Three-Dimensional Flight Trajectories and Impact Damage Prediction Model for Wind-Borne Debris
Abstract
The risk of damage of glass curtain walls in residential areas caused by impact of wind-borne debris has been given increasing importance. In this paper, by incorporating the numerical analysis of three-dimensional (3D) flight trajectories of wind-borne debris and computational fluid dynamics (CFD) simulation of the local wind environment in the context of buildings group, a novel impact damage prediction model for the glass curtain wall of urban buildings is proposed. To this end, the 3D flight trajectories and characteristics of plate-type debris are first studied by solving the 3D equation of motion of debris, of which the aerodynamic coefficients of plate-type debris is obtained by CFD numerical simulation. The flight characteristics of debris with different initial parameters are analyzed, showing that the properties of debris and initial conditions have significant effect on the flight trajectories and impact position of plate-type debris. Further, an impact damage prediction model for the glass curtain wall of an urban building is proposed. In the proposed model, the flight trajectory analysis of the wind-borne debris is embedded in the context of the local wind environment in a residential area obtained by CFD simulation. The damage caused by the impact of debris on the glass curtain wall of the buildings is then analyzed and illustrated by an example. The proposed model is of great significance for the wind damage analysis of urban building glass curtain walls considering local wind environment and real trajectories of debris.
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 that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Financial supports from the National Key R&D Program of China (Grant No. 2017YFC0803300) are highly appreciated.
References
Baker, C. J. 2007. “The debris flight equations.” J. Wind Eng. Ind. Aerodyn. 95 (5): 329–353. https://doi.org/10.1016/j.jweia.2006.08.001.
Barbato, M., F. Petrini, V. U. Unnikrishnan, and M. Ciampoli. 2013. “Performance-based hurricane engineering (PBHE) framework.” Struct. Saf. 45 (Nov): 24–35. https://doi.org/10.1016/j.strusafe.2013.07.002.
Brewick, P., L. Divel, K. Butler, R. Bashor, and A. Kareem. 2009. “Consequence of urban aerodynamics and debris impact in extreme wind events.” In Proc., 11th Americas Conf. on Wind Engineering, 17. Notre Dame, IN: Univ. of Notre Dame.
Chou, J. C. K. 1992. “Quaternion kinematic and dynamic differential equations.” IEEE Trans. Rob. Autom. 8 (1): 53–64. https://doi.org/10.1109/70.127239.
Chou, P. Y. 1952. Theoretical mechanics. [In Chinese.] Beijing: People’s Education Press.
Fehlberg, E. 1969. “Klassische Runge-Kutta-Nystrom-Formeln funfter und siebenter Ordnung mit Schrittweiten-Kontrolle.” Computing 4 (2): 93–106. https://doi.org/10.1007/BF02234758.
Ferziger, J. H., and M. Peric. 2002. Computational methods for fluid dynamics. 3rd ed. Berlin: Springer.
Greenwood, D. T. 2003. Advanced dynamics. London: Cambridge University Press.
Hargreaves, D. M., B. Kakimpa, and J. S. Owen. 2014. “The computational fluid dynamics modelling of the autorotation of square, flat plates.” J. Fluid Struct. 46 (Apr): 111–133. https://doi.org/10.1016/j.jfluidstructs.2013.12.006.
Hatzikyriakou, A., N. Lin, J. Gong, S. Xian, X. Hu, and A. Kennedy. 2016. “Component-based vulnerability analysis for residential structures subjected to storm surge impact from Hurricane Sandy.” Nat. Hazard. Rev. 17 (1): 05015005. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000205.
Holmes, J. D. 2010. “Windborne debris and damage risk models: A review.” Wind Struct. 13 (2): 95–108. https://doi.org/10.12989/was.2010.13.2.095.
Holmes, J. D., C. J. Baker, and Y. Tamura. 2006a. “Tachikawa number: A proposal.” J. Wind Eng. Ind. Aerodyn. 94 (1): 41–47. https://doi.org/10.1016/j.jweia.2005.10.004.
