Skip to main content
Log in

Effect of travelling waves on stochastic seismic response and dynamic reliability of a long-span bridge on soft soil

  • Original Research Paper
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

It is generally known that the variability of earthquake ground motion is mainly in time and space. To investigate the impact of this variability on the seismic performance of a long-span flexible structure, we discuss the seismic dynamic responses of a real bridge subjected to stochastic seismic ground motion. We incorporate the effect of wave passage by means of the method of probability density evolution based on dynamic time-history analysis from the perspective of stochastic dynamics. First, we introduce the theory of probability density evolution and a category of stochastic seismic model. We then conduct a series of deterministic seismic dynamic analyses of the bridge to establish the probability density equation. Eventually, we obtain the probability information at the level of the probability density function of the seismic response by solving the probability-density evolution equation. The results show that the impact of travelling waves on a long-span structure is related to the characteristics of the earthquake ground motion and the structure, and that travelling waves increase the variability of the seismic response.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Aki K, Tsujiura M (1959) Correlational study of near earthquake waves. Bull Earthq Res Inst 37:207–232

    Google Scholar 

  • Behnamfar F, Sayyadpour H (2016) The near-field method: a modified equivalent linear method for dynamic soil-structure interaction analysis. Part I: theory and methodology. Bull Earthq Eng 14(8):2361–2384

    Article  Google Scholar 

  • Bogdanoff JL, Goldberg JE, Schiff AJ (1965) The effect of ground transmission time on the response of long structures. Bull Seismol Soc Am 55(3):627–640

    Google Scholar 

  • Capatti MC, Tropeano G, Morici M, Carbonari S, Dezi F, Leoni G, Silvestri F (2017) Implications of non-synchronous excitation induced by nonlinear site amplification and of soil-structure interaction on the seismic response of multi-span bridges founded on piles. Bull Earthq Eng 15(11):4963–4995

    Article  Google Scholar 

  • Chen JB, Li J (2007) The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Struct Saf 29(2):77–93

    Article  Google Scholar 

  • Chen ZY, Liang SB, He C (2018) Seismic performance of an immersed tunnel considering random soil properties and wave passage effects. Struct Infrastruct Eng 14(1):89–103

    Article  Google Scholar 

  • Clough RW, Penzien J (1975) Dynamics of Structures. McGraw-Hill, New York

    Google Scholar 

  • Code for seismic design of buildings (GB50011-2010) (2010) Ministry of housing and urban-rural of the People’s Republic of China (in Chinese)

  • De Silva CW (2005) Vibration and shock handbook. CRC Press, Boca Raton

    Book  Google Scholar 

  • Falamarz-Sheikhabadi MR, Zerva A (2016) Analytical seismic assessment of a tall long-span curved reinforced-concrete bridge. Part I: numerical modeling and input excitation. J Earthq Eng 00:1–30

    Google Scholar 

  • Geller RJ, Jackson DD, Kagan YY, Mulargia F (1997) Earthquakes cannot be predicted. Science 275(5306):1616

    Article  Google Scholar 

  • Ghiocel DM, Ghanem RG (2002) Stochastic finite-element analysis of seismic soil–structure interaction. J Eng Mech 128(1):66–77

    Article  Google Scholar 

  • Heredia-Zavoni E, Vanmarcke EH (1994) Seismic random-vibration analysis of multisupport-structural systems. J Eng Mech 120(5):1107–1128

    Article  Google Scholar 

  • Hong HP, Liu TJ (2014) Assessment of coherency for bidirectional horizontal ground motions and its application for simulating records at multiple stations. Bull Seismol Soc Am 104(5):2491–2502

    Article  Google Scholar 

  • Housner GW (1957) Interaction of building and ground during an earthquake. Bull Seismol Soc Am 47(6):179–186

    Google Scholar 

  • Huang Y, Xiong M (2017a) Probability density evolution method for seismic liquefaction performance analysis of earth dam. Earthq Eng Struct Dyn 46:925–943

    Article  Google Scholar 

  • Huang Y, Xiong M (2017b) Dynamic reliability analysis of slopes based on the probability density evolution method. Soil Dyn Earthq Eng 94:1–6

    Article  Google Scholar 

  • Huang Y, Yashima A, Sawada K, Zhang F (2008) Numerical assessment of the seismic response of an earth embankment on liquefiable soils. Bull Eng Geol Environ 66(1):31–39

    Article  Google Scholar 

  • Jiao CK, Dong X, Li AQ, Zhou GD, Wu XP (2017) Seismic response of long-span triple-tower suspension bridge under random ground motion. Math Probl Eng 2017(1):1–16

    Article  Google Scholar 

  • Katsanos EI, Sextos AG (2018) Structure-specific selection of earthquake ground motions for the reliable design and assessment of structures. Bull Earthq Eng 16(2):583–611

    Article  Google Scholar 

  • Kim Y, Jhung MJ (2011) Mathematical analysis using two modeling techniques for dynamic responses of a structure subjected to a ground acceleration time history. Nucl Eng Technol 43(4):361–374

    Article  Google Scholar 

  • Lavorato D, Vanzi I, Nuti C, Monti G (2017) Generation of non-synchronous earthquake signals. In: Gardoni P (ed) Risk and reliability analysis: theory and applications. Springer, Berlin

