Abstract
The uncertainties in ground motions may result from several factors, e.g. (i) the fault rupture process, (ii) the wave propagation, (iii) the site amplification from the earthquake bedrock to the ground surface. The uncertainty in the fault rupture slip is taken as a main factor of uncertainties in the present paper and the critical fault rupture slip distribution causing the maximum structural response is found by using the stochastic Green’s function method as a generator of ground motions. Then, a multi-degree-of-freedom (MDOF) building structure is introduced as a model structure and an optimal damper placement problem is discussed for the critical ground motion. The main topic in this paper is the simultaneous determination of the critical fault rupture slip distribution and the optimal damper placement. The sequential quadratic programming method is used in the problem of critical fault rupture slip distribution and a sensitivity-based method is introduced in the optimal damper placement problem. Furthermore, the robustness for the maximum interstory drift in MDOF building structures under the uncertainty in fault rupture slip distributions is presented for resilient building design by using the robustness function. Since the critical case leads to the most unfavorable structural response, the proposed method can provide structural designers with a promising tool for resilient building design.
Highlights
It is well-accepted that earthquake ground motions exhibit diverse aspects, as observed, for example, in Mexico (1985), Northridge (1994), Kobe (1995), Chi-chi (1999), Tohoku (2011), Kumamoto (2016)
A multi-degreeof-freedom (MDOF) building structure is introduced as a model structure and an optimal damper placement problem is discussed for the critical ground motion causing the maximum response (Drenick, 1970; Takewaki, 2007)
A multi-degreeof-freedom (MDOF) building structure was introduced as a model structure and an optimal damper placement problem was investigated for the critical ground motion
Summary
It is well-accepted that earthquake ground motions exhibit diverse aspects, as observed, for example, in Mexico (1985), Northridge (1994), Kobe (1995), Chi-chi (1999), Tohoku (2011), Kumamoto (2016). The Fourier amplitude of ground motions at the earthquake bedrock caused by rupture at a fault element is represented by the Boore’s model (Boore, 1983) and the phase angle is represented by the phase difference method (Yamane and Nagahashi, 2008). The present paper uses the stochastic Green’s function method based on a plane-source model of the fault rupture to produce ground motions. A small ground acceleration at the earthquake bedrock resulting from the slip of a fault element can be obtained by locating a FIGURE 3 | Fault plane and three recording points (replotted based on Kato et al, 2011). Following the investigations by Somerville et al (1999), Eshelby (1957), and Brune (1970), it is assumed that the stress drop σ of large earthquakes and the corner frequency fc are given by the following equations: σ
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