# State-of-the-Art of Research on Seismic Pounding Between Buildings with Aligned Slabs

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## Abstract

Collision between adjoining buildings with aligned slabs is relevant, since the huge impact forces significantly modify the buildings dynamic behavior. The separation required by the regulations avoids pounding; however, even in recent buildings, impact can occur due to not fulfillment of codes and seismicity underestimation. Given the importance of this issue, a significant research effort has been undertaken worldwide, and a considerable number of papers are available. The complexity of this field and this abundance of information might require a review task. This paper presents a summary of the theoretical developments, discusses the most common simulation software, provides an overview of the previous research, offers recommendations to researchers, and identifies research needs.

## Keywords

Seismic pounding Colliding adjoining buildings Numerical simulation## List of Symbols

*A*Cross-section area, integration constant (Eq. 3)

*B, C, D*Integration constants (Eq. 3)

*c*Traveling axial waves velocity \(\left( {c={{\left( {\frac{E}{{\overline {{\varvec{\uprho}}} }}} \right)}^{1/2}}} \right)\), damping coefficient

*d*Gap between two adjoining colliding buildings

*E*Equivalent elastic deformation modulus

*EA*_{1}/*EA*_{2}Axial stiffness of the left/right colliding slabs

*F*Impact force

*k*Stiffness of Kelvin–Voigt model

*L*Length of the colliding slabs (in the pounding direction)

*m*Mass of a building or frame

*m*_{1}/*m*_{2}Equivalent mass of the colliding of slabs of the left/right buildings

*N*Axial force (tension positive)

*q*Time-dependent factor in the eigenvalue analysis of axial vibrations

*r*/*r′*Restitution factor

*t*Time, impact duration

- \({\overline {m} _0}\)
Part of external mass per unit length that is mobilized during the axial vibrations

*t*Time

*u*Axial displacement

*v*_{1}/*v*_{2}Traveling (absolute) velocities of left/right slabs in the beginning of the collision

*v*_{c}Joint velocity, during impact, of the interface between both colliding bodies

- \({v^{\prime}_1}\)
Traveling (absolute) velocity of the left slab at the end of the collision

- \({{{{v^{\prime}}_2}} \mathord{\left/ {\vphantom {{{{v^{\prime}}_2}} {{{v^{\prime\prime}}_2}}}} \right. \kern-0pt} {{{v^{\prime\prime}}_2}}}\)
After-impact velocity of the right slab unstrained segment/After-impact average velocity of the right slab

*x*/*x*_{1}/*x*_{2}Coordinate/coordinates of the colliding of slabs of the left/right buildings

- δ
Axial displacement in the elastic impact analysis

- ε
Axial strain

- \(\phi\)
Modal shape in the eigenvalue analysis of axial vibrations

- \(\lambda\)
Wave length in the eigenvalue analysis of axial vibrations

- ω
Angular frequency, natural frequency

- \({\rho \mathord{\left/ {\vphantom {\rho {\overline {\rho } }}} \right. \kern-0pt} {\overline {\rho } }}\)
Mass/equivalent mass per unit volume

- \(\zeta\)
Damping ratio

- \({\xi \mathord{\left/ {\vphantom {\xi \psi }} \right. \kern-0pt} \psi }\)
Coordinates (

*x*–*c t*/*x*+*c t*) in the elastic impact analysis

## Notes

### Acknowledgements

This work has received financial support from the Spanish Government under Projects BIA2014-60093-R, MAT2014-60647-R and CGL2015-6591. These supports are gratefully acknowledged.

