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Error estimation of closed-form solution for annual rate of structural collapse

机译：年倒塌率封闭形式解的误差估计

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摘要

With the increasing emphasis of performance-based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance-based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed-form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed-form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed-form solution are fit. This study presents a critical review of the closed-form solution for the annual rate of structural collapse. The closed-form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed-form solution. Via a parametric study, the key variables contributing to the error between the closed-form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed-form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution.
机译：随着工程界对基于性能的地震工程的日益重视，提出了几项调查，概述了适用于基于性能的地震设计（PBSD）的简化方法。这些PBSD方法大多数的核心是对表示主要性能指标超出率的概率积分方程使用闭式分析解决方案。这种封闭形式的解决方案不合适的情况主要与外推问题有关，在该区域中，封闭形式的解决方案的参数适用。这项研究对封闭式解决方案的年度结构崩溃率进行了严格的审查。封闭形式的解决方案需要假设坍塌脆性的对数正态性和地面运动危害的幂模型形式，其中就封闭形式解决方案的误差而言，后者更为重要。通过参数研究，说明了导致闭式解与通过数值积分解之间的误差的关键变量。由于这些关键变量无法轻易测量，因此对将来的PBSD中使用这种封闭形式的解决方案产生了怀疑，尤其是考虑到使用直接数值积分来获得解决方案的简单有效的性质。

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