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As a research hotspot in earthquake engineering, the performance-based seismic design concept has achieved mature applications in the seismic damage assessment of bridges, but its implementation in seismic design still needs further research. This study proposes a multi-objective optimization design method for piers based on seismic reliability by integrating the probabilistic seismic risk analysis framework with response surface theory and the improved Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ). First, the method for establishing seismic reliability of bridges is elaborated by combining seismic fragility and seismic hazard theories. A mathematical optimization model is then proposed with the seismic reliability of bridges and the material cost of piers as objective functions. A systematic design workflow for seismic optimization of piers is established by embedding response surface theory and the NSGA-Ⅱ. Subsequently, a typical highway bridge is taken as a case study. In accordance with the seismic design specifications for bridges in China, the seismic hazard curve and seismic vulnerability curve are developed, and the seismic damage characteristics of the bridge are analyzed. Finally, a response surface model for seismic reliability is developed to perform seismic optimization design for the case study bridge. The results show that the response surface model based on the quadratic polynomial can accurately describe the implicit relationship between the design parameters of piers and the seismic reliability of the bridge. The proposed seismic optimization design method in this paper can improve the seismic reliability of the bridge or reduce the material cost of the piers. Incorporating seismic reliability as an objective function directly consider the influence of piers on the seismic damage risk of the bridge. In addition, the multi-objective optimization seismic design can overcome the limitations of traditional empirical design methods and achieve more refined quantitative design. Designers can flexibly obtain the optimal solution from the Pareto solution set based on different optimization strategies.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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