Nonlinear Time History Analysis Research Articles

Nonlinear analysis of reinforced concrete buildings with different heights and floor systems

Most civil structures exhibit nonlinear behavior during moderate to severe earthquakes. Consequently, inelastic analysis is needed for seismic design. Several dynamic and static analysis methods are available for the assessment and design of engineering structures. Two of the available methods in terms of nonlinear dynamic time history analysis and nonlinear static analysis, which is known as pushover analysis, are employed herein to comprehensively study and investigate the seismic performance of multi-story building structures with different floor systems. Moreover, the study is extended to assess the actual values of the response reduction/modification factor (R-factor) for each building model, then evaluate the values with the code-recommended design values. Three-dimensional finite element building models with 5, 10 and 15 stories are developed for the evaluation process. The advanced computer program ETABS is used for developing and analyzing the buildings considering material and geometrical nonlinearity. A suit of seven earthquake records is considered and scaled according to the ASCE-16 seismic design code to excite the building models. The obtained results evidently reveal that the type of floor slab significantly impacts the seismic response of the building. More specifically, the effects of floor slabs on seismic demands are more evident in low- and mid-rise buildings. In addition, the type of slab system and height of the building have more influence on the response modification factors, especially for low-rise building models.

Seismic design and evaluation of controlled rocking outrigger core wall (CROCW) system using equivalent energy design procedure (EEDP)

In this paper, a novel earthquake resilient reinforced concrete core wall system named the controlled rocking outrigger core wall (CROCW) system is proposed. The CROCW consists of two high-performance seismic force resisting systems along its two principal axes. Along one principal axis is the controlled outriggered rocking wall (CORW), where an outrigger is situated at the roof and controlled rocking at the base. Dampers are incorporated within the outrigger and the rocking base to allow CORW to provide stable energy dissipation during earthquake excitation. Along the other principal axis is the self-centering coupled wall (SCCW). In the SCCW system, the self-centering friction dampers are incorporated within the coupling beams to dissipate the earthquake energy, while the base is designed to rock. The proposed CROCW system can be designed using the novel equivalent energy design procedure (EEDP). Four prototype buildings (two different building heights and two different building sites) were designed using the EEDP presented in this paper. The detailed nonlinear time history analysis was conducted to assess the performance of CROCW system. The results demonstrate that the CROCW system can be efficiently designed using the EEDP procedure to achieve a superior performance and low damage response at multiple levels of earthquake shaking intensities.

Numerical study of the seismic performance of fully grouted reinforced masonry shear walls with boundary elements subjected to dynamic loading

Reinforced masonry shear walls with boundary elements (RMSW + BEs) have enhanced curvature and displacement ductility and more energy dissipation than their rectangular counterparts when subjected to quasistatic cyclic loading. However, the behavior of walls tested under quasistatic cyclic loading is different from that under dynamic loading. Although there are many studies in the literature regarding the seismic response of RMSW + BEs, there is a gap in understanding the seismic performance parameters of RMSW + BEs when subjected to dynamic loading. Therefore, in this study, a numerical investigation of the seismic behavior of twelve previously tested half-scaled fully grouted RMSW + BEs was performed to quantify the seismic performance parameters of the walls under quasistatic cyclic loading and incremental dynamic loading. The studied walls have different design parameters that cover different aspect ratios, applied axial stress, horizontal and vertical reinforcement ratios, confinement type in boundary elements (BEs), discontinuity in BEs at upper floors and the presence of interstory slabs. A 2D numerical macromodel was developed using the Extreme Loading for Structures (ELS) software to validate and simulate the nonlinear lateral cyclic response of the studied walls. A nonlinear time-history analysis (NLTHA) was carried out using seven pairs of simulated ground motion records developed by Atkinson to represent Eastern Canada earthquake regions (i.e., Montreal, Quebec). The results showed good agreement between the walls’ results among the two loading protocols to better estimate and correlate the walls’ dynamic performance from quasistatic cyclic testing. The quasistatic loading results showed conservative lateral performance compared to dynamic loading in terms of stiffnesses, lateral capacity and energy dissipation. Moreover, the effect of different design parameters has been inspected on the dynamic performance of RMSW + BEs. Increasing the wall aspect ratio led to lower wall stiffnesses and lateral capacities at different loading stages. More energy dissipation and lateral capacity levels were observed when utilizing higher axial stresses on the walls. This study's findings will help better predict and estimate the lateral behavior of RMSW + BEs to help develop subsequent editions of the North American design standards for masonry structures.

