Quantifying the Error Associated with the Elastic Halfspace Assumption in Site Response Analysis
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 10
Abstract
One of the fundamental decisions when performing one-dimensional (1D) site response analyses (SRA) involves the selection of the depth and dynamic properties of the elastic halfspace (EHS). This boundary condition assumes linear and homogenous material underlying the soil column for an infinite depth. This assumption implies that waves refracted into the EHS are fully absorbed, and as a result, energy from waves that are potentially reflected back toward the surface from deeper impedance contrasts in the actual geologic profile are not accounted for in the SRA. If a strong soil-rock seismic impedance contrast is present at the site of interest, the EHS boundary is typically set at that depth. However, the actual geologic profile below this impedance contrast may not be in accord with the assumed properties of the EHS, which can lead to systematic errors in the SRA. An analytical expression to quantify these errors is derived in this study, verified using an idealized three-layer profile, and compared to case studies of nine real sites in Charleston, South Carolina. Our results show that the presence of a single strong impedance contrast does not suffice as the sole condition to define the EHS boundary. Frequency-dependent errors in site amplification associated with the assumptions inherent to the EHS used in the SRA can be evaluated as a function of multiple impedance contrasts present in the profile. Smaller errors are associated with strong impedance contrasts at shallower layers and/or minimal impedance contrast among layer interfaces at depth. We also find that strong impedance contrasts located at great depths within deep soil deposits introduce nonnegligible errors to site response results.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was partially funded by National Science Foundation (NSF) Grants CMMI-1825189 and CMMI-1937984. This support is gratefully acknowledged. Additionally, this study significantly benefited from the comments of two anonymous reviewers. However, any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF or those that provided review comments.
References
Boore, D. 2003. “Simulation of ground motion using the stochastic method.” Pure Appl. Geophys. 160 (3–4): 635–676. https://doi.org/10.1007/PL00012553.
Boore, D. M., and W. B. Joyner. 1997. “Site amplifications for generic rock sites.” Bull. Seismol. Soc. Am. 87 (2): 327–341.
Building Seismic Safety Council. 2000. The 2000 NEHRP recommended provisions for new buildings and other structures: Part I (Provisions) and Part II (Commentary). Washington, DC: Federal Emergency Management Agency.
Cabas, A., and A. Rodriguez-Marek. 2017. “VS-κ0 correction factors for input ground motions used in seismic site response analyses.” Earthquake Spectra 33 (3): 917–941. https://doi.org/10.1193/22315eqs188m.
Cadet, H., P.-Y. Bard, and A. Rodriguez-Marek. 2010. “Defining a standard rock site: Propositions based on the KiK-net database.” Bull. Seismol. Soc. Am. 100 (1): 172–195. https://doi.org/10.1785/0120090078.
CEN (European Committee for Standardization). 2004. Eurocode 8: Design of structures for earthquake resistance, part 1: General rules, seismic actions and rules for buildings. EN 1998-1. Brussels, Belgium: CEN.
Frankel, A. D., D. L. Carver, and R. A. Williams. 2002. “Nonlinear and linear site response and basin effects in Seattle for the M 6.8 Nisqually, Washington, earthquake.” Bull. Seismol. Soc. Am. 92 (6): 2090–2109. https://doi.org/10.1785/0120010254.
Goulet, C. A., et al. 2021. “PEER NGA-east database.” Supplement, Earthquake Spectra 37 (S1): 1331–1353. https://doi.org/10.1177/87552930211015695.
Hashash, Y. M. A., A. R. Kottke, J. P. Stewart, K. W. Campbell, B. Kim, C. Moss, S. Nikolaou, E. M. Rathje, and W. J. Silva. 2014. “Reference rock site condition for Central and Eastern North America.” Bull. Seismol. Soc. Am. 104 (2): 684–701. https://doi.org/10.1785/0120130132.
Hashash, Y. M. A., M. I. Musgrove, J. A. Harmon, D. R. Groholski, C. A. Phillips, and D. Park. 2015. DEEPSOIL 6.0, user manual. Urbana, IL: Univ. of Illinois at Urbana-Champaign.
