Stochastic Response and Failure Probability Assessment of Unanchored Liquid Storage Tanks Subjected to Artificial Earthquake Accelerograms

The rapid expansion of urban areas, coupled with sustained population growth and the proliferation of critical infrastructure projects, has led to a substantial increase in seismic risk across many regions worldwide. In particular, the Iranian Plateau, characterized by complex fault systems and a history of devastating earthquakes, faces an urgent need for robust seismic design and retrofitting strategies. In this context, the use of time history analyses based on accelerograms that faithfully represent the specific seismotectonic characteristics of a given region is essential for accurate dynamic analysis of structures. However, a major challenge in many seismically active regions, including parts of Iran, is the scarcity of real recorded accelerograms, especially for large-magnitude events at close distances. Consequently, the generation of artificial accelerograms—synthesized from earthquake source parameters (e.g., moment magnitude, stress drop) and local site conditions (e.g., shear wave velocity, attenuation properties)—has become a critical tool in modern earthquake engineering.



This study presents a stochastic model for generating artificial accelerograms specifically calibrated for the Iranian Plateau. The model is based on the widely accepted stochastic point-source method, which simulates ground motion as a band-limited Gaussian white noise modulated by a shaping function that accounts for source, path, and site effects. The dataset used for calibration comprises 260 recorded accelerograms from earthquakes with moment magnitudes (Mw) ranging from 5.0 to 7.3 and Joyner–Boore distances (Rjb) between 10 and 120 km. These records cover a representative range of tectonic settings within the Iranian Plateau, including the Zagros fold-and-thrust belt, Alborz mountain range, and Central Iran. The model parameters—including stress drop, geometric attenuation, anelastic attenuation (Q factor), and kappa (κ0)—were systematically calibrated by minimizing the residual error between simulated and recorded response spectra across all periods of engineering interest (0.05 to 4.0 seconds).



To validate the proposed stochastic model, 50 artificial accelerograms were simulated for each of six independent earthquake events not used in the calibration process. The mean pseudo-acceleration response spectrum (5% damping) of these 50 simulations was then compared with the actual response spectrum of the recorded accelerogram for each event. The comparison was quantified using a goodness-of-fit metric defined as the average absolute relative error across the period range. The results demonstrate that the proposed stochastic model achieves an average accuracy exceeding 95% (i.e., average relative error below 5%) across all six validation events. For periods between 0.2 and 2.0 seconds, which are most critical for ordinary building structures, the accuracy exceeds 97%. These values are significantly higher than those reported in previous stochastic models developed for other tectonic regions, confirming the suitability of the model for the Iranian Plateau.



As a practical engineering application, the response of unanchored liquid storage tanks—critical components of water supply and firefighting systems—was evaluated under various seismic conditions using the generated artificial accelerograms. A probabilistic failure analysis was conducted, defining the probability of failure as the likelihood that the tank's uplifting or sliding response exceeds a safe threshold. The analysis considered varying height-to-radius (H/R) ratios and the presence or absence of seismic isolators. The results reveal two key findings. First, for a given H/R ratio, the use of seismic isolators reduces the probability of failure by up to 100%, which in practical terms implies a reduction to near-zero failure probability (from, for example, 0.30 to less than 0.005). Second, for a specific peak ground acceleration (PGA), increasing the H/R ratio by a factor of two (e.g., from 1.0 to 2.0) leads to a 60% increase in the exceedance probability of the critical response index. This indicates that taller, slender tanks are substantially more vulnerable and require either isolation or stiffening rings to maintain acceptable performance. Based on these findings, design recommendations are proposed, including minimum H/R limits for unanchored tanks in high-seismicity zones of Iran and guidance on the selection of isolation devices.