Analysis of the risk-targeting approach to defining ground motion for seismic design: a case study of Iran

Abstract

Modern seismic codes employed the uniform hazard basis for seismic design, which defines design ground motion with a fixed return period for different sites. Seismic design for uniform hazard ground motion does not lead to the goal of uniform structural safety. As a potential solution to address this problem, the risk-targeting approach has been considered in recent years. This study aims to investigate the changes applied by this approach to the current uniform hazard ground motions. For this purpose, hazard curves for Iran from the Earthquake Model of Middle East (EMME14) have been used. The risk-targeting approach has been performed in two cases, once considering GMs with a 475 year return period and then considering GMs with a 2475 year return period. For each case, a generic fragility function for buildings has been defined. A 1% probability of collapse in 50 years was selected as the target risk in both cases. For each case, the map of the distribution of the theoretical collapse risk is presented. It was discussed that by employing a generic fragility function, the risk-targeting could not guarantee to harmonize risk amongst the sites with different hazard levels, but it could have such an impact for the sites with the same design GM but the different slope of hazard curves. Finally, it was found that basing the seismic design on the 2% in 50 years GMs level leads to a more uniform collapse risk across the country.

Appendix A: Mathematical proof for Eq. (5)

The basic premise of the closed-form solution for the risk integral developed by Cornel (1994) is to fit the hazard curve to a power function such as Eq. (7).

$$H\left( {IM} \right) = K_{0} .IM^{{ - K_{H} }}$$

(7)

where K₀ is an appropriate constant, and K_H is the logarithmic slope of the hazard curve defined by Eq. (4). Assuming a log-normal fragility function with a median collapse capacity, C_50%, and a logarithmic standard deviation, β, the annual collapse risk is obtained using Eq. (8).

$$\lambda_{C} = H\left( {C_{50\% } } \right).e^{{0.5.K_{H}^{2} .\beta^{2} }}$$

(8)

The relation between the 50th-percentile and another percentile (X-percentile) of the collapse capacity is as Equation (9).

$$C_{X} = C_{50\% } .e^{{{\Phi }^{ - 1} \left( X \right).\beta }}$$

(9)

Substituting Eq. (9) into Eq. (8) gives Eq. (5) in the paper.

$$\lambda_{C} = H\left( {C_{X} } \right).e^{{0.5.K_{H}^{2} .\beta^{2} + {\Phi }^{ - 1} \left( X \right).K_{H} .\beta }} .$$

(10)