Holmes, J. D., C. W. Letchford, and N. Lin. 2006b. “Investigations of plate-type windborne debris—Part II: Computed trajectories.” J. Wind Eng. Ind. Aerodyn. 94 (1): 21–39. https://doi.org/10.1016/j.jweia.2005.10.002.
Huang, P., H. T. Lin, and M. Gu. 2020. “Wind tunnel investigation of autorotation of plate: The effects of geometry, Reynolds number and rotation direction.” J. Wind Eng. Ind. Aerodyn. 196 (Jan): 104012. https://doi.org/10.1016/j.jweia.2019.104012.
Huang, P., H. T. Lin, F. Hu, and A. Gu. 2018. “Experimental study and FE analysis of tile roofs under simulated strong wind impact.” Wind Struct. 26 (2): 75–87. https://doi.org/10.12989/was.2018.26.2.075.
Huang, P., F. Wang, A. M. Fu, and A. Gu. 2016. “Numerical simulation of 3-D probabilistic trajectory of plate-type wind-borne debris.” Wind Struct. 22 (1): 17–41. https://doi.org/10.12989/was.2016.22.1.017.
Ji, X., G. Huang, F. Wu, and Z.-H. Lu. 2020. “Wind-induced hazard assessment for low-rise building envelope considering potential openings.” J. Struct. Eng. 146 (4): 04020039. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002553.
Kakimpa, B., D. M. Hargreaves, and J. S. Owen. 2012a. “An investigation of plate-type windborne debris flight using coupled CFD-RBD models. Part I: Model development and validation.” J. Wind Eng. Ind. Aerodyn. 111 (Dec): 95–103. https://doi.org/10.1016/j.jweia.2012.07.008.
Kakimpa, B., D. M. Hargreaves, and J. S. Owen. 2012b. “An investigation of plate-type windborne debris flight using coupled CFD-RBD models. Part II: Free and constrained flight.” J. Wind Eng. Ind. Aerodyn. 111 (Dec): 104–116. https://doi.org/10.1016/j.jweia.2012.07.011.
Kakimpa, B., D. M. Hargreaves, J. S. Owen, P. Martinez-Vazquez, C. J. Baker, M. Sterling, and A. D. Quinn. 2010. “CFD modelling of free-flight and auto-rotation of plate type debris.” Wind Struct. 13 (2): 169–189. https://doi.org/10.12989/was.2010.13.2.169.
Karimpour, A., and N. B. Kaye. 2012. “On the stochastic nature of compact debris flight.” J. Wind Eng. Ind. Aerodyn. 100 (1): 77–90. https://doi.org/10.1016/j.jweia.2011.11.001.
Kordi, B., G. Traczuk, and G. A. Kopp. 2010. “Effects of wind direction on the flight trajectories of roof sheathing panels under high winds.” Wind Struct. 13 (2): 145–167. https://doi.org/10.12989/was.2010.13.2.145.
Launder, B. E., and D. B. Spalding. 1974. “The numerical computation of turbulent flows.” Comput. Methods Appl. Mech. Eng. 3 (2): 269–289. https://doi.org/10.1016/0045-7825(74)90029-2.
Leonard, B. P. 1979. “A stable and accurate convective modelling procedure based on quadratic upstream interpolation.” Comput. Methods Appl. Mech. Eng. 19 (1): 59–98. https://doi.org/10.1016/0045-7825(79)90034-3.
Lin, N., J. D. Holmes, and C. W. Letchford. 2007. “Trajectories of wind-borne debris in horizontal winds and applications to impact testing.” J. Struct. Eng. 133 (2): 274–282. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:2(274).
Lin, N., C. W. Letchford, and J. D. Holmes. 2006. “Investigation of plate-type windborne debris. Part I. Experiments in wind tunnel and full scale.” J. Wind Eng. Ind. Aerodyn. 94 (2): 51–76. https://doi.org/10.1016/j.jweia.2005.12.005.
