Nonstationary Shear-Wave Velocity Randomization Approach to Propagate Small-Scale Spatial Shear-Wave Velocity Heterogeneities into Seismic Response
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 150, Issue 10
Abstract
Recent studies in earthquake engineering have outlined the difficulty of ground response analyses (GRAs) to replicate the observed ground motion and related variability at borehole array sites. Improvement of the seismic site response estimation requires accounting for and propagating the uncertainties in local soil conditions into surface ground motion. Uncertainties in site conditions arise from a number of factors, which include the uncertainties in the shear-wave velocity () that are mainly caused by the natural spatial variability of soils and rocks. In this paper, a novel randomization approach is proposed to propagate the small-scale spatial heterogeneities into samples of profiles within a nonstationary probabilistic framework, to be further used in one-dimensional (1D) GRAs. The nonstationary approach is based on partitioning a borehole base-case profile into several locally stationary layers. The proposed approach was applied at three European sites exhibiting different subsurface soil conditions. Compared with both the classical stationary and an approach from the literature for randomization, the proposed approach provides a set of profiles fully consistent with the pseudoexperimental site signatures in terms of surface-wave dispersion curves, fundamental and higher-mode resonance frequencies, and site amplification. This paper also outlines the importance of the method used to measure profile in both the estimation of depth-dependent variability of at a given site and the prediction of site response variability.
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Data Availability Statement
The codes developed for the spatial variability quantification of the shear-wave velocity and the random field discretization are available online in a GitLab repository with detailed commentary, hosted at https://gricad-gitlab.univ-grenoble-alpes.fr/youssefe/variability-quantification-and-discretization-of-random-fields. The sets of shear-wave velocity profiles developed at the InterPACIFIC sites are also available from the corresponding author upon request.
Acknowledgments
This work benefited from the support and funding provided by the IRD (France) through the ARTS program, the Lebanese University, and the University of Grenoble Alpes. The authors are also thankful for three anonymous reviewers, editorial board member Robb Eric Moss, and an associate editor, for their invaluable feedback, which greatly contributed to improving the quality and clarity of this manuscript.
References
Al-Bittar, T., and A.-H. Soubra. 2013. “Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion.” Int. J. Numer. Anal. Methods Geomech. 37 (13): 2039–2060. https://doi.org/10.1002/nag.2120.
Al-Bittar, T., A.-H. Soubra, and J. Thajeel. 2018. “Kriging-based reliability analysis of strip footings resting on spatially varying soils.” J. Geotech. Geoenviron. Eng. 144 (10): 04018071. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001958.
Assimaki, D., A. Pecker, R. Popescu, and J. Prevost. 2003. “Effects of spatial variability of soil properties on surface ground motion.” J. Earthquake Eng. 7 (1): 1–44. https://doi.org/10.1142/S1363246903000973.
Baise, L., E. M. Thompson, J. Kaklamanos, and L. Dorfmann. 2011. “Complex site response: Does one-dimensional site response work.” In Proc., 4th Int. Sym. on the Effects of Surface Geology on Seismic Motion. Santa Barbara, CA: Univ. of California.
Blatman, G., and B. Sudret. 2010. “An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis.” Probab. Eng. Mech. 25 (2): 183–197. https://doi.org/10.1016/j.probengmech.2009.10.003.
Brown, L. T., D. M. Boore, and K. H. Stokoe. 2002. “Comparison of shear-wave slowness profiles at 10 strong-motion sites from noninvasive SASW measurements and measurements made in boreholes.” Bull. Seismol. Soc. Am. 92 (8): 3116–3133. https://doi.org/10.1785/0120020030.
Comina, C., S. Foti, D. Boiero, and L. V. Socco. 2011. “Reliability of VS30 evaluation from surface-wave tests.” J. Geotech. Geoenviron. Eng. 137 (6): 579–586. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000452.
DeGroot, D. J. 1996. “Analyzing spatial variability of in situ soil properties.” In Uncertainty in the geologic environment: From theory to practice, 210–238. Reston, VA: ASCE.
De la Torre, C., B. Bradley, and C. McGann. 2022. “2D Geotechnical site-response analysis including soil heterogeneity and wave scattering.” Earthquake Spectra 38 (2): 1124–1147. https://doi.org/10.1177/87552930211056667.