Idriss, I. M., and J. I. Sun. 1992. User’s manual for SHAKE91: A computer program for conducting equivalent linear seismic response analyses of horizontally layered soil deposits. Davis, CA: Center for Geotechnical Modeling, Dept. of Civil and Environmental Engineering, Univ. of California at Davis.
Japan Road Association. 1980. Specifications for highway bridges, Part V, Seismic Design. Tokyo: Maruzen Co., Ltd.
Japan Road Association. 1990. Specifications for highway bridges, Part V, Seismic Design. Tokyo: Maruzen Co., Ltd.
Kottke, A. R., and E. M. Rathje. 2008a. Strata, Version alpha, Revision 381. Austin, TX: Univ. of Texas at Austin.
Kottke, A. R., and E. M. Rathje. 2008b. Technical manual for strata. Berkeley, CA: Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley.
Kramer, S. 1996. Geotechnical earthquake engineering. Upper Saddle River, NJ: Prentice Hall.
Laurendeau, A., F. Cotton, O.-J. Ktenidou, L.-F. Bonilla, and F. Hollender. 2013. “Rock and stiff soil site amplification: Dependency on VS30 and kappa (κ0).” Bull. Seismol. Soc. Am. 103 (6): 3131–3148. https://doi.org/10.1785/0120130020.
Markham, C., J. Bray, M. Riemer, and M. Cubrinovski. 2016. “Characterization of shallow soils in the central business district of Christchurch, New Zealand.” Geotech. Test. J. 39 (6): 20150244. https://doi.org/10.1520/GTJ20150244.
NCH 433 mod. D.S. Nº 61 MINVU. 2011. Reglamento que fja el diseño sísmico de edifcios y deroga. [In Spanish.]. Santiago, Chile: Ministerio de Vivienda y Urbanismo.
NGA-West 2. 2013. Next generation attenuation–West 2 database. Berkeley, CA: Pacific Earthquake Engineering Research Center.
Park, D., and Y. M. Hashash. 2004. “Probabilistic seismic hazard analysis with nonlinear site effects in the Mississippi embayment.” In Proc., 13th World Conf. on Earthquake Engineering. Vancouver, BC, Canada: Canadian Association for Earthquake Engineering.
Poggi, V., J. Burjanek, C. Michel, and D. Fah. 2017. “Seismic site-response characterization of high-velocity sites using advanced geophysical techniques: Application to the NAGRA-Net.” Geophys. J. Int. 210 (2): 645–659. https://doi.org/10.1093/gji/ggx192.
Régnier, J., L. F. Bonilla, E. Bertrand, and J.-F. Semblat. 2014. “Influence of the profiles beyond 30 m depth on linear site effects: Assessment from the KiK-net data.” Bull. Seismol. Soc. Am. 104 (5): 2337–2348. https://doi.org/10.1785/0120140018.
Schnabel, P. B., J. Lysmer, and H. B. Seed. 1972. SHAKE: A computer program for earthquake response analysis of horizontally-layered sites. Berkeley, CA: Earthquake Engineering Research Center, Univ. of California at Berkeley.
SNZ (Standards New Zealand). 2004. Structural design actions: Part 5 earthquake actions: New Zealand. Wellington, NZ: SNZ.
Ulmer, K. J., A. Rodriguez-Marek, and R. A. Green. 2021. “Accounting for epistemic uncertainty in site effects in probabilistic seismic hazard analysis.” Bull. Seismol. Soc. Am. 111 (4): 2005–2020. https://doi.org/10.1785/0120200343.
USGS Topographic Maps. 2022. “US topo: Maps for America.” Accessed July 5, 2022. https://www.usgs.gov/programs/national-geospatial-program/us-topo-maps-america.
Zhao, J. X. 1997. “Modal analysis of soft-soil sites including radiation damping.” Earthquake Eng. Struct. Dyn. 26 (1): 93–113. https://doi.org/10.1002/(SICI)1096-9845(199701)26:1%3C93::AID-EQE625%3E3.0.CO;2-A.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 21, 2020
Accepted: May 31, 2022
Published online: Aug 8, 2022
Published in print: Oct 1, 2022
Discussion open until: Jan 8, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.