Lin, N., and E. Vanmarcke. 2008. “Windborne debris risk assessment.” Probab. Eng. Mech. 23 (4): 523–530. https://doi.org/10.1016/j.probengmech.2008.01.010.
Lin, N., and E. Vanmarcke. 2010a. “Windborne debris risk analysis—Part I. Introduction and methodology.” Wind Struct. 13 (2): 191–206. https://doi.org/10.12989/was.2010.13.2.191.
Lin, N., and E. Vanmarcke. 2010b. “Windborne debris risk analysis—Part II. Application to structural vulnerability modeling.” Wind Struct. 13 (2): 207–220. https://doi.org/10.12989/was.2010.13.2.207.
Luo, Y., and X. Q. Ai. 2022. “Wind risk assessment of urban street trees based on wind-induced fragility.” Dis. Prev. Res. 1 (Nov): 7.
Martinez-Vazquez, P., C. J. Baker, M. Sterling, A. Quinn, and P. J. Richards. 2010. “Aerodynamic forces on fixed and rotating plates.” Wind Struct. 13 (2): 127–144. https://doi.org/10.12989/was.2010.13.2.127.
Martinez-Vazquez, P., B. Kakimpa, M. Sterling, C. J. Baker, A. D. Quinn, P. J. Richards, and J. S. Owen. 2012. “Pressure field of a rotating square plate with application to windborne debris.” Wind Struct. 15 (6): 509–529. https://doi.org/10.12989/was.2012.15.6.509.
Martinez-Vazquez, P., M. Sterling, C. J. Baker, A. D. Quinn, and P. J. Richards. 2011. “Autorotation of square plates, with application to windborne debris.” Wind Struct. 14 (2): 167–186. https://doi.org/10.12989/was.2011.14.2.167.
Minor, J. E. 2005. “Lessons learned from failures of the building envelope in windstorms.” J. Archit. Eng. 11 (1): 10–13. https://doi.org/10.1061/(ASCE)1076-0431(2005)11:1(10).
Moghim, F., and L. Caracoglia. 2012a. “A numerical model for wind-borne compact debris trajectory estimation: Part 1—Probabilistic analysis of trajectory in the proximity of tall buildings.” Eng. Struct. 38 (May): 153–162. https://doi.org/10.1016/j.engstruct.2011.11.020.
Moghim, F., and L. Caracoglia. 2012b. “A numerical model for wind-borne compact debris trajectory estimation: Part 2—Simulated vertical gust effects on trajectory and mass momentum.” Eng. Struct. 38 (May): 163–170. https://doi.org/10.1016/j.engstruct.2011.12.032.
Murià-Vila, D., M. Á. Jaimes, A. Pozos-Estrada, A. López, E. Reinoso, M. M. Chávez, F. Peña, J. Sánchez-Sesma, and O. López. 2018. “Effects of Hurricane Odile on the infrastructure of Baja California Sur, Mexico.” Nat. Hazard. 91 (3): 963–981. https://doi.org/10.1007/s11069-017-3165-z.
Ortiz, X., D. Rival, and D. Wood. 2015. “Forces and moments on flat plates of small aspect ratio with application to PV wind loads and small wind turbine blades.” Energies 8 (4): 2438–2453. https://doi.org/10.3390/en8042438.
Richards, P. J. 2012. “Dispersion of windborne debris.” J. Wind Eng. Ind. Aerodyn. 104–106 (May–Jul): 594–602. https://doi.org/10.1016/j.jweia.2012.02.026.
Richards, P. J., N. Williams, B. Laing, M. McCarty, and M. Pond. 2008. “Numerical calculation of the three-dimensional motion of wind-borne debris.” J. Wind Eng. Ind. Aerodyn. 96 (10–11): 2188–2202. https://doi.org/10.1016/j.jweia.2008.02.060.
