Nonlinear Time History Analysis Research Articles

Seismic performance and vulnerability analysis for bifurcated tunnels in soft soil

This paper investigates the seismic performance of complex comprehensive interchange underground structures. As an example, the seismic performance of Nanjing underground bifurcated tunnels constructed in soft soil is analyzed. A three-dimensional (3D) numerical finite element analysis model is established considering soil-tunnel interaction to analyze the seismic response characteristics and failure mechanism of the bifurcated tunnels. The results show that the tunnel damage degree is closely associated with the deformation response, and that the inter-story drift ratio of the lower layer is significantly greater than that of the upper layer. The pushover analysis method is used to obtain the seismic performance curve of the tunnel, and inter-story drift ratio limits are defined. The IDA procedure is then used to conduct multiple non-linear dynamic time history analyses based on the 3D finite element model, and IDA curve clusters are drawn with peak ground acceleration (PGA) as the earthquake intensity measures and the peak inter-story drift ratio as the damage measures of tunnels. The corresponding IDA percentiles lines are calculated, and the seismic fragility curves of the bifurcated tunnels are established. The post-earthquake functional failure probability of the bifurcated tunnels is obtained under different seismic fortification performance level.

Preferred Seismic Performance Attainment in Important Buildings

In the aftermath of earthquakes, hospital buildings are expected to remain occupiable to treat the injured. For the purpose, firstly, an appropriate structural system that ensures no or limited structural damage should be provided in such buildings; wall-frames are the recommended structural systems in hospital buildings. Secondly, it is also essential to adequately design wall-frames to help meet the preferred Occupiability seismic performance. The work presented in this paper examines the contributing factors for failure of structural elements in hospital buildings and explores structural configuration and design strategies for mitigating these failures. Nonlinear analyses studies of a typical hospital building in high seismic region in India are carried out to help provide quantitative guidelines for: (a) Structural Plan Density (SPD) of structural walls, and (b) design parameters, for achieving the preferred performance. Displacement-based limit state of structural damage adopted from traditional displacement demand estimation rules is proposed. Lateral stiffness, strength, and ductility are evaluated of study buildings, and efficacy of results obtained from nonlinear static analyses confirmed by performing nonlinear time history analyses in commercial software PERFORM 3D. Results demonstrate inadequacy of moment frame structural system in hospital buildings under strong earthquake shaking, identifies optimum overall SPD of structural walls and relative column-to-beam strength ratio of frame members, required to achieve Occupiability. A minimum 3% SPD of structural walls in Wall – Special Moment Resisting Frame (WSMRF), 4% SPD in Wall – Ordinary moment resisting frame (WOMRF) hospital buildings, and a minimum column-to-beam strength ratio (CBSR) of 2 is required in hospital buildings to attain Occupiability performance.

Seismic Upgrade of an Existing Reinforced Concrete Building Using Steel Plate Shear Walls (SPSW)

Steel Plate Shear Walls (SPSW) provide significant lateral load capacity and can be utilized in the seismic retrofit and upgrade of existing reinforced concrete (r/c) buildings. In this study, the application of SPSW to retrofit a r/c building designed according to older seismic provisions is presented. Three different options to model SPSW are utilized, i.e., by equivalent braces, by finite elements, and by membrane elements, seeking not only to appropriately simulate the actual behavior of the SPSW but also to achieve the desired seismic behavior of the retrofitted building. Specific seismic response indices, including plastic hinge formations, are derived by non-linear time-history analyses in order to assess the seismic behavior of the retrofitted r/c building. Inspection of the results provided by non-linear analyses in conjunction with the different modeling options of the SPSW leads to the conclusion that the model with the membrane elements exhibits the best performance, implying that for the seismic retrofit and upgrade of existing r/c buildings, the use of membrane elements to model the SPSW is recommended.

