Nonlinear Seismic Analysis Research Articles

Nonlinear seismic response analysis of long-span railway cable-stayed bridges crossing strike-slip faults

Active faults along railways in the mountainous regions of western China pose significant challenges to bridge safety. To ensure the safe operation of long-span railway bridges under complex geological conditions, this study investigates the synthesis of artificial ground motions for bridges crossing strike-slip faults and analyzes their nonlinear seismic response. First, we develop a theoretical method for simulating high- and low-frequency seismic motions using a finite fault and an equivalent velocity pulse model. Next, using a specific long-span railway cable-stayed bridge as a case study, we construct a nonlinear finite element model with OpenSees software. Finally, we assess the seismic response of key bridge components considering various crossing angles, seismic amplitudes, fault rupture directivity, and fling-step effects. The results show that the crossing angle significantly influences the seismic response, with longitudinal and transverse responses exhibiting opposite patterns. Additionally, the scaling factor of seismic motion significantly affects bridge response. For bridges crossing strike-slip faults, the longitudinal response exhibits a sudden increase in displacement due to instantaneous velocity pulses, while the transverse response shows notable residual displacement influenced by the fling-step effect. However, the critical section curvatures of bridge towers and piers remain within the elastic range across all crossing angles, indicating that controlling large displacement deformations is crucial for the seismic design of bridges crossing strike-slip faults.

Failure Probability-Based Optimal Seismic Design of Reinforced Concrete Structures Using Genetic Algorithms

Artificial intelligence (AI) has enabled several optimization techniques for structural design, including machine learning, evolutionary algorithms, as in the case of genetic algorithms, reinforced learning, deep learning, etc. Although the use of AI for weight optimization in steel and concrete buildings has been extensively studied in recent decades, multi-objective optimization for reinforced concrete (RC) and steel buildings remains challenging due to the difficulty in establishing independent objective functions and obtaining Pareto fronts. The well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is an efficient genetic algorithm approach for multi-objective optimization. In this work, the NSGA-II approach is considered for the multi-objective structural optimization of three-dimensional RC buildings subjected to earthquakes. For the objective of this study, two function objectives are considered: minimizing total cost and the probability of structural failure, which are obtained via several nonlinear seismic analyses of the RC buildings. Beams and columns’ cross-sectional dimensions are selected as design variables, and the Mexican Building Code (MBC) specifications are imposed as design constraints. Pareto fronts are obtained for two RC-framed buildings located in Mexico City (soft soil sites), which demonstrate the efficiency and accuracy of NSGA-II for structural optimization.

H∞ optimum design and nonlinear seismic performance assessment of tuned-mass-damper-inerter (TMDI) supported by an auxiliary structure

Tuned Mass Damper Inerter (TMDI) and its simplified form, Tuned Inerter Damper (TID), are highly effective in mitigating seismic responses in buildings, particularly when rigidly connected to the ground. However, practical constraints often limit the feasibility of this ideal setup. This study introduces a novel configuration: the AS-type TMDI, which connects the TMDI to an auxiliary structure (AS) adjacent to the main building to simulate a ground connection. To design the AS-type TMDI, this research builds upon insights from studies on TMDIs in adjacent buildings and develops an analogous 3-DOF model representing the TMDI-linked adjacent-building system. This model incorporates two buildings of different heights, allowing the TMDI to be connected at any floor level. Utilizing fixed-point theory, the study derives an analytical solution for the optimal design of TMDI systems within this novel configuration. Additionally, a method is introduced to determine the optimal stiffness and design procedure for the AS itself. The performance of the proposed AS-type TMDI is evaluated through comprehensive nonlinear seismic analysis of a benchmark nine-story steel frame structure, accounting for material and geometric nonlinearities. Results demonstrate that the AS-type TMDI performs comparably to a virtually grounded TMDI in effectively reducing the seismic responses. Furthermore, this innovative configuration outperforms both a conventional retrofitting technique, where the building is rigidly connected to the AS, and a system where a viscous damper alone connects the main building to the AS. This highlights the AS-type TMDI's potential to significantly improve the building’s seismic performance.

TransFrameNet: A transformer-based approach for generalized seismic performance prediction of building structures

Performing nonlinear seismic analysis on a large number of building structures is challenging. Deep learning offers rapid prediction but still with limitations. One model is generally only applicable to a specific building structure and not easily extended to others. To address this, TransFrameNet, a new method based on Transformer, is proposed. By converting buildings into archetypes, TransFrameNet is able to consider the variations of different buildings in geometric features and component sizes. With hard parameter sharing, multi-task learning further expands the applications for multiple building structures with different designs. TransFrameNet is tested on 100 steel moment resisting frames (SMRFs) to predict floor displacement response using 40 seismic ground motions. Results reveal that TransFrameNet can accurately predict the displacement response of different buildings, with an average mean squared error of 0.0037. Notably, compared to LSTM and Transformer models, TransFrameNet shows significantly improved correlation when tested on a 20-story SMRF structure.

