## 1 Introduction  
At present, the velocity pulse effect caused by near-fault earthquake waves has attracted the extensive attention of researchers. Although the Imperial Valley earthquake in 1979, the Northridge earthquake in 1994, the Kobe earthquake in 1995, the Kocaeli earthquake and Chi-Chi earthquake in 1999 are all moderate earthquakes, they caused serious damage and loss of life and damage to structures [1]. From the existing strong earthquake records, the predominant velocity pulse emerges from either forward directivity or filing step effects [2; 3; 4; 5]. Forward directivity effects show that the component perpendicular to the fault has a strong velocity pulse and filing step effects show residual and irrecoverable displacement due to the relative movements of ruptures [6; 7; 8]. Hence, the velocity pulse effect of near-fault earthquake waves can increase the seismic energy and cause serious damage to the structure and leave a permanent displacement. Different from the common far-field earthquake waves, short-duration and high-energy characteristics of the near-fault earthquake waves are a great potential destructive threat and thus increase the seismic requirement of structures [9]. The unique velocity pulse effect has been studied by many researchers on different structural systems [10]. [PERSON] et al. studied the influence of near-fault earthquake waves on the isolation structure with high damping rubber bearing [11]. At the same time, the comprehensive effects of horizontal and vertical ground motion components are considered and the numerical analysis of the bi-reinforcement concrete buildings is carried out according to the European seismic code. [PERSON] et al. introduced the influence on the seismic performance of the original reinforced concrete (RC)structure and RC structure strengthened by Fiber Reinforced Polymer (FRP)at the near-fault earthquake waves loading [12]. The results showed that the strengthening technology of FPR can improve the rigidity, strength and lateral displacement capacity of the structure. [PERSON] et al. analyzed the important influence of the velocity pulse effect of near-fault earthquake waves on the seismic performance of elastic frame and inelastic frame [13]. The results showed that the early yielding occurs at the higher storied of the structure when the natural vibration period is longer than the pulse period. With the increase of the seismic intensity, the ductility demands move to the bottom stories. The change rule is opposite when the natural vibration period is shorter than the pulse period. [PERSON] et al. studied the influence of near-fault earthquake waves from the Chi-Chi earthquake on the seismic performance of the structure [14]. Based on the test study, the response of a single degree of the freedom inelastic system is calculated by the improved nonlinear hysteretic model. According to the nonlinear elastic response spectrum, the variation of base shear coefficient is discussed. [PERSON] et al. analyzed the impulse effect of near-fault earthquake waves on the multi-story building and 54 near-fault earthquake wave tests were carried out for three kind of multi-story building [15]. Besides, when the ratio of pulse period and the basic period are in the range of 0.5-2.5, the equivalent pulse model can better reflect the influence of forward directionality on the structure. From the aforementioned study, seismic risk assessments of the precast concrete structures under near-fault earthquake waves using the fragility analysis has been little reported in the literature [16]. Since the velocity pulse effect of near-fault earthquake waves can generate more significant inelastic deformation, many structural systems with high ductility and effective seismic energy dissipation have been developed in recent years. The self-centering reinforced concrete frame using the unbonded prestressed tendons have been proposed, which can maintain good self-restoring ability and retain minimal residual deformation [17; 18; 19].