Seismic response prediction using a hybrid unsupervised and supervised machine learning in case of 3D RC frame buildings

The seismic vulnerability assessment represents an important step in monitoring the buildings’ capacity and checking their performance during and after earthquake events. The Nonlinear Time History Analysis (NL-THA) is considered the most reliable method that is used to calculate the exact structural behavior of any building. However, this sophisticated method is known for its complexity, the use of Finite Element (FE) software, and computational time consuming, especially in the case of tall buildings. For that reason, An Artificial Neural network (ANN) is used to develop a new model able to predict the essential Engineering Demand Parameters (EDPs), i.e., the Maximum Base Shear (MBS), the Maximum Inter-story Drift (MIDR) and the Maximum Roof Drift Ratio (RDR). Unsupervised algorithms such as the Principal Component Analysis PCA and the Autoencoder are coupled with the ANN to reduce the dimensionality, improve the dataset quality, and reduce the irrelevant features. More than 192,000 buildings are analyzed using the NL-THA and eighty artificial ground motions (GMs) to generate the dataset. The buildings’ characteristics are generated randomly from the selection range. The results showed that the Autoencoder-ANN model represents the highest performance compared to the PCA-ANN and ANN models. The Autoencoder-ANN model could quickly and accurately predict the seismic responses of unseen ground motions using only the building’s characteristics and the GM parameters without using any FE software.

Seismic response of non-structural components in multi-storey steel frames

This paper investigates the elastic and inelastic seismic response of non-structural components in multi-storey steel moment framed structures and derives predictive relationships for their displacements and spectral accelerations. Within 38 primary structural steel frames, non-structural components characterised by various periods and strength reduction factors, are modelled as single-degree-of-freedom systems which are fixed to individual floors. The primary structures are three, five, and seven-storey steel moment-resisting frames, designed according to the provisions of Eurocode 8. Detailed nonlinear time history analyses are conducted, employing a large set of 100 ground motion records from both far-field and near-field sources. These records are scaled to two distinct levels to simulate the response of primary structures in both elastic and inelastic states. The influence of the ground motion type and the inelasticity level in the non-structural components is examined in detail. The sensitivity to strain hardening and viscous damping considerations is also assessed and discussed. Based on the results, representative relationships for predicting the inelastic displacement ratios are proposed. In addition, various provisions stipulated in European design guidance for determining the spectral accelerations are critically evaluated and improvements are suggested with due consideration for the inelasticity of both the non-structural components and the primary structures.

Mega bracing system with RC multistory based on plate-frame method by sap2000

This study investigates the optimal arrangement of steel braces for a 15-story reinforced concrete building. The analysis is based on a 0.1 mm plate model at the exterior face of the building, which is subjected to nonlinear time history analysis of Elcentro ground motion earthquake. The study focuses on the internal forces path induced by seismic loads and aims to identify the most preferable results for different configurations of steel bracing using sap2000 software. By selecting the moment that led to the maximum internal drift, the study determined the maximum load concentrations. The results indicate that model 4 and 6 produced the optimal results, with a significant increase of 32% and 37% in base shear, as well as a notable improvement of 60.64% and 60.5% in roof displacement, respectively.

Investigation of Seismic Response of Irregular Steel Buildings: A Case Study of U-Shaped Structures

Tills paper presents a dynamic analysis focusing on the influence of plan shape on tall steel structures. The study specifically investigates the seismic behavior of two 22-story buildings, one with a square plan and the other adopting a U-shaped configuration. Utilizing OpenSEES platform for nonlinear time history analysis, the research sheds light on the impact of plan irregularities on fundamental time periods, displacements, drift ratios, and base shear. Results reveal that the U-shaped building experiences liiglier dynamic response compared to the square shaped reference building, the U-shaped building experiences liiglier time periods across all modes due to increased mass and irregular stiffness distribution in the building's grid. Top story displacements reveal an increase in maximum displacement by 30% compared to the reference structure, showing a non-linear pattern. Inter-story drift ratios had peaks at the 8th and 18th floors showing increments of 43% and 117%. respectively. The time liistoiy response illustrates a liiglier response over time for the U-shaped building, indicating distinct behavioral differences. Base shear time liistoiy revealed liiglier values for the U-shaped building over time, including a 48% increase in maximum base shear compared to the reference building. These findings reveal the significant effect of plan regularity in tall steel building design on the seismic response and the importance of considering it in building design.

