Three-Dimensional Seismic Response in Complex Site Conditions: A New Approach Based on an Auxiliary-Model Method

Abstract

In this paper, an auxiliary-model method is proposed for calculating equivalent input seismic loads in research of ground motions. This method can be used to investigate the local effect of 3D complex sites subjected to obliquely incident SV and P waves. Using this method, we build a fictitious auxiliary model along the normal direction of the boundary of the area of interest, with the model’s localized geological features remaining the same along a vector normal to this boundary. This model is divided into five independent auxiliary models, which are then dynamically analyzed to obtain the equivalent input seismic loads. Unlike traditional methods, in this new technique, the mechanical behavior of the auxiliary model can be nonlinear, and its geometry can be arbitrary. In addition, a detailed description of the steps to calculate the equivalent input seismic loads is given. Numerical examples of incident plane-wave propagation at uniform sites with local features validate the effectiveness of this method. It is also applicable to elastic and non-elastic problems.

Keywords

seismic-wave input / topography effect / oblique incidence / equivalent input seismic load / free field motion

References

[1] Ashford S A, Sitar N, Lysmer J, . Topographic Effects on the Seismic Response of Steep Slopes. Bulletin of the Seismological Society of America, 1997, 87(3): 701-709.

[2] Assimaki D. Effects of Local Soil Conditions on the Topographic Aggravation of Seismic Motion: Parametric Investigation and Recorded Field Evidence from the 1999 Athens Earthquake. Bulletin of the Seismological Society of America, 2005, 95(3): 1059-1089.

[3] Assimaki D, Jeong S. Ground-Motion Observations at Hotel Montana during the M _s7.0 2010 Haiti Earthquake: Topography or Soil Amplification?. Bulletin of the Seismological Society of America, 2013, 103(5): 2577-2590.

[4] Assimaki D, Kausel E. Modified Topographic Amplification Factors for a Single-Faced Slope Due to Kinematic Soil-Structure Interaction. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(11): 1414-1431.

[5] Bakavoli M K, Haghshenas E, Kamalian M. Experimental Study of Seismic Behavior of Two Hilly Sites in Tehran and Comparison with 2d and 3d Numerical Modeling. Soil Dynamics and Earthquake Engineering, 2011, 31(5–6): 737-756.

[6] Bathe K J. Finite Element Procedures, 1996, Upper Saddle River: Prentice Hall

[7] Bielak J. Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part I: Theory. Bulletin of the Seismological Society of America, 2003, 93(2): 817-824.

[8] Bouchon M, Barker J S. Seismic Response of a Hill: The Example of Tarzana, California. Bulletin of the Seismological Society of America, 1996, 86(1A): 66-72.

[9] Buech F, Davies T R, Pettinga J R. The Little Red Hill Seismic Experimental Study: Topographic Effects on Ground Motion at a Bedrock-Dominated Mountain Edifice. Bulletin of the Seismological Society of America, 2010, 100(5A): 2219-2229.

[10] Burjánek J, Edwards B, Fäh D. Empirical Evidence of Local Seismic Effects at Sites with Pronounced Topography: A Systematic Approach. Geophysical Journal International, 2014, 197(1): 608-619.

[11] Cremonini M G, Christiano P, Bielak J. Implementation of Effective Seismic Input for Soil-Structure Interaction Systems. Earthquake Engineering & Structural Dynamics, 1988, 16(4): 615-625.

[12] Du X L, Zhao M. A Local Time-Domain Transmitting Boundary for Simulating Cylindrical Elastic Wave Propagation in Infinite Media. Soil Dynamics and Earthquake Engineering, 2010, 30(10): 937-946.

[13] Falcone G, Boldini D, Amorosi A. Site Response Analysis of an Urban Area: A Multi-Dimensional and Non-Linear Approach. Soil Dynamics and Earthquake Engineering, 2018, 109: 33-45.

[14] Falcone G, Boldini D, Martelli L, . Quantifying Local Seismic Amplification from Regional Charts and Site Specific Numerical Analyses: A Case Study. Bulletin of Earthquake Engineering, 2020, 18(1): 77-107.

