Investigation of the most probable critical direction of November 12, 2017 Sarpol-e Zahab earthquake records using Monte Carlo simulation

Earthquake ground motions are generally recorded by digital accelerometers in three orthogonal components (two horizontal and one vertical). The vertical component is typically ignored and two horizontal records are used for the response analysis of most structures. In two-dimensional time history analysis, a stronger horizontal component of the as-recorded ground motion is generally used to evaluate the structural responses. However, the horizontal strong ground motion depends on the orientation of the sensors as installed in the field. Simple trigonometric calculations demonstrate that by rotating the sensors, different waveforms are recorded for a specific ground motion. Considering that the orientation of the sensors is random compared to the orientation of the structures and causative fault, the question arises as to what percentage of confidence the use of as-recorded ground motions leads to the maximum desired responses.     To investigate this issue, based on the information and specifications of embankment dams in the earthquake-stricken areas of Kermanshah and considering the appropriate statistical distributions, 1000 numerical models of embankment dams were simulated using the Monte Carlo simulation method. In the next step, each of the 4 selected records of Sarpol-e Zahab, Kerand, Goorsfeid, and Javanrood were rotated in different angles from 0 to 180 degrees with 10-degree steps and applied to each of the numerical models of the dam. Equivalent linear time history analysis was performed for each of the simulated numerical models of the dam resulting in a total of 72,000 (18 * 4 * 1000) analyses. The values of maximum acceleration, velocity, displacement, and velocity-to-acceleration ratios of the dam crest (and the directions associated with each of these responses) were calculated for different stations. Using the simulation results, the probability that as-recorded accelerations would lead to critical responses was calculated. The results can be summarized as follow: Critical directions depend on the characteristics of the dam, input motions, and the type of the response; The probability of occurrence of critical responses in the case of using recorded accelerations depends on the input motion and the type of response considered; for example, the probability that the Sarpol-e-Zahab record would lead to critical displacement is close to 10%, while the same record with a probability of approximately 30% leads to a critical velocity or acceleration. In Javanrood station, the results are different from the previous results, and in the case of using the recorded acceleration, the probability of occurrence of critical displacement is close to 40%; Histograms of critical directions show that in general, no specific statistical distribution can be considered for critical directions; The higher the PGA value of the record, the lower the scatter of critical directions of the record.