Beam-column joint modeling effects on the seismic response of a non-ductile reinforced concrete building

Seismic performance evaluation of existing reinforced concrete buildings requires numerical approaches that reflect the damage modes that may arise from deficiencies in beam-column joints. In this study, the seismic performance of an existing reinforced concrete building with four stories was investigated by applying elastic and deformable beam-column joint models. The deformable beam-column joint model was verified using an exterior non-ductile beam-column joint test. The model included a rotational spring located at the joint with two connected nodes in a zero-length with rigid elements in the vicinity of frame elements. Moment- rotation relationships represent the joint behavior, and they were defined based on shear stresses and strains. After effective modeling of beam-column joints, it was aimed to obtain the cyclic behavior of the building model using non-linear time history analysis. For this purpose, scaled earthquake records were applied to the three-dimensional numerical model, and the results were compared in terms of inter-storey drift ratios, column and beam chord rotations, and base shear. It was determined that the exterior beam-column joints reached their strength and deformation capacity, while the beam and columns remained below their section deformation limits according to the Turkish Earthquake Code.

The Seismic Performance of Infill and Retrofitted Structural Walls under Earthquakes

To account for the effects of infill walls, the Iranian Code reduces the period of the structure. As a result, filler walls in the plane of structural frames result in significant changes in the properties they possess; therefore, the resistance, stiffness, ductility, distribution of internal forces, and other characteristics of such a frame with an empty frame differ greatly. In this research using 7 far-field earthquakes, a nonlinear time history analysis was performed on reinforced concrete frames with and without masonry infill walls. The maximum relative displacements between the stories were determined. Also, to evaluate the seismic performance of structural masonry walls, the fragility curve of unreinforced masonry walls retrofitted with FRP sheet based on different scenario under the effect of earthquake loads has been investigated by the finite element method. According to the results, the presence of infill walls reduces the number of plastic hinges as well as the maximum relative displacement between the stories. Furthermore, by increasing the number of FRP sheet layers and the reinforced area of the FRP sheet to the entire wall of an unreinforced structural wall, the seismic behaviour of the wall is more effective than other reinforcement patterns and damages the wall less.

Meta databases of steel frame buildings for surrogate modelling and machine learning-based feature importance analysis

Traditionally, nonlinear time history analysis (NLTHA) is used to assess the performance of structures under future hazards which is necessary to develop effective disaster risk management strategies. However, this method is computationally intensive and not suitable for analyzing a large number of structures on a city-wide scale. Surrogate models offer an efficient and reliable alternative and facilitate evaluating the performance of multiple structures under different hazard scenarios. However, creating a comprehensive database for surrogate modelling at the city level presents challenges. To overcome this, the present study proposes meta databases and a general framework for surrogate modelling of steel structures. The dataset includes 30,000 steel moment-resisting frame buildings, representing low-rise, mid-rise and high-rise buildings, with criteria for connections, beams, and columns. Pushover analysis is performed and structural parameters are extracted, and finally, incorporating two different machine learning algorithms, random forest and Shapley additive explanations, sensitivity and explainability analyses of the structural parameters are performed to identify the most significant factors in designing steel moment resisting frames. The framework and databases can be used as a validated source of surrogate modelling of steel frame structures in order for disaster risk management.