[15] Formisano L A, la Rocca M, del Pezzo E, . Topography Effects in the Polarization of Earthquake Signals: A Comparison between Surface and Deep Recordings. Bollettino di Geofisica Teorica ed Applicata, 2012, 53(4): 471-484

[16] Gao Y, Zhang N, Li D, . Effects of Topographic Amplification Induced by a U-Shaped Canyon on Seismic Waves. Bulletin of the Seismological Society of America, 2012, 102(4): 1748-1763.

[17] Gatmiri B, Arson C. Seismic Site Effects by an Optimized 2D BE/FE Method II. Quantification of Site Effects in Two-Dimensional Sedimentary Valleys. Soil Dynamics and Earthquake Engineering, 2008, 28(8): 646-661.

[18] Geli L, Bard P Y, Jullien B. The Effect of Topography on Earthquake Ground Motion: A Review and New Results. Bulletin of the Seismological Society of America, 1988, 78(1): 42-63.

[19] Graff K F. Wave Motion in Elastic Solids, 1975, New York: Dover Publications

[20] Graizer V. Low-Velocity Zone and Topography as a Source of Site Amplification Effect on Tarzana Hill, California. Soil Dynamics and Earthquake Engineering, 2009, 29(2): 324-332.

[21] Hartzell S, Meremonte M, Ramirez-Guzman L, . Ground Motion in the Presence of Complex Topography: Earthquake and Ambient Noise Sources. Bulletin of the Seismological Society of America, 2014, 104(1): 451-466.

[22] Hough S E, Yong A L, Altidor J R, . Site Characterization and Site Response in Port-Au-Prince, Haiti. Earthquake Spectra, 2011, 27(1): 137-155.

[23] Khandan Bakavoli M, Haghshenas E, Kamalian M. Experimental Study of Seismic Behavior of Two Hilly Sites in Tehran and Comparison with 2D and 3D Numerical Modeling. Soil Dynamics and Earthquake Engineering, 2011, 31(5/6): 737-756.

[24] Kuhlemeyer R L, Lysmer J. Finite Element Method Accuracy for Wave Propagation Problems. Journal of the Soil Mechanics and Foundations Division, 1973, 99(5): 421-427.

[25] Lee J. Earthquake Site Effect Modeling in the Granada Basin Using a 3D Indirect Boundary Element Method. Physics and Chemistry of the Earth, Parts A/B/C, 2013, 63: 102-115.

[26] Lee S J, Chen H W, Liu Q, . Three-Dimensional Simulations of Seismic-Wave Propagation in the Taipei Basin with Realistic Topography Based Upon the Spectral-Element Method. Bulletin of the Seismological Society of America, 2008, 98(1): 253-264.

[27] Lee S J, Komatitsch D, Huang B S, . Effects of Topography on Seismic-Wave Propagation: An Example from Northern Taiwan. Bulletin of the Seismological Society of America, 2009, 99(1): 314-325.

[28] Lee S J, Chan Y C, Komatitsch D, . Effects of Realistic Surface Topography on Seismic Ground Motion in the Yangminshan Region of Taiwan Based Upon the Spectral-Element Method and LiDAR DTM. Bulletin of the Seismological Society of America, 2009, 99(2A): 681-693.

[29] Liu J B, Tan H, Bao X, . Seismic Wave Input Method for Three-Dimensional Soil-Structure Dynamic Interaction Analysis Based on the Substructure of Artificial Boundaries. Earthquake Engineering and Engineering Vibration, 2019, 18(4): 747-758.

[30] Liu J B, Bao X, Wang D Y, . The Internal Substructure Method for Seismic Wave Input in 3D Dynamic Soil-Structure Interaction Analysis. Soil Dynamics and Earthquake Engineering, 2019, 127: 105847

[31] Liu J B, Lu Y D. A Direct Method for Analysis of Dynamic Soil-Structure Interaction Based on Interface Idea. Developments in Geotechnical Engineering, 1998, 83 261-276.

[32] Liu J B, Wang Y. A 1D Time-Domain Method for In-Plane Wave Motions in a Layered Half-Space. Acta Mechanica Sinica, 2007, 23(6): 673-680.

[33] Liu J B, Du Y X, Du X L, . 3D Viscous-Spring Artificial Boundary in Time Domain. Earthquake Engineering and Engineering Vibration, 2006, 5(1): 93-102.

[34] Lovati S, Bakavoli M K H, Massa M, . Estimation of Topographical Effects at Narni Ridge (Central Italy): Comparisons between Experimental Results and Numerical Modelling. Bulletin of Earthquake Engineering, 2011, 9(6): 1987-2005.

