## 6 Further Discussion  
To verify the great seismic behavior of the novel SCPC frame under near-fault earthquake waves and the accuracy of seismic risk assessment of numerical model, a five-story four-span cast-in-place RC frame (a reinforced concrete frame) and the traditional SCPC frame (a traditional self-centering precast concrete frame without hysteretic dampers) have been modelled by OpenSees. The section sizes and reinforcements arrangement of the two frames are consistent with the prototype structures. Figure 19(a) displays the analytical connection model of the RC frame; all the structure members are simulated by the Nonlinear Beam Column element. The Joint2D element is adopted in the modelling of the connection core area and is idealized as a parallelogram shaped shear panel with adjacent elements connected to its mid-points. The Joint2D element includes a spring element inside the joint to represent the shear behavior of the core area and four spring elements located at the beam column interface to simulate the sliding the pulling out of reinforcements. The hysteretic curves of force and deformation of each spring can be simulated by the Pinching4 material model [49]. The Pinching4 material model also reflects the pinching effect, degradation effect of stiffness and strength under cyclic loading. The analytical model of the traditional SCPC frame (shown in Figure 19(b)) and the modelling method of the novel joint are close to the aforementioned novel SCPC beam-column connection. The concrete is also assigned to the Concrete 01 material model and the enhancement factor of the stirrup restraint effect is 0.2. The steel bars and PT tendons are also assigned to the Steel 02 material model, which are also based on the Giuffre-Menegotto-Pinto model. Because there are no hysteretic dampers to dissipate energy, the two pairs of zeroLength spring elements simulate the gap of connection opening and closing at the end of the beam under earthquake actions. The shear slip at the beam-column interface is avoided when gap has opened. The rigidlink elements are selected to reflect the coupling characteristics between the node of gaps and the relevant nodes of structural components. The Truss element is also used to simulate the unbonded PT tendons between node 7 and node 12 for connection of the traditional SCPC frame. Figure 22: Annual and 50-year exceeding probabilities of novel SCPC frame under near-fault earthquake waves. The site class and seismic intensity are similar to the prototype structures, 21 near-fault earthquake waves from PEER record database are also chosen for the elastoplastic dynamic analysis for the RC frame and the traditional SCPC frame. The peak ground acceleration of selected ground motions are all satisfy the DBE and MCE levels through linearly scaled. The damping ratio of the Rayleigh damper is 5% for the RC structure and 3% for the traditional SCPC structure, respectively. Tenety second last-time free vibration analysis of the frames are also continued after the applying each near-fault ground motion to calculate the residual deformation. The peak inter-story drift ratios \(\theta_{max}\) of the three frames for each near-fault ground motion and for each story at the DBE and MCE levels are displayed in Figure 13(a),b. Figure 13(a) indicates that the peak inter-story drift ratios of the traditional SCPC frame are the largest and the novel SCPC frame are the smallest subjected to each earthquake wave at the DBE and MCE levels. The maximum difference between the maximum response of the RC frame and the novel SCPC frame subjected to all the earthquake waves are 11.3% and 12.6% at the DBE and MCE level. The maximum difference between the maximum response of the traditional SCPC frame and the novel SCPC frame subjected to all the earthquake waves is 26.4% and 13.8% at the DBE and MCE levels, respectively. The mean value of the peak story drift ratios of the RC structure subjected to all the earthquake waves are 0.36% and 0.88% subjected to the two levels.