Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures have been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single-column concrete box-girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi-class responses (e.g., full contacted or uplifting foundation) and multi-mode damage (e.g., overturning, uplift impact, and column nonlinearity). A multi-step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as-built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time.

中文翻译：

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摇柱式单柱公路桥梁抗震脆弱性

摇摆隔震作为限制土木结构地震破坏的一种有前途的设计理念，越来越受到研究。尽管预测单个地震激发下的摇摆响应存在困难和不确定性（由于负旋转刚度和复杂的冲击能量损失），但在统计意义上，摇摆结构的抗震性能已被证明与实验结果基本一致。为此，本研究以概率方式评估了使用摇摆隔离作为加利福尼亚单柱混凝土箱梁公路桥梁改造策略的有效性。在地震激发下，摇摆桥可能会经历多级响应（例如，完全接触或隆起的基础）和多模态损坏（例如，倾覆、隆起冲击、和列非线性）。开发了一个多步机器学习框架来估计与每个损坏场景相关的损坏概率。该框架由用于地震需求回归的量纲一致广义线性模型、用于不同响应类别分类的逻辑回归以及用于重要地震动和结构参数的特征选择的逐步回归组成。推导了易损性曲线，预测了摇摆隆起和倾覆的响应等级概率，以及柱体振动破坏、摇摆隆起冲击破坏等条件破坏概率。将摇摆桥的脆弱性估计值与竣工桥梁的脆弱性估计值进行比较，表明摇摆隔离能够降低柱损坏的可能性。此外，