## 4 Building Damage Prediction Based on the Calculated Ground Motions
### Results of Building Damage Predictions  
When we predicted building damage distributions based on the synthetic ground motions in the previous section, we restricted the calculation of the damage ratios to the K-NET, KiK-net, and JMA strong motion network sites within 400 km of the assumed fault surface with the PGA higher than 200 cm/s\({}^{2}\). The threshold in PGA was primarily based on our experience that showed that heavy damage or higher does not occur in almost all buildings when the maximum acceleration is 200 cm/s\({}^{2}\) or less. The damage distribution figures in this section onward distinguish sites where no calculation was conducted because the input seismic motion is less than 200 cm/s\({}^{2}\) using black (solid) circles and sites where the damage calculation was conducted but no damage was estimated using white (open) circles. Hereafter, we show the building damage estimation of the hypothesized Tonankai earthquake and the whole rupture scenario along the Nankai Trough. Figures 14-17 show the damage ratio distributions based on the Nagato-Kawase model from the strong ground motion of a hypothesized Tonankai earthquake for wooden houses W02 (Figure 14, together with the estimated seismic intensity distribution), three- and five-storied steel structures, S03 and S05 (Figure 15), three- and six-storied RC structures, R03 and R06 (Figure 16), and nine- and twelve-storied RC structures, R09 and R12 (Figure 17). The old (pre-1981) and new (post-1981) building standard for seismic performance is distinguished except for wooden houses. Figure 18 shows simple average damage ratios at all the sites where the damage ratios are calculated for different structural types, the number of stories, and construction ages. From these figures it is apparent that the old buildings built before 1981 have higher damage ratios than new buildings built after  
Figure 12: An example of the degrading trilinear models used for RC buildings based on the current building standard in Japan (**left**) and the log-normal distribution of existing ratios with different yield capacity ratios for RC buildings based on the field survey by [PERSON] [36] (**right**). Figure 13: A comparison of the reproduced (**left**) and observed (**right**) damage ratio (heavy or higher) distributions during the Hyogo-ken Nanbu earthquake of wooden houses [4]. 1981, low-rise steel structures have the highest damage ratios in lower stories, and old nine-storied RC buildings have highest damage ratio among RC structures. Based on the structural type, the damage ratio is highest in steel structures, followed by wooden houses, and then RC structures. Figure 14: The seismic intensity scale distribution of strong ground motions calculated from the hypothesized Tonankai earthquake in this study (**left**) and the damage ratio distribution for wooden houses calculated from strong ground motions for the hypothesized Tonankai earthquake and the Nagato–Kawase model [4] (**right**). Figure 15: Damage ratio distribution from the hypothesized Tonankai earthquake for steel structures by the Nagato–Kawase model. Top row: three-storied structures (S03), bottom row: five-storied structures (S05); left column: old structures (pre-1981), right column: new structures (post-1981). Figure 16: Damage ratio distribution from the hypothesized Tonankai earthquake for RC structures by the Nagato–Kawase model. Top row: three-storied structures (R03), bottom row: six-storied structures (R06); left column: old structures (pre-1981), right column: new structures (post-1981). Figure 17: Damage ratio distribution from the hypothesized Tonankai earthquake for RC structures by the Nagato–Kawase model. Top row: nine-storied structures (R09), bottom row: twelve-storied structures (R12); left column: old structures (pre-1981), right column: new structures (post-1981).