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Research Article

Formulation and Performance of Multi-Transmitting Formula with Spectral Element Method in 2D Ground Motion Simulations Under Plane-Wave Incidence: SV Wave Problem

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Pages 1837-1860 | Received 20 Jan 2022, Accepted 02 Oct 2023, Published online: 17 Oct 2023

References

  • Ayoubi, P., K. Mohammadi, and D. Asimaki. 2021. “A Systematic Analysis of Basin Effects on Surface Ground Motion.” Soil Dynamics and Earthquake Engineering 141:106490. https://doi.org/10.1016/j.soildyn.2020.106490.
  • Ba, Z. N., and J. W. Liang. 2011. “Diffraction of Plane SV Waves Around an Alluvial Valley in Layered Halfspace.” Journal of Earthquake Engineering and Engineering Vibration 31 (3): 18–26. (in Chinese).
  • Bérenger, J. P. 1994. “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves.” Journal of Computational Physics 114 (2): 185–200. https://doi.org/10.1006/jcph.1994.1159.
  • Boore, D. M., K. L. Larner, and K. Aki. 1971. “Comparison of Two Independent Methods for the Solution of Wave-Scattering Problem: Response of a Sedimentary Basin to Vertically Incident SH Waves.” Journal of Geophysical Research 76 (2): 558–569. https://doi.org/10.1029/JB076i002p00558.
  • Chen, S. L., J. Sun, and X. F. Ke. 2020. “Analysis of Water-Seabed-Structure Dynamic Interaction Excited by Planewaves.” Chinese Journal of Theoretical and Applied Mechanics 52 (2): 578–590. (in Chinese).
  • De Basabe, J. D., and M. K. Sen. 2007. “Grid Dispersion and Stability Criteria of Some Common Finite-Element Methods for Acoustic and Elastic Wave Equations.” GEOPHYSICS 72 (6): 81–95. https://doi.org/10.1190/1.2785046.
  • De Basabe, J. D., and M. K. Sen. 2010. “Stability of the High-Order Finite Elements for Acoustic or Elastic Wave Propagation with High-Order Time Stepping.” Geophysical Journal International 181 (1): 577–590. https://doi.org/10.1111/j.1365-246X.2010.04536.x.
  • Deeks, A. J., and M. F. Randolph. 1994. “Axisymmetric Time-Domain Transmitting Boundaries.” Journal of Engineering Mechanics 120 (1): 25–42. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:1(25).
  • De Martin, F. 2011. “Verification of a Spectral-Element Method Code for the Southern California Earthquake Center LOH. 3 Viscoelastic Case.” Bulletin of the Seismological Society of America 101 (6): 2855–2865. https://doi.org/10.1785/0120100305.
  • Dravinski, M. 2007. “Scattering of Waves by a Sedimentary Basin with a Corrugated Interface.” Bulletin of the Seismological Society of America 97 (1B): 256–264. https://doi.org/10.1785/0120060011.
  • Du, X. L., and M. Zhao. 2009. “A Novel High-Order Spring-Dashpot-Mass Boundary for Cylindrical Symmetry Wave Motions in Infinite Domain.” Chinese Journal of Theoretical and Applied Mechanics 41 (2): 207–215. (in Chinese).
  • Du, X. L., M. Zhao, and J. T. Wang. 2006. “A Stress Artificial Boundary in FEA for Near-Field Wave Problem.” Chinese Journal of Theoretical and Applied Mechanics 38 (1): 49–56. (in Chinese).
  • Feng, K., D. Huang, G. Wang, F. Jin, and Z. Chen. 2022. “Physics-Based Large-Deformation Analysis of Coseismic Landslides: A Multiscale 3D SEM-MPM Framework with Application to the Hongshiyan Landslide.” Engineering Geology 297:106487. https://doi.org/10.1016/j.enggeo.2021.106487.
