Abstract
A modified domain reduction method (MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao’s transmitting boundary and viscous-spring boundary with Liu’s method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ1 and φ2, the rational distance between the observation point and the MDRM boundary is suggested. When φ1>2 or φ2>13, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy.
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References
Berenger and Jean-Pierre (1994), “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” Journal of computational physics, 114(2): 185–200.
Bielak J, Loukakis K, Hisada Y and Yoshimura C (2003), “Domain Reduction Method for Three-dimensional Earthquake Modeling in Localized Regions, Part I: Theory,” Bulletin of the Seismological Society of America, 93(2): 817–824.
Corigliano M, Scandella L, Lai CG and Paolucci R (2011), “Seismic Analysis of Deep Tunnels in Near Fault Conditions: A Case Study in Southern Italy,” Bulletin of Earthquake Engineering, 9(4): 975–995.
Deeks AJ and Randolph MF (1994), “Axisymmetric Time-Domain Transmitting Boundaries,” Journal of Engineering Mechanics, 120(1): 25–42.
Farzanian M, Arbabi F and Pak R (2016), “PML Solution of Longitudinal Wave Propagation in Heterogeneous Media,” Earthquake Engineering and Engineering Vibration, 15(2): 357–368.
Guan Huimin and Liao Zhenpeng (1996), “A Method for the Stability Analysis of Local Artificial Boundaries,” Chinese Journal of Theoretical and Applied Mechanics, 28(3): 121–125. (in Chinese)
Hilber HM, Hughes TJ and Taylor RL (1977), “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Engineering & Structural Dynamics, 5(3): 283–292.
Huang J, Zhao M, Xu C, Du X, Jin L and Zhao X (2018), “Seismic Stability of Jointed Rock Slopes under Obliquely Incident Earthquake Waves,” Earthquake Engineering and Engineering Vibration, 17(3): 527–539.
Idriss IM and Seed HB (1968), “Seismic Response of Horizontal Soil Lauers,” ASCE Journal of Soil Mechanics, 94(4): 1003–1031.
Isbiliroglu Y, Taborda R and Bielak J (2015), “Coupled Soil-Structure Interaction Effects of Building Clusters During Earthquakes,” Earthquake Spectra, 31(1): 463–500.
Jeremić B, Jie G, Preisig M and Tafazzoli N (2009), “Time Domain Simulation of Soil-Foundation-Structure Interaction in Non-Uniform Soils,” Earthquake Engineering & Structural Dynamics, 38(5): 699–718.
Jeremić B, Tafazzoli N, Ancheta T, Orbović N and Blahoianu A (2013), “Seismic Behavior of NPP Structures Subjected to Realistic 3D, Inclined Seismic Motions, in Variable Layered Soil/Rock, on Surface or Embedded Foundations,” Nuclear Engineering and Design, 265: 85–94.
Jeremić B, Yang Z, Cheng Z, Jie G and Sett K (2015), Lecture Notes on Computational Geomechanics: Inelastic Finite Elements for Pressure Sensitive Materials, Department of Civil & Environmental Engineering, University of California at Davis, California.
Jing Liping, Liao Zhenpeng and Zou Jingxiang (2002), “A High-Frequency Instability Mechanism in Numerical Realization of Multi-Transmitting Formula,” Earthquake Engineering and Engineering Vibration, 22(1): 7–13. (in Chinese).
Joyner WB and Chen AT (1975), “Calculation of Nonlinear Ground Response in Earthquakes,” Bulletin of the Seismological Society of America, 65(5): 1315–1336.
Kausel E (1988), “Local Transmitting Boundaries,” Journal of Engineering Mechanics, 114(6): 1011–1027.
Kellezi L (2000), “Local Transmitting Boundaries for Transient Elastic Analysis,” Soil Dynamics and Earthquake Engineering, 19(7): 533–547.
Kontoe S, Zdravkovic L and Potts DM (2008), “The Domain Reduction Method for Dynamic Coupled Consolidation Problems in Geotechnical Engineering,” International Journal for Numerical and Analytical Methods in Geomechanics, 32(6): 659–680.
Kontoe S, Zdravkovic L and Potts DM (2009), “An Assessment of the Domain Reduction Method as an Advanced Boundary Condition and Some Pitfalls in the Use of Conventional Absorbing Boundaries,” International Journal for Numerical and Analytical Methods in Geomechanics, 33(3): 309–330.
Kontoe S, Zdravkovic L, Menkiti CO and Potts DM (2012), “Seismic Response and Interaction of Complex Soil Retaining Systems,” Computers and Geotechnics, 39: 17–26.
