Fréchet-derivative-based global sensitivity analysis of the physical random function model of ground motions

Randomness in earthquake ground motions is prevalent in real engineering practices. Therefore, it is of paramount significance to utilize an appropriate model to simulate random ground motions. In this paper, a physical random function model of ground motions, which considers the source-path-site mechanisms of earthquakes, is employed for the seismic analysis. The probability density evolution method is adopted to quantify the extreme value distribution of structural responses. Then, the sensitivity analysis of the extreme value distribution with respect to basic model parameters is conducted via a newly developed Fréchet-derivative-based approach. A 10-story reinforced concrete frame structure, with nominal deterministic structural parameters and subjected to random ground motions, is studied. The results indicate that when the structure is still in a linear or weakly nonlinear stage in the situation of frequent earthquakes, the model parameter called the equivalent predominate circular frequency is of the most significance, with an importance measure (IM) greater than 0.8. Nonetheless, if the structure exhibits strong nonlinearity, such as in the case of a rare earthquake, the equivalent predominate circular frequency remains highly influential, but the Brune source parameter, which describes the decay process of the fault rupture, becomes important as well, with an IM increased from around 0.2 to around 0.4. These findings indicate that the IMs of basic model parameters are closely related to the embedded physical mechanisms of the structure, and the change in the physical state of the structure may provoke the change of IMs of basic inputs. Furthermore, some other issues are also outlined.