Stochastic Mainshock–Aftershock Simulation and Its Applications in Dynamic Reliability of Structural Systems via DPIM
Publication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
A novel approach for nonlinear stochastic dynamic analysis is proposed and illustrated with nonlinear building structures subjected to mainshock–aftershock sequences. First, a stochastic seismic sequence model with stochastic parameters was established, and its generation method was derived based on the source–path–site mechanism. Then, the representative point sets of seismic parameters could be chosen based on generalized F-discrepancy, and the correlation between the mainshock and aftershock parameters could be determined by using Copula theory. Finally, the stochastic dynamic response was obtained by solving the probability density integral equation (PDIE). Furthermore, the first-passage dynamic reliability could be obtained by the direct probability integral method (DPIM) combined with the absorbing condition approach. This novel approach was used to obtain stochastic dynamic results for four structures subjected to stochastic seismic sequences, which were compared to those using Monte Carlo simulation (MCS) and probability density evolution method (PDEM) to demonstrate the proposed method’s correctness and efficiency. Additionally, the influence of aftershocks on nonlinear structures is explained from the perspective of probability for the first time.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This work was supported by National Key R&D Program of China (2021YFB2601102), China National Natural Science Foundation (Grant Nos. 52279125, 52279096, 52009017, 51979026, and 51890915), Fundamental Research Funds for the Central Universities (DUT21TD106, DUT21RC(3)107), Liaoning Province Science Foundation (2020-BS-06), and Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment (Grant No. FZ213201). The financial support from these sources is gratefully acknowledged.
References
Aas, K., C. Czado, A. Frigessi, and H. Bakken. 2009. “Pair-Copula constructions of multiple dependence.” Math. Econ. 44 (2): 182–198. https://doi.org/10.1016/j.insmatheco.2007.02.001.
Akaike, H. 1981. “Likelihood of a model and information criteria.” J. Econom. 16 (1): 3–14. https://doi.org/10.1016/0304-4076(81)90071-3.
Aurenhammer, F. 1991. “Voronoi diagrams—A survey of a fundamental geometric data structure.” ACM Comput. Surv. 23 (3): 345–405. https://doi.org/10.1145/116873.116880.
Bougioukou, A. P., A. P. Leros, and V. Papakonstantinou. 2008. “Modeling of non-stationary ground motion using the mean reverting stochastic process.” Appl. Math. Modell. 32 (9): 1912–1932. https://doi.org/10.1016/j.apm.2007.06.026.
Brune, J. N. 1970. “Tectonic stress and spectra of seismic shear waves from earthquakes.” J. Geophys. Res. 75 (26): 4997–5009. https://doi.org/10.1029/JB075i026p04997.
Chen, G. H., and D. X. Yang. 2019. “Direct probability integral method for stochastic response analysis of static and dynamic structural systems.” Comput. Methods Appl. Mech. Eng. 357 (Dec): 112612. https://doi.org/10.1016/j.cma.2019.112612.
Chen, G. H., and D. X. Yang. 2021. “A unified analysis framework of static and dynamic structural reliabilities based on direct probability integral method.” Mech. Syst. Sig. Process. 158 (Sep): 107783. https://doi.org/10.1016/j.ymssp.2021.107783.
Chen, J. B., R. Ghanem, and J. Li. 2009. “Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures.” Probab. Eng. Mech. 24 (1): 27–42. https://doi.org/10.1016/j.probengmech.2007.12.017.
Chen, J. B., J. Y. Yang, and J. Li. 2016. “A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters.” Struct. Saf. 59 (Mar): 20–31. https://doi.org/10.1016/j.strusafe.2015.11.001.
Das, S., and V. K. Gupta. 2010. “Scaling of response spectrum and duration for aftershocks.” Soil Dyn. Earthquake Eng. 30 (8): 724–735. https://doi.org/10.1016/j.soildyn.2010.03.003.
Der Kiureghian, A., and T. Dakessian. 1998. “Multiple design points in first and second-order reliability.” Struct. Saf. 20 (1): 37–49. https://doi.org/10.1016/S0167-4730(97)00026-X.
Hainzl, S., G. Zöller, and F. Scherbaum. 2003. “Earthquake clusters resulting from delayed rupture propagation in finite fault segments: Earthquake clustering in finite faults.” J. Geophys. Res. Solid Earth 108 (B1): 1–10. https://doi.org/10.1029/2001JB000610.
Hu, S., P. Gardoni, and L. Xu. 2018. “Stochastic procedure for the simulation of synthetic main shock-aftershock ground motion sequences.” Earthquake Eng. Struct. Dyn. 47 (11): 2275–2296. https://doi.org/10.1002/eqe.3068.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/eqe.495.
Kalkan, E., and V. Graizer. 2007. “Coupled tilt and translational ground motion response spectra.” J. Struct. Eng. 133 (5): 609–619. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:5(609).
