Evaluation of Vector Hazard for Conditional Mean Spectrum with Different Definitions of Multivariate Exceedance Rate

Probabilistic risk assessment for reinforced concrete frame structures subject to mainshock‐aftershock sequences

“…The case building is hypothetically located in Xi'an City, northwest of China. Based on the seismic hazard analysis results from Ji et al, 68,69 the site is targeted with a magnitude of 6.9 and a source-to-site distance of 90 km. Thus, a CMS of the target location with the information of the building is developed.…”

“…where M 0 and M u are the lower and upper bounds of magnitude; Δm is the magnitude interval; β = bln10; b is the seismicity parameters. 69 Assuming that an earthquake with a magnitude of m l occurs at a random point of (x,y) in mth potential source, the P[(x,y)|m l ] can be evaluated as follows:…”

“…According to the fifth-generation Seismic Ground Motion Parameter Zonation Map of China, the GMPE proposed by Yu et al 82 (YLX13) is used in CPSHA to generate the evaluate the probabilistic seismic hazard of the Xi'an region. Further details about the CPSHA can be found in Ji et al 68,69 Figure 9A shows the seismic hazard curve of the MS (𝜆(𝑃𝐺𝑉 MS ))). Substitute the 𝜆(𝑃𝐺𝑉 MS ) and 𝑃[𝑃𝐺𝑉 AS |𝑃𝐺𝑉 MS ] into Equation ( 9), the seismic hazard surface for the MS-AS scenario is shown in Figure 9B.…”

“…The magnitude distribution obeys the truncated Gutenberg‐Richter relation. Thus, the P ( m j ) can be computed by: $$$$\begin{equation}P\left( {{{m}_l}} \right) = \frac{{2\exp \left[ { - \beta ({{m}_l} - {{M}_0})} \right]}}{{1 - \exp \left[ { - ({{M}_u} - {{M}_0})} \right]}} \cdot \sinh \left( {\frac{\beta }{2}\Delta m} \right)\end{equation}$$$$where M 0 and M u are the lower and upper bounds of magnitude; Δ m is the magnitude interval; β = b ln10; b is the seismicity parameters 69 . Assuming that an earthquake with a magnitude of m l occurs at a random point of ( x , y ) in m th potential source, the P [( x , y )| m l ] can be evaluated as follows: $$$$\begin{equation}P\left[ {{{{(x,y)}}_m}|{{m}_l}} \right] = \frac{{{{f}_{m,{{m}_l}}}}}{{{{A}_m}}}\end{equation}$$$$in which $${{f}_{m,{{m}_l}}}$$ denotes the probability of an earthquake with a magnitude of m j in m th potential source; A m is the area of i th potential source.…”

“…(YLX13) is used in CPSHA to generate the evaluate the probabilistic seismic hazard of the Xi'an region. Further details about the CPSHA can be found in Ji et al 68,69 . Figure 9A shows the seismic hazard curve of the MS $$( {\lambda ( {PG{{V}_{{\mathrm{MS}}}}} )} )$$).…”