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

Nonlinear seismic response analysis of liquefiable sites based on effective stress method

In this study, the one-dimensional nonlinear Matasovic model was extended to the two- and three- dimensional stress space by replacing the shear strain with the generalized shear strain. The extended Matasovic model was subsequently combined with Dobry’s excess pore water pressure generation model, and the reliability of the proposed loosely coupled effective stress analysis model was verified through undrained cyclic triaxial tests and a one-dimensional site response analysis. Finally, this method was applied to an engineering site in China to evaluate the nonlinear seismic response of liquefiable sites. The results show that the proposed effective stress analysis method can capture the dynamic behavior of the soil and the generation of pore water pressure during strong shaking. Moreover, there are differences between the proposed effective stress analysis method and the total stress analysis method for liquefiable sites, which indicates the need for careful selection in practical applications.

Nonlinear Seismic Analysis of Concrete Dams Using ABAQUS-Based Scaled Boundary Finite Element Method

ABSTRACT The scaled boundary finite element method (SBFEM) is implemented in ABAQUS through the user subroutine interface. The accuracy of the proposed method and computer program are verified by using two benchmark examples. With the coupled SBFEM and standard finite element method (FEM), the dynamic interaction model of concrete dam – reservoir – foundation considering the geometrical nonlinearity of transverse joints is established using the viscous-spring absorbing boundary conditions. The overlaying element technique is applied to define the contact interface of transverse joints. The dynamic characteristics and linear seismic response of the Koyna gravity dam have been analyzed using polyhedral elements. Finally, nonlinear seismic analysis of the NG5 arch dam has been conducted. The calculated results are in good agreement with those of ABAQUS built-in elements. Moreover, numerical examples demonstrate that proposed method has high computational accuracy and can be applied to the dynamic analysis of complex engineering structures.

Analysis of High-Rise Building Using Opensees

Numerical simulation has increasingly become an effective method and powerful tool for performance-based earthquake engineering research. Most existing numerical analyses use general-purpose commercial software, which can limit in-depth investigations on specific, complex topics. Consequently, this research focuses on the dynamic analysis of high-rise reinforced concrete (RC) frame-core tube structures using the open-source finite element (FE) code OpenSees to perform nonlinear seismic analyses. Various shear walls, a frame-core tube structure, and a tall building are simulated. The rationality and reliability of the proposed analysis method are validated through comparison with available experimental data and the analytical results of a well-validated commercial FE code. The research outcomes will provide a useful reference and an effective tool for further numerical analysis of the seismic behavior of tall buildings.

Design, simulation and energy dissipation evaluating of a new lead shear damper

This study presents a novel design for a lead shear damper (LSD) that features lead blocks encased in laminated steel and rubber plates, intersected by X-shaped steel sticks. It combines the excellent energy dissipation and fatigue resistance of lead with the uniform yielding capabilities of X-shaped steel sticks along their height. Cyclic loading testing and fatigue tests are conducted in order to determine the mechanical properties of the LSD. The test results reveal that the LSD has a variable yielding force, and exhibits stiffness hardening when the damper's deformation direction deviates from the origin. However, when the deformation direction returns to the origin, there is no stiffness hardening observed, and the resistant force remains constant. Furthermore, this LSD can work effectively despite the failure of energy dissipation parts, which improves hysteretic energy dissipation under large deformation. In order to replicate the hysteretic behaviour, a uniaxial constitutive model is formulated and its parameters are determined by the utilization of the differential evolution approach, based on test data. The observed strong concurrence between the experimental and simulated hysteresis curves serves as compelling evidence for the efficacy of the differential evolution method. Meanwhile, a three-story building from the third-generation benchmark problem is employed as the testbed structure to examine the energy dissipation capacity of the developed dampers. Nonlinear seismic analysis on the benchmark model equipped with the proposed dampers is also conducted, and the results are compared to those fitted with conventional dampers, such as mild dampers and friction dampers. The findings of this study indicate that the performance of the LSD in reducing structural displacements is superior to that of mild dampers and friction dampers.

Nonlinear seismic response analysis of slopes considering the coupled effect of slope geometry and soil stratigraphy

SUMMARY To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2-D horizontally layered slope models are constructed. First, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analysed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0–60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0–150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations.

