The objective of this investigation is to develop the damage-based energy factor (gamma) for seismic demand evaluation of Reinforced Concrete (RC) and steel structures under probable future ground motions regarding the energy-balance theorem and use in the Performance-Based Plastic Design (PBPD) procedure. Before this, the energy factor was determined considering different ductility levels, where the procedure could be extended at constant specific damage levels in damage-based design theory to consider the influence of the hysteresis energy, frequency content, ground motions amplitude, and duration for design purposes. Hence, the popular Park-Ang damage index was employed as a damage model to obtain energy factor under 400 far-fault ground motion records by investigating the influence of structural and earthquake properties on it, including period of vibration, damage level, ultimate ductility ratio, stiffness hardening, structural deterioration, beta factor, soil class type, magnitude (Mw), and source-to-site distance. Due to the influence of ground motion characteristics by using statistical analysis, the Ap/Vp ratio is employed to determine the energy factor, which depends on soil class type, magnitude, fault mechanism, and source-to-site distance. Also, a simple equation based on nonlinear regression analysis among data is suggested to estimate the energy factor based on influential structural and earthquake characteristics, and its error is demonstrated by the two concepts of bias and standard deviation. Finally, three empirical structures validated by numerical modeling, consisting of a full-scale RC bridge pier, a full-scale fourstory RC building, and the three-story steel frame, are considered to validate the accuracy of the proposed method and equation. Statistical results illustrate that the difference between estimated displacements and obtained ones from direct time history analysis is not higher than 20 %, especially compared to the existing damage-based coefficient method.
Three-sided underpass culverts are structural systems used to provide passing vehicle or pedestrian. It is of great importance that such infrastructure systems remain useable, especially after disasters such as earthquakes that can cause great destruction, in order to ensure that infrastructure services can be maintained continuously. In this context, the aim of this study is to investigate using finite element method (FEM) the dynamic responses of three-sided underpass culvert system under near-fault ground motions with velocity pulse and far-fault ground motions. For this aim, the modal analysis of the soil-underpass culvert interaction system has been realized using proposed soil-structure interaction (SSI) model. The frequencies of the interaction system obtained from the finite element model developed using proposed approaches have been verified comparing with the results obtained from the literature and the site periods. After showing that the modes of the interaction system can be obtained with the help of the proposed numerical model, the full transient dynamic analyses have been performed in the time history using five near-fault and far-fault records, considering four different soil systems. The comparisons shows that the variations of the soil systems and the ground motion type can significantly affect the top peak relative displacements and the dynamic stresses of the three-sided underpass culvert.