    Google Scholar 

  • Léger P, Idé IM, Paultre P (1990) Multiple-support seismic analysis of large structures. Comput Struct 36(6):1153–1158

    Article  Google Scholar 

  • Li J, Chen JB (2008) The principle of preservation of probability and the generalized density evolution equation. Struct Saf 30(1):65–77

    Article  Google Scholar 

  • Li J, Chen JB, Fan WL (2007) The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf 29(2):112–131

    Article  Google Scholar 

  • Li J, Chen JB, Sun WL, Peng YB (2012) Advances of the probability density evolution method for nonlinear stochastic systems. Probab Eng Mech 28(4):132–142

    Article  Google Scholar 

  • Liu G, Lian J, Liang C (2016a) Completeness verification of complex response spectrum method for underdamped and overdamped multiple-support systems regarding the decoupled damping as mathematical parameter without physical meaning. J Earthq Eng 20(7):1104–1125

    Article  Google Scholar 

  • Liu ZJ, Liu W, Peng YB (2016b) Random function based spectral representation of stationary and non-stationary stochastic processes. Probab Eng Mech 45:115–126

    Article  Google Scholar 

  • Loh CH, Yeh YT (1988) Spatial variation and stochastic modelling of seismic differential ground movement. Earthq Eng Struct Dyn 16(4):583–596

    Article  Google Scholar 

  • Martinelli L, Barbella G, Feriani A (2010) Modeling of Qiandao Lake submerged floating tunnel subject to multi-support seismic input. Proc Eng 4:311–318

    Article  Google Scholar 

  • MIDAS Information Technology Co., Ltd (2017) Midas civil. http://en.midasuser.com/product/civil_overview.asp

  • Nuti C, Vanzi I (2005) Influence of earthquake spatial variability on differential soil displacements and SDF system response. Earthq Eng Struct Dyn 34(11):1353–1374

    Article  Google Scholar 

  • Nuti C, Santini S, Vanzi I (2001) Seismic risk of the Italian hospitals. Eur Earthq Eng 15(1):11–19

    Google Scholar 

  • Pecker A, Paolucci R, Chatzigogos C, Correia AA, Figini R (2014) The role of non-linear dynamic soil-foundation interaction on the seismic response of structures. Bull Earthq Eng 12(3):1157–1176

    Article  Google Scholar 

  • Poulin S, Larsen A (2007) Drag loading of circular cylinders inclined in the along-wind direction. J Wind Eng Ind Aerodyn 95(9):1350–1363

    Article  Google Scholar 

  • Sextos AG, Kappos AJ (2009) Evaluation of seismic response of bridges under asynchronous excitation and comparisons with eurocode 8-2 provisions. Bull Earthq Eng 7(2):519–545

    Article  Google Scholar 

  • Shen X, Camara A, Ye AJ (2015) Effects of seismic devices on transverse responses of piers in the Sutong Bridge. Earthq Eng Eng Vib 14(4):611–623

    Article  Google Scholar 

  • Soyluk K (2004) Comparison of random vibration methods for multi-support seismic excitation analysis of long-span bridges. Eng Struct 26(11):1573–1583

    Article  Google Scholar 

  • Tada K, Jin H, Kitagawa M, Nitta A, Toriumi R (1995) Effect of the southern Hyogo earthquake on the Akashi-Kaikyo bridge. Struct Eng Int 5(3):179–181

    Article  Google Scholar 

  • Tian L, Gai X (2016) Nonlinear seismic behavior of different boundary conditions of transmission line systems under earthquake loading. Shock Vib 2016:1–9

    Google Scholar 

  • Tormann T, Enescu B, Woessner J, Wiemer S (2015) Randomness of megathrust earthquakes implied by rapid stress recovery after the Japan earthquake. Nat Geosci 8(2):152–158

    Article  Google Scholar 

  • Wang Z, Der Kiureghian A (2016) Tail-equivalent linearization of inelastic multi-support structures subjected to spatially varying stochastic ground motion. J Eng Mech 142(8):1–14

    Google Scholar 

  • You Q, He P, Dong X, Zhang X, Wu S (2008) Sutong Bridge—the longest cable-stayed bridge in the world. Struct Eng Int 18(4):390–395

    Article  Google Scholar 

  • Zerva A (1990) Response of multi-span beams to spatially incoherent seismic ground motions. Earthq Eng Struct Dyn 19(6):819–832

    Article  Google Scholar 

  • Zerva A (2016) Spatial variation of seismic ground motions: modeling and engineering applications. CRC Press, Boca Raton

    Google Scholar 

  • Zerva A, Zervas V (2002) Spatial variation of seismic ground motions: an overview. Appl Mech Rev 55(3):271–297

    Article  Google Scholar 

  • Zhang YH, Lin JH, Williams FW, Li QS (2005) Wave passage effect of seismic ground motions on the response of multiply supported structures. Struct Eng Mech 20(6):655–672

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants Nos. 41625011 and 51778467).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu Huang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiong, M., Huang, Y. & Zhao, Q. Effect of travelling waves on stochastic seismic response and dynamic reliability of a long-span bridge on soft soil. Bull Earthquake Eng 16, 3721–3738 (2018). https://doi.org/10.1007/s10518-018-0316-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-018-0316-x

Keywords

Navigation