[35] Luo Y H, Fan X M, Huang R Q, . Topographic and Near-Surface Stratigraphic Amplification of the Seismic Response of a Mountain Slope Revealed by Field Monitoring and Numerical Simulations. Engineering Geology, 2020, 271: 105607

[36] Ma S, Archuleta R J, Page M T. Effects of Large-Scale Surface Topography on Ground Motions, as Demonstrated by a Study of the San Gabriel Mountains, Los Angeles, California. Bulletin of the Seismological Society of America, 2007, 97(6): 2066-2079.

[37] Marzorati S, Ladina C, Falcucci E, . Site Effects “on the Rock”: The Case of Castelvecchio Subequo (L’Aquila, Central Italy). Bulletin of Earthquake Engineering, 2011, 9(3): 841-868.

[38] Massa M, Barani S, Lovati S. Overview of Topographic Effects Based on Experimental Observations: Meaning, Causes and Possible Interpretations. Geophysical Journal International, 2014, 197(3): 1537-1550.

[39] Maufroy E, Cruz-Atienza V M, Cotton F, . Frequency-Scaled Curvature as a Proxy for Topographic Site-Effect Amplification and Ground-Motion Variability. Bulletin of the Seismological Society of America, 2015, 105(1): 354-367.

[40] Moczo P, Kristek J, Bard P Y, . Key Structural Parameters Affecting Earthquake Ground Motion in 2D and 3D Sedimentary Structures. Bulletin of Earthquake Engineering, 2018, 16(6): 2421-2450.

[41] Nguyen K V, Gatmiri B. Evaluation of Seismic Ground Motion Induced by Topographic Irregularity. Soil Dynamics and Earthquake Engineering, 2007, 27(2): 183-188.

[42] Paolucci R. Amplification of Earthquake Ground Motion by Steep Topographic Irregularities. Earthquake Engineering & Structural Dynamics, 2002, 31(10): 1831-1853.

[43] Poursartip B, Fathi A, Kallivokas L F. Seismic Wave Amplification by Topographic Features: A Parametric Study. Soil Dynamics and Earthquake Engineering, 2017, 92 503-527.

[44] Poursartip B, Fathi A, Tassoulas J L. Large-Scale Simulation of Seismic Wave Motion: A Review. Soil Dynamics and Earthquake Engineering, 2020, 129: 105909

[45] Poursartip B, Kallivokas L F. Model Dimensionality Effects on the Amplification of Seismic Waves. Soil Dynamics and Earthquake Engineering, 2018, 113 572-592.

[46] Rathje E M, Bachhuber J, Dulberg R, . Damage Patterns in Port-Au-Prince during the 2010 Haiti Earthquake. Earthquake Spectra, 2011, 27: 117-136. Suppl.)

[47] Sánchez-Sesma F J, Campillo M. Diffraction of P, SV and Rayleigh Waves by Topographic Features: A Boundary Integral Formulation. Bulletin—Seismological Society of America, 1991, 81(6): 2234-2253

[48] Veeraraghavan S, Coleman J L, Bielak J. Simulation of Site and Topographic Effects on Ground Motion in Los Alamos, NM Mesas. Geophysical Journal International, 2020, 220(3): 1504-1520.

[49] Wang X W, Chen J T, Xiao M. Seismic Responses of an Underground Powerhouse Structure Subjected to Oblique Incidence SV and P Waves. Soil Dynamics and Earthquake Engineering, 2019, 119: 130-143.

[50] Wei Z, He H, Shi F, . Topographic Characteristics of Rupture Surface Associated with the 12 May 2008 Wenchuan Earthquake. Bulletin of the Seismological Society of America, 2010, 100(5B): 2669-2680.

[51] Yoshimura C. Domain Reduction Method for Three-Dimensional Earthquake Modeling in Localized Regions, Part II: Verification and Applications. Bulletin of the Seismological Society of America, 2003, 93(2): 825-841.

[52] Zhang X L, Peng X B, Li X J, . 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 M _w7.9 Wenchuan, China Earthquake. Journal of Asian Earth Sciences, 2020, 192 104257

[53] Zhao M, Gao Z, Wang L, . Obliquely Incident Earthquake for Soil-Structure Interaction in Layered Half Space. Earthquakes and Structures, 2017, 13(6): 573-588