De Martin, F., E. Chaljub, P. Thierry, P. Sochala, F. Dupros, E. Maufroy, B. Hadri, A. Benaichouche, and F. Hollender. 2021. “Influential parameters on 3-D synthetic ground motions in a sedimentary basin derived from global sensitivity analysis.” Geophys. J. Int. 227 (3): 1795–1817. https://doi.org/10.1093/gji/ggab304.
Einsele, G. 2000. Sedimentary basins: Evolution, facies, and sediment budget. New York: Springer.
El Haber, E., C. Cornou, D. Jongmans, D. Y. Abdelmassih, F. Lopez-Caballero, and T. Al-Bittar. 2019. “Influence of 2D heterogeneous elastic soil properties on surface ground motion spatial variability.” Soil Dyn. Earthquake Eng. 123 (Aug): 75–90. https://doi.org/10.1016/j.soildyn.2019.04.014.
Fenton, G. 1999. “Random field modeling of CPT data.” J. Geotech. Geoenviron. Eng. 125 (6): 486–498. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:6(486).
Foti, S., et al. 2018. “Guidelines for the good practice of surface wave analysis: A product of the InterPACIFIC project.” Bull. Earthquake Eng. 16 (6): 2367–2420. https://doi.org/10.1007/s10518-017-0206-7.
Garofalo, F., et al. 2016a. “InterPACIFIC project: Comparison of invasive and non-invasive methods for seismic site characterization. Part I: Intra-comparison of surface wave methods.” Soil Dyn. Earthquake Eng. 82 (Mar): 222–240. https://doi.org/10.1016/j.soildyn.2015.12.010.
Garofalo, F., S. Foti, F. Hollender, P. Y. Bard, C. Cornou, B. R. Cox, A. Dechamp, M. Ohrnberger, D. Sicilia, and C. Vergniault. 2016b. “InterPACIFIC project: Comparison of invasive and non-invasive methods for seismic site characterization. Part II: Inter-comparison between surface-wave and borehole methods.” Soil Dyn. Earthquake Eng. 82 (Mar): 241–254. https://doi.org/10.1016/j.soildyn.2015.12.009.
Griffiths, D., J. Huang, and G. Fenton. 2009. “Influence of spatial variability on slope reliability using 2-D random fields.” J. Geotech. Geoenviron. Eng. 135 (10): 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099.
Griffiths, S. C., B. R. Cox, E. M. Rathje, and D. P. Teague. 2016a. “Mapping dispersion misfit and uncertainty in Vs profiles to variability in site response estimates.” J. Geotech. Geoenviron. Eng. 142 (11): 04016062. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001553.
Griffiths, S. C., B. R. Cox, E. M. Rathje, and D. P. Teague. 2016b. “Surface-wave dispersion approach for evaluating statistical models that account for shear-wave velocity uncertainty.” J. Geotech. Geoenviron. Eng. 142 (11): 04016061. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001552.
Haldar, S., and G. S. Babu. 2008. “Effect of soil spatial variability on the response of laterally loaded pile in undrained clay.” Comput. Geotech. 35 (4): 537–547. https://doi.org/10.1016/j.compgeo.2007.10.004.
Hallal, M. M., and B. R. Cox. 2021. “An H/V geostatistical approach for building pseudo-3D Vs models to account for spatial variability in ground response analyses II: Application to 1D analyses at two downhole array sites.” Earthquake Spectra 37 (3): 1931–1954. https://doi.org/10.1177/8755293020981982.
Hallal, M. M., B. R. Cox, S. Foti, A. Rodriguez-Marek, and E. R. Rathje. 2022a. “Improved implementation of the travel time randomization method for incorporating Vs uncertainty in ground response analyses.” Soil Dyn. Earthquake Eng. 157 (Jun): 107277. https://doi.org/10.1016/j.soildyn.2022.107277.
Hallal, M. M., B. R. Cox, and J. Vantasel. 2022b. “Comparison of state-of-the-art approaches used to account for spatial variability in 1D ground response analyses.” J. Geotech. Geoenviron. Eng. 148 (5): 04022019. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002774.
Hallo, M., P. Bergamo, and D. Fäh. 2022. “Stochastic model to characterize high-frequency ground motion at depth validated by KiK-Net vertical array data.” Bull. Seismol. Soc. Am. 112 (4): 1997–2017. https://doi.org/10.1785/0120220038.
Imperatori, W., and P. M. Mai. 2013. “Broad-band near-field ground motion simulations in 3-dimensional scattering media.” Geophys. J. Int. 192 (2): 725–744. https://doi.org/10.1093/gji/ggs041.