Nonlinear seismic analysis of city gate architectural heritages using a sensitive-based model updating method

Due to the unknown accumulation of internal damage and severe degradation of structural mechanisms, updating numerical model related to current damage using Operational Modal Analysis and performing nonlinear seismic analysis pose significant challenges. In this paper, a nonlinear seismic analysis method is proposed involving a three-stage finite element model updating process. This method not only updates the global parameters and local parameters of substructure, but also updates the FEM to true current damage state based on elastic-plastic constitutive model considering current damage. First, on-site vibration and material performance tests were conducted to obtain modal data and material properties of the structure. Second, each component in the model was updated to detect damage, employing a sensitivity-based approach in Stage 1. Then, each element within the severely damaged components obtained from Stage 1 was updated for damage detection, again using a sensitivity-based approach in Stage 2. Finally, the current damage state was updated based on elastoplastic constitutive model considering the current damage and a seismic analysis was performed in Stage 3. The results indicate that, in Stage 1, updating the global parameters of the model aligns the calculated data with the measured data. In Stage 2, updating the local parameters to accurately identify the location and severity of damage within the heavily affected components is demonstrated by a simple example. These results can establish a scientific foundation for the nonlinear seismic analysis of city gate architectural heritages.

Nonlinear seismic response and damage analysis for continuous prestressed concrete rigid-frame bridge considering internal force state under near-fault ground motions

The internal force state of continuous prestressed concrete rigid-frame (CPCR) bridges is significantly influenced by the construction process. To determine the initial internal force state, this study proposed an equivalent load calculation method that is specifically tailored for large-span high-pier CPCR bridges. This method involves calculating equivalent loads that account for the effect of the construction process. Nonlinear dynamic analysis model of a CPCR bridge was established in OpenSees, where the equivalent loads were applied to consider the initial internal force state and the Hertz-damp model was incorporated to simulate the pounding effect. Three groups of near-fault ground motions were selected as three-dimensional inputs for nonlinear time history analysis. Moreover, the paper investigated the seismic damage and the evolution of cracks in the main girder. The results show that the proposed internal equivalent load calculation method can effectively obtain the initial internal force state, which is in good agreement with the actual internal force state. The main girder of the main bridge will pound with the approach bridge and the top of the transition pier in strong earthquakes. The displacement and damage of the transition pier will be greatly underestimated if the pounding effect between the end of the main bridge and the top of the transition pier is neglected. In addition, the cracking damage of the top and bottom plates of the main girders and the distribution of the crack-prone areas were analyzed, and the cracked areas of the top plates of the main girders increased significantly with the increase of the peak ground acceleration.

Nonlinear Seismic Site Response Analysis of Shallow Sites in Dhanbad City, Jharkhand, India

Nonlinear Seismic Site Response Analysis of Shallow Sites in Dhanbad City, Jharkhand, India

New Baseline Correction Method for Near-Fault Ground-Motion Records Based on Continuous Wavelet Transform

Abstract On 6 February 2023, a magnitude 7.8 earthquake struck south-central Türkiye. It was followed by many aftershocks, the largest of which was a magnitude 7.5 aftershock. This earthquake caused considerable loss of life and property. Numerous near-fault ground-motion records were collected during the 2023 Türkiye earthquake. Most existing baseline correction methods for near-fault ground motions disregard the commonly used filtering techniques due to their potential elimination of actual permanent displacement. To address this, a new automatic baseline correction method is proposed based on the continuous wavelet transform, which incorporates filtering while preserving permanent displacement. This method is compatible with existing filtering techniques and demonstrates good applicability. In this approach, the raw record is decomposed into a pulse signal containing permanent displacement and a nonpulse signal. The nonpulse signal is high-pass filtered to obtain the corrected nonpulse signal, and then the true ground motion is obtained by combining the pulse signal with the corrected nonpulse signal. The effectiveness of the proposed method is evaluated across five aspects using the 1999 Chi-Chi earthquake records: time histories, baseline offsets, response spectra, peak ground velocities, and peak ground displacements. Furthermore, the method is applied to 36 station records (108 components) of the 2023 Türkiye earthquake. The analysis results indicate that the corrected displacement time histories exhibit sustained flatness in their tails and demonstrate a closer agreement with the Global Navigation Satellite System (GNSS) measurements than the previous methods. This method can also incorporate static GNSS offsets to accurately determine true ground motions with precise permanent displacements. The corrected results can be utilized for nonlinear seismic calculations and structural damage analysis of fault-crossing structures such as bridges and tunnels.

Fundamental study of damping models with enhanced frequency independence in nonlinear seismic response analysis

AbstractCausal hysteretic damping, extended Rayleigh damping, and uniform damping models exhibit frequency‐independent damping ratios over a wide frequency range. However, several points remain unclear regarding their applicability to inelastic problems. Therefore, in this study, to compare the vibration characteristics of these damping models, analyses are performed by inputting white noise into simple models with various natural frequencies. Results confirm that these damping models are frequency‐independent even under inelastic conditions. Further, the causal hysteretic and extended Rayleigh damping models have the same computation order as that of conventional Rayleigh damping and can therefore be calculated in approximately the same time.

