Rocking response of self-centring wall with viscous dampers under pulse-type excitations

  • Zhang, Lingxin (Institute of Engineering Mechanics, China Earthquake Administration) ;
  • Huang, Xiaogang (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Zhou, Zhen (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
  • Received : 2020.03.25
  • Accepted : 2020.06.10
  • Published : 2020.09.25


A self-centering wall (SCW) is a lateral resistant rocking system that incorporates posttensioned (PT) tendons to provide a self-centering capacity along with dampers to dissipate energy. This paper investigates the rocking responses of a SCW with base viscous dampers under a sinusoidal-type pulse considering yielding and fracture behaviour of the PT tendon. The differences in the overturning acceleration caused by different initial forces in the PT tendon are computed by the theoretical method. The exact analytical solution to the linear approximate equation of motion is also provided for slender SCWs. Finally, the effects of the ductile behaviour of PT tendons on the rocking response of a SCW are analysed. The results demonstrate that SCWs exhibit two overturning modes under pulse excitation. The overturning region with Mode 1 in the PT force cases separates the safe region of the wall into two parts: region S1 with an elastic tendon and region S2 with a fractured tendon. The minimum overturning acceleration of a SCW with an elastic-brittle tendon becomes insensitive to excitation frequency as the PT force increases. After the plastic behaviour of the PT tendon is considered, the minimum overturning acceleration of a SCW is increased significantly in the whole range of the studied wg/p.


  1. Alavi, B. and Krawinkler, H. (2004), "Behavior of momentresisting frame structures subjected to near - fault ground motions", Earthq. Eng. Sructuct. Dyn., 33(6), 687-706.
  2. Aaleti, S. and Sritharan, S. (2009), "A simplified analysis method for characterizing unbonded post-tensioned precast wall systems", Eng. Struct., 31(12), 2966-2975.
  3. Apostolou, M., Gazetas, G. and Garini, E. (2007), "Seismic response of slender rigid structures with foundation uplifting", Soil Dyn. Earthq. Eng., 27(7), 642-654.
  4. Bray, J.D. and Rodriguez-Marek, A. (2004), "Characterization of forward-directivity ground motions in the near-fault region", Soil Dyn. Earthq. Eng., 24(11), 815-828.
  5. Bruce, T.L. and Eatherton, M.R. (2016), "Behavior of posttensioning strand systems subjected to inelastic cyclic loading", J. Struct. Eng., 142(10), 04016067.
  6. Chopra, A.K. (1995), Dynamics of Structures, Prentice-Hall: Englewood Cliffs, N.J.
  7. Dimitrakopoulos, E.G. and Giouvanidis, A.I. (2015), "Seismic response analysis of the planar rocking frame", J. Eng. Mech., 141(7), 04015003.
  8. Dimitrakopoulos, E.G. and DeJong, M.J. (2012), "Overturning of retrofitted rocking structures under pulse-type excitations", J. Eng. Mech., 138(8), 963-972.
  9. ElGawady, M.A., Ma, Q., Butterworth, J.W. and Ingham, J. (2011), "Effects of interface material on the performance of free rocking blocks", Earthq. Eng. Struct. Dyn., 40(4), 375-392.
  10. Eom, T., Kang, S. and Kim, O. (2014), "Earthquake resistance of structural walls confined by conventional tie hoops and steel fiber reinforced concrete", Earthq. Struct., 7(5), 843-859.
  11. Feng, R., Chen, Y. and Cui, G. (2018), "Dynamic response of posttensioned rocking wall-moment frames under near-fault ground excitation", Earthq. Struct., 15(3), 243-251.
  12. Giouvanidis, A.I. and Dimitrakopoulos, E.G. (2017), "Seismic performance of rocking frames with flag-shaped hysteretic behavior", J. Eng. Mech., 143(5), 04017008.
  13. Housner, G.W. (1963), "The behavior of inverted pendulum structures during earthquakes", Bull. Seismol. Soc. Amer., 53(2), 403-417.
  14. Kurama, Y.C., Sause, R., Pessiki, S. and Lu, L.W. (2002), "Seismic response evaluation of unbonded post-tensioned precast walls", ACI Struct. J., 99(5), 641-651.
  15. Lim, W.Y. and Hong, S.G. (2014), "Cyclic loading tests for precast concrete cantilever walls with C-type connections", Earthq. Struct., 7(5), 753-777.
  16. Makris, N. and Vassiliou, M.F. (2014), "Dynamics of the rocking frame with vertical restrainers", J. Struct. Eng., 141(10), 04014245.
  17. Makris, N. and Roussos, Y.S. (2000), "Rocking response of rigid blocks under near-source ground motions", Geotechnique, 50(3), 243-262.
  18. Makris, N. and Zhang, J. (2001), "Rocking response of anchored blocks under pulse-type motions", J. Eng. Mech., 127(5), 484-493.
  19. Mavroeidis, G.P. and Papageorgiou, A.S. (2003), "A mathematical representation of near-fault ground motions", Bull. Seismol. Soc. Amer., 93(3), 1099-1131.
  20. Palermo, D., Vecchio, F.J. and Solanki, H. (2002), "Behavior of three-dimensional reinforced concrete shear walls", ACI Struct. J., 99(1), 81-89.
  21. Perez, F.J., Pessiki, S. and Sause, R. (2004), "Seismic design of unbonded post-tensioned precast concrete walls with vertical joint connectors", PCI J., 49(1), 58-79.
  22. Perez, F.J. Pessiki, S. and Sause, R. (2013), "Experimental lateral load response of unbonded post-tensioned precast concrete walls", ACI Struct. J., 110(6), 1045-1055.
  23. Perez, F.J., Sause, R. and Pessiki, S. (2007), "Analytical and experimental lateral load behavior of unbonded posttensioned precast concrete walls", J. Struct. Eng., 133(11), 1531-1540.
  24. Restrepo, J.I. and Rahman, A. (2007), "Seismic performance of self-centering structural walls incorporating energy dissipators", J. Struct. Eng., 133(11), 1560-1570.
  25. Sritharan, S., Beyer, K., Henry, R.S., Chai, Y.H., Kowalsky, M. and Bull, D. (2014), "Understanding poor seismic performance of concrete walls and design implications", Earthq. Spectra, 30(1), 307-334.
  26. Vassiliou, M.F. and Makris, N. (2015), "Dynamics of the vertically restrained rocking column", J. Eng. Mech., 141(12), 04015049.
  27. Xu, L., Xiao, S. and Li, Z. (2018), "Hysteretic behavior and parametric studies of a self-centering RC wall with disc spring devices", Soil Dyn. Earthq. Eng., 115, 476-488.
  28. Zhang, J. and Makris, N. (2001), "Rocking response of freestanding blocks under cycloidal pulses", J. Eng. Mech., 127(5), 473-483.