Hysteretic energy prediction method for mainshock-aftershock sequences

Structures located in seismically active regions may be subjected to mainshock-aftershock (MSAS) sequences. Strong aftershocks significantly affect the hysteretic energy demand of structures. The hysteretic energy, E (H,seq), is normalized by mass m and expressed in terms of the equivalent velocity, V (D,seq), to quantitatively investigate aftershock effects on the hysteretic energy of structures. The equivalent velocity, V (D,seq), is computed by analyzing the response time-history of an inelastic single-degree-of-freedom (SDOF) system with a varying vibration period subjected to 309 MSAS sequences. The present study selected two kinds of MSAS sequences, with one aftershock and two aftershocks, respectively. The aftershocks are scaled to maintain different relative intensities. The variation of the equivalent velocity, V (D,seq), is studied for consideration of the ductility values, site conditions, relative intensities, number of aftershocks, hysteretic models, and damping ratios. The MSAS sequence with one aftershock exhibited a 10% to 30% hysteretic energy increase, whereas the MSAS sequence with two aftershocks presented a 20% to 40% hysteretic energy increase. Finally, a hysteretic energy prediction equation is proposed as a function of the vibration period, ductility value, and damping ratio to estimate hysteretic energy for mainshock-aftershock sequences.