### Compliance with Ethical Standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- 1.Alfarah B, López-Almansa F, Oller S (2017) Importance of non-simulated failure modes in incremental dynamic analysis (IDA) of non-ductile RC frames. 16WCEE, SantiagoGoogle Scholar
- 2.Anagnostopoulos SA (1988) Pounding of buildings in series during earthquakes. Earthq Eng Struct Dyn 16(3):443–456Google Scholar
- 3.Anagnostopoulos SA (1996) Building pounding re-examined: how serious a problem is it. 11WCEE, AcapulcoGoogle Scholar
- 4.Anagnostopoulos SA (2004) Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems. Earthq Eng Struct Dyn 33(8):897–902Google Scholar
- 5.Anagnostopoulos SA, Karamaneas CE. (2008) Collision shear walls to mitigate seismic pounding of adjacent buildings. 14WCEE, BeijingGoogle Scholar
- 6.Anagnostopoulos SA, Spiliopoulos KV (1992) An investigation of earthquake induced pounding between adjacent buildings. Earthq Eng Struct Dyn 21(4):289–302Google Scholar
- 7.ANSYS
^{®}(2016) Academic Research, Release 16.2, Help System, Coupled Field Analysis Guide, ANSYS, Inc., CanonsburgGoogle Scholar - 8.Arias A (1970) A measure of earthquake intensity. seismic design for nuclear power plants. MIT Press, Cambridge, pp 438–443Google Scholar
- 9.ASCE/SEI 7–10 (2010) Minimum design loads for buildings and other structures. American Society of Civil EngineersGoogle Scholar
- 10.ATC-40 (1996) Seismic evaluation and retrofit of concrete buildings. Applied Technology Council, RestonGoogle Scholar
- 11.Barros RC, Khatami SM (2013) Damping ratios for pounding of adjacent buildings and their consequence on the evaluation of impact forces by numerical and experimental models. Mec Exp 22:119–131Google Scholar
- 12.Barros RC, Naderpour H, Khatami SM, Mortezaei A (2013) Influence of seismic pounding on RC buildings with and without base isolation system subject to near-fault ground motions. J Rehabil Civil Eng 1(1):39–52Google Scholar
- 13.Bothara JK, Jury RD, Wheeler K, Stevens C (2008) Seismic assessment of buildings in Wellington: experiences and challenges. 14th WCEE, BeijingGoogle Scholar
- 14.Boyer F, Labrosse G, Chase JG, Rodgers GW, MacRae GA (2012). Effects of coefficient of restitution, structural yielding and gap ratios on the impact mechanics of building pounding. 15th WCEE, LisbonGoogle Scholar
- 15.Chanda A, Banerjee A, Das R (2016) The application of the most suitable impact model(s) for simulating the seismic response of a straight bridge under impact due to pounding. International Conference on Modern Engineering, TrivandrumGoogle Scholar
- 16.Chase J, Boyer F, Rodgers G, Labrosse G, MacRae G (2015) Linear and nonlinear seismic structural impact response spectral analyses. Adv Struct Eng 18(4):555–570Google Scholar
- 17.Chau KT, Wei XX (2001) Pounding of structures modeled as non-linear impacts of two oscillators. Earthq Eng Struct Dyn 30(5):633–651Google Scholar
- 18.Chau KT, Wei XX, Guo X, Shen CY (2003) Experimental and theoretical simulations of seismic poundings between two adjacent structures. Earthq Eng Struct Dyn 32(4):537–554Google Scholar
- 19.Chopra AK (2012). Dynamics of structures. Prentice-Hall, Upper Saddle RiverGoogle Scholar
- 20.Chouw N (2002) Influence of soil-structure interaction on pounding response of adjacent buildings due to near-source earthquakes. J Appl Mech 5:543–553Google Scholar
- 21.Chouw N, Hao H (2005) Study of SSI and non-uniform ground motion effect on pounding between bridge girders. Soil Dyn Earthq Eng 25(7):717–728Google Scholar