Seismic Vulnerability of Segmental Bridges with Drop-In Span by Pushover Analysis

Insight into the application of pushover analysis to prestressed concrete segmental bridges built in the 1950s–1970s by cantilevering with medium-large span length is provided. Seismic assessment must be carried out considering the whole structural response and, in particular, the task of tall piers, bearings, and drop-in spans with Gerber saddles, which are likely to be subjected to girder pounding and/or unseating. In this paper, the assessment of seismic vulnerability is initially performed by linear modal dynamic analysis; then, the efficiency in assessing the seismic response of different methods of pushover analyses is compared, assuming as a benchmark the results of non-linear time history analysis. The outcomes show that, for the bridge with the drop-in span, criteria for selecting the load pattern considered in pushover analysis, the reliable modeling of the bearings, and tall piers play a dominant role in the assessment of the seismic vulnerability, particularly in longitudinal motion.

Optimal design of self-centering bi-rocking braced frames using metaheuristic algorithms

Residual drift of structural systems after seismic events can make buildings uninhabitable and may cause their collapse in aftershocks, as seen in the 2023 Turkey-Syria earthquake. Self-centering rocking-core systems can eliminate plastic deformation of structures after earthquakes. In the current study, a bi-rocking steel-braced frame was designed using the modified modal superposition (MMS) method. The optimal location of the secondary joint was found to minimize the base shear, overturning moment, peak floor acceleration and inter-story drift. Damage to non-structural components has been considered. The models included 12-, 18- and 24- story frames that were subjected to far-field (FF), near-field-pulse (NP) and near-field-no-pulse (N) ground motion records. The seismic records were scaled to the maximum credible earthquake level. Nonlinear time-history analyses were performed using OpenSees open-source finite element software. Additionally, post-tensioned cables and energy dissipation fuses as variable parameters were optimized using particle swarm optimization. The performance of seven metaheuristic algorithms was compared and the results showed that placing the secondary joint at the mid-height of the structure reduced all seismic demand. The results also suggest that the story moment and FF records were most sensitive to the location of the secondary joint. It was observed that frames with lower stiffness and yield strength of the damper exhibited better seismic performance. Based on this, corrective percentages have been proposed for the design of the cable and dampers. A self-centering ratio of 1.07 was suggested at the mid-height and 1.19 for the base damper. The colliding bodies optimization algorithm performed best for time-history analysis-based optimization.

Dynamic responses of multi-story structural systems with separated gravity and lateral resisting systems under seismic action considering connection semi-rigidity effects

This paper investigates the dynamic behaviour of an innovative structural system with separated gravity and lateral resisting systems (SGLR system), which is proposed for the prefabricated structures in multi-story buildings by enhancing the standardization of beams, under earthquake excitation. The seismic performance of SGLR system is benchmarked against the conventional rigid frame system (RF system) designed with the same maximum inter-story drift ratios, and the influences of connection semi-rigidity on the dynamic responses of SGLR system are focused on. Numerical models are built using the self-developed fiber beam-column elements for composite frames, beam elements for semi-rigid connections and multi-layer shell elements for shear walls based on a six-story prototype structure. The modal analysis indicates that the natural vibration periods of SGLR system are smaller than those of RF system and the connection semi-rigidity will further significantly decrease the periods for the first three orders. Nonlinear time history analysis is conducted under eight sets of ground motions at two different levels in two horizontal directions. The shear walls in SGLR system bear the majority of seismic action with damage concentrated in the bottom. The connection semi-rigidity will decrease the lateral deformation and increase the involvement of the frame part in the lateral resisting mechanism of SGLR system, which can be more significant when the semi-rigidity is higher. SGLR system exhibits better control of inter-story drift ratios considering connection semi-rigidity in low-rise buildings and higher economic efficiency in mid-rise buildings.

