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Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground

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Abstract

Seismic intensity measures (IMs) perform a pivotal role in probabilistic seismic demand modeling. Many studies investigated appropriate IMs for structures without considering soil liquefaction potential. In particular, optimal IMs for probabilistic seismic demand modeling of bridges in liquefied and laterally spreading ground are not comprehensively studied. In this paper, a coupled-bridge-soil-foundation model is adopted to perform an in-depth investigation of optimal IMs among 26 IMs found in the literature. Uncertainties in structural and geotechnical material properties and geometric parameters of bridges are considered in the model to produce comprehensive scenarios. Metrics such as efficiency, practicality, proficiency, sufficiency and hazard computability are assessed for different demand parameters. Moreover, an information theory based approach is adopted to evaluate the relative sufficiency among the studied IMs. Results indicate the superiority of velocity-related IMs compared to acceleration, displacement and time-related ones. In particular, Housner spectrum intensity (HI), spectral acceleration at 2.0 s (S a-20), peak ground velocity (PGV), cumulative absolute velocity (CAV) and its modified version (CAV 5) are the optimal IMs. Conversely, Arias intensity (I a ) and shaking intensity rate (SIR) which are measures often used in liquefaction evaluation or related structural demand assessment demonstrate very low correlations with the demand parameters. Besides, the geometric parameters do not evidently affect the choice of optimal IMs. In addition, the information theory based sufficiency ranking of IMs shows an identical result to that with the correlation measure based on coefficient of determination (R 2). This means that R 2 can be used to preliminarily assess the relative sufficiency of IMs.

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References

  • AASHTO (2012) AASHTO LRFD bridge design specifications, 6th edn. American Association of State Highway and Transportation Officials, Washington DC

    Google Scholar 

  • Acevedo AB, Jaramillo JD, Yepes C et al (2017) Evaluation of the seismic risk of the unreinforced masonry building stock in Antioquia, Colombia. Nat Hazards 86:31–54. doi:10.1007/s11069-016-2647-8

    Article  Google Scholar 

  • ACI committee (2011) Building code requirements for structural concrete (ACI 318-08) and commentary. American Concrete Institute, Farmington Hills

    Google Scholar 

  • Akkar S, Bommer JJ (2010) Empirical equations for the prediction of PGA, PGV, and spectral accelerations in Europe, the Mediterranean Region, and the Middle East. Seismol Res Lett 81:195–206. doi:10.1785/gssrl.81.2.195

    Article  Google Scholar 

  • Altman N, Krzywinski M (2016) Points of significance: p values and the search for significance. Nat Methods 14:3–4. doi:10.1038/nmeth.4120

    Article  Google Scholar 

  • Arias A (1970) A measure of earthquake intensity. In: Hansen RJ (ed) Seismic Design for Nuclear Power Plants. MIT Press, Cambridge, pp 438–483

    Google Scholar 

  • ATC (1978) Tentative provisions for the development of seismic regulations for buildings: a cooperative effort with the design professions, building code interests, and the research community. Department of Commerce, National Bureau of Standards

  • Aviram A, Mackie K, Stojadinović B (2008) Guidelines of nonlinear analysis of bridge structures in California. Pacific Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Aygün B, Dueñas-Osorio L (2011) Efficient longitudinal seismic fragility assessment of a multispan continuous steel bridge on liquefiable soils. J Bridg Eng 16:93–107. doi:10.1061/(ASCE)BE.1943-5592.0000131

    Article  Google Scholar 

  • Baker JW, Cornell CA (2005) A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 34:1193–1217. doi:10.1002/eqe.474

    Article  Google Scholar 

  • Baker JW, Cornell CA (2008) Vector-valued intensity measures for pulse-like near-fault ground motions. Eng Struct 30:1048–1057. doi:10.1016/j.engstruct.2007.07.009