Jaksa, M. B. 1995. “The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Adelaide.
Jamshidi Chenari, R., and H. Kamyab Farahbakhsh. 2015. “Generating non-stationary random fields of auto-correlated, normally distributed CPT profile by matrix decomposition method.” Georisk: Assess. Manage. Risk Eng. Syst. Geohazards 9 (2): 96–108. https://doi.org/10.1080/17499518.2015.1033429.
Jamshidi Chenari, R., H. Kamyab Farahbakhsh, S. Heidarie Golafzani, and A. Eslami. 2018. “Non-stationary realization of CPT data: Considering lithological and inherent heterogeneity.” Georisk: Assess. Manage. Risk Eng. Syst. Geohazards 12 (4): 265–278. https://doi.org/10.1080/17499518.2018.1447675.
Jiang, S., and J. Huang. 2018. “Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis.” Soils Found. 58 (1): 185–198. https://doi.org/10.1016/j.sandf.2017.11.006.
Kaklamanos, J., and B. A. Bradley. 2018. “Challenges in predicting seismic site response with 1D analyses: Conclusions from 114 KiK-net vertical seismometer arrays.” Bull. Seismol. Soc. Am. 108 (5): 2816–2838. https://doi.org/10.1785/0120180062.
Kaklamanos, J., B. A. Bradley, A. N. Moolacattu, and B. M. Picard. 2020. “Physical hypotheses for adjusting coarse profiles and improving 1D site-response estimation assessed at 10 KiK-net sites.” Bull. Seismol. Soc. Am. 110 (3): 1338–1358. https://doi.org/10.1785/0120190263.
Kennet, B. 1983. Seismic wave propagation in stratified media. Canberra, Australia: ANU Press.
Kleiber, W. 2016. “High resolution simulation of nonstationary Gaussian random fields.” Comput. Stat. Data Anal. 101 (Sep): 277–288. https://doi.org/10.1016/j.csda.2016.03.005.
Kottke, A., and E. Rathje. 2009. Technical manual for Strata. Berkley, CA: Pacific Earthquake Engineering Research Center.
Kramer, S. L. 1996. Geotechnical earthquake engineering. Upper Saddle River, NJ: Prentice Hall.
Laurendeau, A., P. Y. Bard, F. Hollender, V. Perron, L. Foundotos, O. J. Ktenidou, and B. Hernandez. 2018. “Derivation of consistent hard rock () GMPEs from surface and down-hole recordings: Analysis of KiK-net data.” Bull. Earthquake Eng. 16 (6): 2253–2284. https://doi.org/10.1007/s10518-017-0142-6.
Li, C.-C., and A. Der Kiureghian. 1993. “Optimal discretization of random fields.” J. Eng. Mech. 119 (6): 1136–1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
Li, W., and D. Assimaki. 2010. “Site-and motion-dependent parametric uncertainty of site-response analyses in earthquake simulations.” Bull. Seismol. Soc. Am. 100 (3): 954–968. https://doi.org/10.1785/0120090030.
Montoya-Noguera, S., T. Zhao, Y. Hu, Y. Wang, and K.-K. Phoon. 2019. “Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen-Loève expansion.” Struct. Saf. 79 (Jul): 66–79. https://doi.org/10.1016/j.strusafe.2019.03.006.
Nour, A., A. Slimani, N. Laouami, and H. Afra. 2003. “Finite element model for the probabilistic seismic response of heterogeneous soil profile.” Soil Dyn. Earthquake Eng. 23 (5): 331–348. https://doi.org/10.1016/S0267-7261(03)00036-8.
Pagliaroli, A., M. Moscatelli, G. Raspa, and G. Naso. 2014. “Seismic microzonation of the central archaeological area of Rome: Results and uncertainties.” Bull. Earthquake Eng. 12 (3): 1405–1428. https://doi.org/10.1007/s10518-013-9480-1.
Parolai, S., D. Bindi, and M. Pilz. 2015. “k0: The role of intrinsic and scattering attenuation.” Bull. Seismol. Soc. Am. 105 (2A): 1049–1052. https://doi.org/10.1785/0120140305.
Passeri, F., C. Comina, L. V. Socco, and S. Foti. 2021. “The Polito Surface Wave flat-file Database (PSWD): Statistical properties of test results and some inter-method comparisons.” Bull. Earthquake. Eng. 19 (6): 2343–2370. https://doi.org/10.1007/s10518-021-01069-1.
