PSI - Issue 13

Zeljko Zugić et al. / Procedia Structural Integrity 13 (2018) 415 – 419 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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additional input parameter — the time elapsed since the previous such event. Due to lack of data and lack of regularity in the occurrence of large earthquakes (either the segment or the magnitude is not repeated), uncertainty in the segmentation, and the interaction between neighboring segments and possibility of a joint rupture in a large earthquake, this time dependent model has been applied to a small number of faults, mostly along the plate boundaries, and the time until the next characteristic event is often modeled as an exponential random variable. probability of exceedance in 50 years. The different lines correspond to estimates when all events contribute to the hazard, and when only the Gutenberg-Richter events or the characteristic events contribute to the hazard. 3.3. One of the possible approaches The above mentioned common assumption is that an earthquake is generated through a random process and it is independent of its last occurrence- the basis for considering earthquake occurrences a Poisson process in PSHA. Similarly, ground motions are a lso characterized by a Poisson’s process. Another assumption is that the annual rate of occurrence (or exceedance) for an event (i.e., T=1 yr) is numerically equal to its annual probability of occurrence (or exceedance). As a result, a conversion is not necessary between rates of occurrence/exceedance and probabilities of occurrence/exceedance, and in the following sections the terms rate and probability are used interchangeably. This approximation is used for rare events (such as earthquakes) where λ is small and is often called the “rare event assumption” proposed by Bazzurro and Cornell (2002).

Fig. 2. Analogy between landslide and seismic fault displacement

Fig. 3. Occurrence of peak deformation as Poisson's process.

Finally, the main assumption of the procedure proposed by Zugic et.al. (2015) is that the occurrence of peak slope permanent displacements in time can be treated as a (generalized) Poisson’s process. It is a widely accepted assumption that strong (characteristic) earthquakes as well as peak ground motions from these earthquakes occur as a generalized Poisson’s process. The slope seismic deformation in this approach is treated as a “peak ground motion” for a certain earthquake (Fig. 2). Every occurrence of peak slope displacement in time is a product of specific combination of seismic, soil and water level conditions (Fig. 3). The idea for this approximation came from Kim and Sitar (2013) who stated that if earthquake events are assumed to be Poisson process, then the failure events caused by earthquakes also become Poisson, thus simplifying the computation. Let be a random variable representing, for an earthquake that has rupture d the soil surface, the absolute value of the displacement across the sliding surface at the ground surface, and •Ž‘’‡ be the same type of displacement at the site ,which may or may not have been affected by the earthquake, and let ’ ( † , – ) be the probability that •Ž‘’‡ exceeds level d during the exposure period. Being a direct consequence of an earthquake occurrence, the probabilistic model for this event (exceedance of a certain level of displacement) has been determined by the probabilistic model of earthquake occurrence, as explained by Zugic et.al (2015). Figure 4 (b) shows that the hazard estimate is quite sensitive to the modeling assumptions affecting the distribution and the number of events over earthquake magnitudes.