    Article  Google Scholar 

  • Baker JW, Shahi SK (2011) New ground motion selection procedures and selected motions for the PEER transportation research program. Pacific Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Barbato M, Gu Q, Conte JP (2010) Probabilistic push-over analysis of structural and soil-structure systems. J Struct Eng 136:1330–1341. doi:10.1061/(ASCE)ST.1943-541X.0000231

    Article  Google Scholar 

  • Billah AHMM, Alam MS (2015) Seismic fragility assessment of highway bridges: a state-of-the-art review. Struct Infrastruct Eng 11:804–832. doi:10.1080/15732479.2014.912243

    Article  Google Scholar 

  • Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185. doi:10.1063/1.1721956

    Article  Google Scholar 

  • Bommer JJ, Acevedo AB (2004) The use of real earthquake accelerograms as input to dynamic analysis. J Earthq Eng 8:43–91. doi:10.1080/13632460409350521

    Google Scholar 

  • Bommer JJ, Martínez-Pereira A (1999) The effective duration of earthquake strong motion. J Earthq Eng 3:127–172. doi:10.1080/13632469909350343

    Google Scholar 

  • Boore DM, Atkinson GM (2008) Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s. Earthq Spectra 24:99–138. doi:10.1193/1.2830434

    Article  Google Scholar 

  • Bora SS, Scherbaum F, Kuehn N et al (2015) Development of a response spectral ground-motion prediction equation (GMPE) for seismic-hazard analysis from empirical fourier spectral and duration models. Bull Seismol Soc Am 105:2192–2218. doi:10.1785/0120140297

    Article  Google Scholar 

  • Bradley BA (2012) Empirical correlations between cumulative absolute velocity and amplitude-based ground motion intensity measures. Earthq Spectra 28:37–54. doi:10.1193/1.3675580

    Article  Google Scholar 

  • Bradley BA, Cubrinovski M, Dhakal RP, MacRae GA (2009a) Intensity measures for the seismic response of pile foundations. Soil Dyn Earthq Eng 29:1046–1058. doi:10.1016/j.soildyn.2008.12.002

    Article  Google Scholar 

  • Bradley BA, Cubrinovski M, MacRae GA, Dhakal RP (2009b) Ground-motion prediction equation for SI based on spectral acceleration equations. Bull Seismol Soc Am 99:277–285. doi:10.1785/0120080044

    Article  Google Scholar 

  • Bray J, Frost D, others (2010) Geo-engineering reconnaissance of the 2010 Maule, Chile earthquake. Report No. GEER-022, the NSF Sponsored GEER Association Team

  • Celarec D, Dolšek M (2013) The impact of modelling uncertainties on the seismic performance assessment of reinforced concrete frame buildings. Eng Struct 52:340–354. doi:10.1016/j.engstruct.2013.02.036

    Article  Google Scholar 

  • Chang D, Boulanger R, Brandenberg S, Kutter B (2013) FEM analysis of dynamic soil-pile-structure interaction in liquefied and laterally spreading ground. Earthq Spectra 29:733–755. doi:10.1193/1.4000156

    Article  Google Scholar 

  • Cornell CA, Jalayer F, Hamburger RO, Foutch DA (2002) Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. J Struct Eng 128:526–533. doi:10.1061/(ASCE)0733-9445(2002)128:4(526)

    Article  Google Scholar 

  • Cox BR, Boulanger RW, Tokimatsu K et al (2013) Liquefaction at Strong Motion Stations and in Urayasu City during the 2011 Tohoku-Oki Earthquake. Earthq Spectra 29:S55–S80. doi:10.1193/1.4000110

    Article  Google Scholar 

  • Danciu L, Tselentis GA (2007) Engineering ground-motion parameters attenuation relationships for Greece. Bull Seismol Soc Am 97:162–183. doi:10.1785/0120040087

