Nonlinear Time History Analysis Research Articles

Performance-Based Seismic Design for Bridge Bents Retrofitted with BRBs Using the Ductility Demand Spectra of SDOF Oscillators with Bilinear Fuses

ABSTRACT Reinforced concrete bridge bents with double columns in bridge substructures are commonly used, but it has suffered severe damage during strong earthquakes. The seismic retrofit with structural fuses is used to effectively mitigate seismic damage of bridge bents. To obtain the displacement ductility demand for dual systems including the primary structure (PS) and structural fuses (SF), the corresponding ductility demand factor spectra were developed. The interaction between the PS and SF is described by defining two parameters of dual systems: the yield displacement ratio (α) and the initial stiffness ratio (β), and the influence of α, β, and strength reduction factor on the ductility demand factor spectra are also analyzed. For seismic retrofitting in bridge bents, buckling-restrained braces (BRBs) are used as energy dissipation fuses, and the steel core lengath of BRBs with three configurations forms, including diagonal, inverted-V, and toggle systems, are also explored. Then, based on the structural fuses concept and ductility demand factor spectra of dual systems, a performance-based seismic design procedure is proposed for bridge bents retrofitted with BRBs to ensure that the bridge bents maintain the target ductility under design-level earthquakes. Finally, the procedure was utilized to design the bridge bents with BRBs, and the procedure’s feasibility was verified by nonlinear time-history analysis.

Seismic behavior analysis of long-span cable-stayed bridge under bi-directional near-fault ground motions

In this paper, the seismic behaviors of a long-span cable-stayed bridge subjected to bi-directional near-fault ground motions are analyzed. The cable-stayed bridge with a main span of 432 m is selected as the research object and appropriately modeled using the OpenSees software. Ten sets of historical near-fault and far-field ground motions associated with the same earthquake event and site class are utilized as input excitations. Nonlinear time-history analyses are conducted to explore three key aspects: the influence of ground motion directionality, the effectiveness of the percentage rule and simplified Square-Root-of-Sum-of-Squares (SRSS) rule, and the main influential factors. The findings reveal that near-fault ground motions induce larger seismic responses compared to far-field ground motions. Moreover, the effects of ground motion directionality are more pronounced in near-fault scenarios than in far-field events. The percentage rule and simplified SRSS rule demonstrate minor significance in predicting the critical seismic responses. The bi-directional peak ground velocity (PGV) of seismic motions in the principal directions of the cable-stayed bridge may emerge as the primary factor influencing the seismic responses, making it a suitable intensity measure for bi-directional seismic fragility assessment.

Advanced tree-based machine learning methods for predicting the seismic response of regular and irregular RC frames

In this study, predicting the maximum drift ratio (MDR) for two types of structures: 8-story regular (R8) and vertically irregular (IR8) reinforced concrete (RC) frames are focused. To accomplish this, advanced tree-based machine learning (ML) methods, namely Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Stochastic Gradient Boosting (SGB) are utilized. 2300 ground motion (GM) records, includes twenty-one input parameters and their nonlinear time history analyses results are considered as a dataset. The performance of the RF, XGBoost, and SGB models was examined considering the impact of the data pre-processing issue to test whether the use of data pre-processing approaches in model development could improve the prediction performance of the advanced ML models. Various data pre-processing techniques, including outlier detection using boxplot, missing data imputation using RF, data transformation using log transformation, and feature selection using Hill Climbing are employed as part of ML pipeline. The models' performance is evaluated using six different well-established statistical evaluation metrics. Subsequently, the results are systematically compared to identify the most effective prediction model. Our findings highlight the substantial impact of data pre-processing on the performance of ML models when predicting seismic responses, specifically the MDR of RC frames. Notably, RF consistently outperformed other ML models for both R8 and IR8 structures in the case of the simple ML pipeline strategy and data pre-processing approach. The RF model achieved R2 scores of R2 = 0.87 and R2 = 0.91 on the test data before implementing data pre-processing for R8 and IR8, respectively. After data pre-processing, R2 scores showed an improvement of 12% and 6.22% in the cases of R8 and IR8. In contrast, the performance scores of SGB consistently fell behind those of RF and XGBoost models.