Seismic Risk Analysis of Existing Link Slab Bridges Using Novel Fragility Functions

In this paper, a comprehensive probabilistic framework is proposed and adopted to perform seismic reliability and risk analysis of existing link slab (LS) bridges, representing a widely diffused structural typology within the infrastructural networks of many countries worldwide. Unlike classic risk analysis methods, innovative fragility functions are used in this work to retrieve more specific and detailed information on the possible failure modes, without limiting the analysis to the global failure conditions but also considering several intermediate damage scenarios (including one or more damage mechanisms), and providing insights on the numerosity of elements involved within a given damage scenario. Reliability analyses are performed on a set of LS bridges with different geometries (total lengths and pier heights) designed according to the Italian codes enforced in the 1970s. Accurate numerical models are developed in OpenSees and Multiple-Stripe nonlinear time–history analyses are carried out to build proper demand models, from which fragility functions are determined according to two limit states: damage onset and near-collapse. Mean annual rates of exceeding are thus estimated through the convolution between the hazard and the fragility. The results shed light on the main failure mechanisms characterizing this bridge typology, highlighting how different levels of risk (hence safety margins) can be associated with failure scenarios that differ in terms of elements/mechanisms involved and damage extension. Such a higher level of detail in the risk analysis may be useful to better quantify post-earthquake consequences (e.g., costs and losses) and define more tailored retrofit interventions. A comparison of the reliability levels associated with bridges of the same class with different geometries is finally presented.

Enhancing Seismic Performance of Multi-story Steel Buildings Using Inner Mega Braced Frames

damage to buildings. In this study, a multi-story steel building is designed using the ETABS v16 software under vertical loads only. Subsequently, seismic performance was enhanced by employing five different Mega braced frames (MBFs) systems in two cases: in the first case, the five bracing systems are placed within a frame located 6 meters away from the outer frame, while in the second case; the bracing systems were placed within a frame located 12 meters away from the outer frame. The building was then analyzed using nonlinear time history analysis with SAP 2000 V20 software, utilizing seismic data from the El-Centro earthquake available in SAP 2000 V20. The results were compared based on various parameters such as maximum roof displacement, maximum inter-story drift ratio, and maximum base shear. The findings demonstrated an improvement in the building's response, in the first case maximum roof displacement reduction ranging from 36.08% to 48.29% in both directions, and from 36% to 44% for maximum roof displacement in the second case. Maximum inter story- drift ratio also reduced by percentages ranging from 25% to 46% in the first case and 25% to 39% in the second case. From the analysis results, it is evident that the best pattern in the first case is pattern5, while in the second case pattern4 is the best.

Seismic Fragility Analysis of Retaining Walls Dependent on Initial Conditions

Fragility curves of retaining walls constitute an efficient tool for the estimation of seismic risk and can be utilized for prevention from potential damage or for immediate decision-making. In this work, fragility curves for cantilever retaining walls of three different heights are proposed, considering cohesionless soil materials. The seismic response of the soil-wall system, in terms of permanent vertical ground displacement of the backfill soil and permanent horizontal displacement of the wall’s base, is estimated by conducting non-linear time history analyses, through the 2D finite element simulation method. Five initial conditions are investigated regarding the value of the global factor of safety (FS) under static conditions. An initial value of FS equal to 1.5 is considered for dry conditions. If the presence of the water table is taken into account, the corresponding FS drops to values ranging from 1.4 to 1.1. Parameters that characterize seismic intensity are evaluated based on criteria, in order to identify the intensity measures that best correlate with the system’s response. Three damage states are adopted, corresponding to minor, moderate, and extensive damage. The approach of combined damage criteria is also investigated. Finally, fragility curves are derived demonstrating the degree of dependency on initial conditions.

Near-fault ground motion effect on self-centering modular bracing panels considering soil-structure interaction

This study investigates the nonlinear seismic response behavior of self-centering modular steel bracing panel (SCMBP) systems subjected to near-fault ground motion records, considering the soil-structure interaction (SSI) effect. Analytical formulas for the load-displacement relationship of an SCMBP were validated through nonlinear 3D continuum finite element analysis while a simplified 2D wireframe model utilizing a constitutive spring model was verified by the 2D refined finite element model and subsequently adopted for time history analysis of the SCMBP structures with SSI effect. Based on the nonlinear time history analysis of a 6-story prototype building subjected to a suite of near-fault ground motions, the prototype structure is found to be able to re-center itself even under near-fault ground motion scaled to the design basis earthquake (DBE) level while frame members remain undamaged, except for fuse devices. Additionally, SSI reduces inter-story drift ratios under both far-field and near-fault ground motions. The findings provide insights into the promising performance of using SCMBP systems as a seismic strengthening system for sites with potential SSI effects and near-fault earthquake impact. The findings of this study can be insightful to other self-centering systems with flag-shaped story shear hysteresis.

