Abstract
Soil properties vary in space even within a soil layer. Nevertheless, site response analyses are typically conducted using a best-characterized shear wave velocity (Vs) profile without considering its fluctuation. In this study, the random field theory is adopted to model heterogeneous Vs profiles for a range of coefficient of variations (COVs) and correlation lengths (CLs). Linear 1D site responses are analyzed with the randomized profiles to quantify the influence of spatial Vs variation on the propagated ground motions. Results reveal that a higher COV of randomized Vs profiles leads to a lower mean ground response compared with a homogeneous Vs profile. The variation of CL does not significantly affect the surface response and peak ground acceleration profile, but is shown to influence the degree of fluctuation of the maximum shear strain profiles. For idealized profiles, the effect of heterogeneous Vs on ground response can be approximately predicted by using reduced Vs and enlarged small strain damping that are dependent on COV.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- Cov :
-
Covariation matrix
- COV:
-
Coefficient of variation
- d i :
-
Displacement of layer i
- f :
-
Frequency
- f thres :
-
Threshold frequency
- h :
-
Separation distance between two points
- h i :
-
Thickness of layer i
- Vs:
-
Shear wave velocity
- \(\overline {\rm{V}} {\rm{s}}\) :
-
Equivalent shear wave velocity
- Vs,i:
-
Shear wave velocity of layer i
- w :
-
Variability function
- γ i :
-
Strain of layer i
- λ :
-
Wavelength
- μ :
-
Local mean property
- ξ heter :
-
Additional damping owing to heterogeneity
- ρ ij :
-
Correlation for any point i and j in the space
- σ :
-
Standard deviation
- σ i :
-
Standard deviation of point i
- σ j :
-
Standard deviation of point j
References
Assimaki A, Pecker A, Popescu R, Prevost J (2003) Effects of spatial variability of soil roperties on surface ground motion. Journal of Earthquake Engineering 7(SP1):1–44, DOI: https://doi.org/10.1080/13632460309350472
Bazzurro P, Cornell CA (2004) Ground-motion amplification in nonlinear soil sites with uncertain properties. Bulletin of the Seismological Society of America 94(6):2090–2109, DOI: https://doi.org/10.1785/0120030215
Chen Q, Seifried A, Andrade JE, Baker JW (2012) Characterization of random fields and their impact on the mechanics of geosystems at multiple scales. International Journal for Numerical and Analytical Methods in Geomechanics 36:140–165, DOI: https://doi.org/10.1002/nag.999
DeGroot DJ, Baecher GB (1993) Estimating autocovariance of in-situ soil properties. Journal of Geotechnical Engineering 119:147–166, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147)
El Haber E, Cornou C, Jongmans D, Abdelmassih DY, Lopez-Caballero F, Al-Bittar T (2019) Influence of 2D heterogeneous elastic soil properties on surface ground motion spatial variability. Soil Dynamics and Earthquake Engineering 123:75–90, DOI: https://doi.org/10.1016/j.soildyn.2019.04.014
EPRI (1993) Guidelines for determining design basis ground motions. EPRI TR-102293, Electric Power Research Institute, Palo Alto, CA, USA
Fenton GA, Griffiths DV (2003) Bearing capacity prediction of spatially random c-ϕ soils. Canadian Geotechnical Journal 40:54–65, DOI: https://doi.org/10.1139/t02-086
Fenton GA, Griffiths DV (2008) Risk assessmentin geotechnical engineering. John Wiley & Sons, Inc., Hoboken, NJ, USA
Field EH, Jacob KH (1993) Monte Carlo simulation of the theoretical site response variability at Turkey Flat, California, given the uncertainty in the geotechnically derived input parameters. Earthquake Spectra 9(4):669–701, DOI: https://doi.org/10.1193/1.1585736
Griffiths SC, Cox BR, Rathje EM, Teague DP (2016) Mapping dispersion misfit and uncertainty in Vs profiles to variability in site response estimates. Journal of Geotechnical Engineering 142(11), DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0001553