- 22.Chouw N, Hao H (2012) Pounding damage to buildings and bridges in the 22 February 2011 Christchurch earthquake. Int J Prot Struct 3(2):123–140Google Scholar
- 23.Cole G, Dhakal RP, Carr AJ, Bull D (2009) The effect of diaphragm wave propagation on the analysis of pounding structures. COMPDYN 2009 Conference, RhodesGoogle Scholar
- 24.Cole G, Dhakal RP, Carr AJ, Bull D (2010) Building pounding state of the art: Identifying structures vulnerable to pounding damage. 2010 NZSEE Conference, WellingtonGoogle Scholar
- 25.Cole G, Dhakal R, Carr A, Bull D (2011) An investigation of the effects of mass distribution on pounding structures. Earthquake Engineering Structural Dynamics 40(6):641–659Google Scholar
- 26.Cole GL, Dhakal RP, Turner FM (2012) Building pounding damage observed in the 2011 Christchurch earthquake. Earthq Eng Struct Dyn 41(5):893–913Google Scholar
- 27.Comartin CD, Greene M, Tubbesing SK (1995) The Hyōgo-ken Nanbu Earthquake: Great Hanshin Earthquake Disaster, January 17, 1995: Preliminary Reconnaissance Report. Earthquake Engineering ResearchGoogle Scholar
- 28.Correia AA, Virtuoso FBE (2006) Nonlinear analysis of space frames. III European Conference on Computational Mechanics, LisbonGoogle Scholar
- 29.DesRoches R, Muthukumar S (2002) Effect of pounding and restrainers on seismic response of multiple-frame bridges. J Struct Eng 128(7):860–869Google Scholar
- 30.Dimitrakopoulos E, Kappos AJ, Makris N (2009) Dimensional analysis of yielding and pounding structures for records without distinct pulses. Soil Dyn Earthq Eng 29(7):1170–1180Google Scholar
- 31.Dimitrakopoulos E, Makris N, Kappos AJ (2009) Dimensional analysis of the earthquake induced pounding between adjacent structures. Earthq Eng Struct Dyn 38(7):867–886Google Scholar
- 32.Doğan M, Günaydin A (2009) Pounding of adjacent RC buildings during seismic loads. J Eng Archit Fac Eskişehir Osman Univ 22(1):129–145Google Scholar
- 33.EERI (1989) Loma Prieta earthquakeGoogle Scholar
- 34.Efraimiadou S, Hatzigeorgiou GD, Beskos DE (2013) Structural pounding between adjacent buildings subjected to strong ground motions. Part I: the effect of different structures arrangement. Earthq Eng Struct Dyn 42(10):1509–1528Google Scholar
- 35.Elwardany H, Seleemah A, Jankowski R (2017) Seismic pounding behavior of multi-story buildings in series considering the effect of infill panels. Eng Struct 144:139–150Google Scholar
- 36.EQE (1994) The January 17, 1994 Northridge, California Earthquake, An EQE Summary Report. Retrieved from http://www.absconsulting.com/resources/Catastrophe_Reports/1994 Northridge EQ.pdf
- 37.Filiatrault A, Wagner P, Cherry S (1996) An experimental study on the seismic pounding of buildings. 11WCEE, AcapulcoGoogle Scholar
- 38.Goldsmith W (1960). Impact: the theory and physical behavior of colliding solids. ArnoldGoogle Scholar
- 39.Graff KF (1975). Wave motion in elastic solids. Courier Corporation, North ChelmsfordzbMATHGoogle Scholar
- 40.Guo A, Li Z, Li H, Ou J (2009) Experimental and analytical study on pounding reduction of base-isolated highway bridges using MR dampers. Earthq Eng Struct Dyn 38(11):1307–1333Google Scholar
- 41.Guo AX, Cui LL, Li H (2012) Impact stiffness of the contact-element models for the pounding analysis of highway bridges: experimental evaluation. J Earthquake Eng 16(8):1132–1160Google Scholar
