Journal of Earthquake and Tsunami

The Probabilistic Seismic Demand Analysis (PSDA) which is frequently implemented in the first generation performance-based earthquake engineering quantifies seismic behavior of a structure by computing mean annual frequency of exceeding a specific value of a desired demand parameter given all anticipated earthquakes. This framework, based on the total probability integration formula, provides a technical basis on which aleatory uncertainties, uncertainties originated due to inherent randomness of the phenomena, are explicitly addressed. However, variability in the mean value of different model parameters, referred to as epistemic uncertainties and mainly due the finite-sample size of observations, is neglected. In this study, as an alternative to total probability integration, a reliability-based formulation tailored to effortlessly reflect both aleatory and epistemic uncertainties is put-forward to perform unified PSDA. Next, as an application of the proposed methodology, a reliability-based seismic demand curve of a 4-story example building is developed. Results demonstrate that the Second-Order Reliability Method (SORM) and important sampling method (ISM) along with multi-step Monte Carlo simulation (MSMCS) methods are appropriate candidates for computing reliability-based PSDA with differentiable and nondifferentiable performance functions, respectively.

Based on a rectangle underground station structure, two-dimensional finite element models are established in this study to explore the effectiveness of different seismic reduction and isolation measures for underground structure, where Davidenkov model is adopted to consider the soil nonlinearity and the underground structure is considered elastic. The performances of the seismic reduction and isolation measures are evaluated by assessing the structure internal force and deformation responses. Depending on the ratio of wave impedance between the isolation layer and the structure, the isolation layers are divided into rigid and flexible types. The effects of the length and elastic modulus of rigid isolation layer as well as that of the thickness and shear modulus of flexible isolation layer are investigated. The results show that the seismic reduction effect of rigid isolation layer is better with the increase of stiffness, and the effect of flexible isolation layer is more obvious with the decrease of stiffness, which are consistent with the classical impedance theory. Furthermore, the middle column of subway station is usually the most vulnerable during seismic shakings, and one viable way to improve its seismic behavior is to reduce the column end constraints. Therefore, different column constraints consisting of swing, hinge, sliding connection and isolation bearing are considered. The numerical results suggest that among the different column end constraints considered, the sliding connection is comparatively more favorable, which can effectively limit the lateral deformation of column while imposing no horizontal reaction force.

In this research, we have implemented a numerical algorithm to identify the seismic wave parameters: P phase, S phase, amplitude, period and seismic signal duration. We have used the Matlab programming language and the digital signal processing toolbox to conduct the automatic picking of seismic signal parameters. As a mathematical tool, we have used the discrete Fourier transform to study the frequency components of the signal and the Hilbert transform to obtain the envelope signal. The Butterworth filter was used to bandpass the seismic signal, in case of a noisy signal. We have implemented a graphical user interface in Matlab to pick the seismic signals (with options of automatic picking and manual picking). In this way, the routine of picking a great set of seismic signals is easier. The results of the automatic algorithm agree very well with that of a human operator for a Signal/Noise ratio greater than 50, according to the sensitivity test, with an accuracy of around $\pm$0.05s.

Shallow footings are the most preferred foundations for buildings due to low cost and ease of construction. However, under seismic loads, these foundations may suffer excessive settlements, particularly when there is a risk of soil liquefaction. This paper explores the effectiveness of granular columns in mitigating the liquefaction-induced ground deformations under shallow foundations, using FLAC2D program. PM4Sand, a critical state-based bounding surface plasticity model is used to simulate the stress–strain response of sand to cyclic loading. The responses of granular columns are also simulated using the same soil model. Validation of the numerical model is presented against the experimental results of mildly sloping ground. The application of granular column groups resulted in maximum reduction of the settlement of footing by 60% when soil densification is included along with drainage and stress redistribution effects. Though excess pore water pressure is relatively low in treated deposit compared to the untreated deposit, its contribution to the reduction in settlement of footing is found to be minimal.

$b$-value of the Gutenberg–Richter relation as an earthquake precursor depends on the tectonic setting features. This paper presents an alternative method to calculate $b$-value in the presence of characteristic earthquakes. The proposed equation is based on the maximum likelihood method applied on the probability density function of the characteristic earthquake model. Data from real and simulated catalogs were used to evaluate the accuracy of the proposed model. For this purpose, 224 seismic event catalogs with various properties including catalogs’ sample size, the ratios of characteristic earthquakes number to catalog’s sample size $(R_{\mathrm{\text{nc}}})$ and different magnitude of characteristic earthquakes were simulated. According to the estimated $b$-values, the earthquake occurrence probability was calculated and discussed. The results indicate that the proposed method of estimation for $b$-value has more adaptable consideration of the characteristic earthquake behavior.