A practical approach for seismic risk assessment of underground structures: A case study of Iranian subway tunnels

Active geological and young faulted zones have made Iran’s territory one of the most seismological active areas in the world according to recent historical earthquakes. Some of the deadliest earthquakes such as Gilan 1990 and Kermanshah 2018 caused tens of thousands fatalities. If such violent earthquakes affect strategical structures of a country, indirect losses would be more concerning than direct losses. Nowadays there is no doubt about the vital role of tunnels and underground structures in urban areas. These facilities serve as nonstop functional structures for human transportation, water and sewage systems and underground pedestrian ways. Any external hazard subjected to underground spaces, such as earthquake could directly affect passenger’s lives and significantly decrease whole system reliability of public transportation. Commonly two earthquake levels of intensities, Maximum Design Earthquake (MDE) and Operating Design Earthquake (ODE) were used in seismic design of underground structures. However, uncertain nature of earthquakes in terms of frequency content, duration of strong ground motion, and level of intensity indicate that only the two levels of earthquake (ODE and MDE) cannot cover the all range of possible seismic responses of structures during a probable earthquake. It is important to evaluate the behavior of tunnel under a wide range of earthquake intensities. For this purpose, a practical risk-based approach which is obtained using the total probability rule was used. This study illustrates a framework for evaluation seismic stability of tunnels. Urban railway tunnels of Tehran, Shiraz, Ahwaz, Mashhad, Isfahan and Tabriz were considered as study cases. Nominal value of seismic risk for three main damage states, including minor, moderate and major were calculated.     

A test sensitive to extreme hidden periodicities

A modified version of the widely used Kolmogorov-Smirnov (K-S) test of null hypothesis is constructed, that a given time series is Gaussian white noise, against the alternative hypothesis that the time series contains an added or multiplicative deterministic-periodic component of unspecified frequency. The usual KS test is treated as a special case. The proposed test is more powerful than the ordinary K-S test in detecting extreme (low or high) hidden periodicities. Computational procedure necessary for implementation are also given.     

A test sensitive to extreme hidden periodicities

A modified version of the widely used Kolmogorov-Smirnov (K-S) test of null hypothesis is constructed, that a given time series is Gaussian white noise, against the alternative hypothesis that the time series contains an added or multiplicative deterministic-periodic component of unspecified frequency. The usual KS test is treated as a special case. The proposed test is more powerful than the ordinary K-S test in detecting extreme (low or high) hidden periodicities. Computational procedure necessary for implementation are also given.