    Article  Google Scholar 

  • Dashti S, Bray JD, Pestana JM et al (2010) Centrifuge testing to evaluate and mitigate liquefaction-induced building settlement mechanisms. J Geotech Geoenviron Eng 136:918–929. doi:10.1061/(ASCE)GT.1943-5606.0000306

    Article  Google Scholar 

  • Ebrahimian H, Jalayer F, Lucchini A et al (2015) Preliminary ranking of alternative scalar and vector intensity measures of ground shaking. Bull Earthq Eng. doi:10.1007/s10518-015-9755-9

    Google Scholar 

  • Elenas A, Meskouris K (2001) Correlation study between seismic acceleration parameters and damage indices of structures. Eng Struct 23:698–704. doi:10.1016/S0141-0296(00)00074-2

    Article  Google Scholar 

  • Esposito S, Iervolino I (2011) PGA and PGV spatial correlation models based on European multievent datasets. Bull Seismol Soc Am 101:2532–2541. doi:10.1785/0120110117

    Article  Google Scholar 

  • Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Gidaris I, Padgett JE, Barbosa AR et al (2017) Multiple-hazard fragility and restoration models of highway bridges for regional risk and resilience assessment in the United States: state-of-the-art review. J Struct Eng 143:4016188. doi:10.1061/(ASCE)ST.1943-541X.0001672

    Article  Google Scholar 

  • Giovenale P, Cornell CA, Esteva L (2004) Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses. Earthq Eng Struct Dyn 33:951–979. doi:10.1002/eqe.386

    Article  Google Scholar 

  • Housner GW (1959) Behavior of structures during earthquakes. J Eng Mech Div 85:109–130

    Google Scholar 

  • Hutchinson TC, Chai YH, Boulanger RW, Idriss IM (2004) Inelastic seismic response of extended pile-shaft-supported bridge structures. Earthq Spectra 20:1057–1080. doi:10.1193/1.1811614

    Article  Google Scholar 

  • Jalayer F, Beck JL, Zareian F (2012) Analyzing the sufficiency of alternative scalar and vector intensity measures of ground shaking based on information theory. J Eng Mech 138:307–316. doi:10.1061/(ASCE)EM.1943-7889.0000327

    Article  Google Scholar 

  • Jones A, Kramer S, Arduino P (2002) Estimation of uncertainty in geotechnical properties for performance-based earthquake engineering. Pacific Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Kale O, Padgett JE, Shafieezadeh A (2017) A ground motion prediction equation for novel peak ground fractional order response intensity measures. Bull Earthq Eng. doi:10.1007/s10518-017-0122-x

    Google Scholar 

  • Kamai R, Boulanger R (2009) Characterizing localization processes during liquefaction using inverse analyses of instrumentation arrays. In: Hatzor YH, Sulem J, Vardoulakis I (eds) Meso-scale shear physics in earthquake and landslide mechanics. CRC Press, Boca Raton, pp 219–238

    Chapter  Google Scholar 

  • Kawashima K, MacRae GA, Hoshikuma J, Nagaya K (1998) Residual displacement response spectrum. J Struct Eng 124:523–530. doi:10.1061/(ASCE)0733-9445(1998)124:5(523)

    Article  Google Scholar 

  • Kayen RE, Mitchell JK (1997) Assessment of liquefaction potential during earthquakes by arias intensity. J Geotech Geoenviron Eng 123:1162–1174. doi:10.1061/(ASCE)1090-0241(1997)123:12(1162)

    Article  Google Scholar 

  • Khosravifar A, Boulanger RW, Kunnath SK (2014) Effects of liquefaction on inelastic demands on extended pile shafts. Earthq Spectra 30:1749–1773. doi:10.1193/032412EQS105M

    Article  Google Scholar 

  • Kohrangi M, Bazzurro P, Vamvatsikos D (2016) Vector and scalar IMs in structural response estimation, Part I: hazard analysis. Earthq Spectra 32:1507–1524. doi:10.1193/053115EQS080M

