the under-excavation technique---I. Theory. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 31 (1994), 439-446. DOI 10.1016/0148-9062(94)90147-3
[12] Wiles, T. D., Kaiser, P. K.: {\it In situ} stress determination using the under-excavation technique---II. Applications. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 31 (1994), 447-456. DOI 10.1016/0148-9062(94)90148-1
Search
Partner of
