A polyhedral scaled boundary finite element method for three-dimensional dynamic analysis of saturated porous media. (English) Zbl 1464.76068
Summary: This paper presents a polyhedral scaled boundary FEM (SBFEM) to investigate three-dimensional seismic response of saturated porous media. The displacement interpolation functions and the pore-pressure interpolation functions are derived using enhanced SBFEM. The spatial discretization formula of generalized Biot equations is achieved by Galerkin method, and subsequently solved via time-domain solving approach. The proposed method can be applied directly over arbitrary polyhedron and octree grids, possessing desirable flexibility in investigating complex geometries and high-efficiency in discretization, which makes it more versatility for engineering simulation compared to traditional numerical methods. The reliability and advantages of the developed method are validated using three numerical examples.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
scaled boundary finite element method; saturated porous media; generalized Biot consolidation; polyhedron; octreeReferences:
| [1] | Terzaghi, K., Theoretical soil mechanics (1943), John Wiley & Sons, inc: John Wiley & Sons, inc New York, USA |
| [2] | Biot, M. A., General theory of three-dimensional consolidation, J Appl Phys, 12, 2, 155-164 (1941) · JFM 67.0837.01 |
| [3] | Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range, J Acoust Soc Am, 28, 2, 168-178 (1956) |
| [4] | Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range, J Acoust Soc Am, 28, 2, 179-191 (1956) |
| [5] | Zienkiewicz, O. C.; Chang, C. T.; Bettess, P., Drained, undrained, consolidating and dynamic behaviour assumptions in soils, Géotechnique, 30, 4, 385-395 (1980) |
| [6] | Zienkiewicz, O. C.; Shiomi, T., Dynamic behaviour of saturated porous media; the generalized Biot formulation and its numerical solution, Int J Numer Anal Methods Geomech, 8, 1, 71-96 (1984) · Zbl 0526.73099 |
| [7] | Simon, B. R.; Zienkiewicz, O. C.; Paul, D. K., An analytical solution for the transient response of saturated porous elastic solids, Int J Numer Anal Methods Geomech, 8, 4, 381-398 (1984) · Zbl 0539.73128 |
| [8] | Boer, R. D.; Ehlers, W.; Liu, Z., One-dimensional transient wave propagation in fluid-saturated incompressible porous media, Arch Appl Mech, 63, 1, 59-72 (1993) · Zbl 0767.73013 |
| [9] | Gajo, A.; Mongiovi, L., An analytical solution for the transient response of saturated linear elastic porous media, Int J Numer Anal Methods Geomech, 19, 6, 399-413 (1995) · Zbl 0830.73015 |
| [10] | Schanz, M.; Cheng, A. H.D., Wave propagation in a one-dimensional poroelastic column, Acta Mech, 145, 1-4, 1-18 (2000) · Zbl 0987.74039 |
| [11] | Shan, Z.; Ling, D.; Ding, H., Exact solutions for one-dimensional transient response of fluid-saturated porous media, Int J Numer Anal Methods Geomech, 35, 4, 461-479 (2011) · Zbl 1274.74113 |
| [12] | Ghaboussi, J.; Wilson, E. L., Variation formulation of dynamics of fluid-saturated porous elastic solids, J Eng Mech Div, 98, 4, 947-963 (1972) |
| [13] | Zienkiewicz, O.; Leung, K.; Hinton, E.; Chang, C., Liquefaction and permanent deformation under dynamic conditions-numerical solution and constitutive relations, Soil mechanics-transient and cyclic loads: constitutive relations and numerical treatment, 71-104 (1982), Wiley: Wiley London · Zbl 0584.73135 |