Assessment of seismic inelastic displacement profiles of steel MRFs by means of modal behavior factors

A new method for the estimation of inelastic displacements of steel moment resisting frames (MRFs) under strong seismic ground motions is presented. The method comes as an extension of previous work of the authors from reinforced concrete to steel MRFs. Key-elements of the present method are the modal behavior (strength reduction) factors, accounting for the first four modes of significance. These factors are expressed in terms of natural period, interstorey drift ratio and/or plastic rotation, soil type and performance level. These factors are multiplied by the corresponding elastic modal displacements to generate the inelastic modal displacement profile. Eventually, the inelastic displacements can be calculated after combining the modal responses through any combination rule (e.g. SRSS). The results of the presented method are compared with that of the well-known equal displacement rule and three others and attested through nonlinear time history analyses.

Nonlinear Dynamic Analysis of Lumped Soil Mass Model against Seismic Loading

Soil yielding mechanisms and seismic load responses are the key areas of study. The true behavior of soil is revealed by nonlinear analysis. A clump of dirt is used for the analysis. In this study, the Finite Element Model (FEM) forms the basis for the mathematical formulas. Soil analysis in the case of a lumped mass takes into account the soil's one DOF, two DOF, and multi DOF degrees of freedom. In order to determine soil characteristics for MDOF, a soil bore log must be employed. In the instance of MDOF, the soil is composed of 12 distinct layers. SAP 2000 is used to conduct a nonlinear time-history analysis for this research. The hysteresis loops of nonlinear elastic, completely flexible soil undergo permanent deformation. Therefore, it is possible to get insight into the behavior of soil mass during an earthquake by studying lumped soil mass. The soil's nonlinear behavior is investigated using a variety of linear completely plastic hysteretic loops. Soil characteristics are shown to be crucial in this regard. Inadequate soil stiffness may result in persistent deformation, which in turn can lead structures to lean out of alignment. It is also noted that near the soil's surface, amplification is greatest.

Progressive collapse analysis of steel frames via a nonlinear SDOF model

AbstractProgressive collapse is a dynamic loading incident triggered by the sudden loss of critical elements. Design codes provide simplified rules to consider the dynamic effects via the use of Dynamic Increased Factors in order to avoid complex and time‐consuming nonlinear time history analyses. In this paper, a nonlinear single degree of freedom (SDOF) system is presented that captures the dynamic response of steel frames subjected to a column removal scenario. The model takes into account inertia, damping effects and assumes an elastoplastic nonlinear resistance for the system. A closed‐form analytical solution for the dynamic equation of motion is derived and then is applied to a frame to simulate the response under a column removal scenario. A nonlinear finite element model developed in OpenSees was used to verify the accuracy of the analytical model. The results showed that the nonlinear response of the frame for the selected hazard event can be well captured with the proposed model.

Numerical analysis of inclined demountable precast concrete walls with rocking-based composite columns for seismic protection of building structures

With the aim of simultaneously reducing all seismic demands, this paper proposes a novel structural system comprising inclined demountable walls with rocking base composite columns (IDWC). The proposed IDWC system combines the concepts of using inclined demountable walls in each story and rocking-based concrete filled steel tube (CFST) columns as the wall boundary elements. In particular, through inclined walls, the number of walls in each story is reduced, while with the use of rocking CFST columns, damage to the boundary elements can be mitigated. In total, 18 two-dimensional numerical models are developed and static as well as dynamic analyses are conducted to evaluate the performance of conventional and demountable wall systems of 4-, 10- and 15-stories height. For each height, 4 IDWC models, with various wall arrangements, and a vertical demountable wall model are analyzed and compared with a conventional reinforcement concrete wall model. For the studied models, micro and macro numerical models are developed and verified through experimental data. After performing cyclic and time history nonlinear analyses, it is shown that IDWC models have lower initial stiffness and higher energy dissipation capacity than the conventional model. According to these results, inter-story drift, floor acceleration, and base shear in IDWC models are reduced by up to 30%, 41%, and 45%, respectively, compared to the conventional model. Also, it is demonstrated that with the use of rocking CFST columns, the wall boundaries remain undamaged, which ensures any residual drifts after severe earthquakes are insignificant. Meanwhile, as the incremental dynamic analysis results show, the collapse capacity of IDWC models is up to 53.5% higher than that of conventional models.