Bayesian-optimized interpretable surrogate model for seismic demand prediction of urban highway bridges

Urban highway bridges are crucial for regional economic development and population mobility, but they are vulnerable to seismic hazards. Accurately predicting the seismic demands of bridges is essential. Several commonly-used methods for seismic demand estimates, such as cloud analysis, incremental dynamic analysis, and multiple stripe analysis, are computationally expensive and subject to theoretical assumptions and convergence issues, especially for portfolios of bridges. Machine learning techniques can be effective, but their lack of interpretability hinders understanding of the surrogate model's predictions. To address these challenges, this study develops a Bayesian-optimized interpretable ensemble learning surrogate model for predicting and interpreting the critical seismic demands of urban highway bridges.Thousands of continuous prestressed concrete girder bridges with typical geometric configurations in China are generated, and 120 ground motion records with different frequency, waveform, and duration characteristics are chosen. The seismic demand dataset is established based on nonlinear time-history analyses for urban highway bridges, accounting for different types of uncertainties. The surrogate models are developed based on the XGBoost ensemble learning method, with hyperparameters automatically and efficiently determined by Bayesian optimization technique. Compared to the random search and grid search methods, Bayesian optimization is approximately 8 times and 29 times faster, respectively, and it also achieves the highest prediction accuracy. Meanwhile, the relationship of each hyperparameter in the surrogate model is also revealed. The prediction results of the proposed model are compared with other machine learning models. The SHAP algorithm is subsequently used to explain the model predictions regarding the feature importance, global interpretations, and feature dependency analysis. The study quantifies the contribution of each structural feature and seismic intensity measure to the selected critical seismic demand and identifies the interaction effects between different input variables in the prediction.

Seismic isolation effect of tunable friction pendulum system in bridge

ABSTRACT A Tunable Friction Pendulum System (TFPS) was proposed to investigate its seismic isolation control performance in bridge structures. First, the structural design and theoretical model of TFPS are given. Second, the mechanical properties of TFPS are studied through finite element simulation. Then, the above TFPS is introduced into the bridge structure, and the analysis model is established based on SAP2000. Finally, a nonlinear time-history analysis is carried out on the bridge structure, and the seismic isolation performance of TFPS is evaluated by using the dynamic characteristic response index of the bridge structure. Theoretical derivation and finite element analysis results show that TFPS can adjust the dynamic characteristics in real time according to the spectral characteristics of the ground motion input and the response of the structure itself, so that the friction force can be continuously adjusted and energy consumption can be adjusted.

Evaluation of Steel Diagrid Structural System Under Near-Fault Earthquakes

ABSTRACTThe diagrid structural system has become popular in the construction of high-rise buildings in light of significant advantages over other structural systems. The present study explores the effects of the vertical near-fault earthquake component on the axial forces of diagonal elements in steel diagrid structures. Nonlinear time-history analysis was carried out using 11 near-fault earthquake records. A total of nine three-dimensional models of 12, 18, and 24 stories, each with diagonal angles of 45, 63.4, and 71.5 degrees, were designed and analyzed. Due to the three-dimensional modeling complexities of diagrid structures, a method was developed to transform three-dimensional models into two-dimensional ones. Finally, the scenarios with and without the vertical earthquake component were compared. It was found that the incorporation of the vertical earthquake component into the analysis of diagrid structures substantially influenced the axial forces of diagonal elements. This can affect the design load estimation of diagonal elements as the main components of a diagrid structure.