Griffiths DV, Fenton GA (2000) Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. Geo-Denver 2000, August 5–8, Denver, CO, USA, DOI: https://doi.org/10.1061/10.1061/40512(289)14
Griffiths DV, Fenton GA, Monoharan N (2002) Bearing capacity of rough rigid strip footing on a cohesive soil: Probabilistic study. Journal of Geotechnical and Geoenvironmental Engineering 128:743–755, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743)
Haji-Soltani A, Pezeshk S (2017) A comparison of different approaches to incorporate site effects into PSHA: A case study for a liquefied natural gas tank. Bulletin of the Seismological Society of America 107(6):2927–2947, DOI: https://doi.org/10.1785/0120170026
Haldar S, Babu GLS (2007) Effects of soil variability on the response of lateral loaded pile in undrained clay. Computers and Geotechnics 35:537–547, DOI: https://doi.org/10.1016/j.compgeo.2007.10.004
Hashash YMA, Musgrove MI, Harmon JA, Groholski DR, Phillips CA, Park D (2016) DEEPSOIL6.1, User manual and tutorial. Board of Trustees of University of Illinois at Urbana-Champaign, Urbana, IL, USA
Hashash YMA, Tsai CC, Phillips C, Park D (2008) Soil-column depth-dependent seismic site coefficients and hazard maps for the Upper Mississippi Embayment. Bulletin of the Seismological Society of America 98(4):2004–2021, DOI: https://doi.org/10.1785/0120060174
Johari A, Momeni M (2015) Stochastic analysis of ground response using non-recursive algorithm. Soil Dynamics and Earthquake Engineering 69:57–82, DOI: https://doi.org/10.1016/j.soildyn.2014.10.025
Kottke A, Rathje EM (2009) Technical manual for strata. Pacific Earthquake Engineering Research Center, Berkeley, CA, USA
Koutsourelakis S, Prevost JH, Deodatis G (2002) Risk assessment of an interacting structure-soil system due to liquefaction. Earthquake Engineering Structural Dynamics 31:851–879, DOI: https://doi.org/10.1002/eqe.125
Kwok AOL, Stewart JP, Hashash YMA (2008) Nonlinear ground-response analysis of Turkey flat shallow stiff-soil site to strong ground motion. Bulletin of the Seismological Society of America 98(1):331–343, DOI: https://doi.org/10.1785/0120070009
Li W, Assimaki D (2010) Site- and motion-dependent parametric uncertainty of siteresponse analyses in earthquake simulations. Bulletin of the Seismological Society of America 100(3):954–968, DOI: https://doi.org/10.1785/0120090030
Nadi B, Tavasoli O, Esfeh PK, Kontoni DPN (2020) Characteristics of spatial variability of shear wave velocity on seismic response of slopes. Arabian Journal of Geosciences 13(16):800, DOI: https://doi.org/10.1007/s12517-020-05797-7
Nour A, Slimani A, Laouami N, Afra H (2003) Finite element model for the probabilistic seismic response of heterogeneous soil profile. Soil Dynamics and Earthquake Engineering 23(5):331–348, DOI: https://doi.org/10.1016/S0267-7261(03)00036-8
Paice GM, Griffiths DV, Fenton GA (1996) Finite element modelling of settlement on spatially random soil. Journal of Geotechnical Engineering 122:777–779, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(777)
Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Canadian Geotechnical Journal 36(4):612–624, DOI: https://doi.org/10.1139/t99-038
Popescu R, Prevost JH, Deodatis G (1997) Effects of spatial variability on soil liquefaction: Some design considerations. Géotechnique 47(5):1019–1036, DOI: https://doi.org/10.1680/geot.1997.47.5.1019
Popescu R, Prevost JH, Deodatis G (2005) 3D effects in seismic liquefaction of stochastically variable soil deposits. Géotechnique 55:21–31, DOI: https://doi.org/10.1680/geot.2005.55.1.21
Rathje EM, Kottke AR, Trent WL (2010) Influence of input motion and site property variabilities on seismic site response analysis. Journal of Geotechnical and Geoenvironmental Engineering 136(4):607–619, DOI: https://doi.org/10.1061/(Asce)Gt.1943-5606.0000255