Effect of uncertainties on seismic fragility for out-of-plane collapse of unreinforced masonry walls

A new approach for the evaluation of fragility curves of UnReinforced Masonry (URM) walls is proposed. Uncertainties on geometrical and mechanical properties, as well as on magnitude and position of the applied loads, are considered using fuzzy set theory. Fuzzy set theory has been broadly applied to civil engineering problems, particularly to reinforced concrete structures, though its application to masonry, to the authors’ knowledge, is investigated here for the first time to evaluate the seismic response of masonry walls in the presence on vague and imprecise information. The proposed procedure allows computing fragility curves based on available typological databases, integrated with experimental tests and survey data. One of the main advantages of this procedure is that it can account for the variability of structural typologies on a territorial scale. The effectiveness of the method is shown through numerical examples concerning walls made of fired clay bricks and lime mortar, which are typical construction materials in the Po River Plain, in Northern Italy. Linear kinematic and nonlinear time-history analyses are used to calculate the seismic response. The computed fuzzy-like fragility curves include both aleatory and epistemic uncertainties. An extensive sensitivity analysis based on suitable sets of representative input parameters is carried out to validate the proposed procedure.

Dynamic Soil-Structure Interaction Through 2-D Site-Specific Response Analysis

Seismic response of structures involved soil-structure-interaction (SSI) that need to consider both inertial and kinematic interaction. Many underground SSI has been developed such as modelling the structures and soils as continuum with seismic load simplified as pseudo-static or static equivalent. More recent and more realistic SSI model consider non-linear time-history analysis in the form of 2-D site-specific response analysis (SSRA), in which both inertial and kinematic interaction in combination with non-linear soil model, as well as time-history ground-motions are simulated. This paper presents simplified pseudo-static soil-structure interaction finite-element (FE) response of underground box-station structure under prescribed maximum strain displacement as resulted from 1-D site-specific response analysis under various ground-motions characteristics of subduction and shallow crustal earthquakes. More complex model of SSI system of basement is also presented. This basement SSI model incorporates non-linear time-history analysis with dynamic soil properties considered through 2-D SSRA simulating seismic wave propagation from reference base-rock to ground surface. Various base-rock seismic ground-motions are simulated from results of de-aggregation analysis from probabilistic seismic hazard analysis considering both subduction and shallow crustal earthquakes scaled at various ground-motion periods. The analysis adopts dynamic soil model with non-linear modulus and damping using FLAC computer program.

Seismic Performance of Multistory Chevron‐braced Steel Structures with Yielding Beams

AbstractLateral loads are resisted by braces in concentrically braced frames. Therefore, braces meet the demand for the load combination based on the seismic provisions. The rest of the system including the connections are determined according to the capacity‐based design, where the brace members yield under tension and buckle under compression. Chevron or inverted V‐braced frames are generally preferred because they allow large openings for doors and windows. However, the seismic‐design requirements in current building codes lead to deep, heavy chevron beams to resist the unbalanced load at beam members due to pre‐ and post‐buckling compressive strength deterioration and full tensile yielding of the braces. This results in uneconomical design. Recent large‐scale experiments of chevron‐braced frames have demonstrated that limited beam yielding is not detrimental to chevron‐braced frame behavior and on the contrary, it utilizes a second yielding mechanism and thereby increases the story drift capacity at which the braces fracture. Also, they propose a new design method for chevron braced frame with yielded beam. This paper expands the previous findings by investigating the seismic performance of 9‐story structures which are designed according to provisions and proposed method. Structural analysis program SAP2000 is utilized for linear design by modelling the full‐scale 9‐story building. Nonlinear finite element analysis software Perform 3D is utilized for the nonlinear time history analysis in which only a single chevron braced frame is modelled. Results show that the proposed building design has larger interstory drift ratios. However, the adjusted collapse margin ratio and the collapse probability for maximum considered earthquake satisfy the required limitations. In other words, the proposed chevron frame design offers a more economical alternative with no significant tradeoff in seismic performance.