Robinson, A. C. 1958. On the use of quaternions in simulation of rigid-body motion. Dayton, OH: Aeronautical Research Laboratory, Wright Air Development Centre.
Sauer, T. 2006. Numerical analysis. London: Pearson Education.
Scarabino, A., and P. Giacopinelli. 2010. “Analysis of the two dimensional sheet debris flight equations: Initial and final state.” Wind Struct. 13 (2): 109–125. https://doi.org/10.12989/was.2010.13.2.109.
Shetty, M. S., L. R. Dharani, J. Wei, and D. S. Stutts. 2014. “Failure probability of laminated architectural glazing due to combined loading of wind and debris impact.” Eng. Fail. Anal. 36 (Jan): 226–242. https://doi.org/10.1016/j.engfailanal.2013.10.005.
Song, F. F., and J. P. Ou. 2010. “Windborne debris damage prediction analysis.” Front. Archit. Civ. Eng. China 4 (3): 326–330. https://doi.org/10.1007/s11709-010-0067-5.
Standohar-Alfano, C. D., S. Freyne, A. J. Graettinger, R. W. Floyd, and T. N. Dao. 2015. “Performance of residential shelters during the May 20, 2013, Tornado in Moore, Oklahoma.” J. Perform. Constr. Facil. 29 (5): 04014143. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000636.
Stathopoulos, T., and B. A. Baskaran. 1996. “Computer simulation of wind environmental conditions around buildings.” Eng. Struct. 18 (11): 876–885. https://doi.org/10.1016/0141-0296(95)00155-7.
Stuelpnagel, J. 1964. “On the parametrization of the three-dimensional rotation group.” SIAM 6 (4): 422–430. https://doi.org/10.1137/1006093.
Tachikawa, M. 1983. “Trajectories of flat plates in uniform flow with application to wind-generated missiles.” J. Wind Eng. Ind. Aerodyn. 14 (1–3): 443–453. https://doi.org/10.1016/0167-6105(83)90045-4.
Tachikawa, M. 1988. “A method for estimating the distribution range of trajectories of wind-borne missiles.” J. Wind Eng. Ind. Aerodyn. 29 (1–3): 175–184. https://doi.org/10.1016/0167-6105(88)90156-0.
Talay, T. A. 1975. Introduction to the aerodynamics of flight. Washington, DC: Scientific & Technical Information Office.
Tohidi, A., and N. B. Kaye. 2017. “Aerodynamic characterization of rod-like debris with application to firebrand transport.” J. Wind Eng. Ind. Aerodyn. 168 (Sep): 297–311. https://doi.org/10.1016/j.jweia.2017.06.019.
Uchibori, K., and T. Tamura. 2019. “LES study on aerodynamics of auto-rotating square flat plate by IBM and SAMR.” J. Fluid Struct. 89 (Aug): 108–122. https://doi.org/10.1016/j.jfluidstructs.2019.04.013.
Visscher, B. T., and G. A. Kopp. 2007. “Trajectories of roof sheathing panels under high winds.” J. Wind Eng. Ind. Aerodyn. 95 (8): 697–713. https://doi.org/10.1016/j.jweia.2007.01.003.
Wills, J. A. B., B. E. Lee, and T. A. Wyatt. 2002. “A model of wind-borne debris damage.” J. Wind Eng. Ind. Aerodyn. 90 (4–5): 555–565. https://doi.org/10.1016/S0167-6105(01)00197-0.
Xu, F., L. Yin, W. L. Chen, Z. D. Duan, and Y. Q. Xiao. 2020. “Numerical study on coupling flight characteristics of a plate-type windborne debris.” J. Wind Eng. Ind. Aerodyn. 205 (Oct): 104319. https://doi.org/10.1016/j.jweia.2020.104319.
Information & Authors
Information
Published In
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jul 3, 2022
Accepted: Nov 22, 2022
Published online: Jan 18, 2023
Published in print: May 1, 2023
Discussion open until: Jun 18, 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.