Lee, Y. T., K. F. Ma, M. C. Hsieh, Y. T. Yen, and Y. S. Sun. 2016. “Synthetic ground-motion simulation using a spatial stochastic model with slip self-similarity: Toward near-source ground-motion validation.” Terr. Atmos. Oceanic Sci. 27 (3): 397. https://doi.org/10.3319/TAO.2015.11.27.01(TEM).
Li, J., and J. B. Chen. 2009. Stochastic dynamics of structures. New York: Wiley. https://doi.org/10.1002/9780470824269.
Li, L. X., M. X. Fang, G. H. Chen, and D. X. Yang. 2022. “Reliability-based stochastic optimal control of frame building under near-fault ground motions.” Mech. Syst. Sig. Process. 163 (Jan): 108098. https://doi.org/10.1016/j.ymssp.2021.108098.
Li, X. L., G. H. Chen, H. C. Cui, and D. X. Yang. 2021. “Direct probability integral method for static and dynamic reliability analysis of structures with complicated performance functions.” Comput. Methods Appl. Mech. Eng. 374 (Feb): 113583. https://doi.org/10.1016/j.cma.2020.113583.
Liu, Z. J., W. Liu, and Y. B. Peng. 2016. “Random function based spectral representation of stationary and non-stationary stochastic processes.” Probab. Eng. Mech. 45 (Jul): 115–126. https://doi.org/10.1016/j.probengmech.2016.04.004.
Lu, T. J., X. S. Tang, D. Q. Li, and X. H. Qi. 2020. “Modeling multivariate distribution of multiple soil parameters using vine Copula model.” Comput. Geotech. 118 (Feb): 103340. https://doi.org/10.1016/j.compgeo.2019.103340.
Ohsaki, Y. 1979. “On the significance of phase content in earthquake ground motions.” Earthquake Eng. Struct. Dyn. 7 (5): 427–439. https://doi.org/10.1002/eqe.4290070504.
Pang, R., B. Xu, X. J. Kong, Y. Zhou, and D. G. Zou. 2018a. “Seismic performance evaluation of high CFRD slopes subjected to near-fault ground motions based on generalized probability density evolution method.” Eng. Geol. 246 (Nov): 391–401. https://doi.org/10.1016/j.enggeo.2018.09.004.
Pang, R., B. Xu, X. J. Kong, D. G. Zou, and Y. Zhou. 2018b. “Seismic reliability assessment of earth-rockfill dam slopes considering strain-softening of rockfill based on generalized probability density evolution method.” Soil Dyn. Earthquake Eng. 107 (Apr): 96–107. https://doi.org/10.1016/j.soildyn.2018.01.020.
Pang, R., B. Xu, X. Zhang, Y. Zhou, and X. J. Kong. 2019a. “Seismic performance investigation of high CFRDs subjected to mainshock-aftershock sequences.” Soil Dyn. Earthquake Eng. 116 (Jan): 82–85. https://doi.org/10.1016/j.soildyn.2018.09.049.
Pang, R., B. Xu, Y. Zhou, and L. F. Song. 2021. “Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations.” Comput. Geotech. 136 (Aug): 104245. https://doi.org/10.1016/j.compgeo.2021.104245.
Pang, R., B. Xu, Y. Zhou, X. Zhang, and X. L. Wang. 2020. “Fragility analysis of high CFRDs subjected to mainshock-aftershock sequences based on plastic failure.” Eng. Struct. 206 (Mar): 110152. https://doi.org/10.1016/j.engstruct.2019.110152.
Pang, R., B. Xu, D. Zou, and X. J. Kong. 2019b. “Seismic performance assessment of high CFRDs based on fragility analysis.” Sci. China Technol. Sci. 62 (4): 635–648. https://doi.org/10.1007/s11431-017-9220-8.
Pitarka, A. 2000. “Simulation of near-fault strong-ground motion using hybrid green’s functions.” Bull. Seismol. Soc. Am. 90 (3): 566–586. https://doi.org/10.1785/0119990108.
Sharbati, R., F. Khoshnoudian, H. R. Ramazi, and H. R. Amindavar. 2018. “Stochastic modeling and simulation of ground motions using complex discrete wavelet transform and Gaussian mixture model.” Soil Dyn. Earthquake Eng. 114 (Nov): 267–280. https://doi.org/10.1016/j.soildyn.2018.07.003.
Sharbati, R., H. R. Ramazi, F. Khoshnoudian, H. R. Amindavar, and H. Rabbani. 2021. “Stochastic model for simulation of ground-motion sequences using kernel-based smoothed wavelet transform and Gaussian mixture distribution.” J. Earthquake Eng. 25 (11): 2147–2177. https://doi.org/10.1080/13632469.2019.1605948.
Shen, J., J. Chen, and D. Guo. 2020. “Random field model of sequential ground motions.” Bull. Earthquake Eng. 18 (11): 5119–5141. https://doi.org/10.1007/s10518-020-00901-4.
Sklar, A. 1959. Fonctions de repartition a n dimensions et Leurs Marges, 229–231. Paris, France: de l′Institut de Statistique de l′Université de Paris.
Song, L. F., B. Xu, X. J. Kong, D. G. Zou, X. Yu, and R. Pang. 2021. “Reliability analysis of 3D rockfill dam slope stability based on the copula function.” Int. J. Geomech. 21 (3): 04021001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001932.