- 42.Guo A, Cui L, Li S, Li H (2015) A phenomenological contact-element model considering slight non-uniform contact for pounding analysis of highway bridges under seismic excitations. Earthq Eng Struct Dyn 44(11):1677–1695Google Scholar
- 43.Hibbett, Karlsson, Sorensen (1998) ABAQUS/standard: User’s Manual, vol 1. Hibbitt, Karlsson & Sorensen, PhiladelphiaGoogle Scholar
- 44.Hunt KH, Crossley FRE (1975) Coefficient of restitution interpreted as damping in vibroimpact. J Appl Mech 42(2):440–445Google Scholar
- 45.Jankowski R, Wilde K, Fujino Y (1998) Pounding of superstructure segments in isolated elevated bridge during earthquakes. Earthq Eng Struct Dyn 27(5):487–502Google Scholar
- 46.Jankowski R (2005) Non-linear viscoelastic modeling of earthquake-induced structural pounding. Earthq Eng Struct Dyn 34(6):595–611Google Scholar
- 47.Jankowski R (2006) Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding. Earthq Eng Struct Dyn 35(4):517–524Google Scholar
- 48.Jankowski R (2006) Pounding force response spectrum under earthquake excitation. Eng Struct 28(8):1149–1161Google Scholar
- 49.Jankowski R (2008) Comparison of numerical models of impact force for simulation of earthquake-induced structural pounding. International Conference on Computational Science, Springer, Berlin, pp 710–717Google Scholar
- 50.Jankowski R (2008b) Earthquake-induced pounding between equal height buildings with substantially different dynamic properties. Eng Struct 30(10):2818–2829Google Scholar
- 51.Jankowski R (2010) Experimental study on earthquake-induced pounding between structural elements made of different building materials. Earthq Eng Struct Dyn 39(3):343–354Google Scholar
- 52.Jankowski R, Seleemah A, Elkhoriby S, Elwardany H (2015) Experimental study on pounding between structures during damaging earthquakes. Key Eng Mater 627:249–252Google Scholar
- 53.Jeng V, Tzeng WL (2000) Assessment of seismic pounding hazard for Taipei City. Eng Struct 22(5):459–471Google Scholar
- 54.Kagermanov A, Ceresa P, Morales E, Poveda J, O’Connor J (2017) Seismic performance of RC buildings during the MW7.8 Muisne (Ecuador) earthquake on April 2016: field observations and case study. Bull Earthquake Eng. doi: 10.1007/s10518-017-0182-y Google Scholar
- 55.Karayannis CG, Favvata MJ (2005) Earthquake-induced interaction between adjacent reinforced concrete structures with non-equal heights. Earthq Eng Struct Dyn 34(1):1–20Google Scholar
- 56.Kasai K, Maison BF (1997) Building pounding damage during the 1989 Loma Prieta earthquake. Eng Struct 19(3):195–207Google Scholar
- 57.Kharazian A (2017) Analysis of seismic pounding of moderate height RC buildings with aligned slabs. Doctoral Dissertation, Technical University of CataloniaGoogle Scholar
- 58.Kharazian A, López-Almansa F (2017) Study on pounding effect between short-to-mid height RC buildings with aligned slabs. 16WCEE Santiago, ChileGoogle Scholar
- 59.Khatiwada S, Chouw N, Butterworth JW (2011) Development of pounding model for adjacent structures in earthquakes. Ninth Pacific Conference on Earthquake Engineering, AucklandGoogle Scholar
- 60.Khatiwada S, Chouw N, Butterworth JW (2013) Evaluation of numerical pounding models with experimental validation. Bull N Z Soc Earthq Eng 46(3):117–130Google Scholar
- 61.Khatiwada S, Chouw N, Larkin T (2013). An experimental study on pounding force between reinforced concrete slabs. Australian Earthquake Engineering Society Conference, HobartGoogle Scholar
- 62.Khatiwada S, Chouw N, Larkin T (2013) Simulation of structural pounding with the sears impact model. 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos IslandGoogle Scholar