    Article  Google Scholar 

  • Kostadinov MV, Towhata I (2002) Assesement of liquefaction-inducing peak ground velocity and frequency of horizontal ground shaking at onset of phenomenon. Soil Dyn Earthq Eng 22:309–322. doi:10.1016/S0267-7261(02)00018-0

    Article  Google Scholar 

  • Kostadinov MV, Yamazaki F (2001) Detection of soil liquefaction from strong motion records. Earthq Eng Struct Dyn 30:173–193. doi:10.1002/1096-9845(200102)30:2<173:AID-EQE3>3.0.CO;2-7

    Article  Google Scholar 

  • Kostinakis K, Fontara I-K, Athanatopoulou AM (2016) Scalar structure-specific ground motion intensity measures for assessing the seismic performance of structures: a review. J Earthq Eng. doi:10.1080/13632469.2016.1264323

    Google Scholar 

  • Kramer SL (1996) Geotechnical earthquake engineering. Upper Saddle River, NJ

    Google Scholar 

  • Kramer SL (2008) Using OpenSees for performance-based evaluation of bridges on liquefiable soils. Pacific Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Kramer SL, Mitchell RA (2006) Ground motion intensity measures for liquefaction hazard evaluation. Earthq Spectra 22:413–438. doi:10.1193/1.2194970

    Article  Google Scholar 

  • Kulasingam R, Malvick EJ, Boulanger RW, Kutter BL (2004) Strength loss and localization at silt interlayers in slopes of liquefied sand. J Geotech Geoenviron Eng 130:1192–1202. doi:10.1061/(ASCE)1090-0241(2004)130:11(1192)

    Article  Google Scholar 

  • Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:79–86. doi:10.1214/aoms/1177729694

    Article  Google Scholar 

  • Kwon O-S, Elnashai AS (2010) Fragility analysis of a highway over-crossing bridge with consideration of soil–structure interactions. Struct Infrastruct Eng 6:159–178. doi:10.1080/15732470802663870

    Article  Google Scholar 

  • Luco N, Cornell CA (2007) Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions. Earthq Spectra 23:357–392. doi:10.1193/1.2723158

    Article  Google Scholar 

  • Mackie K, Stojadinovic B (2004) Residual displacement and post-earthquake capacity of highway bridges. In: Proceedings of 13th world conference on earthquake engineering. Vancouver, BC, Canada

  • Mackie K, Stojadinović B (2001) Probabilistic seismic demand model for California highway bridges. J Bridg Eng 6:468–481. doi:10.1061/(ASCE)1084-0702(2001)6:6(468)

    Article  Google Scholar 

  • Mackie K, Stojadinović B (2003) Seismic demands for performance-based design of bridges. Pacific Earthquake Engineering Research Center, Berkeley

    Google Scholar 

  • Malvick E, Kutter B, Boulanger R (2008) Postshaking shear strain localization in a centrifuge model of a saturated sand slope. J Geotech Geoenviron Eng 134:164–174. doi:10.1061/(ASCE)1090-0241(2008)134:2(164)

    Article  Google Scholar 

  • Mander JB, Priestley MJN, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng 114:1804–1826. doi:10.1061/(ASCE)0733-9445(1988)114:8(1804)

    Article  Google Scholar 

  • Maurer BW, Green RA, Cubrinovski M, Bradley BA (2014) Evaluation of the liquefaction potential index for assessing liquefaction hazard in Christchurch, New Zealand. J Geotech Geoenviron Eng 140:1–11. doi:10.1061/(ASCE)GT.1943-5606.0001117

    Article  Google Scholar 

  • McKenna F (2011) OpenSees: a framework for earthquake engineering simulation. Comput Sci Eng 13:58–66. doi:10.1109/MCSE.2011.66

    Article  Google Scholar 

  • Midorikawa S, Wakamatsu K (1988) Intensity of earthquake ground motion at liquefied sites. Soils Found 28:73–84. doi:10.3208/sandf1972.28.2_73