Passeri, F., S. Foti, and A. Rodriguez-Marek. 2020. “A new geostatistical model for shear wave velocity profiles.” Soil Dyn. Earthquake Eng. 136 (Sep): 106247. https://doi.org/10.1016/j.soildyn.2020.106247.
Peng, B., J. Xu, and Y. Peng. 2022. “Efficient simulation of multivariate non-stationary ground motions based on a virtual continuous process and EOLE.” Mech. Syst. Signal Process. 184(Feb): 109722. https://doi.org/10.1016/j.ymssp.2022.109722.
Phoon, K.-K., and F. H. Kulhawy. 1996. “On quantifying inherent soil variability.” Geotech. Spec. Publ. 1996 (58 I): 326–340.
Phoon, K.-K., and F. H. Kulhawy. 1999a. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Phoon, K.-K., and F. H. Kulhawy. 1999b. “Evaluation of geotechnical property variability.” Can. Geotech. J. 36 (4): 625–639. https://doi.org/10.1139/t99-039.
Pilz, M., and F. Cotton. 2019. “Does the one-dimensional assumption hold for site response analysis? A study of seismic site responses and implication for ground motion assessment using KiK-net strong-motion data.” Earthquake Spectra 35 (2): 883–905. https://doi.org/10.1193/050718EQS113M.
Pilz, M., and D. Fäh. 2017. “The contribution of scattering to near-surface attenuation.” J. Seismol. 21 (4): 837–855. https://doi.org/10.1007/s10950-017-9638-4.
Popescu, R. 1995. “Stochastic variability of soil properties: Data analysis, digital simulation, effects on system behavior.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Princeton Univ.
Rathje, E. M., A. R. Kottke, and W. L. Trent. 2010. “Influence of input motion and site property variabilities on seismic site response analysis.” J. Geotech. Geoenviron. Eng. 136 (4): 607–619. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000255.
Rodriguez-Marek, A., E. M. Rathje, J. J. Bommer, F. Scherbaum, and P. J. Stafford. 2014. “Application of single-station sigma and site-response characterization in a probabilistic seismic-hazard analysis for a new nuclear site.” Bull. Seismol. Soc. Am. 104 (4): 1601–1619.
Salloum, N. 2015. “Evaluation de la variabilité spatiale des paramètres géotechniques du sol à partir de mesures géophysiques: Application à la plaine alluviale de Nahr-Beyrouth (Liban).” Ph.D. thesis, Institut des Sciences de la Terre, Univ. Joseph Fourier.
Shi, J., and D. Assimaki. 2018. “A generic velocity profile for basin sediments in California conditioned on VS30.” Seismol. Res. Lett. 89 (4): 1397–1409. https://doi.org/10.1785/0220170268.
Socco, L. V., and C. Strobbia. 2004. “Surface-wave method for near-surface characterization: A tutorial.” Near Surf. Geophys. 2 (4): 165–185. https://doi.org/10.3997/1873-0604.2004015.
Soubra, A.-H., and D. Youssef Abdel Massih. 2009. “Probabilistic analysis and design at the ultimate limit state of obliquely loaded strip footings.” Géotechnique 60 (4): 275–285. https://doi.org/10.1680/geot.7.00031.
Stewart, J., K. Afshari, and Y. Hashash. 2014. Guidelines for performing hazard-consistent one-dimensional ground response analysis for ground motion prediction. Berkeley, CA: Pacific Earthquake Engineering Research Center.
Sudret, B., and A. Der Kiureghian. 2000. Stochastic finite element methods and reliability: A state-of-the-art report. Berkeley, CA: Dept. of Civil and Environmental Engineering, Univ. of California.
Tao, Y., and E. Rathje. 2019. “Insights into modeling small-strain site response derived from downhole array data.” J. Geotech. Geoenviron. Eng. 145 (7): 04019023. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002048.
Tao, Y., and E. Rathje. 2020. “Taxonomy for evaluating the site-specific applicability of one-dimensional ground response analysis.” Soil Dyn. Earthquake Eng. 128 (Jan): 288–294. https://doi.org/10.1016/j.soildyn.2019.105865.