| [14] | Zienkiewicz, O., Basic formulation of static and dynamic behaviour of soil and other porous media, Numerical methods in geomechanics, 39-55 (1982), Springer · Zbl 0539.73127 |
| [15] | Zienkiewicz, O. C.; Huang, M.; Wu, J.; Wu, S., A new algorithm for the coupled soil-pore fluid problem, Shock Vib, 1, 1, 3-14 (1993) |
| [16] | Huang, M.; Zienkiewicz, O. C., New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems, Int J Numer Methods Eng, 43, 6, 1029-1052 (2015) · Zbl 0945.74069 |
| [17] | Huang, M.; Wu, S.; Zienkiewicz, O. C., Incompressible or nearly incompressible soil dynamic behaviour—a new staggered algorithm to circumvent restrictions of mixed formulation, Soil Dyn Earthq Eng, 21, 2, 169-179 (2001) |
| [18] | Pastor, M.; Li, T.; Merodo, J. A.F., Stabilized finite elements for harmonic soil dynamics problems near the undrained-incompressible limit, Soil Dyn Earthq Eng, 16, 3, 161-171 (1997) |
| [19] | Predeleanu, M., Development of boundary element method to dynamic problems for porous media ☆, Appl Math Modell, 8, 6, 378-382 (1984) · Zbl 0583.76112 |
| [20] | Dargush, G. F.; Chopra, M. B., Dynamic Analysis of Axisymmetric foundations on Poroelastic media, J Eng Mech, 122, 7, 623-632 (1996) |
| [21] | Nguyen, K. V.; Gatmiri, B., Numerical implementation of fundamental solution for solving 2D transient poroelastodynamic problems, Wave Motion, 44, 3, 137-152 (2007) · Zbl 1231.74112 |
| [22] | Karim, M. R.; Nogami, T.; Wang, J. G., Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method, Int J Solids Struct, 39, 24, 6011-6033 (2002) · Zbl 1032.74585 |
| [23] | Soares, Delfim, A time-domain meshless local Petrov-Galerkin formulation for the dynamic analysis of nonlinear porous media, Comput Model Eng Sci, 66, 3, 227-248 (2010) · Zbl 1231.76164 |
| [24] | Boal, N.; Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N., Finite-difference analysis of fully dynamic problems for saturated porous media, J Comput Appl Math, 236, 6, 1090-1102 (2011) · Zbl 1375.76106 |
| [25] | Song, C.; Wolf, J. P., The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics, Comput Methods Appl Mech Eng, 147, 3-4, 329-355 (1997) · Zbl 0897.73069 |
| [26] | Wolf, J. P.; Song, C., The scaled boundary finite-element method - a primer: derivations, Comput Struct, 78, 1, 191-210 (2000) |
| [27] | Song, C.; Wolf, J. P., The scaled boundary finite-element method - a primer: solution procedures, Comput Struct, 78, 1, 211-225 (2000) |
| [28] | Birk, C.; Behnke, R., A modified scaled boundary finite element method for three-dimensional dynamic soil-structure interaction in layered soil, Int J Numer Methods Eng, 89, 3, 371-402 (2012) · Zbl 1242.74095 |
| [29] | Yang, Z., Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method, Eng Fract Mech, 73, 12, 1711-1731 (2006) |
| [30] | Yang, Z., Application of scaled boundary finite element method in static and dynamic fracture problems, Acta Mech Sin, 22, 3, 243-256 (2006) · Zbl 1202.74187 |
| [31] | Deeks, A. J.; Cheng, L., Potential flow around obstacles using the scaled boundary finite-element method, Int J Numer Methods Fluids, 41, 7, 721-741 (2003) · Zbl 1107.76348 |
| [32] | Bazyar, M. H.; Graili, A., A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows, Int J Numer Anal Methods Geomech, 36, 16, 1793-1812 (2012) |
| [33] | Bazyar, M. H.; Talebi, A., Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite-element method, Int J Numer Anal Methods Geomech, 39, 1, 1-22 (2015) |
