Horacio Florez

[3] Li S, Feng XT, Li Z, Chen B, Zhang C, Zhou H. In situ monitoring of rockburst nucleation and evolution in the deeply buried tunnels of Jinping II hydropower station. Engineering

[4] Cai M. Principles of rock support in burst-prone ground. Tunnelling and Underground

[5] Ortlepp WD, Stacey TR. Rockburst mechanisms in tunnels and shafts. Tunnelling and

[6] Tarasov BG, Randolph MF. Frictionless shear at great depth and other paradoxes of hard rocks. International Journal of Rock Mechanics and Mining Sciences. 2008;45(3):316-328

[7] Wang JA, Park HD. Comprehensive prediction of rockburst based on analysis of strain energy in rocks. Tunnelling and Underground Space Technology. 2001;16(1):49-57

[8] Cook NGW. Origin of rockbursts. In: Richards L, editor. Rockbursts; Prediction and

[9] Wattimena RK, Sirait B, Widodo NP, Matsui K. Evaluation of rockburst potential in a cutand-fill mine using energy balance. International Journal of the Japanese Committee for

[10] Mitri HS, Tang B, Simon R. FE modelling of mining-induced energy release and storage rates. The Journal of the South African Institute of Mining and Metallurgy. 1999;99(2):103-110

[11] Novozhilov VV. Foundations of the Nonlinear Theory of Elasticity. Graylock. Mineola,

[12] Ranzi G, Gilbert R. Structural Analysis: Principles, Methods and Modelling. Boca Raton.

[13] Ranzi G, Dall Asta A, Ragni L, Zona A. A geometric nonlinear model for composite

[14] Xie HP, Li L, Peng R, Ju Y. Energy analysis and criteria for structural failure of rocks.

beams with partial interaction. Engineering Structures. 2010;32(5):1384-1396

Journal of Rock Mechanics and Geotechnical Engineering. 2009;1(1):11-12

Control. London: Institute of Mining and Metallurgy; 1983. pp. 1-9

Geology. 2012;137–138:85-96

Space Technology. 2013;36:46-56

Rock Mechanics. 2012;8(1):19-23

New York; 1999

Florida: CRC Press; 2015

Underground Space Technology. 1994;9(1):59-65

222 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

Additional information is available at the end of the chapter Horacio Florez Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71873

### Abstract

Most engineering applications estimate the deformation induced by loads by using the linear elasticity theory. The discretization process starts with the equilibrium equation and then develops a displacement formulation that employs the Hooke's law. Problems of practical interest encompass designing of large structures, buildings, subsurface deformation, etc. These applications require determining stresses to compare them with a given failure criteria. One often tackles this way a design or material strength type of problems. For instance, Geomechanics applications in the oil and gas industry assess the induced stresses changes that hydrocarbon production or the injection of fluids, i.e., artificial lift, in a reservoir produce in the surrounding rock mass. These studies often include reservoir compaction and subsidence that pose harmful and costly effects such as in wells casing, cap-rock stability, faults reactivation, and environmental issues as well. Estimating these stress-induced changes and their consequences require accurate elasticity simulations that are usually carried out through finite element (FE) simulations. Geomechanics implies that the flow in porous media simulation must be coupled with mechanics, which causes a substantial increase in CPU time and memory requirements.

Keywords: elasticity, single-phase flow, geomechanics, Dirichlet-Neumann, mortar methods, continuous Galerkin
