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http://dx.doi.org/10.5000/EESK.2018.22.7.379

Practical Numerical Model for Nonlinear Analyses of Wave Propagation and Soil-Structure Interaction in Infinite Poroelastic Media  

Lee, Jin Ho (Department of Ocean Engineering, Pukyong National University)
Publication Information
Journal of the Earthquake Engineering Society of Korea / v.22, no.7, 2018 , pp. 379-390 More about this Journal
Abstract
In this study, a numerical approach based on mid-point integrated finite elements and a viscous boundary is proposed for time-domain wave-propagation analyses in infinite poroelastic media. The proposed approach is accurate, efficient, and easy to implement in time-domain analyses. In the approach, an infinite domain is truncated at some distance. The truncated domain is represented by mid-point integrated finite elements with real element-lengths and a viscous boundary is attached to the end of the domain. Given that the dynamic behaviors of the proposed model can be expressed in terms of mass, damping, and stiffness matrices only, it can be implemented easily in the displacement-based finite-element formulation. No convolutional operations are required for time-domain calculations because the coefficient matrices are constant. The proposed numerical approach is applied to typical wave-propagation and soil-structure interaction problems. The model is verified to produce accurate and stable results. It is demonstrated that the numerical approach can be applied successfully to nonlinear soil-structure interaction problems.
Keywords
Soil-structure interaction; Wave propagation; Poroelastic medium; Mid-point integrated finite element; Viscous boundary; Caisson breakwater;
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1 Schanz M. Poroelastodynamics: Linear models, analytical solutions, and numerical methods. Applied Mechanics Review. 2009;62.
2 Kausel E. Forced vibrations of circular foundations on layered media, Research Report R74-11. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, c1974.
3 Beskos DE. Boundary element methods in dynamic analysis. Applied Mechanics Review. 1987;40:1-23.   DOI
4 Beskos DE. Boundary element methods in dynamic analysis: Part II (1986-1996). Applied Mechanics Review. 1998;50:149-197.
5 Astley RJ. Infinite elements for wave propagation: a review of current formulations and an assessment of accuracy. International Journal for Numerical Methods in Engineering. 2000;49:951-976.   DOI
6 Givoli D. High-order local non-reflecting boundary conditions: a review. Wave Motion. 2004;39:319-326.   DOI
7 Basu U, Chopra AK. Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Computer Methods in Applied Mechanics in Engineering. 2003;192:1337-1375.   DOI
8 Basu U, Chopra AK. Perfectly matched layers for transient elastodynamics of unbounded domains. International Journal for Numerical Methods in Engineering. 2004;59:1039-1074.   DOI
9 Lee JH, Kim JK, Kim JH. Nonlinear analysis of soil-structure interaction using perfectly matched discrete layers. Computers and Structures. 2014;142:28-44.   DOI
10 Lee JH, Kim JH, Kim JK. Perfectly Matched Discrete Layers for Three-Dimensional Nonlinear Soil-Structure Interaction Analyses. Computers and Structures. 2016;165:34-47.   DOI
11 Lee JH. Nonlinear Soil-Structure Interaction Analysis in Poroelastic Soil Using Mid-Point Integrated Finite Elements and Perfectly Matched Discrete Layers. Soil Dynamics and Earthquake Engineering. 2018;108:160-176.   DOI
12 Meza-Fajardo KC, Papageorgiou AS. Study of the accuracy of the multiaxial perfectly matched layer for the elastic-wave equation. Bulletin of the Seismological Society of America. 2012;102:2458-2467.   DOI
13 Guddati MN, Tassoulas JL. Continued-fraction absorbing boundary conditions for the wave equation. Journal of Computational Acoustics. 2000;8:139-156.   DOI
14 Guddati MN, Lim K-W. Continued fraction absorbing boundary conditions for convex polygon domains. International Journal of Numerical Methods in Engineering. 2006;66:949-977.   DOI
15 Astaneh AV, Guddati MN. Efficient computation of dispersion curves for multilayered waveguides and half-spaces. Computer Methods in Applied Mechanics and Engineering. 2016; 200: 27-46.
16 Savadatti S, Guddati MN. Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling. Journal of Computational Physics. 2010;229:6644-6662.   DOI
17 Duru K, Kreiss G. Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides. Wave Motion. 2014;51:445-465.   DOI
18 Baffet D, Bielak J, Givoli D, Hagstrom T, Rabinovich D. Long-time stable high-order absorbing boundary conditions for elastodynamics. Computer Methods in Applied Mechanics and Engineering. 2012;241-244:20-37.   DOI
19 Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. Journal of Acoustical Society of America. 1956;28:168-178.   DOI
20 Lewis RW, Schrefler BA. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. Wiley. c1998.
21 Lysmer J, Kuhlemeyer RL. Finite dynamic model for infinite media. ASCE. Journal of the Engineering Mechanics Division. 1969;95:859-877.
22 Guddati M, Savadatti S. Efficient and accurate domain-truncation techniques for seismic soil-structure interaction. Earthquakes and Structures. 2012; 3: 563-580.   DOI
23 Lee JH, Tassoulas JL. Root-Finding Absorbing Boundary Conditions for Problems of Wave Propagation in Infinite Media. Computer Methods in Applied Mechanics and Engineering. c2018.
24 Chen W-F. Constitutive Equations for Engineering Materials, Volume 2: Plasticity and Modeling. Elsevier. c1994.
25 Rabinovich D, Givoli D, Bielak J, Hagstrom T, The Double Absorbing Boundary method for a class of anisotropic elastic media. Computer Methods in Applied Mechanics and Engineering. 2017; 315:190-221.   DOI
26 Westergaard HM. Water Pressures on Dams during Earthquakes. Transaction ASCE. 1933;98:418-433.
27 Savadatti S, Guddati MN. A finite element alternative to infinite elements. Computer Methods in Applied Mechanics and Engineering. 2010;199:2204-2223.   DOI
28 Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T. Computational Geomechanics with Special Reference to Earthquake Engineering. Wiley. c1999.