Seismic isolated bridge performance evaluation and design proposal using artificial neural network

AbstractSeismic isolators such as rubber bearings and other dampers are critical components of seismic design. The hysteresis behavior of such bearings is complicated, and engineers are using a bilinear model or equivalent linearization method in design practice. The response evaluation and initial design parameter assumptions are highly dependent on engineers' expertise and need repeated analysis. Therefore, this study proposed a machine learning‐based approach to conduct bridge seismic isolation performance evaluation and design parameters proposal without repeating the nonlinear simulations. The training data were generated by conducting a nonlinear time history analysis of the bridge structure model with input design earthquakes. Four trained three‐layer neural network models could perform bridge seismic response evaluation, predict the structure's seismic response, and suggest design proposal using some input parameters.

Nonlinear time history analysis evaluation of optimized design for medium to high rise buildings using performance-based design

Nonlinear time history analysis evaluation of optimized design for medium to high rise buildings using performance-based design

Probabilistic residual displacement-based design for enhancing seismic resilience of BRBFs using self-centering braces

Buckling-restrained braces (BRBs) can effectively control the structural maximum displacements. However, their full hysteresis tends to cause significant residual drifts after strong earthquakes, resulting in massive economic loss. To improve the resilience of the buckling-restrained braced frames (BRBFs) by reducing the residual drifts, self-centering braces (SCBs) are introduced to BRBFs based on the probabilistic residual displacement-based design (PRDBD) method in this study. Parametric analyses are first carried out on single-degree-of-freedom (SDOF) systems to represent the retrofitted BRBFs subjected to near-fault pulse-like earthquakes, wherein the isotropic strain hardening of BRBs is considered. The probabilistic prediction models for maximum and residual displacement are subsequently developed by employing an artificial neural network (ANN) machine learning algorithm. Subsequently, the PRDBD method is proposed. A benchmark BRBF is retrofitted by SCBs to demonstrate the PRDBD’s effectiveness. System-level nonlinear time-history analyses (THAs) are performed to study the dynamic performance of the enhanced BRBFs. It can be observed from the analysis results that the proposed PRDBD is efficient in controlling residual displacements of the enhanced BRBFs within the prescribed guarantee rate. Moreover, the analysis results confirm that the retrofitted BRBF with partial self-centering behavior can achieve remarkable post-earthquake repairability, as evidenced by residual inter-story drifts below 0.5% with 99% probability subjected to the maximum considered earthquakes.

A method for automated development of model and fragility inventories of nonductile reinforced concrete buildings

The nonductile reinforced concrete building (NDRCB) stock—typically, pre-1974 structures in the U.S.—is a well-known high-risk group for seismic hazards. Prior studies indicate that there are approximately 1500 NDRCBs in Los Angeles. Through various ordinances, the owners are currently required to choose between demolition and, when appropriate, seismic retrofitting. Because fulfilling these ordinances will take decades, the potential risk of major losses will persist. In this study, a method for automated development of structural analysis models and damage fragilities for non-ductile moment-resisting frames is established. This capability enables seismic risk assessment at a regional scale using relatively limited building metadata and the era-specific seismic design code. The approach is used first to develop archetypal models in OpenSees, verified through static pushover and nonlinear time-history analyses against prior detailed studies. Fragility curves for discrete damage states are developed through a probabilistic seismic demand model. Additional investigations are carried out to consider the influence of soil-structural interaction effects and to determine the most suitable seismic intensity measures to quantify the seismic damage levels of NDRCB frames. The sensitivity of the proposed modeling method to variations/uncertainties in building configurations and properties is also examined through parametric studies. The method is limited to a particular subcategory of NDRBCs—namely, moment-resisting frames—but extensions to other types appear straightforward.

