On the Effect of Near and Far Field Earthquakes on Strength Reduction Factor and Inelastic to Elastic Displacement Ratio, Demand Ductility Concept

The experience of previous earthquakes shows that the inelastic response of structure relates to the intensity and content of ground motion. In this case, the evaluation of nonlinear response of structure demonstrates the reduction in the base shear force. This reduction leads to inelastic base shear is defined by Behavior Factor (strength reduction factor) in seismic codes. One of the important parts in R factor is ductility reduction factor Rμ or. While Rμ is related to type of earthquake, it seems that for near fault motions there would be a different value in comparison to ordinary earthquakes. Fir the near fault earthquakes, due to direction of fault rupture from the site, the directivity effect becomes an important parameter. Previous researches show that for forward directivity effect, there would be two components for earthquakes. One is strike normal and the other is strike parallel. In this paper these components are named as the SN and SP. Also, in concept of performance -based design, to calculate target displacement, the ratio between inelastic and elastic response of structure is an important index. In this paper, this ratio is named as CR. It is good to mention that CR factor is defined as a C1 coefficient in FEMA440. In the previous research, the evaluation of CR for near and far fault motions has less considered.
To evaluate Rμ and CR, the extended number of SDOF systems (from 0.2 to 4 Sec.) for four levels of target ductility (2, 3, 4 and 5) have been considered. Then, Rμ and CR calculated for near field (normal and parallel component) and far fault earthquakes. At the end, for the strike normal component, a sensitivity analysis was carried out due to strain hardening ratio and inherent damping. To perform the analysis in Opensees, the nonlinear time history analysis was selected. During the assessment of Rμ and CR, the strain hardening slope and damping have been selected 3% and 5% respectively. The steel material was defined as bilinear. To set the demand ductility with prescribed target ductility, during trial and error procedure, the yield strength of SDOF was changed since the target ductility achieved. To evaluate sensitivity of Rμ and CR to the effect of strain hardening slope, this factor was selected as 0, 3, 5 and 10%. In the case of damping sensitivity, inherent damping were selected as 2, 5. 10 and 20%. To solve the inelastic equation of motion, the Newmark-Beta method was selected. The inelasticity in Opensees was modeled with distributed plasticity using the fiber element. Finally to calculate Rμ and CR for near and far field motions, approximately 84000 nonlinear time history analysis have been carried out. Also, to study sensitivity of Rμ and CR to damping and strain hardening ratio for the strike normal earthquake, approximately 22400 nonlinear time history analysis have been carried out.
The results show that for all three sets of the earthquake, the Rμ increases and then constant while the fundamental period (T) increases. For small value of ductility (μ), increasing T may lead that Rμ converges to target ductility. In the near field, while T and μ increase, Rμ is almost greater than μ. Also, for small value of T, Rμ is not depend on demand μ. The study shows using far field value of Rμ for near field motions may lead to Non-conservative value. Furthermore, while T increases, the CR value converges to the unit. In the short period, CR depends on μ and T severely. Using CR of far field against SN component leads to Non-conservative result. For a constant value of μ and T, increasing damping increases CR. Using C1 for near field motions is Non-conservative for near field motions. Also, for short periods and high ductility demand, CR, corresponding to SN component is 40% greater than C1. Evaluation of ratio between displacement modification factor and behavior factor shows (Cd/R) for T greater than 1 Sec. this ratio converges to the unit. For small period value, this ratio is dependent to period significantly. Also, using Cd/R of far field for near field motions may lead to inaccurate results.