  • Godinho, L., P. Amado Mendes, A. Tadeu, A. Cadena-Isaza, C. Smerzini, F. J. Sanchez-Sesma, R. Madec, et al. 2009. “Numerical Simulation of Ground Rotations Along 2D Topographical Profiles Under the Incidence of Elastic Plane Waves.” Bulletin of the Seismological Society of America 99 (2B): 1147–1161. https://doi.org/10.1785/0120080096.
  • Higdon, R. L. 1987. “Numerical Absorbing Boundary Conditions for the Wave Equations.” Mathematics of Computation 49 (179): 65–90. https://doi.org/10.1090/S0025-5718-1987-0890254-1.
  • Higdon, R. L. 1991. “Absorbing Boundary Conditions for Elastic Waves.” Geophysics 56 (2): 231–241. https://doi.org/10.1190/1.1443035.
  • Higdon, R. L. 1992. “Absorbing Boundary Conditions for Acoustic and Elastic Waves in Stratified Media.” Journal of Computational Physics 101 (2): 386–418. https://doi.org/10.1016/0021-9991(92)90016-R.
  • Huang, J. J. 2018. “An Incrementation-Adaptive Multi-Transmitting Boundary for Seismic Fracture Analysis of Concrete Gravity Dams.” Soil Dynamics and Earthquake Engineering 110:145–158. https://doi.org/10.1016/j.soildyn.2017.12.002.
  • Huang, D., G. Wang, C. Du, and F. Jin. 2021. “Seismic Amplification of Soil Ground with Spatially Varying Shear Wave Velocity Using 2D Spectral Element Method.” Journal of Earthquake Engineering 25 (14): 2834–2849. https://doi.org/10.1080/13632469.2019.1654946.
  • Huang, D., G. Wang, C. Du, F. Jin, K. Feng, and Z. Chen. 2020. “An Integrated SEM-Newmark Model for Physics-Based Regional Coseismic Landslide Assessment.” Soil Dynamics and Earthquake Engineering 132:106066. https://doi.org/10.1016/j.soildyn.2020.106066.
  • Jiang, P. L., H. Jiang, T. Y. Yu, Sun, TY, Zhang, L. 2020. “Influence of 3D Urban Dense Building Groups on Magnification of Ground Motion in Homogeneous Sedimentary Basin.” Shock and Vibration 2020:1–14. https://doi.org/10.1155/2020/8812424.
  • Komatitsch, D., and J. Tromp. 1999. “Introduction to the Spectral Element Method for Three-Dimensional Seismic Wave Propagation.” Geophysical Journal International 139 (3): 806–822. https://doi.org/10.1046/j.1365-246x.1999.00967.x.
  • Komatitsch, D., S. Tsuboi, and J. Tromp. 2005. “The spectral-element method in seismology.”in Seismic Earth: Array Analysis of Broadband Seismograms, In A. Levander and G. Nolet (edited by), American Geophysical Monograph, Vol. 157: 205–227. https://doi.org/10.1029/157GM13.
  • Komatitsch, D., and J. P. Vilotte. 1998. “The Spectral Element Method: An Efficient Tool to Simulate the Seismic Response of 2D and 3D Geological Structures.” Bulletin of the Seismological Society of America 88 (2): 368–392. https://doi.org/10.1785/BSSA0880020368.
  • Kong, X. J., H. J. Xing, H. J. Li, Z. Zhenghua. 2021. “An Approach to Controlling Drift Instability of Multi-Transmitting Formula.” Chinese Journal of Theoretical and Applied Mechanics 53 (11): 3097–3109. (in Chinese).
  • Lee, V. W., H. Luo, and J. Liang. 2006. “Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution.” Journal of Engineering Mechanics 132 (10): 1106–1114. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1106).
  • Liao, Z. P. 2002. Introduction to Wave Motion Theories for Engineering. Beijing: Science Press. (in Chinese).