Ideal-Pulse-Based Strong-Motion Duration for Multi-Pulse Near-Fault Records

ABSTRACT Serious damage to near-fault structures is caused mainly by velocity pulses in a ground motion, hence, the necessity to develop a pulse-related definition of strong-motion duration to adequately describe the intensity of near-fault ground motion. For a multipulse record, an ideal-pulse-based strong-motion duration, which is defined as the time interval between the beginning of the first pulse and the end of the last pulse in an ideal-pulse signal, is proposed. This strong-motion duration corresponds with the time interval of the occurrence of strong vibrations and energy accumulations in the original record. For near-fault records, pulselike characteristics can be completely presented within this duration. Meanwhile, the ideal-pulse-based strong-motion duration shows good performance in the estimation of structural responses. The elastic and inelastic displacement spectra of the original records agree well with those of the records shortened according to the proposed duration. The validity of applying the proposed duration to structural analysis is further verified by the nonlinear time history analyses of 3-, 9-, and 20-story steel moment-resisting frame structures. The proposed strong-motion duration accurately estimates nonlinear structural responses. It is proven that the ideal-pulse-based strong-motion duration can adequately describe the intensity of near-fault ground motions, both from the perspective of the energy accumulation process in a ground-motion record and that of the structural analyses subjected to these ground motions.

Fuzzy Multivariate Regression Models for Seismic Assessment of Rocking Structures

The assessment of rocking response is a challenging task due to its high nonlinearity. The present study investigates two methodologies to evaluate finite rocking rotations and overturn of three typical rocking systems. In particular, fuzzy linear regression (FLR) with triangular fuzzy numbers and a hybrid model combining logistic regression and fuzzy logic were adopted. To this end, three typical rocking structures were considered, and nonlinear time history analyses were performed to obtain their maximum response. Eighteen seismic intensity measures (IMs) extracted from recorded seismic accelerograms were considered to predict the responses. In the absence of rocking overturn, the finite rocking rotations and similarity ratios were calculated by adopting the FLR method. Moreover, extensive analysis was performed to evaluate the influence of each IM on the model’s predictions. On the other hand, rocking overturn was evaluated by logistic regression to compute the probability of collapse, followed by the FLR method to estimate the similarity between the different rocking-based structural systems. The root mean square error (RMSE) parameter and the log loss function were determined for every model to assess the predictions that emerged from the two fuzzy methods. As indicated, both methods demonstrated satisfactory results, presenting minimal deviations from the observed values. Finally, in the case of finite rocking rotation predictive models, remarkably high similarity ratios were observed among the various structures, with a median value of 0.96.

System fragility evaluation of a curved highway bridge structure considering multi-direction seismic excitations

This paper presents the impact of varying the input seismic excitation directions on the system fragility of a geometrically complex highway bridge structure. The traditional approach of fragility derivation in the principal loading directions (longitudinal and transverse) results in an under/overestimation of the system fragility. To reduce such errors, the contribution of all major vulnerable components to the system fragility in the critical loading direction must be considered. For this purpose, a series of nonlinear time-history analyses were conducted for a testbed configured geometrically curved highway bridge structure in Japan. Shear strain, ductility, and distortion strain were considered as engineering demand parameters for bearings, concrete pier, and steel piers, respectively. The demand dependency among the components was considered using the correlation coefficient matrix for fragility estimation. Subsequently, fragility functions with respect to the input loading directions were generated for the bridge components and system to quantify their sensitivity to seismic input excitation directions. The results show that the component fragility is significantly influenced by the input excitation direction. A relative comparison of the system fragility for different loading directions indicated that a 150° loading direction yielded a higher fragility demand. The findings suggest that the critical fragility assessment should not always be decided only along the principal loading directions.

