Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

Gaede, Oliver, Karpfinger, Florian, Jocker, Jeroen, & Prioul, Romain (2012) Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock. International Journal of Rock Mechanics and Mining Sciences, 51, pp. 53-63.

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Abstract

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

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11 citations in Web of Science®

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ID Code: 60077
Item Type: Journal Article
Refereed: Yes
Keywords: Elastic Anisotropy, Borehole Stresses, Finite Element Method, Analytical Solution
DOI: 10.1016/j.ijrmms.2011.12.010
ISSN: 1873-4545
Subjects: Australian and New Zealand Standard Research Classification > EARTH SCIENCES (040000)
Australian and New Zealand Standard Research Classification > EARTH SCIENCES (040000) > GEOPHYSICS (040400)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Numerical Computation (080205)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > RESOURCES ENGINEERING AND EXTRACTIVE METALLURGY (091400) > Geomechanics and Resources Geotechnical Engineering (091402)
Divisions: Current > Schools > School of Earth, Environmental & Biological Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier
Deposited On: 20 May 2013 01:09
Last Modified: 22 May 2013 07:15

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