Abstract
Soil exhibits inherent spatial variability, creating a significant source of uncertainty in geotechnical assessments. This variability becomes particularly critical when evaluating the seismic performance of infrastructure such as multi-span highway bridges, since traditional methodologies in bridge design often oversimplify soil properties by assuming uniformity. This approach, however, may lead to considerable inaccuracies in determining structural response under seismic activity. The complexity of soil–structure interaction (SSI) in such multi-span structures further exacerbates the influence of soil spatial variability on the overall structural response to seismic events. Although numerous studies have explored the impact of spatial variation in ground motions on seismic performance, a noticeable gap exists in the literature addressing soil spatial variability in the SSI modeling and its impact in the seismic response of multi-span bridges. Accordingly, this research aims to address this gap by proposing a numerical framework that integrates the inherent spatial variability of soil in SSI modeling by means of random fields theory and 3D nonlinear dynamic finite element models into the seismic performance analysis of multi-span bridges. The findings from a case study reveals a significant influence of soil spatial variability on structural response, leading to discrepancies in vulnerability assessment between different bridge components and highlighting the importance of incorporating spatial variability in soil parameters into seismic assessments of bridges. Moreover, soil variability appeared to slightly impact system-level vulnerability. Although the main conclusions are developed from a case study and are applicable to bridges with similar characteristics and seismic demand, the proposed approach can readily be applied to other bridge configurations and seismic environments.
Similar content being viewed by others
Data availability
Some or all data, models, or codes that support the findings of this study are available from the corresponding authors or other authors upon reasonable request.
References
AASHTO 2nd L (2017) Bridge design specifications. American Association of State Highway and Transportation Officials, Washington, DC
Akhoondi MR, Behnamfar F (2021) Seismic fragility curves of steel structures including soil–structure interaction and variation of soil parameters. Soil Dyn Earthq Eng 143:106609. https://doi.org/10.1016/J.SOILDYN.2021.106609
Aldea S, Bazaez R, Astroza R, Hernandez F (2021) Seismic fragility assessment of Chilean skewed highway bridges. Eng Struct 249:113300. https://doi.org/10.1016/J.ENGSTRUCT.2021.113300
Bakalis K, Vamvatsikos D (2018) Seismic fragility functions via nonlinear response history analysis. J Struct Eng 144:4018181. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002141
Baker J (2011) Conditional Mean spectrum: tool for ground-motion selection. J Struct Eng 137:322–3311943. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000215
Baker JW (2015) Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 31:579–599. https://doi.org/10.1193/021113EQS025M
Birrell M, Astroza R, Carreño R et al (2021a) Bayesian parameter and joint probability distribution estimation for a hysteretic constitutive model of reinforcing steel. Struct Saf 90:102062. https://doi.org/10.1016/J.STRUSAFE.2020.102062
Birrell M, Astroza R, Restrepo JI et al (2021b) Bayesian inference for calibration and validation of uniaxial reinforcing steel models. Eng Struct 243:112386. https://doi.org/10.1016/J.ENGSTRUCT.2021.112386
Boulanger RW, Curras CJ, Kutter BL et al (1999) Seismic soil-pile-structure interaction experiments and analyses. J Geotech Geoenviron Eng 125:750–759. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:9(750)
Bozorgzadeh A, Ashford SA, Restrepo JI, Nimityongskul N (2008) Experimental and analytical investigation on stiffness and ultimate capacity of bridge abutments. Structural Systems Research Project, University of California, San Diego Report No. SSRP-07/12,
Candia G, Macedo J, Jaimes MA, Magna-Verdugo C (2019) A new state-of-the-art platform for probabilistic and deterministic seismic hazard assessment. Seismol Res Lett 90:2262–2275. https://doi.org/10.1785/0220190025