    Article  Google Scholar 

  • Moehle J, Deierlein GG (2004) A framework methodology for performance-based earthquake engineering. In: Proceedings of 13th world conference on earthquake engineering. Vancouver, BC, Canada

  • Mollaioli F, Lucchini A, Cheng Y, Monti G (2013) Intensity measures for the seismic response prediction of base-isolated buildings. Bull Earthq Eng 11:1841–1866. doi:10.1007/s10518-013-9431-x

    Article  Google Scholar 

  • Nuttli OW (1979) The relation of sustained maximum ground acceleration and velocity to earthquake intensity and magnitude, Report No. S-73-1, US Army Waterways Experimental Station, Vicksburg, MS

  • Padgett JE, Nielson BG, DesRoches R (2008) Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthq Eng Struct Dyn 37:711–725. doi:10.1002/eqe.782

    Article  Google Scholar 

  • Padgett JE, Ghosh J, Dueñas-Osorio L (2010) Effects of liquefiable soil and bridge modelling parameters on the seismic reliability of critical structural components. Struct Infrastruct Eng 9:59–77. doi:10.1080/15732479.2010.524654

    Google Scholar 

  • Pang Y, Wu X, Shen G, Yuan W (2014) Seismic fragility analysis of cable-stayed bridges considering different sources of uncertainties. J Bridg Eng 19:4013015. doi:10.1061/(ASCE)BE.1943-5592.0000565

    Article  Google Scholar 

  • Park Y, Ang AHS, Wen YK (1985) Seismic damage analysis of reinforced concrete buildings. J Struct Eng 111:740–757. doi:10.1061/(ASCE)0733-9445(1985)111:4(740)

    Article  Google Scholar 

  • Parra E (1996) Numerical modeling of liquefaction and lateral ground deformation including cyclic mobility and dilation response in soil systems. PhD Dissertation, Rensselaer Polytechnic Institute, Troy, New York

  • Reed JW, Kassawara RP (1990) A criterion for determining exceedance of the operating basis earthquake. Nucl Eng Des 123:387–396. doi:10.1016/0029-5493(90)90259-Z

    Article  Google Scholar 

  • Riddell R (2007) On ground motion intensity indices. Earthq Spectra 23:147–173. doi:10.1193/1.2424748

    Article  Google Scholar 

  • Scott MH, Fenves GL (2010) Krylov subspace accelerated Newton algorithm: application to dynamic progressive collapse simulation of frames. J Struct Eng 136:473–480. doi:10.1061/(ASCE)ST.1943-541X.0000143

    Article  Google Scholar 

  • Shafieezadeh A. (2011) Seismic vulnerability assessment of wharf structures. PhD Dissertation, Georgia Institute of Technology, Atlanta, GA

  • Shafieezadeh A, Ramanathan K, Padgett JE, DesRoches R (2012) Fractional order intensity measures for probabilistic seismic demand modeling applied to highway bridges. Earthq Eng Struct Dyn 41:391–409. doi:10.1002/eqe.1135

    Article  Google Scholar 

  • Shome N (1999) Probabilistic seismic demand analysis of nonlinear structures. PhD Dissertation, Stanford University, Stanford, CA

  • Sica S, Mylonakis G, Simonelli AL (2013) Strain effects on kinematic pile bending in layered soil. Soil Dyn Earthq Eng 49:231–242. doi:10.1016/j.soildyn.2013.02.015

    Article  Google Scholar 

  • Somerville P, Smith N, Punyamurthula S, Sun J (1997) Development of ground motion time histories for phase 2 of the FEMA/SAC steel project. Report No. SAC/DB-97/04, Sacramento, CA

  • Stein M (1987) Large sample properties of simulations using latin hypercube sampling. Technometrics 29:143–151