  • Liao, Z. P., and H. L. Wong. 1984. “A Transmitting Boundary for the Numerical Simulation of Elastic Wave Propagation.” International Journal of Soil Dynamics and Earthquake Engineering 3 (4): 174–183. https://doi.org/10.1016/0261-7277(84)90033-0.
  • Liao, Z. P., Z. H. Zhou, and Y. H. Zhang. 2002. “Stable Implementation of Transmitting Boundary in Numerical Simulation of Wave Motion.” Chinese Journal of Geophysics 45 (4): 554–568. (in Chinese). https://doi.org/10.1002/cjg2.269.
  • Liu, J. B., Y. X. Du, X. L. Du, Z. Wang, and J. Wu. 2006. “3D Viscous-Spring Artificial Boundary in Time Domain.” Earthquake Engineering and Engineering Vibration 5 (1): 93–102. https://doi.org/10.1007/s11803-006-0585-2.
  • Liu, Z., J. Liang, Y. Huang, and L. Liu. 2016. “IBIEM Modelling of the Amplification of Seismic Waves by a Three-Dimensional Layered Alluvial Basin.” Geophysical Journal International 204 (2): 999–1023. https://doi.org/10.1093/gji/ggv473.
  • Liu, Q. F., Y. Y. Yu, D. Y. Yin, and X. Zhang. 2018. “Simulations of Strong Motion in theWeihe Basin During the Wenchuan Earthquake by Spectral Element Method.” Geophysical Journal International 215 (2): 978–995. https://doi.org/10.1093/gji/ggy320.
  • Liu, Q. J., M. J. Zhao, and Z. Liu. 2019. “Liu Zx.Wave Function Expansion Method for the Scattering of SH Waves by Two Symmetrical Circular Cavities in Two Bonded Exponentially Graded Half Spaces.” Engineering Analysis with Boundary Elements 106:389–396. https://doi.org/10.1016/j.enganabound.2019.05.015.
  • Luzón, F., S. A. Gil-Zepeda, F. J. Sánchez-Sesma, and C. Ortiz-Alemán. 2004. “Three-Dimensional Simulation of Ground Motion in the Zafarraya Basin (Southern Spain) Up to 1.335 Hz Under Incident Plane Waves.” Geophysical Journal International 156 (3): 584–594. https://doi.org/10.1111/j.1365-246X.2004.02142.x.
  • Lysmer, J., and R. L. Kuhlemeyer. 1969. “Finite Dynamic Model for Infinite Media.” Journal of the Engineering Mechanics Division 95 (4): 859–878. https://doi.org/10.1061/JMCEA3.0001144.
  • Manolis, G. D., S. L. Parvanova, K. Makra, and P. S. Dineva. 2015. “Seismic Response of Buried Metro Tunnels by a Hybrid FDM-BEM Approach.” Bulletin of Earthquake Engineering 13 (7): 1953–1977. https://doi.org/10.1007/s10518-014-9698-6.
  • Olsen, K. B. 2000. “Site Amplification in the Los Angeles Basin from Three-Dimensional Modeling of Ground Motion.” Bulletin of the Seismological Society of America 90 (6B): S77–S94. https://doi.org/10.1785/0120000506.
  • Poursartip, B., A. Fathi, and L. F. Kallivokas. 2017. “Seismic Wave Amplification by Topographic Features: A Parametric Study.” Soil Dynamics and Earthquake Engineering 92:503–527. https://doi.org/10.1016/j.soildyn.2016.10.031.
  • Pozrikidis, C. 2014. Introduction to Finite and Spectral Element Methods Using MATLAB. 2nd ed. Boca Raton: CRC Press.
  • Sahar, D., J. P. Narayan, and N. Kumar. 2015. “Study of Role of Basin Shape in the Site–City Interaction Effects on the Ground Motion Characteristics.” Natural Hazards 75 (2): 1167–1186. https://doi.org/10.1007/s11069-014-1366-2.