Carreño R, Lotfizadeh KH, Conte JP, Restrepo JI (2020) Material model parameters for the Giuffrè-Menegotto-Pinto uniaxial steel stress–strain model. J Struct Eng 146:04019205. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002505
Castro S, Benavente R, Crempien JGF et al (2022) A consistently processed strong-motion database for Chilean earthquakes. Seismol Res Lett 93:2700–2718. https://doi.org/10.1785/0220200336
Conde Bandini PA, Padgett JE, Paultre P, Siqueira GH (2022) Seismic fragility of bridges: an approach coupling multiple-stripe analysis and Gaussian mixture for multicomponent structures. Earthq Spectra 38:254–282. https://doi.org/10.1177/87552930211036164
Davis JC, Sampson RJ (1986) Statistics and data analysis in geology. Wiley, New York
DeGroot DJ, Baecher GB (1993) Estimating autocovariance of insitu soil properties. J Geotechn Eng 119:147–166. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147)
Deodatis G, Shinozuka M (1989) Simulation of seismic ground motion using stochastic waves. J Eng Mech 115:2723–2737. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2723)
Duncan M, Mokwa R (2001) Passive Earth Pressures: Theories and Tests. Journal of Geotechnical and Geoenvironmental Engineering 127(3):248–257. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:3(248)
Der Kiureghian A, Bin KJ (1988) The stochastic finite element method in structural reliability. Probab Eng Mech 3:83–91. https://doi.org/10.1016/0266-8920(88)90019-7
Fayaz J, Medalla M, Zareian F (2020) Sensitivity of the response of Box-Girder seat-type bridges to the duration of ground motions arising from crustal and subduction earthquakes. Eng Struct 219:110845. https://doi.org/10.1016/J.ENGSTRUCT.2020.110845
Fenton GA, Griffiths DV (2003) Bearing-capacity prediction of spatially random c–φ soils. Can Geotechn J 40(1):54–65. https://doi.org/10.1139/t02-086
Fenton GA, Griffiths DV et al (2008) Risk assessment in geotechnical engineering. Wiley, New York
Ghosh J, Sood P (2016) Consideration of time-evolving capacity distributions and improved degradation models for seismic fragility assessment of aging highway bridges. Reliability Engineering & System Safety 154:197–218. https://doi.org/10.1016/j.ress.2016.06.001
Griffiths DV, Huang J, Fenton GA (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotechn Geoenviron Eng 135:1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099
Griffiths DV, Fenton GA (2000) Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. In: Proceedings of sessions of geo-denver 2000: slope stability 2000, GSP 101 289, pp 184–193. https://doi.org/10.1061/40512(289)14
Haldar S, Babu GLS (2008) Effect of soil spatial variability on the response of laterally loaded pile in undrained clay. Comput Geotech 35:537–547. https://doi.org/10.1016/j.compgeo.2007.10.004
Haldar S, Sharma J, Basu D (2018) Probabilistic analysis of monopile-supported offshore wind turbine in clay. Soil Dyn Earthq Eng 105:171–183. https://doi.org/10.1016/j.soildyn.2017.11.028
Hedayati Dezfuli F, Alam MS (2017) Effect of different steel-reinforced elastomeric isolators on the seismic fragility of a highway bridge. Struct Control Health Monit 24: https://doi.org/10.1002/stc.1866
Hu H, Huang Y (2019) PDEM-based stochastic seismic response analysis of sites with spatially variable soil properties. Soil Dyn Earthq Eng 125: https://doi.org/10.1016/j.soildyn.2019.105736
Idini B, Rojas F, Ruiz S, Pastén C (2017) Ground motion prediction equations for the Chilean subduction zone. Bull Earthq Eng 15:1853–1880. https://doi.org/10.1007/s10518-016-0050-1
Johari A, Hosseini SM, Keshavarz A (2017) Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method. Comput Geotech 91:203–217. https://doi.org/10.1016/J.COMPGEO.2017.07.019
Jones AL, Kramer SL, Arduino P (2002) Estimation of uncertainty in geotechnical properties for performance-based earthquake engineering. Pacific Earthquake Engineering Research Center, College of Engineering
Kim S-H, Feng MQ (2003) Fragility analysis of bridges under ground motion with spatial variation. Int J Non Linear Mech 38:705–721. https://doi.org/10.1016/S0020-7462(01)00128-7
Koutsourelakis S, Prévost JH, Deodatis G (2002) Risk assessment of an interacting structure-soil system due to liquefaction. Earthq Eng Struct Dyn 31:851–879. https://doi.org/10.1002/eqe.125
Li D-Q, Jiang S-H, Cao Z-J et al (2015) A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Eng Geol 187:60–72. https://doi.org/10.1016/j.enggeo.2014.12.003
