Conditional simulation of non-stationary spatially variable ground motions for long-span bridges across non-uniform site conditions

Jubin Lu1, Hu Liang2, Zili Xia3, Songye Zhu1
1Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
2School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei province, China
3Hong Kong-Zhuhai-Macao Bridge Authority, Zhuhai, Guangdong Province, China

Tóm tắt

AbstractNon-stationary spatially variable ground motions (SVGMs) are commonly modelled as multivariate oscillatory processes based on evolutionary power spectral density (EPSD) functions. The existing conditional simulation algorithms require the known EPSD functions. The EPSD functions are usually assumed to be identical for all locations, which is unreasonable for long-span bridges because variable soil conditions are practically observed at different bridge piers. This paper proposes a conditional simulation algorithm for non-stationary SVGMs in consideration of non-uniform site conditions. The spatial interpolation tool, termed inverse-distance-weighted (IDW) interpolation, is introduced to estimate the EPSD functions at sites without ground motion measurement. Subsequently, the covariance matrix of the random Fourier coefficients of the multivariate oscillatory processes can be calculated. The Kriging estimation is adopted to obtain the unknown random Fourier coefficients, from which the time histories of the non-stationary SVGMs can be conditionally simulated. The proposed conditional simulation algorithm is first validated through a numerical example, in which the EPSD functions of non-uniform sites are represented by a non-stationary Kanai-Tajimi spectrum with different soil parameters. Then, the algorithm is applied to the Jiuzhou Channel Bridge, a navigation channel bridge of the Hong Kong-Zhuhai-Macau Bridge (HZMB), with complex soil and water conditions. Based on the limited in-situ seismic measurement data, the site characteristics in the bridge area are analysed, and the ground motion time histories at all piers can be generated.

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Tài liệu tham khảo

Bi K, Hao H, Ren W (2010) Response of a frame structure on a canyon site to spatially varying ground motions. Struct Eng Mech 36:111–127

Bi K, Hao H, Chouw N (2011) Influence of ground motion spatial variation, site condition and SSI on the required separation distances of bridge structures to avoid seismic pounding. Earthquake Eng Struct Dynamics 40:1027–1043

Bi K, Hao H (2012) Modelling and simulation of spatially varying earthquake ground motions at sites with varying conditions. Probabilistic Eng Mech 29:92–104

Chen Q, Hong N (2019) Depth coherency analysis for strong seismic motions from KiK-net. J Earthq Eng 25:1762–1787

Cheng Q, Tian Y, Lu X, Huang Y, Ye L (2021) Near-real-time prompt assessment for regional earthquake-induced landslides using recorded ground motions. Comput Geosci 149:1–11

Cui XZ, Hong HP (2020) Conditional simulation of spatially varying multicomponent nonstationary ground motions: Bias and ill condition. J Eng Mech 146:1–13

Deodatis G (1996) Non-stationary stochastic vector processes: seismic ground motion applications. Probabilistic Eng Mech 11:149–167

Hao H, Oliveira CS, Penzien J (1989) Multiple-station ground motion processing and simulation based on smart-1 array data. Nucl Eng Des 111:293–310

Harichandran RS, Vanmarcke EH (1986) Stochastic variation of earthquake ground motion in space and time. J Eng Mech 112:154–174

Heredia-Zavoni E, Santa-Cruz S (2000) Conditional simulation of a class of nonstationary space-time random fields. J Eng Mech 126:398–404

Hu L, Xu YL, Zheng Y (2012) Conditional simulation of spatially variable seismic ground motions based on evolutionary spectra. Earthq Eng Struct Dyn 41:2125–2139

Hu L, Xu Z, Xu YL, Li L, Kareem A (2017) Error analysis of spatially varying seismic ground motion simulation by spectral representation method. J Eng Mech 143:1–13

Huang D, Wang G (2015) Stochastic simulation of regionalized ground motions using wavelet packets and cokriging analysis. Earthq Eng Struct Dyn 44:775–794

Kameda H, Morikawa H (1992) An interpolating stochastic process for simulation of conditional random fields. Probabilistic Eng Mech 7:243–254

Kameda H, Morikawa H (1994) Conditioned stochastic processes for conditional random fields. J Eng Mech 120:855–875

