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A machine learning (ML) based method is presented in this paper for obtaining tangent stiffness of a complicated three-dimensional wheel-rail interaction element that is able to practically and effectively simulate the complicated dynamic responses of vehicle-track problems. The element tangent stiffness, defined as differentiation of element insisting force to nodal displacement, is important in improving efficiency when Newton’s method is used to solve implicit nonlinear finite element equations. However, deriving and software implementing the tangent stiffness require significant efforts, and calculating the tangent stiffness in each iteration of the Newton method is usually time consuming. On the other hand, ML can directly obtain the implicit mapping between inputs and outputs of complex calculation process with limited programming effort and high computational efficiency, and is potentially a good alternative way to calculate the tangent stiffness of complicated element. In this paper, a feedforward artificial neural network is trained for obtaining the tangent stiffness, while inputs are the displacement and velocity of the element and outputs are the entries of the tangent stiffness matrix. The ML based tangent stiffness are implemented in an open source finite element software framework, OpenSees, and verified by application examples of a wheelset and a light rail vehicle running on straight rigid rail. The accuracy and efficiency are compared between the use of ML based tangent stiffness (MLTS) and the consistent tangent stiffness obtained at different speeds. The results demonstrate the MLTS can ensure the calculation accuracy and significantly improve the calculation efficiency.

Seismic fragility assessment widely uses a probabilistic measure for assessing the seismic performance of structural components or systems. This article proposes a copula-based seismic fragility (CBSF) method to derive the system-level damage probabilities of reinforced concrete bridges and to consider the correlation among seismic demands of components. First, the marginal distribution functions of the random variables are calibrated, and three Archimedean copula models are considered. Subsequently, the relevant parameters of the copula models are estimated using the semi-parametric maximum likelihood method. Next, the damage probabilities of a bridge system are calculated based on the joint distribution model with the most suitable copula model and the calibrated marginal distribution functions. Finally, the CBSF method is used to estimate the damage probability of a simply supported box girder bridge. The performance of the CBSF method is validated by a comparison of fragility curves obtained using the CBSF method and the probabilistic seismic demand analysis (PSDA) method. The comparative results demonstrate that the fragility curves obtained by the CBSF method are better than those obtained using the PSDA method. The proposed CBSF model can serve as a tool for assessing the seismic performance of structures and estimating the economic loss of existing bridge systems.

The exposure of a reinforced concrete (RC) bridge to a chloride environment can cause strength reduction and even change the failure modes of RC piers during an earthquake. This research proposes a novel and practical resilience assessment framework for aging bridges considering the different failure modes of RC piers. A probability approach is used for estimating the performance degradation of bridge columns due to the decreases in diameter and yield strength of the corroded reinforcement, bond degradation of longitudinal reinforcement, and the compressive strength deterioration of the cover concrete. The seismic responses of the RC piers with different failure modes (i.e., shear and flexural failure) are simulated using the finite element (FE) model. Six existing results of static cyclic-loading experiments are used for validating the accuracy of the used FE models. The effects of the component deterioration mechanisms are assessed within the resilience framework for a typical three-span simply supported T-beam bridge throughout its service year. The results of this study illustrate the following: (1) The FE model with the nonlinear shear spring provides an acceptably accurate solution for simulating the hysteretic response of aging bridge columns with different failure modes. (2) The resilience index of the RC bridge system decreases significantly when the intensity measures of the ground motion increase. (3) Chloride-induced corrosion will reduce the ability of the bridge system to withstand and rapidly recover from an earthquake hazard.

Soil–structure interaction (SSI) plays an important role in the analysis of seismic structural responses. This study significantly extends an efficient linear SSI analysis method presented previously by the authors and co-workers to realistic nonlinear SSI systems, that is, systems with nonlinear soil, nonlinear structures, and flexible foundations (e.g. single- or multiple-pile foundations). The flexible foundations lying on half-space nonlinear soil are represented by frequency-dependent compliance functions that are fitted numerically instead of obtained by closed-form solution. These functions are then transferred to the time domain using the discrete-time recursive filtering method. A non-iterative algorithm is applied to guarantee the boundary conditions between soil and structure, that is, the displacement continuity and force equilibrium between them. The proposed method is implemented on an open-source FE software framework, called OpenSees. The accuracy and efficiency of the extended coupling method are investigated in detail through the seismic response analyses of typical soil–foundation–structure systems while considering the cases of linear or nonlinear soil, linear or nonlinear structures, and single- or multiple-pile foundations. Results show that the extended coupling method is significantly faster than the traditional FE method and provides acceptably accurate solutions for SSI systems with linear or low-to-moderate nonlinear soil. The paper provides a method for fast evaluation of nonlinear SSI effects in seismic structural response analysis.

The uncertainty of a structural capacity plays an important role in regional fragility, risk, and resilient estimation. This paper proposes an artificial neural network (ANN)-based predicting capacity model to consider the uncertainty of the seismic performance of the reinforced concrete (RC) bridge columns. The seismic fragility of three typical RC bridges is studied. A database that includes 78 testing results is used to train, validate, and test the ANN model. The capacity measures of RC bridges are predicted using the constructed ANN model. Case studies are conducted for three typical simply supported T-beam bridges, and nonlinear time history analysis is performed to obtain the structural responses of the RC bridges. Seismic fragility models are established and a comparison is performed to study the discrepancies of damage probability for RC bridges with and without considering the uncertainty of the capacity model. The main results of the paper are as follows: (1) the ANN-based predicting capacity model can provide an acceptable capacity measure for seismic fragility estimation and (2) the damage probability of RC bridges is related to the uncertainty of seismic performance that needs to be considered for structural fragility estimation.

Risk assessment plays an important role in quantifying earthquake loss and has been widely used in the field of seismic engineering. However, current studies of the risk assessment rarely consider the different failure modes of piers (i.e., flexure failure, flexure-shear failure and shear failure), which will lead to an excessive estimation for the seismic performance and collapse safety of the reinforced concrete girder bridges. This paper focuses on studying the seismic behavior of bridges considering different failure modes and comparing the seismic collapse risk of the bridges with and without ductile detailing. The numerical analysis is performed in an open source finite element (FE) software framework, Open Sees. Nonlinear shear springs are introduced into the FE models of reinforced concrete (RC) columns to accommodate the shear and flexural-shear effect of the bridges. The accuracy of the FE models is validated by using the existing results of static cyclic-loading experiments. Case studies are conducted for two categories of the girder bridges, which are designed based on new and old seismic design criteria in China, respectively. The collapse fragility curves are developed by using the incremental dynamic analysis method, which considers the uncertainties of the ground-motion characteristics and the structural material parameters. Based on the seismic hazard curve of a designated region, a comparative assessment of the seismic collapse risk is performed regarding mean annual collapse rate for the non-ductile and ductile bridges. The main results of the paper are: (1) The FE model with the nonlinear shear spring provides an acceptably accurate solution for simulating the initial stiffness, shear failure point, strength degradation slope and residual shear strength of the RC columns; (2) The structural collapse safety is shown to be related not only to the collapse probability of the bridges but also to the occurring probability of the ground motion intensity exceeding a given threshold; (3) The mean annual collapse rate of the ductile girder bridges is significantly smaller than that of the non-ductile girder bridges. The results can be used as a reference to implement specific policies for appraising and mitigating the seismic risk of existing RC bridges.