## 4 Numerical Comparisons between FPBs and SRBs
### Comparison Results and Discussions
In addition, by comparing FPB-6-2M (FPB-6-2) with FPB-3-2M (FPB-3-2) and FPB-6-3M (FPB-6-3) with FPB-3-3M (FPB-3-3) in terms of maximum horizontal acceleration, with the same acceleration control performance, the FPB models designed with a larger design displacement, a smaller curvature radius, and a smaller damping force might potentially have a better horizontal acceleration control performance than those designed with a smaller design displacement, a larger curvature radius, and a larger damping force. Figure 12: Comparisons of maximum horizontal acceleration responses of SRBs and FPBs subjected to different ground motions. Figure 13: Comparisons of maximum horizontal displacement responses of SRBs and FPBs subjected to different ground motions. Figure 14: Comparisons of residual displacement responses of SRBs and FPBs subjected to different ground motions. As observed from Figures 13, 15 and 16, under 14 (13) and 18 (21) sets (i.e., the majority) of far-field ground motions, FPB-3-2M (FPB-3-2) and FPB-6-2M (FPB-6-2) had smaller horizontal isolation displacement than SRB-3 and SRB-6, respectively, in particular, the latter. Under 29 (28) sets and 37 (36) sets (i.e., the majority) of pulse-like near-fault ground motions, FPB-3-3M (FPB-3-3) and FPB-6-3M (FPB-6-3) had smaller horizontal isolation displacement than SRB-3 and SRB-6, respectively, in particular, the latter. Note that the amounts for FPB-3-2 and FPB-6-2 shown in Figure 13 are the same as those shown in Figure 12. It is reasonable because FPB-3-2 and FPB-6-2 were designed based on the maximum horizontal displacement responses of SRB-3 and SRB-6 subjected to each ground motion, i.e., Benchmark II. If FPB-3-2 (FPB-6-2) had a larger horizontal acceleration response than SRB-3 (or SRB-6)  
Figure 16: Numerical results of SRB-3, FPB-3-3, SRB-6, and FPB-6-3 under 1999 Taiwan Chi-Chi, TCU052 (EW) (Group 3). Figure 15: Numerical results of SRB-3, FPB-3-2, SRB-6, and FPB-6-2 under 1999 Taiwan Chi-Chi, TCU074 (EW) (Group 2). under a given ground motion, it also meant that FPB-3-2 (FPB-6-2) had a larger horizontal displacement response than SRB-3 (SRB-6), and vice versa. Without considering the extremes, the response ratios on average, regardless of being subjected to far-field or pulse-like near-fault ground motions, were less than unity. To sum up, under the ground motions considered, if simply observing the amount or the average of the response ratios, the FPB models might be potentially more effective than the SRB models in reducing maximum horizontal displacement responses. By comparing FPB-6-2M (FPB-6-2) with FPB-3-2M (FPB-3-2) and FPB-6-3M (FPB-6-3) with FPB-3-3M (FPB-3-3) in terms of maximum horizontal displacement, with the same acceleration control performance, the horizontal displacement control performances of the different FPB models seemed to be not very different. As observed from Figures 14-16, only under 9 (11) and 5 (10) sets (i.e., the minority) of far-field ground motions, FPB-3-2M (FPB-3-2) and FPB-6-2M (FPB-6-2) had superior re-centering performances to SRB-3 and SRB-6, respectively. Only under 16 (13) sets (i.e., the minority) and 2 (1) sets (i.e., the minority and even almost none) of pulse-like near-fault ground motions, FPB-3-3M (FPB-3-3) and FPB-6-3M (FPB-6-3) had superior re-centering performances to SRB-3 and SRB-6, respectively. Without considering the extremes, the response ratios on average, regardless of being subjected to far-field or pulse-like near-fault ground motions, were larger than unity. To sum up, under the ground motions considered, if simply observing the amount or the average of the response ratios, the SRB models, SRB-6 (i.e., the design with a larger sloping angle and a smaller damping force) in particular, might be potentially more effective than the FPB models in controlling residual displacement responses.