An automated a priori knowledge-based p-adaptive three-dimensional finite element mesh improvement method for stress analysis of underground excavations with prismatic cross-sections

References

• Abaqus, 2007. Abaqus/Standard user’s manual. Version 6.7. Hibbitt, Karlsson, & Sorensen, Inc. Providence: HKS
   Google Scholar
• Brown, E.T. and Bray, J., 1987. Analytical and computational methods in engineering rock mechanics. London: Allen and Unwin.
   Google Scholar
• Daniel, P., et al., 2018. An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. Computers & Mathematics with Applications, 76 (5), 967–983. doi:https://doi.org/10.1016/j.camwa.2018.05.034.
   Web of Science ®Google Scholar
• Davis, R.O. and Selvadurai, A.P.S., 1996. Elasticity and geomechanics. New York: Cambredge University Press.
   Google Scholar
• Franke, D., et al., 2010. A comparison of the h, p, hp, and rp version of the FEM for the solution of the 2d hertzian contact problem. Computational Mechanics, 45 (5), 513–522. doi:https://doi.org/10.1007/s00466-009-0464-6.
   Web of Science ®Google Scholar
• Garcia Rosero, D.F. and Zsaki, A.M., 2013. Finite element mesh optimization using local p-refinement for stress analysis of underground excavations. CSCE 2013 General Conference - Congrès général 2013 de la SCGC, Montreal, Quebec, Canada: CSCE, GEN-014:1–10.
   Google Scholar
• Gupta, A.K., 1978. A finite element for transition from a fine to a coarse grid. International Journal for Numerical Methods in Engineering, 12, 35–45. doi:https://doi.org/10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• Hazegh, M. and Zsaki, A.M., 2012. A framework for automatic modeling of underground excavations and optimizing 3D boundary and finite element meshes derived from them — framework. International Journal for Numerical and Analytical Methods in Geomechanics, 37 (6), 641–660. doi:https://doi.org/10.1002/nag.1130.
   Web of Science ®Google Scholar
• Hoek, E., 2007. Practical rock engineering. Toronto: Rocscience inc.
   Google Scholar
• Jones, B.W.S., 2015. Mesh adaptation through r-refinement using a truss network analogy. Master’s dissertation, University of Capetown, S. Africa.
   Google Scholar
• Martin, C.D. and Kozak, E.T., 1992. Flow measurements in the excavation disturbed zone of Room 209. Rock characterization: ISRM symposium, Eurock ’92, Chester, UK, 402–407.
   Google Scholar
• Morton, D.J., Tyler, J.M., and Dorroh, J.R., 1995. A new 3D finite element for adaptive h-refinement of 1irrigular meshes. International Journal for Numerical Methods in Engineering, 38 (4), 3989–4008. doi:https://doi.org/10.1002/nme.1620382306.
   Google Scholar
• Owen, S.J., et al., 2007, New Strategies for Unstructured All-Hexahedral Mesh Generation, APCOM’07 in conjunction with EPMESC XI, 3–6 December Kyoto, Japan. doi:https://doi.org/10.1094/PDIS91-4-0467B.
   Google Scholar
• PLAXIS, 2018. PLAXIS 3D connect Ed V20 reference manual. Delft, The Netherlands: PLAXIS.
   Google Scholar
• Ramamurthy, T., 2007. Engineering in rocks for slopes, foundations and tunnels. 2nd ed. Delhi: PHI.
   Google Scholar
• Rocscience Inc, 2016. Developer’s tip. https://rocscience.com/documents/pdfs/uploads/8492.pdf. [Accessed July 2019].
   Google Scholar
• Rocscience Inc, 2019. RS2 user manual. Toronto, ON: Rocscience Inc.
   Google Scholar
• Sandia National Laboratories, 2016, Albuquerque, NM 87185, USA, CUBIT 15.1 User Documentation.
   Google Scholar
• SIMULIA, 2016. Abaqus analysis user’s manual. 6.9 ed. Providence: SIMULIA.
   Google Scholar
• Sonnenhof Holdings, 2012. LISA Version 7.7.1. LISA-Finite Element Technologies. http://www.lisa-fet.com
   Google Scholar
• Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z., 2013. The finite element method: its basis and fundamentals. 6th ed. Burlington: Elsevier Ltd.
   Google Scholar
• Zienkiewicz, O.C. and Zhu, J.Z., 1987. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering, 24 (1), 337–357. doi:https://doi.org/10.1002/nme.1620240206.
   Google Scholar
• Zsaki, A.M., 2010. sim|FEM [Software]. Montreal: Concordia University.
   Google Scholar
• Zsaki, A.M. and Curran, J.H., 2005a. A continuum mechanics based framework for optimizing boundary and finite element meshes associated with underground excavations – framework. International Journal for Numerical and Analytical Methods in Geomechanics, 29 (13), 1271–1298. doi:https://doi.org/10.1002/(ISSN)1096-9853.
   Web of Science ®Google Scholar
• Zsaki, A.M. and Curran, J.H., 2005b. A continuum mechanics based framework for optimizing boundary and finite element meshes associated with underground excavations - accuracy, efficiency and applications. International Journal for Numerical and Analytical Methods in Geomechanics, 29 (13), 1299–1315. doi:https://doi.org/10.1002/(ISSN)1096-9853.
   Web of Science ®Google Scholar