### A Mathematical Approach for Predicting Sufficient Separation Gap between Adjacent Buildings to Avoid Earthquake-Induced Pounding

Yazan Jaradat, Harry Far, Mina Mortazavi

#### Abstract

Studies on earthquake-related damage underscore that buildings are vulnerable to significant harm or even collapse during moderate to strong ground motions. Of particular concern is seismic-induced pounding, observed in numerous past and recent earthquakes, often resulting from inadequate separation gaps between neighboring structures. This study conducted an experimental and numerical investigation to develop a mathematical equation to calculate a sufficient separation gap in order to avoid the collision between adjacent mid-rise steel-frame buildings during seismic excitation. In this study, the coupled configuration of 15-storey & 10-storey, 15-storey & 5-storey, and 10-storey & 5-storey steel frame structures was considered in the investigation. The investigation concluded with a large number of data outputs. The outputs were used to predict structural behavior during earthquakes. The obtained data were categorized into three main categories according to the earthquake's Peak Ground Acceleration (PGA) levels. Also, the derived equations were divided into three different equations to estimate the required seismic gap between neighboring buildings accordingly. The derived equations are distilled to empower engineers to rigorously evaluate non-irregular mid-rise steel frame buildings.

Full Text: PDF

#### Keywords

Separation Gap; Earthquake Induced Pounding; Seismic Response; Steel Structures; Peak Ground Acceleration; Multiple Linear Regression; Finite Element Analysis.

#### References

Miari, M., Choong, K. K., & Jankowski, R. (2019). Seismic pounding between adjacent buildings: Identification of parameters, soil interaction issues and mitigation measures. Soil Dynamics and Earthquake Engineering, 121, 135–150. doi:10.1016/j.soildyn.2019.02.024.

Jankowski, R. (2015). Pounding between Superstructure Segments in Multi-Supported Elevated Bridge with Three-Span Continuous Deck under 3D Non-Uniform Earthquake Excitation. Journal of Earthquake and Tsunami, 9(4), 1550012. doi:10.1142/S1793431115500128.

Khatami, S. M., Naderpour, H., Barros, R. C., Jakubczyk-Gałczyńska, A., & Jankowski, R. (2019). Effective formula for impact damping ratio for simulation of earthquake-induced structural pounding. Geosciences (Switzerland), 9(8), 347. doi:10.3390/geosciences9080347.

Abdel Raheem, S. E., Hayashikawa, T., & Dorka, U. (2011). Ground motion spatial variability effects on seismic response control of cable-stayed bridges. Earthquake Engineering and Engineering Vibration, 10(1), 37–49. doi:10.1007/s11803-011-0045-5.

Abdel Raheem, S. E. (2009). Pounding mitigation and unseating prevention at expansion joints of isolated multi-span bridges. Engineering Structures, 31(10), 2345–2356. doi:10.1016/j.engstruct.2009.05.010.

Luo, Y., Li, Y., Wang, X., & Lu, G. (2021). Influence of Restrainer Piers on the Seismic Performance of Long Bridges with Equal-Height Piers. Mathematical Problems in Engineering, 2021. doi:10.1155/2021/6651215.

Rosenblueth, E., & Meli, R. (1986). The 1985 Mexico earthquake. Concrete international, 8(5), 23-34.

Kasai, K., & Maison, B. F. (1997). Building pounding damage during the 1989 Loma Prieta earthquake. Engineering Structures, 19(3), 195–207. doi:10.1016/S0141-0296(96)00082-X.

Anagnostopoulos, S. A. (1996, June). Building pounding re-examined: how serious a problem is it. Eleventh world conference on earthquake engineering, 23-28 June, 1996, Acapulco, Mexico.

Lin, J., & Weng, C. (2002). A study on seismic pounding probability of buildings in Taipei metropolitan area. Journal of the Chinese Institute of Engineers, 25(2), 123–135. doi:10.1080/02533839.2002.9670687.

Lin, C. C. J., Hung, H. H., Liu, K. Y., & Chai, J. F. (2010). Reconnaissance observation on bridge damage caused by the 2008 Wenchuan (China) earthquake. Earthquake Spectra, 26(4), 1057–1083. doi:10.1193/1.3479947.

Kazemi, F., Miari, M., & Jankowski, R. (2021). Investigating the effects of structural pounding on the seismic performance of adjacent RC and steel MRFs. Bulletin of Earthquake Engineering, 19(1), 317–343. doi:10.1007/s10518-020-00985-y.

Cole, G., Dhakal, R., Carr, A. J., & Bull, D. (2010). Building pounding state of the art: Identifying structures vulnerable to pounding damage. 2010 New Zealand Society of Earthquake Engineerings (NZSEE) Conference, 26-28 March, 2010, Wellington, New Zealand.