- 63.Khatiwada S, Chouw N (2014) Limitations in simulation of building pounding in earthquakes. Int J Prot Struct 5(2):123–150Google Scholar
- 64.Khatiwada S, Chouw N, Butterworth JW (2014) A generic structural pounding model using numerically exact displacement proportional damping. Eng Struct 62:33–41Google Scholar
- 65.Khatiwada S, Larkin T, Chouw N (2014) Influence of mass and contact surface on pounding response of RC structures. Earthq Struct 7(3):385–400Google Scholar
- 66.Khatiwada S, Chouw N, Larkin T (2015) Discussion on “relaxation method for pounding action between adjacent buildings at expansion joint”. Earthq Eng Struct Dyn 44(1):159–162Google Scholar
- 67.Komodromos P, Polycarpou PC, Papaloizou L, Phocas MC (2007) Response of seismically isolated buildings considering poundings. Earthq Eng Struct Dyn 36(12):1605–1622Google Scholar
- 68.Kun Y, Li L, Hongping Z (2009) A modified Kelvin impact model for pounding simulation of base-isolated building with adjacent structures. Earthq Eng Eng Vib 8(3):433–446Google Scholar
- 69.Kun Y, Li L, Hongping Z (2009) A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthq Eng Struct Dyn 38(9):1135–1142Google Scholar
- 70.Lankarani HM, Nikravesh PE (1990) A contact force model with hysteresis damping for impact analysis of multibody systems. J Mech Des 112(3):369Google Scholar
- 71.Li B, Bi K, Chouw N, Butterworth JW, Hao H (2012) Experimental investigation of spatially varying effect of ground motions on bridge pounding. Earthq Eng Struct Dyn 41(14):1959–1976Google Scholar
- 72.Liu Y, Liu WG, Wang X, He WF, Yang QR (2014) New equivalent linear impact model for simulation of seismic isolated structure pounding against moat wall. Shock Vibration. doi: 10.1155/2014/151237 Google Scholar
- 73.López-Almansa F, Kharazian A (2014) Parametric study of the pounding effect between adjacent RC buildings with aligned slabs. 15 ECEE Istanbul, TurkeyGoogle Scholar
- 74.Madani B, Behnamfar F, Tajmir Riahi H (2015) Dynamic response of structures subjected to pounding and structure–soil–structure interaction. Soil Dyn Earthq Eng 78:46–60Google Scholar
- 75.Mahmoud S, Jankowski R (2011) Modified linear viscoelastic model of earthquake-induced structural pounding. Iran J Sci Technol 35:51–62Google Scholar
- 76.Mahmoud S, Abd-Elhamed A, Jankowski R (2013) Earthquake-induced pounding between equal-height multi-storey buildings considering soil-structure interaction. Bull Earthq Eng 11(4):1021–1048Google Scholar
- 77.Maison BF, Kasai K (1990) Analysis for a type of structural pounding. J Struct Eng 116(4):957–977Google Scholar
- 78.Maison BF, Kasai K (1992) Dynamics of pounding when two buildings collide. Earthq Eng Struct Dyn 21(9):771–786Google Scholar
- 79.Malhotra PK (1998) Dynamics of seismic pounding at expansion joints of concrete bridges. J Eng Mech 124(7):794–802Google Scholar
- 80.Marin AV (2014). Development and implementation of a biaxial contact element to analyze pounding in highway bridges with deck rotation under bidirectional seismic excitation. MsC Thesis, Technical University of CataloniaGoogle Scholar
- 81.Masroor A, Mosqueda G (2012) Experimental simulation of base-isolated buildings pounding against moat wall and effects on superstructure response. Earthq Eng Struct Dyn 41:2093–2109Google Scholar
- 82.Mavronicola EA, Polycarpou PC, Komodromos P (2015). The effect of modified linear viscoelastic impact models on the pounding response of a base isolated building with adjacent structures. 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, CreteGoogle Scholar