Seismic performance assessment of RC bridge piers with variable hysteresis performance dampers

A novel variable hysteresis performance damper (VHD)—multi-stage slip friction damper is developed and applied to implement multi-level seismic resistance of structures. Different from the conventional slip friction dampers, which feature only a single type of slip friction surface, this innovative damper incorporates two types: a flat slip surface and a wedge slip surface. The quasi-static cyclic loading tests of the VHD were carried out to investigate its variable hysteresis performance. The test results revealed that the developed damper presented excellent adaptive performance, and its hysteresis behavior changed from a complete rectangle with efficient energy dissipation to a flag-shaped curve with exceptional self-centering capacity as deformation increases. Subsequently, the developed VHD with unique adaptive performance was applied in RC bridge piers (BP) to improve the seismic performance. Nonlinear time history and fragility analysis methods were employed to assess the seismic performance of the RC bridge piers with VHDs (BP-VHD) in deterministic and probabilistic manners, considering maximum and residual deformations as performance indicators. For comparison, seismic responses of RC bridge piers with traditional buckling restrained braces (BRBs) and self-centering energy dissipation braces (SCEBs) were also presented. The analysis and comparison results demonstrate that the developed VHD is as effective as BRB in reducing maximum deformation at small PGAs, meanwhile, it can effectively reduce the residual deformation of the structure to allowable values when the PGA is large. Furthermore, the failure probability of BP-VHDs is lower compared to piers with BRBs and SCEBs, particularly concerning maximum and residual drift ratios as performance indicators. The application of the VHD can effectively achieve the goal of multi-level seismic resistance for RC bridge piers.

Modal-Based Fragility Analysis of High-Rise Tubular Structures: A Methodology for Vulnerability Assessment

This study addresses the limitations of current vulnerability assessment processes for tall buildings, which fail to incorporate the effects of higher modes and the resulting structural vulnerability to seismic hazards. Additionally, the extensive computational resources required for assessing tubular high-rise buildings make vulnerability assessments almost impossible. This study proposes a new methodology for assessing the modal-based structural vulnerability of high-rise reinforced concrete (RC) tubular buildings by incorporating nonlinear response and reducing computational effort. The proposed methodology discreetly develops the vulnerability information of each structural vibrational mode separately using nonlinear time history analysis rather than the linear Modal Response Spectrum Analysis (MRSA). The methodology includes steps for establishing vulnerability information for high-rise tubular buildings, and a case study of a 55-story RC building with core wall is presented to demonstrate the methodology. The vibrational modes of the building were decoupled and analyzed separately using single degree of freedom (SDOF) systems, and fragility curves were developed for three different limit states using various intensity measures. The obtained fragility relationships were compared with the curves of another structure of similar class. The results indicated good compatibility and significance of incorporating higher vibrational modes in assessment of structural vulnerability, thus, proposed methodology can be extended to any structural configuration of tubular buildings.

Open Ground Story Mid-Rise Buildings Represented by Simplified Systems

Open Ground Story Mid-Rise Buildings Represented by Simplified Systems

Comparative seismic performance evaluation of friction, self-centering and hybrid self-centering dampers

This study explores comparative seismic performance of a shape memory alloy (SMA)-only device, a friction damper, and a hybrid self-centering device. The self-centering device considered in this study, named as superelastic friction dampers (SFDs), is a hybrid damper operating on a mechanism where SMA cables and frictional components are arranged in parallel. A detailed description of the device and an experimental characterization of mechanical behavior are presented first. Then, an 8-story archetype steel frame building is designed and modeled with each seismic protection device (SMA-only, hybrid self-centering, and friction only). To enable comparative performance assessment, each device is designed to have similar initial stiffness and the same maximum force at design displacement. Nonlinear time history analyses are conducted using a total of 44 ground motion records. The results are evaluated to compare performance of each frame design at design-basis and maximum considered earthquake hazard levels. Next, a risk-based seismic hazard demand analysis framework that involves comprehensive incremental dynamic analyses is employed for further assessing the performance of each system. The experimental results validate the parallel working mechanism of SMA cables and frictional components in the SFD, with 90% of the damper deformations recovered. Comparative analysis of seismic responses demonstrates the excellent performance of the SFDs in reducing interstory drift ratio, residual interstory drift ratio, and absolute acceleration responses. Furthermore, fragility analysis and risk-based seismic hazard assessment further reveal that the SFDs provide a well-balanced combination of energy dissipation capability and self-centering ability, thereby enhancing the seismic resilience of structures.