Tchawe, F. N., C. Gelis, L. F. Bonilla, and F. Lopez-Caballero. 2021. “Effects of 2-D random velocity perturbations on 2-D SH short-period ground motion simulations in the basin of Nice, France.” Geophys. J. Int. 226 (2): 847–861. https://doi.org/10.1093/gji/ggab141.
Teague, D. P., and B. R. Cox. 2016. “Site response implications associated with using non-unique Vs profiles from surface wave inversion in comparison with commonly used methods of accounting for Vs uncertainty.” Soil Dyn. Earthquake Eng. 91 (Dec): 87–103. https://doi.org/10.1016/j.soildyn.2016.07.028.
Teague, D. P., B. R. Cox, and E. M. Rathje. 2018. “Measured vs. predicted site response at the Garner Valley downhole array considering shear wave velocity uncertainty from borehole and surface wave methods.” Soil Dyn. Earthquake Eng. 113 (Oct): 339–355. https://doi.org/10.1016/j.soildyn.2018.05.031.
Thompson, E., L. Baise, Y. Tanaka, and R. Kayen. 2012. “A taxonomy of site response complexity.” Soil Dyn. Earthquake Eng. 41 (Oct): 32–43. https://doi.org/10.1016/j.soildyn.2012.04.005.
Thompson, E. M., L. G. Baise, R. E. Kayen, and B. B. Guzina. 2009. “Impediments to predicting site response: Seismic property estimation and modeling simplifications.” Bull. Seismol. Soc. Am. 99 (5): 2927–2949. https://doi.org/10.1785/0120080224.
Toro, G. 1995. Probabilistic models of the site velocity profiles for generic and site-specific ground-motion amplification studies. Technical Rep. No. 79574. New York: Brookhaven National Laboratory.
Toro, G. 2022. “Uncertainty in shear-wave velocity profiles.” J. Seismol. 26 (4): 713–730. https://doi.org/10.1007/s10950-022-10084-x.
Vanmarcke, E. 1983. Random fields: Analysis & synthesis. Cambridge, MA: MIT Press.
Vantassel, J. P., and B. R. Cox. 2021. “A procedure for developing uncertainty-consistent vs profiles from inversion of surface wave dispersion data.” Soil Dyn. Earthquake Eng. 145 (Jun): 106622. https://doi.org/10.1016/j.soildyn.2021.106622.
Wathelet, M., J.-L. Chatelain, C. Cornou, G. Di Giulio, B. Guillier, M. Ohrnberger, and A. Savvaidis. 2020. “Geopsy: A user-friendly open-source tool set for ambient vibration processing.” Seismol. Res. Lett. 91 (3): 1878–1889. https://doi.org/10.1785/0220190360.
Wathelet, M., D. Jongmans, and M. Ohrnberger. 2004. “Surface-wave inversion using a direct search algorithm and its application to ambient vibration measurements.” Near Surf. Geophys. 2 (4): 211–221. https://doi.org/10.3997/1873-0604.2004018.
Youssef Abdel Massih, D. 2007. “Analyse du comportement des fondations superficielles filantes par des approches fiabilistes.” Ph.D. thesis, Faculté des Sciences et des Techniques, Univ. of Nantes.
Zalachoris, G., and E. Rathje. 2015. “Evaluation of one-dimensional site response techniques using borehole arrays.” J. Geotech. Geoenviron. Eng. 141 (12): 04015053. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001366.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 150 • Issue 10 • October 2024
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© 2024 American Society of Civil Engineers.
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Received: Apr 27, 2023
Accepted: May 7, 2024
Published online: Aug 12, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 12, 2025
ASCE Technical Topics:
- Chemical properties
- Chemistry
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Environmental engineering
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fluid velocity
- Geomechanics
- Geotechnical engineering
- Geotechnical investigation
- Ground motion
- Heterogeneity
- Hydraulic engineering
- Hydrologic engineering
- Motion (dynamics)
- Seismic tests
- Seismic waves
- Shear waves
- Soil mechanics
- Soil properties
- Solid mechanics
- Tests (by type)
- Uncertainty principles
- Water and water resources
- Wave velocity
- Waves (fluid mechanics)
- Waves (mechanics)
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- E. Youssef, C. Cornou, D. Youssef Abdel Massih, T. Al-Bittar, A. Yong, F. Hollender, Application of non-stationary shear-wave velocity randomization approach to predict 1D seismic site response and its variability at two downhole array recordings, Soil Dynamics and Earthquake Engineering, 10.1016/j.soildyn.2024.108945, 186, (108945), (2024).