Abstract
In this chapter the principles and algorithms of the BEA are further extended to cover the reinforcement analysis, stochastic analysis, and seismic analysis. This is an important step towards more widespread and practical use of the BEA in hydraulic structures. Looked at as line segments penetrating through or embedding on discontinuities, the positions and/or the intersecting points of reinforcement components (bolts, piles, keys) with regard to discontinuities are pinpointed by the same pre-processor towards block system identification. The force and moment equilibrium equation, deformation compatibility equation and constitutive equation, are employed to establish the governing equation set for such a reinforced block system. In order to assess the reliability of a complex block system, stochastic analysis algorithms with the BEA are formulated using the approaches of the first-order second moment method and the Monte-Carlo method. Seismic analysis algorithm is implemented using a procedure similar to the dynamic FEM, in which the mass matrix, damping matrix and visco-elastic artificial boundary, are employed.
Keywords
- Deformation Compatibility Equation
- Moment Equilibrium Equation
- Rock Block System
- Reinforcement Components
- Hydraulic Structures
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Al-Homoud AS, Tahtamoni WW. Reliability analysis of three-dimensional dynamic slope stability and earthquake-induced permanent displacement. Soil Dyn Earthq Eng. 2000;19(2):91–114.
Ang AHS, Newmark NM. A probabilistic seismic safety assessment of the Diablo Canyon Nuclear Power Plant. Washington, DC, USA: US Nuclear Regulatory Commission; 1977.
Ayyub BM, Klir GJ. Uncertainty modeling and analysis in engineering and the sciences. Boca Raton, USA: Chapman & Hall/CRC, Taylor & Francis Group; 2006.
Bardet JP, Scott RF. Seismic stability of fractured rock masses with the distinct element method. In: Proceedings of the 26th US symposium on rock mechanics. Rapid City, SD, USA; 1985. p. 139–49.
Bathe KJ. Finite element procedures in engineering analysis. New Jersey, USA: Prentice-Hall; 1982.
Ben-Gal I, Herer Y, Raz T. Self-correcting inspection procedure under inspection errors. IIE Trans Qual Reliab. 2002;34(6):529–40.
Bjerager P. Probability integration by directional simulation. J Eng Mech, ASCE. 1988;114(8):1285–302.
Bucher CG, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Struct Safety. 1990;7(1):57–66.
Cambou B. Applications of first-order uncertainty analysis in the finite element method in linear elasticity. In: Proceedings of 2nd international conference on applications of statistics and probability in soil and structural engineering. Aachen, Germany; 1975. p. 67–87.
Chen SH. Analysis of reinforced rock foundation using elastic-viscoplastic block theory. In: Ribeiro e Sousa L, Grossmann NF, editors. Proceedings on 1993 ISRM International Symposium—EUROCK 93. Rotterdam, The Netherlands: A.A. Balkema; 1993. p. 45–51.
Chen SH. Hydraulic structures. Berlin, Germany: Springer; 2015.
Chen SH, Lian HD, Yang XW. Interval static displacement analysis for structures with interval parameters. Int J Numer Meth Eng. 2002;53(2):393–407.
Chen SH, Shen BK, Huang MH. Stochastic elastic-viscoplastic analysis for discontinuous rock masses. Int J Numer Meth Eng. 1994;37(14):2429–44.
Chen SH, Wang WM, Zheng HF, Shahrour I. Block element method for the seismic stability of rock slopes. Int J Geotech Geoenviron Eng, ASCE. 2010;136(12):1610–7.
Chen SH, Xiong WL. An elastic-viscoplastic stochastic FEM for geotechnical engineering. In: Proceedings of 2nd National symposium on computer geomechanics. Shanghai, China; 1990. p. 256–66 (in Chinese).
Clayton RW, Engquist B. Absorbing boundary conditions for wave equation migration. Geophysics. 1980;45(5):895–904.
Corotis RB. An overview of uncertainty concepts related to mechanical and civil engineering. ASCE-ASME J Risk Uncertain Eng Syst, Part B: Mech Eng. 2015;1(4):040801.
Cundall PA, Hart DH. Numerical modelling of discontinua. Eng Comput. 1992;9(2):101–13.
Deeks AJ, Randolph MF. Axisymmetric time-domain transmitting boundaries. J Eng Mech, ASCE. 1994;120(1):25–42.
Elishakoff I, Ohsaki M. Optimization and anti-optimization of structures under uncertainty. London, UK: Imperial College Press; 2010.
Eringen AC, Suhubi ES. Elastodynamics. NY, USA: Academic Press; 1974.
Ghanem R, Spanos PD. Stochastic finite elements: a spectral approach. NY, USA: Springer; 1991.
Hasofer AM, Lind NC. Exact and invariant second-moment code format. J Eng Mech, ASCE. 1974;100(1):111–21.
Higdon RL. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation. Math Comp. 1986;47(176):437–59.
Kramer SL. Geotechnical Earthquake Engineering. NJ, USA: Prentice-Hall; 1996.
Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media. J Eng Mech Div, ASCE. 1969;95(4):859–77.
Mahadevan S, Zhang R, Smith N. Bayesian networks for system reliability reassessment. Struct Saf. 2001;23(3):231–51.
Melchers RE. Structural reliability analysis and prediction. NY, USA: Wiley; 1987.
Moens D, Hanss M. Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: recent advances. Finite Elem Anal Des. 2011;47(1):4–16.
Moens D, Vandepitte D. A survey of non-probabilistic uncertainty treatment in finite element analysis. Comput Meth Appl Mech Eng. 2005;194(14–16):1527–55.
Moore RE. Interval analysis. Englewood Cliffs, USA: Prentice-Hall; 1966.
Pearl J. Probabilistic reasoning in intelligent systems. San Francisco, CA, USA: Morgan Kaufmann; 1988.
Provan JW. Probabilistic fracture mechanics and reliability. Dordrecht, The Netherlands: Martinus Nijhoff; 1987.
Rackwitz R, Fiessler B. Structural reliability under combined random load sequences. Comput Struct. 1978;9(5):489–94.
Rao SS, Berke L. Analysis of uncertain structural systems using interval analysis. AIAA J. 1997;35(4):727–35.
Shi GH. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Eng Comput. 1992;9(2):157–68.
Sofi A, Muscolino G, Elishakoff I. Special issue on nonprobabilistic treatments of uncertainty: recent developments. ASCE-ASME J Risk Uncertain Eng Syst, Part B: Mech Eng. 2015;1(4):040301.
Torres-Toledano JG, Sucar LE. Bayesian networks for reliability analysis of complex systems. In: Proceedings of 6th Ibero-American conference on AI (IBERAMIA 98). Lecture notes inartificial intelligence, vol. 1484. Berlin, Germany: Springer; 1998. p. 195–206.
Zhao GF, Jin WL. The theory of structural reliability. Beijing, China: Chinese Industrial Architecture Publishing House; 2000 (in Chinese).
Zhao WT, Qiu ZP. An efficient response surface method and its application to structural reliability and reliability-based optimization. Finite Elem Anal Des. 2013;67:34–42.
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Chen, Sh. (2019). Expanding Study on the Block Element Analysis. In: Computational Geomechanics and Hydraulic Structures. Springer Tracts in Civil Engineering . Springer, Singapore. https://doi.org/10.1007/978-981-10-8135-4_12
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