Sekkour, H., Belounar, L., Belounar, A., Boussem, F., & Fortas, L. (2022). A Triangular Shell Element Based on Higher-order Strains for the Analysis of Static and Free Vibration. Civil Engineering Journal, 8(10), 2096-2109. doi:10.28991/CEJ-2022-08-10-06.

Efraimiadou, S., Hatzigeorgiou, G. D., & Beskos, D. E. (2013). Structural pounding between adjacent buildings subjected to strong ground motions. Part I: The effect of different structures arrangement. Earthquake Engineering & Structural Dynamics, 42(10), 1509-1528. doi:10.1002/eqe.2285.

Raheem, S. E. A., Fooly, M. Y. M., Omar, M., & Zaher, A. K. A. (2019). Seismic pounding effects on the adjacent symmetric buildings with eccentric alignment. Earthquake and Structures, 16(6), 715–726. doi:10.12989/eas.2019.16.6.715.

Polycarpou, P. C., Papaloizou, L., & Komodromos, P. (2014). An efficient methodology for simulating earthquake-induced 3D pounding of buildings. Earthquake Engineering and Structural Dynamics, 43(7), 985–1003. doi:10.1002/eqe.2383.

Leibovich, E., Rutenberg, A., & Yankelevsky, D. Z. (1996). On eccentric seismic pounding of symmetric buildings. Earthquake Engineering and Structural Dynamics, 25(3), 219–233. doi:10.1002/(SICI)1096-9845(199603)25:3<219::AID-EQE537>3.0.CO;2-H.

Jankowski, R. (2008). Earthquake-induced pounding between equal height buildings with substantially different dynamic properties. Engineering Structures, 30(10), 2818–2829. doi:10.1016/j.engstruct.2008.03.006.

Jankowski, R. (2010). Experimental study on earthquake-induced pounding between structural elements made of different building materials. Earthquake Engineering & Structural Dynamics, 39(3), 343–354. doi:10.1002/eqe.941.

Kazemi, F., Mohebi, B., & Yakhchalian, M. (2020). Predicting the seismic collapse capacity of adjacent structures prone to pounding. Canadian Journal of Civil Engineering, 47(6), 663–677. doi:10.1139/cjce-2018-0725.

Raheem, S. A., Fooly, M. Y., Shafy, A. A., Abbas, Y. A., Omar, M., Latif, M. M. S. A., & Mahmoud, S. (2018). Seismic pounding effects on adjacent buildings in series with different alignment configurations. Steel and Composite Structures, 28(3), 289-308. doi:10.12989/scs.2018.28.3.289.

Anagnostopoulos, S. A. (1988). Pounding of buildings in series during earthquakes. Earthquake Engineering & Structural Dynamics, 16(3), 443–456. doi:10.1002/eqe.4290160311.

Skrekas, P., Sextos, A., & Giaralis, A. (2014). Influence of bi-directional seismic pounding on the inelastic demand distribution of three adjacent multi-storey R/C buildings. Earthquake and Structures, 6(1), 71–87. doi:10.12989/eas.2014.6.1.071.

Sołtysik, B., & Jankowski, R. (2013). Non-linear strain rate analysis of earthquake-induced pounding between steel buildings. International Journal of Earth Sciences and Engineering, 6(3), 429–433.

Elwardany, H., Seleemah, A., & Jankowski, R. (2017). Seismic pounding behavior of multi-story buildings in series considering the effect of infill panels. Engineering Structures, 144, 139–150. doi:10.1016/j.engstruct.2017.01.078.

Khatami, S. M., Naderpour, H., Barros, R. C., Jakubczyk-Gałczyńska, A., & Jankowski, R. (2020). Determination of peak impact force for buildings exposed to structural pounding during earthquakes. Geosciences (Switzerland), 10(1), 18. doi:10.3390/geosciences10010018.

Anagnostopoulos, S. A. (1995). Earthquake induced pounding: State of the art. Proceedings of the 10th European Conference on Earthquake Engineering, 28 August-2 September, 1995, Vienna, Austria.

ICBO. (1997). Uniform building code. International Conference of Building Officials, California, United States.

EN 1998-1:2004. (2004). Design of structures for earthquake resistance-part 1: General rules, seismic actions and rules for buildings. European Committee for Standardization, Brussels, Belgium.

IBC. (2009). International Building Code. International Code Council, Illinois, United States.

Jeng, V., Kasai, K., & Maison, B. F. (1992). A Spectral Difference Method to Estimate Building Separations to Avoid Pounding. Earthquake Spectra, 8(2), 201–223. doi:10.1193/1.1585679.