Li C, Diao Y, Li HN et al (2023) Seismic performance assessment of a sea-crossing cable-stayed bridge system considering soil spatial variability. Reliab Eng Syst Saf 235:109210. https://doi.org/10.1016/J.RESS.2023.109210
Mackie K, Stojadinovic B (2003) Seismic demands for performance-based design of bridges, PEER Report 2003–16. California
Mangalathu S, Jeon J-S (2019) Machine learning–based failure mode recognition of circular reinforced concrete bridge columns: comparative study. J Struct Eng 145:4019104. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002402
Martínez A, Hube MA, Rollins KM (2017) Analytical fragility curves for non-skewed highway bridges in Chile. Eng Struct 141:530–542. https://doi.org/10.1016/J.ENGSTRUCT.2017.03.041
McKenna F, Fenves GL, Scott MH, Jeremic B (2000) Open system for earthquake engineering simulation (OpenSees). Pacific Earthquake Engineering Research Center, University of California, Berkeley
Montalva G, Bastias N, Rodriguez-Marek A (2017) Ground-motion prediction equation for the Chilean subduction zone. Bull Seismol Soc Am 107:901–911. https://doi.org/10.1785/0120160221
Poulos A, Monsalve M, Zamora N, De la Llera JC (2019) An updated recurrence model for Chilean subduction seismicity and statistical validation of its Poisson nature. Bulletin of the Seismological Society of America 109(1):66–74. https://doi.org/10.1785/0120170160
Rubilar F (2015) Modelo no lineal para predecir la respuesta sísmica de pasos superiores. Pontificia Universidad Catolica de Chile (Chile)
Nazmy AS, Abdel-Ghaffar AM (1992) Effects of ground motion spatial variability on the response of cable-stayed bridges. Earthq Eng Struct Dyn 21:1–20. https://doi.org/10.1002/eqe.4290210101
Nour A, Slimani A, Laouami N, Afra H (2003) Finite element model for the probabilistic seismic response of heterogeneous soil profile. Soil Dyn Earthq Eng 23:331–348. https://doi.org/10.1016/S0267-7261(03)00036-8
O’Reilly GJ (2021) Seismic intensity measures for risk assessment of bridges. Bull Earthq Eng 19:3671–3699. https://doi.org/10.1007/S10518-021-01114-Z
Paice GM, Griffiths DV, Fenton GA (1996) Finite element modeling of settlements on spatially random soil. J Geotechn Eng 122:777–779. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(777)
Phoon K-K, Kulhawy FH (1999a) Characterization of geotechnical variability. Can Geotech J 36:612–624. https://doi.org/10.1139/t99-038
Phoon K-K, Kulhawy FH (1999b) Evaluation of geotechnical property variability. Can Geotech J 36:625–639. https://doi.org/10.1139/t99-039
Phoon K-K, Cao Z-J, Ji J et al (2022) Geotechnical uncertainty, modeling, and decision making. Soils Found 62: https://doi.org/10.1016/j.sandf.2022.101189
Pinto FJ, Toledo J, Birrell M et al (2023) Uncertainty quantification in constitutive models of highway bridge components: seismic bars and elastomeric bearings. Materials 16:1792. https://doi.org/10.3390/ma16051792
Popescu R (1995) Stochastic variability of soil properties: data analysis, digital simulation, effects on system behavior. Princeton University
Popescu R, Prevost JH, Deodatis G (1996) Effects of spatial variability on soil liquefaction: some design recommendations. Geotechnique. https://doi.org/10.1680/geot.1997.47.5.1019
Popescu R, Deodatis G, Nobahar A (2005a) Effects of random heterogeneity of soil properties on bearing capacity. Probab Eng Mech 20:324–341. https://doi.org/10.1016/j.probengmech.2005.06.003
Popescu R, Prevost JH, Deodatis G (2005b) 3D effects in seismic liquefaction of stochastically variable soil deposits. Géotechnique 55:21–31. https://doi.org/10.1680/geot.2005.55.1.21
Popescu R, Chakrabortty P, Prevost JH (2005) Fragility curves for tall structure on stochastically variable soil. Proc of 9th International Conference on Structural Safety and Reliability (ICOSSAR), Rome, Italy.
Puła W, Chwała M (2015) On spatial averaging along random slip lines in the reliability computations of shallow strip foundations. Comput Geotech 68:128–136. https://doi.org/10.1016/J.COMPGEO.2015.04.001
Robertson PK (1990) Soil classification using the cone penetration test. Can Geotech J 27:151–158. https://doi.org/10.1139/t90-014
Robertson PK (2010) Soil behaviour type from the CPT: an update. Proc 2nd international symposium on cone penetration testing, Huntington Beach, CA, USA.