Song, R. Q., Y. Li, and J. W. Van de Lindt. 2016. “Loss estimation of steel buildings to earthquake mainshock–aftershock sequences.” Struct. Saf. 61 (Jul): 1–11. https://doi.org/10.1016/j.strusafe.2016.03.002.
Song, S., J. Liu, Y. J. Qian, F. Zhang, and G. Wu. 2018. “Dependence analysis on the seismic demands of typical components of a concrete continuous girder bridge with the Copula technique.” Adv. Struct. Eng. 21 (12): 1826–1839. https://doi.org/10.1177/1369433218757234.
Wang, D., and J. Li. 2011. “Physical random function model of ground motions for engineering purposes.” Sci. China Technol. Sci. 54 (1): 175–182. https://doi.org/10.1007/s11431-010-4201-3.
Wang, Z. H., and C. S. Gu. 2011. “A new non-stationary stochastic seismic ground motion model and its application.” Adv. Mater. Res. 243–249: 4627–4633. https://doi.org/10.4028/www.scientific.net/AMR.243-249.4627.
Wong, H. L., and M. D. Trifunac. 1979. “Generation of artificial strong motion accelerograms.” Earthquake Eng. Struct. Dyn. 7 (6): 509–527. https://doi.org/10.1002/eqe.4290070602.
Yang, D. X., and J. L. Zhou. 2015. “A stochastic model and synthesis for near-fault impulsive ground motions: Stochastic model and synthesis for near-fault impulsive ground motions.” Earthquake Eng. Struct. Dyn. 44 (2): 243–264. https://doi.org/10.1002/eqe.2468.
Yang, J., J. Tao, B. Sudret, and J. Chen. 2020. “Generalized F-discrepancy-based point selection strategy for dependent random variables in uncertainty quantification of nonlinear structures.” Int. J. Numer. Methods Eng. 121 (7): 1507–1529. https://doi.org/10.1002/nme.6277.
Yoder, M. R., J. Van Aalsburg, D. L. Turcotte, S. G. Abaimov, and J. B. Rundle. 2013. “Statistical variability and Tokunaga branching of aftershock sequences utilizing BASS model simulations.” Pure Appl. Geophys. 170 (1–2): 155–171. https://doi.org/10.1007/s00024-011-0411-2.
Zakharova, O., S. Hainzl, and C. Bach. 2013. “Seismic moment ratio of aftershocks with respect to main shocks: Seismic moment ratio of aftershocks.” J. Geophys. Res. Solid Earth 118 (11): 5856–5864. https://doi.org/10.1002/2013JB010191.
Zhang, H., T. Sun, S. W. Hou, Q. M. Gao, and X. Li. 2021a. “Effect of aftershocks on seismic fragilities of single-story masonry structures.” Front. Phys. 9 (May): 695111. https://doi.org/10.3389/fphy.2021.695111.
Zhang, L. J., Y. F. Zhai, B. H. Cui, Y. J. Tang, and Z. H. Bi. 2021b. “A novel method for constructing main-aftershock sequences and its application in the global damage accumulation effects analysis of gravity dams.” Shock Vibr. 2021: 1–12. https://doi.org/10.1155/2021/9356540.
Zhong, M., T. Zeng, T. Jiang, H. Wu, X. H. Chen, and Y. Hong. 2021. “A copula-based multivariate probability analysis for flash flood risk under the compound effect of soil moisture and rainfall.” Water Resour. Manage. 35 (1): 83–98. https://doi.org/10.1007/s11269-020-02709-y.
Zhou, T., and A. Q. Li. 2019. “Seismic fragility assessment of highway bridges using D-vine Copulas.” Bull. Earthquake Eng. 17 (2): 927–955. https://doi.org/10.1007/s10518-018-0474-x.
Zhou, Y., M. Y. Jing, R. Pang, B. Xu, F. Jiang, and X. Yu. 2021. “Stochastic dynamic response and seismic reliability analysis of nuclear power plant’s vertical retaining wall based on plastic failure.” Structures. 31: 513–539. https://doi.org/10.1016/j.istruc.2021.02.012.
Zhou, Y., B. Xu, R. Pang, D. G. Zou, and X. J. Kong. 2018. “Stochastic seismic response and stability reliability analysis of a vertical retaining wall in front of the pumping station of a nuclear power plant using the probability density evolution method.” Nucl. Eng. Des. 334 (Aug): 110–120. https://doi.org/10.1016/j.nucengdes.2018.05.008.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 9, 2022
Accepted: Aug 20, 2022
Published online: Nov 11, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 11, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Arash Rayegani, Omid Karimzade Soureshjani, Seyed Ali Moayed Alaee, Imad H. Mualla, Fariba Nemati, Seismic Performance of Buildings Equipped with Four-Joint Rotational Friction Dampers in Mainshock–Aftershock Sequences, Journal of Structural Engineering, 10.1061/JSENDH.STENG-12980, 150, 3, (2024).