A novel modular CFS composite frame-wall structure: Experimental investigation and numerical analysis

Due to the advantages with short-time installation and waste reduction, modular structures are promising. In the process of applying cold-formed steel (CFS) structures in multi-rise buildings, the combination of steel frames and CFS walls can improve the lateral performance of the structures. A novel modular CFS composite frame-wall structure was proposed, which was comprised by modular steel frames and modular CFS shear walls. Five full-scale modular CFS frame-wall components derived from the composite structures were tested under cyclic loads. The layout of sheathings, configuration of CFS diagonal bracings and door openings were varied to study their effects on lateral performance of the modular CFS composite structures. The results indicate the modular steel frames and CFS shear walls can do well in working cooperatively. The bearing capacity of the specimens with sheathings is more than twice that of the specimens without sheathings. In contrast, the effect of the diagonal bracings is not so significant due to the failure of the screw in the ends. Besides, the simplified models based on equivalent line elements was put forward and verified by experiments. A 6-story CFS composite frame-wall archetype structure was designed and its 3D numerical model was built on basis of the mentioned above simplified approaches. The nonlinear time-history analyses were carried out to evaluate the seismic response of the structures. Results show that the inter-story drifts of the designed structures under the earthquake waves of collapse levels are less than the drift limits 1/50. The designed structures have good seismic performance.

Optimal seismic design for self-centering concrete wall structures equipped with U-shaped flexural plate dissipaters

In self-centering wall (SCW) structural system, additional energy dissipation devices are crucial members that are expected to provide both partial lateral force resistance and energy dissipation capacity aiming at mitigating structural response. This research aims to develop a seismic design framework based on particle swarm optimization algorithm for SCW structures equipped with U-Shaped Flexural Plates (UFPs), which can be used to seek out the optimal configuration of UFPs of each floor to reduce seismic response, while maintaining a constant total lateral force resistance provided by all UFPs. For validation, a 10-story SCW structure is chosen as the design case. Specifically, two configurations are considered: a 10-story SCW structure equipped with identical UFPs following conventional design (SCF10-Original) and one equipped with UFPs from optimized configuration (SCF10-Optimized). Their drift and acceleration response are calculated and compared under different seismic intensities through nonlinear time history analysis (NATH). The results demonstrate that the optimized configuration of UFPs can significantly mitigate the drift response in SCW structure. For instance, the maximum inter-story drift ratios of SCF10-Optimized are 0.2 % smaller than those of SCF10-Original under maximum considered earthquake, while the maximum residual inter-story drift ratios of SCF10-Optimized are only half those of SCF10-Original under Extremely Rare Earthquake. Furthermore, the optimized UFPs can effectively reduce the maximum floor acceleration response under various seismic intensities. Therefore, the optimized configuration of UFPs is more effective in reducing both structural and non-structural damage for SCW structural systems compared to conventional configuration. It is also found that greater energy dissipation levels in SCW structure equipped with UFPs may not always result in smaller seismic response, while the configuration of UFPs may play a major influencing factor due to different inter-story lateral force resistance and inter-story energy dissipation demands of SCW structure.

