Intensity Measures (IMs) provide the relationship between Engineering Demand Parameters (EDPs) and seismic hazard characteristics for different structures and hence, their role in performance-based bridge design is significant. A few studies have investigated the optimal IMs for bridges under horizontal ground motions, however, detailed studies to explore the optimal IMs for isolated-bridges under the coupled vertical and horizontal records are very rare. This paper presents a procedure for the selection of optimal IMs for seismic-isolated bridges under the combined strong Horizontal Component (HC) and Vertical Component (VC) seismic excitations. Soil-Structure-Interaction (SSI) effects, the high level of uncertainties for soil properties, uncertainties for structural and geotechnical issues and advanced plasticity model for non-liquefied soil are included to explore the optimal vector-valued IMs. Four individual situations are considered to investigate the geometry effects on the selected optimal IMs. Optimal IMs criteria including efficiency, practicality, proficiency and sufficiency are investigated and developed to achieve a set of optimal vector-valued IMs for critical EDPs: drift ratio, pile-cap displacement and bearing displacement, which are affected by both HC and VC in isolated Soil-Pile-Bridge (SPB) systems. The results show that velocity-related IMs: peak ground velocity (PGV_H), Housner spectrum intensity (HI_H) and root mean square of velocity (V_RMSH) are optimal IMs as representative of HCs. In addition, structure-dependent spectral IMs: vertical spectral acceleration at T = 0.2 s (\({\text{S}}_{\text{a}0.2}^{\text{V}}\)) and square-root-of-the-sum-of-square of vertical spectral acceleration at the first and second vertical periods (\({\text{S}}_{\text{a}}^{\text{V}}\left({\text{T}}_{\text{s}}\right)\)) are the appropriate optimal IMs as representative of VCs. However, the displacement-related IM, peak ground displacement of HCs (PGD_H), may be treated as optimal IMs for SPB system supported by inclined pile foundations to investigate pile-cap displacement. In addition, the sufficiency term is investigated extensively with respect to seismological parameters.

强度度量（IM）提供了工程需求参数（EDP）与不同结构的地震危害特征之间的关系，因此，它们在基于性能的桥梁设计中的作用非常重要。一些研究调查了水平地面运动下桥梁的最佳IM，但是，很少有研究探讨垂直和水平耦合记录下的隔离桥梁的最佳IM。本文提出了在强水平地震分量和垂直地震分量激励共同作用下为地震隔离桥梁选择最佳IM的程序。土壤-结构-相互作用（SSI）效应，土壤特性的高度不确定性，包括结构和岩土问题的不确定性以及非液化土壤的高级可塑性模型，以探索最佳的矢量值IM。考虑了四种情况，以研究几何形状对所选最佳IM的影响。研究并开发了包括效率，实用性，熟练程度和充分性在内的最佳IM准则，以实现针对关键EDP的一组最佳矢量值IM：漂移率，桩帽位移和轴承位移，这些变量均受HC和VC的影响。土桩桥（SPB）系统。结果表明，与速度有关的IM：峰值地面速度（PGV）研究和开发了包括效率，实用性，熟练程度和充分性在内的最佳IM准则，以实现针对关键EDP的一组最佳矢量值IM：漂移率，桩帽位移和轴承位移，这些变量均受HC和VC的影响。土桩桥（SPB）系统。结果表明，与速度有关的IM：峰值地面速度（PGV）研究并开发了包括效率，实用性，熟练程度和充分性在内的最佳IM准则，以实现针对关键EDP的一组最佳矢量值IM：漂移率，桩帽位移和轴承位移，这些变量均受HC和VC的影响。土桩桥（SPB）系统。结果表明，与速度有关的IM：峰值地面速度（PGV）_H），霍斯纳谱强度（HI _H）和速度均方根（V _RMSH）是代表_HC的最佳IM。此外，取决于结构的光谱IM：T  = 0.2 s时的垂直光谱加速度（\（{\ text {S}} _ {\ text {a} 0.2} ^ {\ text {V}} \））和平方第一个和第二个垂直周期的垂直光谱加速度的平方和的平方根（\（{\ text {S}} _ {\ text {a}} ^ {\ text {V}} \ left （{\ text {T}} _ {\ text {s}} \ right）\））是代表VC的最佳IM。但是，与位移有关的IM，HCs的峰值地面位移（PGD _H），可以视为由倾斜桩基支撑的SPB系统的最佳IM，以研究桩帽位移。另外，关于地震学参数，对充分性术语进行了广泛的研究。