Interpretable Machine Learning for Assessing the Cumulative Damage of a Reinforced Concrete Frame Induced by Seismic Sequences

Recently developed Machine Learning (ML) interpretability techniques have the potential to explain how predictors influence the dependent variable in high-dimensional and non-linear problems. This study investigates the application of the above methods to damage prediction during a sequence of earthquakes, emphasizing the use of techniques such as SHapley Additive exPlanations (SHAP), Partial Dependence Plots (PDPs), Local Interpretable Model-agnostic Explanations (LIME), Accumulated Local Effects (ALE), permutation and impurity-based techniques. Following previous investigations that examine the interdependence between predictors and the cumulative damage caused by a seismic sequence using classic statistical methods, the present study deploy ML interpretation techniques to deal with this multi-parametric and complex problem. The research explores the cumulative damage during seismic sequences, aiming to identify critical predictors and assess their influence on the cumulative damage. Moreover, the predictors contribution with respect to the range of final damage is evaluated. Non-linear time history analyses are applied to extract the seismic response of an eight-story Reinforced Concrete (RC) frame. The regression problem’s input variables are divided into two distinct physical classes: pre-existing damage from the initial seismic event and seismic parameters representing the intensity of the subsequent earthquake, expressed by the Park and Ang damage index (DIPA) and Intensity Measures (IMs), respectively. In addition to the interpretability analysis, the study offers also a comprehensive review of ML methods, hyperparameter tuning, and ML method comparisons. A LightGBM model emerges as the most efficient, among 15 different ML methods examined. Among the 17 examined predictors, the initial damage, caused by the first shock, and the IMs of the subsequent shock—IFVF and SIH—emerged as the most important ones. The novel results of this study provide useful insights in seismic design and assessment taking into account the structural performance under multiple moderate to strong earthquake events.

Inelastic Behavior of Steel and Composite Frame Structure Subjected to Earthquake Loading

Steel construction is used more often these days as an alternative to the R.C.C. when lightweight, high-strength, large-span structures with a faster erection are required. Extensive studies have been conducted by researchers to study the seismic performance of reinforced concrete and steel structures, both in terms of elastic and inelastic behavior. Composite construction is also a recent advancement in the building industry with similar advantages. However, no emphasis has been given to the comparison between the inelastic behavior of steel and composite structures when subjected to lateral loads. This study compares the inelastic behavior of steel and a composite frame designed to have the same plastic moment capacity for structural members. The responses, such as the formation of hinges, story drifts, story displacements, lateral stiffness, ductility, maximum strength, energy dissipated, joint accelerations, and performance points, are compared with the aid of the building analysis and design software ETABS-18. For this, response spectrum analysis, pushover analysis, and nonlinear direct integration time history analysis have been performed on both frames. For design and analysis, international codes, such as IS 800-2007, IS 875 (Part I, II, IV), IS 1893-2002, AISC 360 (16 and 10), and FEMA 440, have been used. Part of this study also aims at comparing the response of these frames when subjected to near-field and far-field earthquakes. It can be concluded from the results that the post-yield performance of the composite frame is superior to that of the steel frame when seismically excited.

Seismic fragility analysis of steel moment frames using machine learning models

This study develops machine learning (ML) models for seismic fragility analysis of steel moment frames. Four ML methods – random forest, adaptive boosting, gradient boosting regression tree (GBRT), and extreme gradient boosting (XGBoost) – were employed for this purpose. Probabilistic seismic demand models, each representing the relationship between the seismic response of a type of structure and ground motion intensity, were used to construct the fragility curves based on nonlinear time history analyses of 616 steel moment frames subjected to 240 ground motions. The first three natural periods of steel moment frames and a capacity limit state defined by the maximum interstory drift were selected as input variables for the ML models. Two parameters (median and logarithmic standard deviation) of a fragility function were considered as output variables for the ML models. For each steel frame, the capacity limit state values considered for maximum interstory drift cover a wide range to generalize the fragility curve outcomes. The interquartile range method was used to ensure the quality of the dataset, and consequently 56,479 data points were used for the development of ML models. Based on model performance, the GBRT (R2 = 0.9986, for the testing dataset) and XGBoost (R2 = 0.9987) models are proposed as the best models for fragility analysis of steel moment frames. Finally, a graphical user interface for fragility analysis of steel moment frames was built based on the two proposed models, for easy access by practicing engineers. This study demonstrates the applicability of ML methods in practical design.