  • Schuberth, B. 2003. “The Spectral Element Method for Seismic Wave Propagation.” Department Für, Geo-Und Umweltwissenschaften, Sektion Ge-ophysik, 23–25.
  • Seriani, G., and S. P. Oliveira. 2008. “Dispersion Analysis of Spectral Element Methods for Elastic Wave Propagation.” Wave Motion 45 (6): 729–744. https://doi.org/10.1016/j.wavemoti.2007.11.007.
  • Stacey, R. 1988. “Improved Transparent Boundary Formulations for the Elastic-Wave Equation.” Bulletin of the Seismological Society of America 78 (6): 2089–2097. https://doi.org/10.1785/BSSA0780062089.
  • Tang, H. 2011. Numerical Simulation of Earthquake Wave and Stability of Calculation. Institute of Engineering Mechanics, China Earthquake Administration. (in Chinese)
  • Tang, H., and M. S. Rong. 2020. “An Improved Wave Motion Input Method for Application of Multi-Transmitting Boundary.” Wave Motion 97:102600. https://doi.org/10.1016/j.wavemoti.2020.102600.
  • Tarinejad, R., M. Isari, and A. T. Ghalesari. 2019. “A New Boundary Element Solution to Evaluate the Geometric Effects of the Canyon Site on the Displacement Response Spectrum.” Earthquake Engineering and Engineering Vibration 18 (2): 267–284. https://doi.org/10.1007/s11803-019-0503-z.
  • Vasilev, G., S. Parvanova, P. Dineva, and F. Wuttke. 2015. “Soil-Structure Interaction Using BEM–FEM Coupling Through ANSYS Software Package.” Soil Dynamics and Earthquake Engineering 70:104–117. https://doi.org/10.1016/j.soildyn.2014.12.007.
  • Wang, Y., H. Takenaka, and T. Furumura. 2000. “Effect of Vertical Velocity Gradient on Ground Motion in a Sediment-Filled Basin Due to Incident SV Wave.” Earth, Planets and Space 52 (1): 13–24. https://doi.org/10.1186/BF03351609.
  • Wang, T., and X. Tang. 2003. “Finite-Difference Modeling of Elastic Wave Propagation: A Nonsplitting Perfectly Matched Layer Approach.” Geophysics 68 (5): 1749–1755. https://doi.org/10.1190/1.1620648.
  • Wong, H. L. 1982. “Effect of Surface Topography on the Diffraction of P, SV, and Rayleigh Waves.” Bulletin of the Seismological Society of America 72 (4): 1167–1183.
  • Xie, Z. N. 2014. “Explanation for Amplification Mode of Instable Numerical Solutions in Multi-Transmitting Formula Induced Zero-Frequency Drift Instability.” Earthquake Engineering and Engineering Dynamics 34 (4): 15–20. (in Chinese).
  • Xie, Z. N., and Z. P. Liao. 2012. “Mechanism of High Frequency Instability Caused by Transmitting Boundary and Method of Its Elimination: SH Wave.” Chinese Journal of Theoretical and Applied Mechanics 44 (4): 745–752. (in Chinese).
  • Xie, Z., R. Matzen, P. Cristini, D. Komatitsch, and R. Martin. 2016. “A Perfectly Matched Layer for Fluid-Solid Problems: Application to Ocean- Acoustics Simulations with Solid Ocean Bottoms.” The Journal of the Acoustical Society of America 140 (1): 165–175. https://doi.org/10.1121/1.4954736.
  • Xie, Z. N., and X. B. Zhang. 2017. “Analysis of High-Frequency Local Coupling Instability Induced by Multi-Transmitting Formula: P-SV Wave Simulation in a 2D Waveguide.” Earthquake Engineering and Engineering Vibration 16 (1): 1–10. https://doi.org/10.1007/s11803-017-0364-2.