Sextos AG, Pitilakis KD, Kappos AJ (2003) Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion, site effects and soil–structure interaction phenomena. Part 1: methodology and analytical tools. Earthq Eng Struct Dyn 32:607–627. https://doi.org/10.1002/eqe.241
Stefanidou SP, Kappos AJ (2017) Methodology for the development of bridge-specific fragility curves. Earthq Eng Struct Dyn 46:73–93. https://doi.org/10.1002/eqe.2774
Stefanidou SP, Kappos AJ (2019) Bridge-specific fragility analysis: When is it really necessary? Bull Earthq Eng 17:2245–2280. https://doi.org/10.1007/s10518-018-00525-9
Stefanidou SP, Kappos AJ (2021) Fragility-informed selection of bridge retrofit scheme based on performance criteria. Eng Struct 234: https://doi.org/10.1016/j.engstruct.2021.111976
Stefanidou SP, Paraskevopoulos EA, Papanikolaou VK, Kappos AJ (2022) An online platform for bridge-specific fragility analysis of as-built and retrofitted bridges. Bull Earthq Eng 20:1717–1737. https://doi.org/10.1007/S10518-021-01299-3
Vanmarcke E (2010) Fundamentals of analysis of random fields. Random Fields. https://doi.org/10.1142/9789814307598_0002
Vanmarcke E, Shinozuka M, Nakagiri S et al (1986) Random fields and stochastic finite elements. Struct Saf 3:143–166. https://doi.org/10.1016/0167-4730(86)90002-0
Wijaya H, Rajeev P, Gad E (2019) Effect of seismic and soil parameter uncertainties on seismic damage of buried segmented pipeline. Transp Geotech 21: https://doi.org/10.1016/j.trgeo.2019.100274
Wilches J, Santa María H, Riddell R, Arrate C (2019) Effects of changes in seismic design criteria in the transverse and vertical response of Chilean highway bridges. Eng Struct 191:370–385. https://doi.org/10.1016/j.engstruct.2019.04.064
Xiao T, Li D-Q, Cao Z-J et al (2016) Three-dimensional slope reliability and risk assessment using auxiliary random finite element method. Comput Geotech 79:146–158. https://doi.org/10.1016/j.compgeo.2016.05.024
Xiao-ling Z, Bo-han J, Yan H, Shong-loong C, Xiu-yu L (2021) Random field model of soil parameters and the application in reliability analysis of laterally loaded pile. Soil Dynamics and Earthquake Engineering 147: https://doi.org/10.1016/j.soildyn.2021.106821
Yamazaki F, Shinozuka M (1988) Digital generation of non-Gaussian stochastic fields. J Eng Mech 114:1183–1197. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:7(1183)
Yoon S, Lee DH, Jung H-J (2019) Seismic fragility analysis of a buried pipeline structure considering uncertainty of soil parameters. Int J Press Vessels Pip 175:103932. https://doi.org/10.1016/j.ijpvp.2019.103932
Zerva A (1991) Effect of spatial variability and propagation of seismic ground motions on the response of multiply supported structures. Stoch Struct Dyn 2:307–336. https://doi.org/10.1007/978-3-642-84534-5_17
Zerva A (1992) Seismic ground motion simulations from a class of spatial variability models. Earthq Eng Struct Dyn 21:351–361. https://doi.org/10.1002/EQE.4290210406
Acknowledgements
This research was funded by the National Research and Development Agency (ANID) through the FONDECYT project 1200277 “Uncertainty-informed multi-hazard risk evaluation of degrading civil structures” and the FONDECYT POSTDOCTORAL project 3230313 “Elucidating the effects of dynamic nonlinear soil–structure interaction of structures through high-fidelity FE modeling”. The “Fondo de Ayuda a la Investigación” of the Universidad de los Andes (Chile) through a Postdoctoral fellowship also partially funded the present study.
Funding
ANID FONDECYT Projects #1200277 and #3230313, and Universidad de los Andes FAI Postdoctoral Fellowship.
Author information
Authors and Affiliations
Contributions
Conceptualization: FJP, RA; methodology: FP, RA; Formal analysis and investigation: BG, FP, RA; Writing—original draft preparation: BG, FP; Writing—review and editing: FP, RA; Funding acquisition: RA, FP; Resources: RA, FP; Supervision: FP, RA.
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Guajardo, B., Pinto, F. & Astroza, R. Effects of soil spatial variability on the seismic response of multi-span simply-supported highway bridges. Bull Earthquake Eng 22, 2643–2675 (2024). https://doi.org/10.1007/s10518-024-01872-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-024-01872-6