For the evaluation of structures with known ductility demands,the constant-ductility displacement ratio spectra(CDDRS) are particularly useful for providing inelastic displacement ratios to estimate maximum lateral inelastic displacement demands from maximum elastic displacement demands.The CDDRS are computed for single-degree-of-freedom systems(SDOF) by considering or ignoring P-Δ effect for different ductility levels when subjected to 344 earthquake ground motions recorded in four site classes.The modified expressions of CDDRS for P-Δ effect are proposed.It is concluded that the P-Δ effect on CDDRS is significant,and the effect increases with the increase of ductility level.In the long-period region,the CDDRS ignoring P-Δ effect almost conforms to the equal-displacement rule.But in the case of higher ductility level,the CDDRS considering P-Δ effect are much higher than 1.0,which do not conform to the equal-displacement rule.
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construc- tion process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investi- gated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in corner and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computa- tional efficiency of PML boundary is only a little lower than MTF boundary.
In the last twenty years, near-field problems became an important topic for both seismologists and civil engineers. The one aspect is to illuminate mechanisms of earthquakes and explain new phenomena. The another aspect is the ground motions, which are usually assigned by engineers as a type of input load for seismic design of structures, sometimes can control the final design results. The experiments, performance evaluations and other related aspects are all based on the specified type of load. As a result, many aspects related to civil engineering will be influenced by changes of the type of load. Hence, the characteristics of the load and the corresponding response of structures are desired for studying. In this paper, the state-of-the-art of near-field problems in civil engineering is comprehen- sively reviewed, which include inherent characteristics of near-field ground motions and influences of these ground motions on civil structures. The existing problems are pointed out and work needed to be further investi- gated in the future is suggested. It is believed that the information in this paper can be useful to advance the state of investigation on near-field problems.