Penzien, J. (1997). Evaluation of building separation distance required to prevent pounding during strong earthquakes. Earthquake Engineering & Structural Dynamics, 26(8), 849–858. doi:10.1002/(SICI)1096-9845(199708)26:8<849::AID-EQE680>3.0.CO;2-M.

Lopez-Garcia, D., & Soong, T. T. (2009). Assessment of the separation necessary to prevent seismic pounding between linear structural systems. Probabilistic Engineering Mechanics, 24(2), 210–223. doi:10.1016/j.probengmech.2008.06.002.

Filiatrault, A., & Cervantes, M. (1995). Separation between buildings to avoid pounding during earthquakes. Canadian Journal of Civil Engineering, 22(1), 164–179. doi:10.1139/l95-015.

Garcia, D. L. (2004). Separation between adjacent nonlinear structures for prevention of seismic pounding. Proceedings of the 13th World Conference on Earthquake Engineering, 1-6 August, 2004, Vancouver, Canada.

Hong, H. P., Wang, S. S., & Hong, P. (2003). Critical building separation distance in reducing pounding risk under earthquake excitation. Structural Safety, 25(3), 287–303. doi:10.1016/s0167-4730(02)00080-2.

Wang, S. S., & Hong, H. P. (2006). Quantiles of critical separation distance for nonstationary seismic excitations. Engineering Structures, 28(7), 985–991. doi:10.1016/j.engstruct.2005.11.003.

Khatami, S. M., Naderpour, H., Barros, R. C., & Jankowski, R. (2019). Verification of Formulas for Periods of Adjacent Buildings Used to Assess Minimum Separation Gap Preventing Structural Pounding during Earthquakes. Advances in Civil Engineering, 2019. doi:10.1155/2019/9714939.

Naderpour, H., Khatami, S. M., & Barros, R. C. (2017). Prediction of critical distance between two MDOF systems subjected to seismic excitation in terms of artificial neural networks. Periodica Polytechnica Civil Engineering, 61(3), 516–529. doi:10.3311/PPci.9618.

Shrestha, B. (2013). Effects of separation distance and nonlinearity on pounding response of adjacent structures. International Journal of Civil and Structural Engineering, 3(3), 603.

Favvata, M. J. (2017). Minimum required separation gap for adjacent RC frames with potential inter-story seismic pounding. Engineering Structures, 152, 643–659. doi:10.1016/j.engstruct.2017.09.025.

Barbato, M., & Tubaldi, E. (2013). A probabilistic performance-based approach for mitigating the seismic pounding risk between adjacent buildings. Earthquake Engineering and Structural Dynamics, 42(8), 1203–1219. doi:10.1002/eqe.2267.

Abdel Raheem, S. E. (2014). Mitigation measures for earthquake induced pounding effects on seismic performance of adjacent buildings. Bulletin of Earthquake Engineering, 12(4), 1705–1724. doi:10.1007/s10518-014-9592-2.

Khatami, S. M., Naderpour, H., Mortezaei, A., Razavi, S. M. N., Lasowicz, N., & Jankowski, R. (2021). Effective gap size index for determination of optimum separation distance preventing pounding between buildings during earthquakes. Applied Sciences (Switzerland), 11(5), 1–15. doi:10.3390/app11052322.

Tena-Colunga, A., & Sánchez-Ballinas, D. (2022). Required building separations and observed seismic pounding on the soft soils of Mexico City. Soil Dynamics and Earthquake Engineering, 161, 107413, 1-33. doi:10.1016/j.soildyn.2022.107413.

Kamal, M., & Inel, M. (2022). Simplified approaches for estimation of required seismic separation distance between adjacent reinforced concrete buildings. Engineering Structures, 252, 113610. doi:10.1016/j.engstruct.2021.113610.

Kamal, M., & Inel, M. (2022). A new equation for prediction of seismic gap between adjacent buildings located on different soil types. Journal of Building Engineering, 57, 104784. doi:10.1016/j.jobe.2022.104784.

AS1170.4. (2007). Structural Design Actions Part 4: Earthquake Actions in Australia. Standards Australia, Sydney, Australia.

Jaradat, Y., Sobhi, P., & Far, H. (2023). An investigation into adequacy of separation gap to preclude earthquake-induced pounding. Structural Engineering and Mechanics, 86(1), 29–48. doi:10.12989/sem.2023.86.1.029.

Jaradat, Y., Far, H., & Saleh, A. (2021). Examining the adequacy of separation gaps between adjacent buildings under near-field and far-field earthquakes. The Thirteenth International Conference on Earthquake Resistant Engineering Structures, 26–28 May, 2021.

