地震超材料於橋墩基礎之設計架構研發與應用

Abstract

隨著對結構耐震性能要求的提升，地震超材料近年來逐漸被視為一項具發展潛力的創新抗震解決方案，能夠削弱地震波傳遞時所攜帶的震動能量，進而保護結構物不受地震災害所破壞。然而，現有的地震超材料設計方法多仰賴耗時的反覆試誤程序，使得帶隙特性的精確控制以及單元晶格數量之最佳配置難以達成，進而限制其後續之應用發展。本研究提出一套以局部共振機制為基礎的理論導向設計框架，基於理論公式所揭示的關鍵見解，協助工程師依據不同應用場景調整單元晶格之材料性質與幾何參數，進而設計出具備目標帶隙的地震超材料。同時，透過無因次位移包絡線的推導，可以有效率地估算達成使用者所設定衰減效能所需的單元晶格數量。為有效衰減低頻地震波，本研究開發出一種三維地震超材料單元晶格，具備1.6至2.7Hz的帶隙頻率範圍，並推導其對應之無因次位移包絡線，作為設計框架的應用範例之一。另一方面，為驗證其工程應用之可行性，進一步將該單元晶格嵌入於傳統橋梁結構中的淺基礎與沉箱基礎系統，構建地震超材料嵌入式橋梁模型（seismic metamaterial-embedded bridge models），作為新型耐震橋梁設計之應用實例，並透過頻率掃描分析與時間歷時分析評估其波動衰減效能。頻率掃描分析結果顯示，兩種橋梁模型皆在帶隙範圍內展現顯著的波動衰減能力，在特定激振方向下，最大衰減率超過98%，且所有方向之衰減效能皆維持在86%以上。此外，歷時分析亦顯示，在多組地震加速度紀錄下，橋面板、橋墩帽與橋柱等構件的加速度反應皆明顯降低。其中，淺基礎模型之最大衰減率分別為49%、87%與80%；沉箱基礎模型則為39%、90%與79%。整體而言，本研究所提出之設計框架及其橋梁應用案例，不僅促進地震超材料的發展與工程實務之應用，也展現其在基礎設施中的抗震韌性提升效果，以及作為未來耐震設計方案之潛力。

With increasing emphasis on improving structural resilience, seismic metamaterials have emerged as a promising and innovative solution for earthquake protection. By attenuating vibrational energy during wave propagation, they help safeguard structures against earthquake-induced damage. Despite their potential, designing such materials remains challenging due to reliance on time-intensive trial-and-error methods, which hinder precise control over bandgap characteristics and the optimal configuration of unit cells for effective wave attenuation. In this study, a theory-driven design framework for seismic metamaterials is proposed, grounded in the local resonance mechanism. The proposed framework allows engineers to customize material properties and geometric parameters to achieve a desired bandgap, while also utilizing dimensionless displacement envelopes to efficiently estimate the required number of unit cells to meet user-defined attenuation targets. A three-dimensional seismic metamaterial unit cell is developed, exhibiting a bandgap between 1.6 and 2.7 Hz. To demonstrate their feasibility for engineering implementation, the unit cells are embedded into conventional shallow and caisson foundation systems to construct seismic metamaterial-integrated (SM-embedded) bridge models. Frequency sweep analysis reveals that both SM-embedded models achieve significant wave attenuation within the bandgap, with peak attenuation rates surpassing 98% in certain excitation directions and maintaining over 86% across all directions. Time history analyses under various ground motion records further confirm notable reductions in structural accelerations at the deck, pier cap, and column. Maximum attenuation rates reach 49%, 87%, and 80% for the shallow foundation model, and 39%, 90%, and 79% for the caisson foundation model. Overall, these findings underscore the effectiveness of the proposed design framework in advancing the development and real-world integration of seismic metamaterials for earthquake-resilient infrastructure.