| [34] | Lin, G.; Du, J.; Hu, Z., Dynamic dam-reservoir interaction analysis including effect of reservoir boundary absorption, Sci China Ser E: Technol Sci, 50, 1, 1-10 (2007) · Zbl 1220.76043 |
| [35] | Xu, H.; Zou, D.; Kong, X.; Hu, Z.; Su, X., A nonlinear analysis of dynamic interactions of CFRD-compressible reservoir system based on FEM-SBFEM, Soil Dyn Earthq Eng, 112, 24-34 (2018) |
| [36] | Xu, H.; Zou, D.; Kong, X.; Su, X., Error study of Westergaard’s approximation in seismic analysis of high concrete-faced rockfill dams based on SBFEM, Soil Dyn Earthq Eng, 94, 88-91 (2017) |
| [37] | Xu, H.; Zou, D.; Kong, X.; Hu, Z., Study on the effects of hydrodynamic pressure on the dynamic stresses in slabs of high CFRD based on the scaled boundary finite-element method, Soil Dyn Earthq Eng, 88, 223-236 (2016) |
| [38] | Ooi, E. T.; Song, C.; Tin-Loi, F., A scaled boundary polygon formulation for elasto-plastic analyses, Comput Methods Appl Mech Eng, 268, 1, 905-937 (2014) · Zbl 1295.74102 |
| [39] | Chen, K.; Zou, D.; Kong, X.; Chan, A.; Hu, Z., A novel nonlinear solution for the polygon scaled boundary finite element method and its application to geotechnical structures, Comput Geotech, 82, 201-210 (2017) |
| [40] | Chen, K.; Zou, D.; Kong, X.; Yu, X., An efficient nonlinear octree SBFEM and its application to complicated geotechnical structures, Comput Geotech, 96, 226-245 (2018) |
| [41] | Chen, K.; Zou, D.; Kong, X., A nonlinear approach for the three-dimensional polyhedron scaled boundary finite element method and its verification using Koyna gravity dam, Soil Dyn Earthq Eng, 96, 1-12 (2017) |
| [42] | Kai, C.; Degao, Z.; Xianjing, K.; Jingmao, L., Elasto-plastic fne-scale damage failure analysis of metro structures based on coupled SBFEM-FEM, Comput Geotech, 108, 280-294 (2019) |
| [43] | Lu, S.; Liu, J.; Lin, G.; Wang, W., Time-domain analyses of the layered soil by the modified scaled boundary finite element method, Struct Eng Mech, 55, 5, 1055-1086 (2015) |
| [44] | Liu, J.; Lin, G., A scaled boundary finite element method applied to electrostatic problems, Eng Anal Boundary Elem, 36, 12, 1721-1732 (2012) · Zbl 1351.78048 |
| [45] | Lin, G.; Liu, J.; Li, J.; Hu, Z., A scaled boundary finite element approach for sloshing analysis of liquid storage tanks, Eng Anal Boundary Elem, 56, 70-80 (2015) · Zbl 1403.65209 |
| [46] | Ye, W.; Liu, J.; Lin, G.; Zhou, Y.; Yu, L., High performance analysis of lateral sloshing response in vertical cylinders with dual circular or arc-shaped porous structures, Appl Ocean Res, 81, 47-71 (2018) |
| [47] | Li, P.; Liu, J.; Lin, G.; Zhang, P.; Yang, G., A NURBS-based scaled boundary finite element method for the analysis of heat conduction problems with heat fluxes and temperatures on side-faces, International Journal of Heat & Mass Transfer, 113, 764-779 (2017) |
| [48] | Lu, S.; Liu, J.; Lin, G.; Zhang, P., Modified scaled boundary finite element analysis of 3D steady-state heat conduction in anisotropic layered media, Int J Heat Mass Transf, 108, 2462-2471 (2017) |
| [49] | Li, P.; Lin, G.; Liu, J.; Zhou, Y.; Xu, B., Solution of steady-state thermoelastic problems using a scaled boundary representation based on nonuniform rational B-splines, J Therm Stress, 41, 2, 1-25 (2018) |