- 83.Mavronicola EA, Polycarpou PC, Komodromos P (2016) Effect of planar impact modeling on the pounding response of base-isolated buildings. Front Built Environ 2:11Google Scholar
- 84.Mavronicola EA, Polycarpou PC, Komodromos P (2017) Spatial seismic modeling of base-isolated buildings pounding against moat walls: effects of ground motion directionality and mass eccentricity. Earthq Eng Struct Dyn 46:1161–1179Google Scholar
- 85.Muthukumar S, Des Roches R (2006) A Hertz contact model with non-linear damping for pounding simulation. Earthq Eng Struct Dyn 35(7):811–828Google Scholar
- 86.Naderpour H, Khatami SM, Barros RC (2017) Prediction of critical distance between two MDOF systems subjected to seismic excitation in terms of artificial neural networks. Period Polytech Civil Eng 61(3):516–529Google Scholar
- 87.Naserkhaki S, Aziz FNAA, Pourmohammad H (2012) Earthquake induced pounding between adjacent buildings considering soil-structure interaction. Earthq Eng Eng Vib 11(3):343–358Google Scholar
- 88.Pant DR, Wijeyewickrema AC, Ohmachi T (2010). Three-dimensional nonlinear analysis of seismic pounding between multi-story reinforced concrete buildings. 7CUEE 5ICEE, TokyoGoogle Scholar
- 89.Pant DR, Wijeyewickrema AC, Ohmachi T (2010) Seismic pounding between reinforced concrete buildings: a study using two recently proposed contact element models. 14ECEE, BeijingGoogle Scholar
- 90.Pant DR, Wijeyewickrema AC (2012). Pounding of seismically isolated reinforced concrete buildings subjected to near-fault ground motions. 15WCEE, LisbonGoogle Scholar
- 91.Pantelides CP, Ma X (1998) Linear and nonlinear pounding of structural systems. Comput Struct 66(1):79–92Google Scholar
- 92.Papadrakakis M, Mouzakis H (1995) Earthquake simulator testing of pounding between adjacent buildings. Earthq Eng Struct Dyn 24:811–834Google Scholar
- 93.Papadrakakis M, Apostolopoulou C, Zacharopoulos A, Bitzarakis S (1996) Three-dimensional simulation of structural pounding during earthquakes. J Eng Mech 122(5):423–431Google Scholar
- 94.PEER (2015). Open system for earthquake engineering simulation (OpenSEES). Pac Earthq Eng Res Cent, BerkeleyGoogle Scholar
- 95.Polycarpou PC, Komodromos P (2010) Earthquake-induced poundings of a seismically isolated building with adjacent structures. Eng Struct 32(7):1937–1951Google Scholar
- 96.Polycarpou PC, Komodromos P (2010b) On poundings of a seismically isolated building with adjacent structures during strong earthquakes. Earthq Eng Struct Dyn 39(8):933–940Google Scholar
- 97.Polycarpou PC, Komodromos P (2011) Numerical investigation of potential mitigation measures for poundings of seismically isolated buildings. Earthq Struct 2(1):1–24Google Scholar
- 98.Polycarpou PC, Komodromos P, Polycarpou AC (2013) A nonlinear impact model for simulating the use of rubber shock absorbers for mitigating the effects of structural pounding during earthquakes. Earthq Eng Struct Dyn 42(1):81–100Google Scholar
- 99.Polycarpou PC, Papaloizou L, Komodromos P (2014) An efficient methodology for simulating earthquake-induced 3D pounding of buildings. Earthq Eng Struct Dyn 43(7):985–1003Google Scholar
- 100.Polycarpou PC, Papaloizou L, Komodromos P, Charmpis DC (2015) Effect of the seismic excitation angle on the dynamic response of adjacent buildings during pounding. Earthq Struct 8(5):1127–1146Google Scholar