A Novel Approach to Linear and Nonlinear Time-History Analysis of Structures: Gauss–Lobatto–Hermite 4-Point (GLH-4P) Method

AbstractAn efficient time integration scheme has been devised for conducting time-history dynamic analysis of single-degree-of-freedom (SDOF) structural systems. The developed scheme belongs to Runge-Kuta family. The primary innovation of the new formulation lies in the constructive cooperation between the Hermite interpolation and the Gauss–Lobatto integration, linked to address the second-order ordinary differential equation of motion (DEOM). To put the idea into practice, several Hermite interpolators are generated to exploit the information of the internal points of Gauss-Lobatto integrator. The 4-point Gauss–Lobatto formula is employed to numerically integrate acceleration and velocity functions. This novel methodology has been designated the Gauss–Lobatto–Hermite 4-point (GLH-4P) method. GLH-4P furnishes a generally applicable implicit algorithm for conducting both linear and nonlinear analyses of structures subjected to seismic excitation. The advantage of the proposed algorithm over the conventional techniques is its higher accuracy level. Besides, it offers better stability compared with the conventional methods such as the Newmark-β and Wilson-θ methods. Unlike the other methods, GLH-4P can handle high-frequency systems without reducing the step size. Numerical examples reveal the efficacy of the GLH-4P method when juxtaposed against existing methodologies.

Different Soil-Structure Interaction Modelling Strategies for Seismic Analysis of a Masonry Church

ABSTRACT Masonry structures can be damaged different external reasons such as war, flood, earthquake etc. For protecting and transfer to the next generations, these structures can be examined detailed. Finite element analysis has generally been used for the seismic evaluation of masonry structures. The fixed base assumption has been used in traditional finite element analysis of masonry structures. Interacting with the surrounding soil and structure was generally ignored. The seismic behavior of masonry structures is significantly influenced by the soil-structure interaction (SSI). There are various soil structure interaction modelling strategies in the recent studies. In this paper, the dimensions, mechanical properties and material model of the soil are considered constant. One of them had no soil-structure interaction. The others, roller support case, fixed support case, absorbing boundary case, free field columns and Winkler supports. Variations in the seismic response of a historical masonry church were investigated using 4 different SSI models and a fixed base (SSI ignored) model. Nonlinear time history analyses were employed for the finite element analysis. The soil borehole provided the material characteristics of the surrounding soil. According to the analysis results, higher response amplitudes were obtained when SSI was considered.

Effectiveness of composite energy dissipation restrainer on mitigating pounding and unseating failure of highway bridges

In earthquake-prone regions, large relative displacement between piers and girders may lead to pounding damage and unseating failure in highway bridges. To mitigate these effects, this study presents a composite energy dissipation restrainer (CEDR) that incorporates a composite energy tube (CET) as a fundamental component (comprising an aluminum honeycomb buffer and an expansion tube). The energy absorption characteristics of the CET are analyzed, and the influence of the aluminum honeycomb is thoroughly discussed. Furthermore, a design procedure and mechanical model for the CEDR, considering rare earthquakes, are developed. Finally, the effectiveness of the proposed design method and the behavior of limiting displacement of the CEDR are demonstrated through nonlinear time history analysis of an implemented project. The results reveal that the aluminum honeycomb buffer exhibits superior energy absorption capability, enhancing buffering efficiency and reducing damage. Compared to common cable-type restrainers (CCR), the CEDR reduces the relative peak displacement of the bridge by 40%, decreases the frequency of reciprocating displacement by 30% on average, and mitigates impacts on the abutment by 80%.

Seismic Fragility Reduction for Base Isolated RC Frame Buildings by Curved Surface Sliding Bearings with Over-Stroke Displacement Capacity

ABSTRACT Recently, experimental studies on failure conditions of buildings equipped with curved surface sliding isolators have shown that when no displacement restraining elements are employed and the concave plates feature a flat rim, the inner slider can run on the edge of the sliding surfaces producing lateral displacement larger than the nominal isolator capacity. The over-stroke displacement capacity reduces the probability of seismic collapse of code-conforming base-isolated buildings for earthquake stronger than the design one. In order to quantify the benefit of the over-stroke displacement capacity of double concave curved surface slider (DCCSS) bearings on the seismic fragility of base isolated buildings, four case studies of six-storey reinforced concrete framed structures, consisting of new constructions and retrofit of existing structures located in high and medium hazard seismic sites, have been investigated in this paper. In all cases, two configurations of the isolation system have been considered, with end-stop displacement or with over-stroke displacement capacity. The seismic performance of the buildings has been investigated by multi-stripe nonlinear time-history analysis. The results of the nonlinear dynamic analysis at the collapse limit state have been compared with nonlinear static analysis in terms of maximum displacement and corresponding base shear. Fragility curves highlight a higher safety margin against collapse for seismic intensities beyond the design limit state of the isolation system with over-stroke capacity.