  • Xing, H. J., and H. J. Li. 2017. “Implementation of Multi-Transmitting Boundary Condition for Wave Motion Simulation by Spectral Element Method: 2-D Case.” Chinese Journal of Theoretical and Applied Mechanics 49 (4): 894–906. ( in Chinese).
  • Xing, H. J., X. J. Li, H. J. Li, and A. Liu. 2021. “Spectral-Element Formulation of Multi-Transmitting Formula and Its Accuracy and Stability in 1D and 2D Seismic Wave Modeling.” Soil Dynamics and Earthquake Engineering 140:106218. https://doi.org/10.1016/j.soildyn.2020.106218.
  • Xu, J., J. Bielak, O. Ghattas, and J. Wang. 2003. “Three-Dimensional Nonlinear Seismic Ground Motion Modeling in Basins.” Physics of the Earth and Planetary Interiors 137 (1–4): 81–95. https://doi.org/10.1016/S0031-9201(03)00009-8.
  • Yu, Y Y, H PX. Ding, and Q F. Liu. 2017. “Integration of transmitting boundary and spectral element method and improvement on the accuracy of wave motion simulation.” Journal of Vibration and Shock 36 (2): 13–22. (in Chinese). https://doi.org/10.1155/2017/4132092.
  • Yu, Y. Y., H. P. Ding, and X. B. Zhang. 2021. “Simulations of Ground Motions Under Plane Wave Incidence in 2D Complex Site Based on the Spectral Element Method (SEM) and Multi-Transmitting Formula (MTF): SH Problem.” Journal of Seismology 25 (3): 967–985. https://doi.org/10.1007/s10950-021-09995-y.
  • Zeng, C., J. Xia, R. D. Miller, and G. P. Tsoflias. 2011. “Application of the Multiaxial Perfectly Matched Layer (M-PML) to Near-Surface Seismic Modeling with Rayleigh Waves.” Geophysics 76 (3): T43–T52. https://doi.org/10.1190/1.3560019.
  • Zhang, N., Y. Gao, and R. Y. S. Pak. 2017. “Soil and Topographic Effects on Ground Motion of a Surficially Inhomogeneous Semi-Cylindrical Canyon Under Oblique Incident SH Waves.” Soil Dynamics and Earthquake Engineering 95:17–28. https://doi.org/10.1016/j.soildyn.2017.01.037.
  • Zhang, X. B., Z. P. Liao, and Z. N. Xie. 2015. “Mechanism of High Frequency Coupling Instability and Stable Implementation for Transmitting Boundary: SH Wave Motion.” Chinese Journal Geophysics 58 (10): 3639–3648.(in. Chinese).
  • Zhang, X. L., X. B. Peng, X. J. Li, Z. Zhou, A. Mebarki, Z. Dou, and W. Nie. 2020. “Seismic Effects of a Small Sedimentary Basin in the Eastern Tibetan Plateau Based on Numerical Simulation and Ground Motion Records from Aftershocks of the 2008 Mw7.9 Wenchuan, China Earthquake.” Journal of Asian Earth Sciences 192:104257. https://doi.org/10.1016/j.jseaes.2020.104257.
  • Zhang, X. B., and Z. N. Xie. 2022.“Stability Analysis of Transmitting Boundary in Wave Spectral Element Simulation.”Engineering Mechanics,39 (10): 26–35. https://doi.org/10.6052/j.issn.1000-4750.2021.06.0428. (in Chinese).
  • Zhou, Z. H., and Z. P. Liao. 2001. “A Measure for Eliminating Drift Instability of the Multi-Transmitting Formula.” Acta Mechanica Sinica 33 (4): 550–554.
  • Zhu, C., and D. Thambiratnam. 2016. “Interaction of Geometry and Mechanical Property of Trapezoidal Sedimentary Basins with Incident SH Waves.” Bulletin of Earthquake Engineering 14 (11): 2977–3002. https://doi.org/10.1007/s10518-016-9938-z.

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