- 101.Rahman AM, Carr AJ, Moss PJ (2001) Seismic pounding of a case of adjacent multiple-storey buildings of differing total heights considering soil flexibility effects. Bull N Z Natl Soc Earthq Eng 34(1):40–59Google Scholar
- 102.Rezavandi A, Moghadam AS (2007) Experimental and numerical study on pounding effects and mitigation techniques for adjacent structures. Adv Struct Eng 10(2):121–134Google Scholar
- 103.Rosenblueth E (1986) The 1985 earthquake: causes and effects in Mexico City. Concr Int 8:23–34Google Scholar
- 104.Ruangrassamee A, Kawashima K (2001) Relative displacement response spectra with pounding effect. Earthq Eng Struct Dyn 30(10):1511–1538Google Scholar
- 105.Ruangrassamee A, Kawashima K (2003) Control of nonlinear bridge response with pounding effect by variable dampers. Eng Struct 25(5):593–606Google Scholar
- 106.Sasaki T, Sato E, Fukuyama K, Kajiwara K (2017) Enhancement of base-isolation based on E-defense full-scale shake table experiments: dynamic response of base-isolated building under impact due to pounding. 16WCEEGoogle Scholar
- 107.Schmid G, Chouw N (1992) Soil-structure interaction effects on structural pounding. 10WCEE, MadridGoogle Scholar
- 108.Sears J (1912) On longitudinal impact of metal rods II. Trans Camb Phys Soc 21:49–106Google Scholar
- 109.SeismoSoft (2016) A computer program for static and dynamic nonlinear analysis of framed structures. Available from SeismoSoft.comGoogle Scholar
- 110.Stronge WJ. (2004) Impact mechanics. Cambridge University Press, CambridgezbMATHGoogle Scholar
- 111.Shakya M, Kawan CK (2016) Reconnaissance based damage survey of buildings in Kathmandu valley: an aftermath of 7.8
*M*_{w}, 25 April 2015 Gorkha (Nepal) earthquake. Eng Fail Anal 59:161–184Google Scholar - 112.Takabatake H, Yasui M, Nakagawa Y, Kishida A (2014) Relaxation method for pounding action between adjacent buildings at expansion joint. Earthq Eng Struct Dyn 43(9):1381–1400Google Scholar
- 113.Takabatake H, Yasui M, Nakagawa Y, Kishida A (2015) Response to short communication on relaxation method for pounding action between adjacent buildings at expansion joint. Earthq Eng Struct Dyn 44(1):163–165Google Scholar
- 114.Valles RE, Reinhorn AM (1997) Evaluation, prevention and mitigation of pounding effects in building structures. 11WCEE, AcapulcoGoogle Scholar
- 115.Van Mier JGM, Pruijssers AF, Reinhardt HW, Monnier T (1991) Load-time response of colliding concrete bodies. J Struct Eng 117(2):354–374Google Scholar
- 116.Watanabe G, Kawashima K (2004) Numerical simulation of pounding of bridge decks. 13WCEE, VancouverGoogle Scholar
- 117.Weimin D (2000) Chi-Chi, Taiwan Earthquake Event Report. Risk Management Solutions, 16. Retrieved from http://forms2.rms.com/rs/729-DJX-565/images/eq_chi_chi_taiwan_eq.pdf
- 118.Wilson EL, Hollings JP, Dovey HH. (1979). Etabs: three dimensional analysis of building systems. Earthquake Engineering Research Center, University of California, OaklandGoogle Scholar
- 119.Yaghmaei-Sabegh S, Jalali-Milani N (2012) Pounding force response spectrum for near-field and far-field earthquakes. Sci Iran 19(5):1236–1250Google Scholar
- 120.Zhai C, Jiang S, Li S, Xie L (2015) Dimensional analysis of earthquake-induced pounding between adjacent inelastic MDOF buildings. Earthq Eng Eng Vib 14(2):295–313Google Scholar
- 121.Zhu P, Abe M, Fujino Y (2002) Modelling three-dimensional non-linear seismic performance of elevated bridges with emphasis on pounding of girders. Earthq Eng Struct Dyn 31(11):1891–1913Google Scholar