Kim T, Kwon O-S, Song J (2021) Seismic performance of a long-span cable-stayed bridge under spatially varying bidirectional Spectrum-compatible ground motions. J Struct Eng 147:1–19

Kiureghian AD (1996) A coherency model for spatially varying ground motions. Earthq Eng Struct Dyn 25:99–111

Konakli K, Der Kiureghian A (2012) Simulation of spatially varying ground motions including incoherence, wave-passage and differential site-response effects. Earthq Eng Struct Dyn 41:495–513

Konakli K, Der Kiureghian A, Dreger D (2014) Coherency analysis of accelerograms recorded by the UPSAR array during the 2004 Parkfield earthquake. Earthq Eng Struc Dyn 43:641–659

Li C, Hao H, Li H, Bi K (2015) Theoretical modeling and numerical simulation of seismic motions at seafloor. Soil Dyn Earthq Eng 77:220–225

Li C, Li H, Hao H, Bi K, Chen B (2018a) Seismic fragility analyses of sea-crossing cable-stayed bridges subjected to multi-support ground motions on offshore sites. Eng Struct 165:441–456

Li C, Li H, Hao H, Bi K, Tian L (2018b) Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites. Earthq Eng Eng Vib 17:475–490

Li C, Li H, Hao H, Bi K (2018c) Simulation of spatially varying seafloor motions using onshore earthquake recordings. J Eng Mech 144:1–14

Lu X, Cheng Q, Tian Y, Huang Y (2021) Regional ground-motion simulation using recorded ground motions. Bull Seismol Soc Am 111:825–838

Luco JE, Wong HL (1986) Response of a rigid foundation to a spatially random ground motion. Earthq Eng Struct Dyn 14:891–908

Oliveira CS, Hao H, Penzien J (1991) Ground motion modeling for multiple-input structural analysis. Struct Saf 10:79–93

Priestley MB (1965) Evolutionary spectra and non-stationary processes. J R Stat Soc Ser B Methodol 27:204–229

Priestley MB (1966) Design relations for non-stationary processes. J R Stat Soc Ser B Methodol 28:228–240

Priestley MB (1967) Power spectral analysis of non-stationary random processes. J Sound Vib 6:86–97

Rodda GK, Basu D (2020) Spatially correlated vertical ground motion for seismic design. Eng Struct 206:1–22

Suzuki W, Aoi S, Kunugi T, Kubo H, Morikawa N, Nakamura H, Kimura T, Fujiwara H (2017) Strong motions observed by K-NET and KiK-net during the 2016 Kumamoto earthquake sequence. Earth Planets Space 69:1–12

Svay A, Perron V, Imtiaz A, Zentner I, Cottereau R, Clouteau D, Bard PY, Hollender F, Lopez-Caballero F (2017) Spatial coherency analysis of seismic ground motions from a rock site dense array implemented during the Kefalonia 2014 aftershock sequence. Earthq Eng Struct Dyn 46:1895–1917

Thráinsson H, Kiremidjian AS, Winterstein SR (2000) Modeling of earthquake ground motion in the frequency domain. John A. Blume Earthquake Engineering Center Rep No 134, Dept of Civil and Environmental Engineering, Stanford Univ, Stanford

Vanmarcke EH, Fenton GA (1991) Conditioned simulation of local fields of earthquake ground motion. Struct Saf 10:247–264

Vanmarcke EH, Heredia‐Zavoni E, Fenton GA (1993) Conditional Simulation of Spatially Correlated Earthquake Ground Motion. J Eng Mech 119:2333–2352

Wu Y, Gao Y (2019) A modified spectral representation method to simulate non-Gaussian random vector process considering wave-passage effect. Eng Struct 201:1–15

Zerva A (2009) Spatial variation of seismic ground motions: molldeing and engineering application. CRC Press, Boca Raton

Zerva A, Zervas V (2002) Spatial variation of seismic ground motions: an overview. Appl Mech Rev 55:271–297

Zhong J, Jeon J-S, Ren W-X (2018) Risk assessment for a long-span cable-stayed bridge subjected to multiple support excitations. Eng Struct 176:220–230