The strain demand of reinforced concrete bridge columns under seismic loading

The steel in reinforced concrete (RC) members that form plastic hinges must possess sufficient strain capacity to dissipate seismic deformation demands. Unfortunately, there is limited information on the seismic strain demands of bridge column plastic hinges. Instead, designers rely on a perception of cyclic strain capacity that is an approximate rule of thumb. A standard methodology needs to be established for quantifying the strain demand on these structural members as a function of the expected seismic hazard. To develop this methodology, 1944 columns were analyzed with nonlinear time-history analyses (NLTHAs) using ground motions from a range of earthquakes. This study evaluates the strain demand on RC bridge columns by defining the relationship between the strain demand and earthquake intensity. The results of the model are defined in terms of the peak tensile strain of the reinforcing bar, [Formula: see text]. The earthquake intensity with the highest correlation to the [Formula: see text] was determined to be the elastic spectral displacement at the optimal period ([Formula: see text]), which is defined as 75% of the effective period. The relationship between [Formula: see text] and [Formula: see text] can be used to predict the strain demand for an RC bridge column at a given geographic location. Results are presented as a probability density function (PDF), representing strain demand, compared to a PDF of the column capacity. The intersection of the capacity curve and demand curve represents the maximum acceptable strain given as a function of [Formula: see text]. This methodology can help understand the demand placed on a structural system given a region’s seismicity.

Correction to: Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Correction to: Optimized Gauss–Legendre–Hermite 2-point (O-GLH-2P) method for nonlinear time-history analysis of structures

Study on the mechanical properties of a viscoelastic self-centering brace with rotational displacement amplification and its application in RC frames

This paper introduces a novel viscoelastic self-centering brace with a rotational displacement amplification function (VSB-RA), developed to address the issue of limited energy dissipation in traditional self-centering braces. The basic structure and working mechanism of the VSB-RA are detailed. Low-cycle reciprocating loading tests were performed on two types of VSB-RA specimens with different initial amplification angles, and a comprehensive analysis was conducted on their bearing capacity, energy dissipation performance, self-centering capability, and frequency correlation. A refined finite element model was developed in ABAQUS software to simulate the complete test loading process. Nonlinear dynamic time history analysis is then performed on an 8-story reinforced concrete (RC) frame structure with the VSB-RAs using different initial amplification angles. The results demonstrate that the hysteresis curves of the VSB-RA exhibit distinct flag-shaped characteristics and excellent self-centering performance, and its energy dissipation capacity increases exponentially with the decrease of the initial amplification angle. The numerical simulation results of the hysteresis curves align well with experimental findings. The inter-story drift, residual inter-story drift, floor acceleration, and base shear force are effectively controlled in the VSB-RA frame structures compared to the uncontrolled structure. Under rare earthquake actions, the base shear forces of the structure are reduced by 27.2 %, 27.9 %, and 30.7 % at initial amplification angles of 45°, 37.5°, and 30°, respectively.

A response‐compatible ground motion generation method using physics‐guided neural networks

AbstractSelecting or generating ground motions (GMs) that elicit seismic responses matching specific standards or expected benchmarks for nonlinear time‐history analysis (NLTHA) is crucial for ensuring the rationality of structural seismic design and analysis. Typical GM inputs for NLTHA, either natural or artificial, are normally spectrum‐compatible, which may produce significant variations in analysis results, even using multiple GMs. This paper introduces a response‐compatible ground motion generation (RCGMG) method for generating GMs that are tailored to be response‐compatible. NLTHA results using only a few of these artificial GMs can closely approximate the mean responses from a large set of natural spectrum‐compatible GMs or target responses. The RCGMG method adopts the response diagram in the time domain (RDTD) to characterize the nonstationary features of GMs and their impacts on structural dynamic responses. A physics‐guided conditional generative adversarial network is developed to produce artificial RDTDs with features and impacts of RDTDs of natural GMs. These generated RDTDs are then mapped into response‐compatible GMs through a feedforward neural network. To verify the effectiveness of RCGMG, NLTHA of different structure models under various site conditions and target spectra is conducted. Seismic responses of NLTHA using RCGMG‐generated GMs are compared with responses from spectrum‐compatible natural GMs. The results demonstrate that responses from RCGMG GMs are closer to the target responses, with fewer GM inputs and robust generalization performance.