Nonlinear seismic analysis of a reinforced concrete frame building using fibre distributed plasticity element model and fibre hinge model

Nonlinear seismic analysis of a reinforced concrete frame building using fibre distributed plasticity element model and fibre hinge model

Research on Dynamic Characteristics of Loess Homogeneous Dam under Seismic Waves

Based on the relevant provisions of the seismic design code, the three-dimensional nonlinear seismic response analysis of an actual loess homogeneous dam engineering is carried out. The seismic waves use the ground motion time history generated by the relevant design response spectrum of the set seismic site. The research results show that the homogeneous dam in the V-shaped valley has a significant amplification effect in the middle of the valley. The acceleration amplification area of the dam is above 4/5 of the dam height and within the range of 1/3 of the dam axis length. The regularity shows obvious "whiplash effect" and three-dimensional river valley effect.

Hybrid‐simulation‐based model calibration method for nonlinear seismic analysis

AbstractThe calibration of parameters of hysteretic models that simulate the hysteretic behavior of key structural components is a crucial task in the nonlinear seismic analysis of structures to ensure accurate analysis results. For complicated systems, a direct calibration of model parameters at the system level is almost impossible due to the lack of test data. Consequently, the calibration is usually conducted using test results with lower levels of complexity. Currently, a widely accepted practice in calibrating hysteretic model parameters in structural models is to utilize standardized cyclic tests of a single component. However, due to the simplified and unrealistic loading profile of standardized cyclic tests, the relevance between the calibration and the system‐level prediction capabilities can be weak. In other words, a well‐tuned hysteretic model that matches the standardized cyclic test results very well may not be able to produce the same level of accuracy in estimating the system‐level structural dynamic response where the calibrated components will experience more random and complicated loadings. In this paper, a method is proposed to calibrate hysteretic models in a test method with more realistic loading histories through hybrid simulations. The proposed calibration method is then validated by conducting a large number of hybrid simulations on a type of small‐scale buckling‐restrained brace (BRB) specimen. A framework is also proposed to evaluate the relevance between the calibration and the system‐level response considering uncertainties in hysteretic model parameters. The results demonstrate the superiority of the hybrid‐simulation‐based calibration method over the conventional cyclic‐test‐based calibration method.

Nonlinear dynamic response analysis of a hybrid concrete‐filled steel tubular truss lightweight bridge under strong earthquakes

AbstractConcrete‐filled steel tubular (CFST) trusses have seen recent development and application in bridges found in mountainous regions with deep valleys, and especially in seismic zones. In this study, a hybrid CFST truss lightweight bridge was selected as the research object. This bridge is composited of CFST composite truss girders (superstructure) and CFST lattice piers (substructure). Two different finite element models (FEM) for nonlinear seismic response analysis, one is detailed model and the other is simplified model, were established. By comparing with the detailed model, the results of the shaking table test as well as the real bridge test, the simplified model was found to be accurate. Considering the CFST columns' edge strain, the most unfavorable input direction of horizontal ground motion was perpendicular to the connection line of the bearings at both ends of the main girder. Also, the simultaneous influence of vertical ground motion and horizontal ground motion needs to be taken into consideration. By increasing the intensity of input ground motion, the yielding order of CFST lattice piers and its effect on the seismic response were also discussed. Results indicated that the bridge was in the elastic stage for the designed seismic ground motion. After the CFST lattice piers reached the plastic stage, the displacement and in‐plane bending moment had larger amplification coefficients compared to the increase coefficient of the input ground motion, while had a much smaller axial force amplification coefficient. Moreover, the in‐plane bending moment had a larger amplification coefficient in high piers compared to short piers.

Optimization of diagrid tall buildings for seismic response using the parameter space multi-objective method

The development in structural optimization of diagrid buildings is emerged recently due to the urgent need to fulfil environmental sustainability. Despite this, little work has so far been undertaken to optimize diagrid buildings with various heights under nonlinear seismic analysis. This paper studies the optimization of diagrid buildings using parameter space investigation (PSI) to find out the optimum size of diagonal adopting the minimization of diagonals weight. The PSI was utilized among Python script connected with ABAQUS software and visual basic program to generate the feasible and Pareto sets for the studied buildings. Optimal Pareto solutions which is extracted from the proposed method are compared with the referential stiffness-based method to evaluate the efficiency and applicability of the methods. The results concluded that the optimization of diagrid buildings using PSI is a powerful tool for structural engineers to determine the design parameters and can achieve sustainable and resilient structures. In additions, the PSI method could decrease the tension damage in the slabs drastically.