AS/NZS3678. (2011). Structural steel—Hot-rolled plates, floorplates and slabs. Standards Australia, Sydney, Australia.

Tabatabaiefar, S., Fatahi, B., & Samali, B. (2014). Numerical and experimental investigations on seismic response of building frames under influence of soil-structure interaction. Advances in Structural Engineering, 17(1), 109–130. doi:10.1260/1369-4332.17.1.109.

Tabatabaiefar, H. R., & Mansoury, B. (2015). Detail design, building and commissioning of tall building structural models for experimental shaking table tests. The Structural Design of Tall and Special Buildings, 25(8), 357–374. doi:10.1002/tal.1262.

Tabatabaiefar, H. R. (2016). Detail design and construction procedure of laminar soil containers for experimental shaking table tests. International Journal of Geotechnical Engineering, 10(4), 328–336. doi:10.1080/19386362.2016.1145419.

Chopra A. (2007). Dynamics of Structures (3rd Ed.). Prentice Hall, New Jersey, United States.

Saleh, A., Far, H., & Mok, L. (2018). Effects of different support conditions on experimental bending strength of thin walled cold formed steel storage upright frames. Journal of Constructional Steel Research, 150, 1–6. doi:10.1016/j.jcsr.2018.07.031.

Jaradat, Y., & Far, H. (2023). Impact Stiffness of Linear Viscoelastic Model for Seismic Pounding Simulation: An Experimental Evaluation. Civil Engineering Journal (Iran), 9(6), 1289–1311. doi:10.28991/CEJ-2023-09-06-01.

Kramer S. L. (1996). Geotechnical earthquake engineering. Prentice Hall, New Jersey, United States.

K-karamodin, A., & H-Kazemi, H. (2010). Semi-active control of structures using neuro-predictive algorithm for MR dampers. Structural Control and Health Monitoring, 17(3), 237–253. doi:10.1002/stc.278.

Computers and Structures INC (CSI). (2000). SAP2000 Integrated Software for Structural Analysis and Design. Computers and Structures Inc., Berkeley, United States.

Jaradat, Y., Far, H., & Mortazavi, M. (2022). Experimental Evaluation of Theoretical Impact Models for Seismic Pounding. Journal of Earthquake Engineering, 2022, 1–21. doi:10.1080/13632469.2022.2131654.

Jaradat Y, & Far H. (2021). Project Title: Seismic Behaviour of High-rise and Mid-rise Buildings. University of Technology Sydney, Australia

Far, H., & Flint, D. (2017). Significance of using isolated footing technique for residential construction on expansive soils. Frontiers of Structural and Civil Engineering, 11(1), 123–129. doi:10.1007/s11709-016-0372-8.

Jaradat, Y., & Far, H. (2021). Optimum stiffness values for impact element models to determine pounding forces between adjacent buildings. Structural Engineering and Mechanics, 77(2), 293–304. doi:10.12989/sem.2021.77.2.293.

Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models. McGraw-Hill, New York, United States.

Far, C., & Far, H. (2019). Improving energy efficiency of existing residential buildings using effective thermal retrofit of building envelope. Indoor and Built Environment, 28(6), 744–760. doi:10.1177/1420326X18794010.

Shao, J. (1993). Linear model selection by cross-validation. Journal of the American Statistical Association, 88(422), 486–494. doi:10.1080/01621459.1993.10476299.

Cox, D. R. (1984). Interaction. International Statistical Review, 52(1), 1-24. doi:10.2307/1403235.

Ostertagová, E. (2012). Modelling using polynomial regression. Procedia Engineering, 48, 500–506. doi:10.1016/j.proeng.2012.09.545.

Jeng, V., Kasai, K., & Jagiasi, A. (1992). The separation to avoid seismic pounding. Proceedings of the Tenth World Conference on Earthquake Engineering, 19-24 July, Madrid, Spain.

Kasai, K., Jagiasi, A. R., & Jeng, V. (1996). Inelastic Vibration Phase Theory for Seismic Pounding Mitigation. Journal of Structural Engineering, 122(10), 1136–1146. doi:10.1061/(asce)0733-9445(1996)122:10(1136).

Denham, D. (1992). Earthquake attack in the Sydney basin: What is the risk? Exploration Geophysics, 23(4), 579–587. doi:10.1071/EG992579.

Zhang, X., & Far, H. (2022). Effects of dynamic soil-structure interaction on seismic behaviour of high-rise buildings. Bulletin of Earthquake Engineering, 20(7), 3443–3467. doi:10.1007/s10518-021-01176-z.

Full Text: PDF

DOI: 10.28991/CEJ-2023-09-10-02

### Refbacks

• There are currently no refbacks.