Assessing structural performance under seismic hazard requires accounting for both damage accumulation and post-event recovery. In current performance-based earthquake engineering (PBEE), recovery is generally treated as a post-processing attribute, while structural performance is modeled using Poissonian exceedance assumptions that imply renewability and memorylessness. These assumptions hinder a unified treatment of reliability and resilience under repeated seismic loading. This study proposes a generalized PBEE framework in which damage and recovery are embedded directly into the system dynamics through a continuous-time Markov chain. A single generator matrix governs state-dependent transitions, providing a unified description of structural reliability and resilience while remaining compatible with standard PBEE metrics. Time-dependent failure probabilities and reliability indices are derived from the transient system dynamics, whereas resilience is quantified through the expected fraction of operational time before collapse. The framework exploits the spectral properties of the generator matrix to compute both metrics efficiently and transparently. The methodology is illustrated on a three-state example and applied to two structural archetypes: a braced frame and a base-isolated system. Results show that recovery dynamics can strongly affect long-term resilience even when conventional reliability measures exhibit limited sensitivity, emphasizing the need to explicitly account for recovery in life-cycle seismic performance assessment.

翻译：评估地震危险下的结构性能需要考虑损伤累积和灾后恢复。在当前的基于性能的地震工程中，恢复通常被视为后处理属性，而结构性能则采用泊松超越假设建模，该假设蕴含可更新性和无记忆性。这些假设阻碍了在重复地震荷载作用下对可靠性和韧性的统一处理。本研究提出一个通用基于性能的地震工程框架，其中损伤和恢复通过连续时间马尔可夫链直接嵌入系统动力学。单个生成矩阵控制状态依赖转移，为结构可靠性和韧性提供统一描述，同时与标准基于性能的地震工程指标保持兼容。随时间变化的失效概率和可靠性指标从瞬态系统动力学中推导，而韧性则通过倒塌前的预期运行时间比例进行量化。该框架利用生成矩阵的谱特性高效且透明地计算这两个指标。研究方法通过一个三状态示例进行说明，并应用于两种结构原型：支撑框架和基础隔震系统。结果表明，即使传统可靠性指标表现出有限敏感性，恢复动力学也会强烈影响长期韧性，这突显了在生命周期地震性能评估中显式考虑恢复的必要性。