| [50] | Ooi, E. T.; Shi, M.; Song, C.; Tin-Loi, F.; Yang, Z. J., Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique, Eng Fract Mech, 106, 1-21 (2013) |
| [51] | Dai, S.; Augarde, C.; Du, C.; Chen, D., A fully automatic polygon scaled boundary finite element method for modelling crack propagation, Eng Fract Mech, 133, 163-178 (2015) |
| [52] | Shi, M.; Zhong, H.; Ooi, E. T.; Zhang, C.; Song, C., Modelling of crack propagation of gravity dams by scaled boundary polygons and cohesive crack model, Int J Fract, 183, 1, 29-48 (2013) |
| [53] | Chiong, I.; Ooi, E. T.; Song, C.; Tin-Loi, F., Scaled boundary polygons with application to fracture analysis of functionally graded materials, Int J Numer Methods Eng, 98, 8, 562-589 (2014) · Zbl 1352.74020 |
| [54] | Chen, K.; Zou, D.; Kong, X.; Zhou, Y., Global concurrent cross-scale nonlinear analysis approach of complex CFRD systems considering dynamic impervious panel-rockfill material-foundation interactions, Soil Dyn Earthq Eng, 114, 51-68 (2018) |
| [55] | Zou, D.; Chen, K.; Kong, X.; Liu, J., An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis, Eng Anal Boundary Elem, 84, 87-107 (2017) · Zbl 1403.74273 |
| [56] | Talebi, H.; Saputra, A.; Song, C., Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements, Comput Mech, 58, 4, 697-715 (2016) · Zbl 1398.74409 |
| [57] | Natarajan, S.; Ooi, E. T.; Saputra, A.; Song, C., A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra, Eng Anal Boundary Elem, 80, 218-229 (2017) · Zbl 1403.65217 |
| [58] | Ooi, E. T.; Song, C.; Natarajan, S., A scaled boundary finite element formulation for poroelasticity, Int J Numer Methods Eng (2018) · Zbl 07878389 |
| [59] | Zou, D.; Teng, X.; Chen, K.; Yu, X., An extended polygon scaled boundary finite element method for the nonlinear dynamic analysis of saturated soil, Eng Anal Boundary Elem, 91, 150-161 (2018) · Zbl 1403.74274 |
| [60] | Zienkiewicz, O. C.; Chan, A. H.C.; Pastor, M.; Schrefler, B. A.; Shiomi, T., Computational geomechanics with special reference to earthquake engineering (1999), John Wiley & Sons Ltd.: John Wiley & Sons Ltd. New York, USA · Zbl 0932.74003 |
| [61] | Floater, M. S., Mean value coordinates, Comput Aided Geom Des, 20, 1, 19-27 (2003) · Zbl 1069.65553 |
| [62] | Wolf, J. P., The scaled boundary finite element method (2004), Wiley: Wiley Chichester, UK |
| [63] | Zou, D.; Kong, X.; Xu, B., User manual for geotechnical dynamic nonlinear analysis (2005), Institute of earthquake engineering, Dalian University of Technology: Institute of earthquake engineering, Dalian University of Technology Dalian |
| [64] | http://www.mfcad.com/tuzhi/20147/413074.html; http://www.mfcad.com/tuzhi/20147/413074.html |
| [65] | Syahrom, A.; Abdul Kadir, M. R.; Abdullah, J.; Ochsner, A., Permeability studies of artificial and natural cancellous bone structures, Med Eng Phys, 35, 6, 792-799 (2013) |
| [66] | Malachanne, E.; Dureisseix, D.; Canadas, P.; Jourdan, F., Experimental and numerical identification of cortical bone permeability, J Biomech, 41, 3, 721-725 (2008) |
| [67] | Valliappan, S.; Svensson, N. L.; Wood, R. D., Three dimensional stress analysis of human femur, Comput Biol Med, 7, 4, 253-264 (1977) |
| [68] | Lee, K. I.; Yoon, S. W., Comparison of acoustic characteristics predicted by Biot’s theory and the modified Biot-Attenborough model in cancellous bone, J Biomech, 39, 2, 364-368 (2006) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