Li Xiaojun and Liao Zhenpeng (1996), “Calculate the Drift Instability of Local Transmitting Boundary in Time Domain,” Chinese Journal of Theoretical and Applied Mechanics, 28(5): 627–632. (in Chinese)
Liang F, Chen H and Huang M (2017), “Accuracy of Three-Dimensional Seismic Ground Response Analysis in Time Domain Using Nonlinear Numerical Simulations,” Earthquake Engineering and Engineering Vibration, 16(3): 487–498.
Liao ZP and Wong HL (1984), “A Transmitting Boundary for the Numerical Simulation of Elastic Wave Propagation,” Soil Dynamics and Earthquake Engineering, 3(4): 174–183.
Liao ZP and Liu JB (1992), “Numerical Instabilities of a Local Transmitting Boundary,” Earthquake Engineering & Structural Dynamics, 21(1): 65–77.
Liao ZP, Wong HL, Yang BP and Yuan YF (1984), “A Transmitting Boundary for Transient Wave Analysis,” Scientia Sinica, 27(10): 1063–1076.
Liao ZP, Zhou ZH and Zhang YH (2002), “Stable Implementation of Transmitting Boundary in Numerical Simulation of Wave Motion,” Chinese Journal of Geophysics, 45(4): 554–568.
Liu JB and Lv YD (1998), “A Direct Method for Analysis of Dynamic Soil-Structure Interaction Based on Interface Idea.” Dynamic Soil-Structure Interaction-Current Research in China and Switzerland, Elsevier.
Lindman EL (1975), “Free-Space Boundary-Conditions for Time-Dependent Wave-Equation,” Journal of Computational Pysics, 18(1): 66–78.
Liu JB, Du YX, Du XL, Wang ZY and Wu J (2006), “3D Viscous-spring Artificial Boundary in Time Domain,” Earthquake Engineering and Engineering Vibration, 5(1): 93–102.
Lysmer J (1978), Analytical Procedures in Soil Dynamics, University of California at Berkeley, Earthquake Engineering Research Center, Richmond, CA.
Lysmer J and Kuhlemeyer RL (1969), “Finite Dynamic Model for Infinite Media,” Journal of the Engineering Mechanics Division, 95(4): 859–878.
Mavroeidis GP and Papageorgiou AS (2003), “A Mathematical Representation of Near-Fault Ground Motions,” Bulletin of the Seismological Society of America, 93(3): 1099–1131.
Newmark NM (1959), “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, 85(3): 67–94.
Poursartip B, Fathi A and Kallivokas LF (2017), “Seismic Wave Amplification by Topographic Features: A Parametric Study,” Soil Dynamics and Earthquake Engineering, 92: 503–527.
Smerzini C, Paolucci R and Stupazzini M (2011), “Comparison of 3D, 2D and 1D Numerical Approaches to Predict Long Period Earthquake Ground Motion in the Gubbio Plain, Central Italy,” Bulletin of Earthquake Engineering, 9(6): 2007–2029.
Solberg JM, Hossain Q and Mseis G (2016), “Nonlinear Time-domain Soil-Structure Interaction Analysis of Embedded Reactor Structures Subjected to Earthquake Loads,” Nuclear Engineering and Design, 304: 100–124.
Xie ZN and Zhang XB (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.
Yasui Y, Takano S, Takeda T, Miyamoto A, Kurimoto O and Ishikawa R (1988), “Finite Element Method for Obliquely Incident Seismic Wave Problems,” Proceedings of the Ninth World Conference on Earthquake Engineering, Japan.
Yoshimura C, Bielak J, Hisada Y and Fernandez A (2003), “Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part II: Verification and Applications,” Bulletin of the Seismological Society of America, 93(2): 825–840.
Zhou Zhenghua and Liao Zhenpeng (2001), “A Measure for Eliminating Drift Instability of the Multi-Transmitting Formula,” Chinese Journal of Theoretical and Applied Mechanics, 33(4): 550–554. (in Chinese)
Acknowledgement
The financial support provided by the China Scholarship Council for Dr. Luo Chao′s two-year visit in the University of California, Davis is greatly appreciated. This work presented was sponsored by the National Natural Science Foundation of China under grant Nos. 91315301, 51478279 and the State Key Laboratory Basic Theory Foundation of the Ministry of Science and Technology of China under the grant SLDRCE08-A-07. These supports are gratefully acknowledged.
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Supported by: National Natural Science Foundation of China under Grant Nos. 91315301, 51478279 and the State Key Laboratory Basic Theory Foundation of the Ministry of Science and Technology of China under the Grant SLDRCE08-A-07
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Luo, C., Lou, M., Gui, G. et al. A modified domain reduction method for numerical simulation of wave propagation in localized regions. Earthq. Eng. Eng. Vib. 18, 35–52 (2019). https://doi.org/10.1007/s11803-019-0488-7
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DOI: https://doi.org/10.1007/s11803-019-0488-7