Roblee C, Silva W, Toro G, Abrahamson N (1996) Variability in site-specific seismic ground-motion design predictions. In: Shackelford CD, Nelson PP, Roth MJS (eds) Uncertainty in the geologic environment: From theory to practice. ASCE Geotech Special Publication 58, 1113–1133
Rodriguez-Marek A, Rathje EM, Bommer JJ, Scherbaum F, Stafford PJ (2014) Application of single-station sigma and site-response characterization in a probabilistic seismic hazard analysis for a new nuclear site. Bulletin of the Seismological Society of America 104(4):1601–1619, DOI: https://doi.org/10.1785/0120130196
Salloum N, Jongmans D, Cornou C, Massih DYA, Chehade FH, Voisin C, Mariscal A (2014) The shear wave velocity structure of the heterogeneous alluvial plain of Beirut (Lebanon): Combined analysis of geophysical and geotechnical data. Geophysical Journal International 199(2):894–913, DOI: https://doi.org/10.1093/gji/ggu294
Song KI, Cho GC, Lee SW (2011) Effects of spatially variable weathered rock properties on tunnel behavior. Probabilistic Engineering Mechanics 26:413–426, DOI: https://doi.org/10.1016/j.probengmech.2010.11.010
Tao YM, Rathje E (2019) Insights into modeling small-strain site response derived from downhole array data. Journal of Geotechnical and Geoenvironmental Engineering 145(7), DOI: https://doi.org/10.1061/(Asce)Gt.1943-5606.0002048
Teague DP, Cox BR, Rathje EM (2018) Measured vs. predicted site response at the Garner Valley Downhole Array considering shear wave velocity uncertainty from borehole and surface wave methods. Soil Dynamics and Earthquake Engineering 113:339–355, DOI: https://doi.org/10.1016/j.soildyn.2018.05.031
Thompson EM, Baise LG, Kayen RE (2007) Spatial correlation of shear-wave velocity in the San Francisco Bay Area sediments. Soil Dynamics and Earthquake Engineering 27(2):144–152, DOI: https://doi.org/10.1016/j.soildyn.2006.05.004
Thompson EM, Baise LG, Kayen RE, Guzina BB (2009) Impediments to predicting site response: Seismic property estimation and modeling simplifications. Bulletin of the Seismological Society of America 99(5):2927–2949, DOI: https://doi.org/10.1785/0120080224
Toro G (1995) Probabilistic models of the site velocity profiles for generic and sitespecific ground-motion amplification studies. Technical Report No. 779574, Brookhaven National Laboratory, Upton, NY, USA
Tsai CC, Chang WS, Chiou JS (2017) Enhancing prediction of ground response at the Turkey Flat geotechnical array. Bulletin of the Seismological Society of America 107(5):2043–2054, DOI: https://doi.org/10.1785/0120160324
Tsai CC, Hashash YMA (2009) Learning of dynamic soil behavior from downhole arrays. Journal of Geotechnical and Geoenvironmental Engineering 135(6):745–757, DOI: https://doi.org/10.1061/(Asce)Gt.1943-5606.0000050
Tsai CC, Liu HW (2017) Site response analysis of vertical ground motion in consideration of soil nonlinearity. Soil Dynamics and Earthquake Engineering 102:124–136, DOI: https://doi.org/10.1016/j.soildyn.2017.08.024
Vanmarcke EH (1977) Probabilistic modeling of soil profiles. Journal of Geotechnical Engineering Division 119(1):147–166, DOI: https://doi.org/10.1061/AJGEB6.0000517
Vanmarcke EH (1983) Random fields: Analysis and synthesis. The MIT Press, London, UK
Yee E, Stewart JP, Tokimatsu K (2013) Elastic and large-strain nonlinear seismic site response from analysis of vertical array recordings. Journal of Geotechnical and Geoenvironmental Engineering 139(10): 1789–1801, DOI: https://doi.org/10.1061/(Asce)Gt.1943-5606.0000900
Acknowledgments
This work was supported by the Ministry of Science and Technology, Taiwan under Award No. 108-2628-E-005-001-MY3.
The authors gratefully acknowledge such support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, YH., Tsai, CC., Huang, CC. et al. Effect of Intra-layer Vs Fluctuation on Linear Seismic Site Response. KSCE J Civ Eng 25, 3701–3713 (2021). https://doi.org/10.1007/s12205-021-2047-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-021-2047-9