Effect of Bearing Friction on Seismic Performance of Bridges with Massive Piers Isolated by Friction Pendulum Bearings

Although seismic isolation is a well-accepted design strategy for bridges to provide structural earthquake resistance, for bridges with massive piers, it may unexpectedly pose an abnormal influence on the seismic response of bridges due to the effect of substructure mass. This study investigates the effects of bearing friction and pier mass on the seismic performance of bridges isolated by friction pendulum bearings (FPBs). Nonlinear time history analysis is conducted to demonstrate the variation of the bridge peak responses with different bearing frictional coefficients and pier mass. The inherent influential mechanism of the frictional coefficient of FPBs is also discussed in the current study. The results of the analysis show that for FPB-isolated bridges with massive piers, the peak base shear forces of piers first decrease and then increase with the increase of the bearing frictional coefficient. Such a phenomenon may be attributed to the fact that the inertia force of the massive piers will be altered by the variation of bearing friction. The outcome of this study provides a useful reference for practical engineering that the seismic base force of massive bridge piers calculated under a specified bearing frictional coefficient may be smaller than the actual response and cause reduced safety to bridges.

A clustering-based analysis method for simulating seismic damage of buildings in large cities

Earthquakes are major threats to cities. Refined simulations of urban earthquake damage are significant for disaster prevention planning, including post-earthquake emergency rescue operations. However, this approach is time-consuming and computationally demanding. This study presents a novel machine learning method for simulating seismic damage of large urban building groups, thus minimizing the computational time and resources associated with the simulation process. First, the proposed method clusters building structures based on their seismic damage index (DI) under specific ground motions. Subsequently, one structure is selected from each cluster for seismic analysis. This approach significantly reduces the number of analyzed structures. The efficiency and accuracy of this method are studied based on a parametric study that involved an improved K-means clustering algorithm and a grid-based clustering algorithm. A batch-clustering algorithm is also developed to further improve the speed of clustering and efficiency of regional seismic simulations. A large Chinese city is considered as research application example. The results indicated the following: (1) the method based on the improved K-means clustering algorithm was superior; (2) the batch-clustering algorithm significantly speeded up clustering analysis and enhanced efficiency of the seismic simulation; (3) the clustering-based simulation method demonstrated high efficiency and accuracy, with a significant decrease of 90.5% in the calculation time compared with direct nonlinear time history analysis. In addition, the average relative error of the DI was only 11.0%. Moreover, over 85.0% of the structures were estimated to be in the correct damage state.

Relationships between ground motion parameters and energy demands for regular low-rise RC frame buildings

AbstractThe present study aims to analyze the correlation between ground motion parameters and energy demands of low-rise RC buildings without shear walls. Two regular 4- and 7-story residential buildings were seismically designed to represent low-rise RC buildings. In order to establish the requirements of single degree of freedom (SDOF) systems as well as multi degree of freedom (MDOF) systems, the dynamic features of “equivalent” SDOF systems were defined by using MDOF systems. The correlation of 20 ground motion parameters (GMPs) of 44 records with the energy demands obtained from a total of 176 nonlinear time history analyses was examined for the SDOF and MDOF systems within the scope of this study. The ground motion parameters (GMPs) were taken as intensity measures (IMs). In contrast, maximum input energy was used as a demand measure (DM) and these energy values were normalized with the masses of the buildings for cases, where the buildings were evaluated together. Parameters related to acceleration and velocity are generally found to yield better results in comparison to the ones related to frequency and displacement. Velocity Spectrum Intensity (VSI) and Arias Intensity (Ia) were obtained to have the highest correlation values as a single parameter. This study suggested new equations by combining multiple ground motion parameters for SDOF and MDOF systems to better reflect damage potential than a single parameter. The use of multiple parameters in combination results in better correlation coefficients.