    Article  Google Scholar 

  • Tang WH, Ang A (2007) Probability concepts in engineering: Emphasis on applications to civil and environmental engineering, 2nd edn. Wiley, Hoboken

    Google Scholar 

  • Tubaldi E, Barbato M, Dall’Asta A (2012) Influence of model parameter uncertainty on seismic transverse response and vulnerability of steel—concrete composite bridges with dual load path. J Struct Eng 138:363–374. doi:10.1061/(ASCE)ST.1943-541X.0000456

    Article  Google Scholar 

  • Von Thun JL, Roehm LH, Scott GA, Wilson JA (1988) Earthquake ground motions for design and analysis of dams. In: Earthquake engineering and soil dynamics II—recent advances in ground-motion evaluation. American Society of Civil Engineers, pp 463–481

  • Wang Z, Dueñas-Osorio L, Padgett JE (2012) Optimal intensity measures for probabilistic seismic response analysis of bridges on liquefiable and non-liquefiable soils. Structures congress 2012. ASCE, Reston, pp 527–538

    Chapter  Google Scholar 

  • Wang Z, Padgett JE, Dueñas-Osorio L (2013) Influence of vertical ground motions on the seismic fragility modeling of a bridge-soil-foundation system. Earthq Spectra 29:937–962. doi:10.1193/1.4000170

    Article  Google Scholar 

  • Wang X, Luo F, Su Z, Ye A (2017) Efficient finite-element model for seismic response estimation of piles and soils in liquefied and laterally spreading ground considering shear localization. Int J Geomech 17:6016039. doi:10.1061/(ASCE)GM.1943-5622.0000835

    Article  Google Scholar 

  • Watson-Lamprey J, Abrahamson N (2006) Selection of ground motion time series and limits on scaling. Soil Dyn Earthq Eng 26:477–482. doi:10.1016/j.soildyn.2005.07.001

    Article  Google Scholar 

  • Yakut A, Yılmaz H (2008) Correlation of deformation demands with ground motion intensity. J Struct Eng 134:1818–1828. doi:10.1061/(ASCE)0733-9445(2008)134:12(1818)

    Article  Google Scholar 

  • Yang Z (2000) Numerical modeling of earthquake site response including dilation and liquefaction. PhD Dissertation, Columbia University, New York, NY

  • Zhang J, Huo Y (2009) Evaluating effectiveness and optimum design of isolation devices for highway bridges using the fragility function method. Eng Struct 31:1648–1660. doi:10.1016/j.engstruct.2009.02.017

    Article  Google Scholar 

  • Zhang J, Huo Y, Brandenberg SJ, Kashighandi P (2008) Effects of structural characterizations on fragility functions of bridges subject to seismic shaking and lateral spreading. Earthq Eng Eng Vib 7:369–382. doi:10.1007/s11803-008-1009-2

    Article  Google Scholar 

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Acknowledgements

Funding for this study is provided by the National Natural Science Foundation of China (Grant No. 51278375), the Ministry of Science and Technology of China (Grant No. SLDRCE 15-B-05), and National Science Foundation of the United States (Grant No. CMMI-1462183). The first author also thanks to the financial support from the China Scholarship Council (CSC). Special thanks to Mr. Ruiwei Feng for providing comments that improved the manuscript. The authors would also acknowledge the anonymous reviewers who have contributed to improving and enriching the paper. Any opinions, findings, and conclusions expressed are those of the authors, and do not necessarily reflect those of the sponsoring organization.

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  1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China

    Xiaowei Wang & Aijun Ye

  2. Department of Civil, Environmental and Geodetic Engineering, Ohio State University, Columbus, OH, 43210, USA

    Xiaowei Wang & Abdollah Shafieezadeh

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Wang, X., Shafieezadeh, A. & Ye, A. Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground. Bull Earthquake Eng 16, 229–257 (2018). https://doi.org/10.1007/s10518-017-0199-2

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