Nonlinear Time History Analysis Research Articles

Optimal intensity measures and probabilistic fragility assessment for the long-span aqueduct structure with four-column bents

The intensity measure (IM) is a key factor in determining the accuracy of seismic performance assessment, which can represent the power of ground motion. However, the optimal IMs selection for long-span aqueduct structures with four-column bents has not been investigated in the previous study. This study aims to evaluate the optimal IMs for use in probabilistic seismic demand model (PSDM) and propose the scalar- and vector-valued fragility methods of the long-span aqueduct structure. To achieve this goal, taking the long-span aqueduct structure with four-column bents in the Central Yunnan Water Diversion Project in Southwest China as a typical case, a series of nonlinear dynamic time history analysis are conducted. Then, the 21 commonly-used IMs are tested and evaluated based on the different metrics (e.g. correlation, efficiency, practicality and proficiency). The optimal vector-valued IMs for the fragility analysis of the long-span aqueduct structure with four-column bents is proposed. Meanwhile, the PSDMs of optimal vector-valued IMs are also established and compared. Finally, the scalar- and vector-valued fragility functions are developed in terms of the optimal IMs. A method for seismic fragility analysis of the long-span aqueduct structure with four-column bents based on vector-valued IMs is proposed. The numerical results reveal that peak ground acceleration (PGA), peak pseudo acceleration spectrum (PSA), root-mean-square of acceleration (Arms) and characteristic intensity (Ic) are relatively appropriate IMs for seismic performance evaluation of the long-span aqueduct structure with four-column bents. In particular, PGA is considered to be the optimal IM due to its highest correlation, better efficiency, practicality and proficiency. The scalar-valued fragility curves can only describe the impact of the single IM on the damage probability of the aqueduct structure, which may overestimate or underestimate its damage probability. Furthermore, the vector-valued IMs can significantly increase the fitting ability of the PSDMs. The fragility surfaces are superior to scalar-valued fragility curve due to the vector-valued IMs can more accurately describe the ground motion information. In summary, the findings of this study highlight the significance of proposing the optimal IMs and developing vector-valued fragility surfaces when evaluating the seismic performance of the long-span aqueduct structure with four-column bents.

An Evaluation of the Structural Behaviour of Historic Buildings Under Seismic Action: A Multidisciplinary Approach Using Two Case Studies

The evaluation of the structural behaviour of iconic historic buildings represents one of the most current structural engineering research topics. However, despite the various research works carried out during recent decades, several issues still remain open. One of the most important aspects is related to the correct reconstruction of the complex geometries that characterise this type of construction and that influence structural behaviour, especially in the presence of the horizontal loads caused by seismic action. For these reasons, different techniques have been proposed based on the use of laser scanners, Unmanned Aerial Vehicles (UAVs), and terrestrial photogrammetry. At the same time, several analysis methods have been developed that include the use of linear and non-linear approaches. In this present paper, the seismic performance of the Santa Maria Novella basilica and Santa Maria di Collemaggio basilica (before the partial collapse due to the 2009 L’Aquila earthquake) were investigated in detail by means of several numerical analyses. In particular, a series of non-linear time history analyses (NTHAs) were carried out, as reported in the Italian Building Code. To represent the non-linear behaviour of the main structural elements, smeared cracking (CSC) constitutive law was adopted. The geometry of the structures was reconstructed from a complete laser scanner survey of the churches, in order to consider all the intrinsic irregularities that characterise the heritage buildings. Finally, a comparison between the structural behaviour of the two case studies was carried out, highlighting the differences and similar aspects, focusing on possible collapse mechanisms and the identification of the most critical structural elements represented, in both cases analysed, by the main pillars of the transept.

Application of one-dimensional periodic layers with elastomeric seismic isolators for three-dimensional isolation

Three-dimensional (3D) seismic isolation is an appealing idea to protect structures and their components from earthquake-induced horizontal and vertical ground motions. Past attempts to develop 3D isolation systems were ineffective due to their complexity and reliability issues. One-dimensional periodic material-based isolation systems (1D-PIS) have been extensively researched for applications as raft foundations due to their simple and construction-friendly unit cell designs. These systems aim to attenuate seismic excitations in both horizontal and vertical directions. However, the effectiveness of 1D-PIS in mitigating 3D excitations may be limited due to the potential mismatch between the frequency content of horizontal and vertical vibrations. The present study proposes to combine a conventional horizontal isolation system with a 1D-PIS in the vertical direction to achieve a simple, passive, and efficient three-dimensional isolation system for structures and components. The 1D-PIS is strengthened by incorporating steel shims within the rubber layers and implementing steel casings at its periphery, enabling its utilization as an isolated system. Small-scale experimental and numerical investigations were conducted on strengthened 1D-PIS to study its isolation characteristics in the vertical directions. The study reveals that infinite boundary conditions required for the efficacy of 1D-PIS were achieved through lateral restraint provided by steel shims and steel casings. Notably, the individual isolation characteristics of the conventional and the 1D-PIS are not compromised in the combined isolation system. Nonlinear time history analysis on a prototype combined isolation system confirms its effectiveness in attenuating the seismic response under simultaneous horizontal and vertical ground motions.

Scalar- and vector-valued seismic fragility assessment of segmental shield tunnel lining in liquefiable soil deposits

Seismic fragility analysis can quantitatively evaluate the seismic performance of structures from a probabilistic viewpoint and accurately characterize the relationship between the degree of structural damage and ground motion intensity. This study investigates the seismic fragility of shield tunnels in three different liquefiable and non-liquefiable soils. A plane-strain finite element model of the saturated soil and shield tunnel is established via the OpenSees computational platform employing the multi-yield surface elastoplastic PressureDependMultiYield and PressureIndependMultiYield models to simulate the constitutive behaviour of liquefiable and non-liquefiable soils. The developed model is utilized to conduct nonlinear dynamic effective stress time history analyses to generate the seismic fragility curves and surfaces based on the incremental dynamic analysis method. Meanwhile, appropriate scalar- and vector-valued intensity measures are identified based on their correlation, efficiency, practicality and proficiency. Compared with the fragility curves based on scalar-valued intensity measures, the fragility surfaces based on the vector-valued intensity measures can better describe the effect of ground motion characteristics on the structural seismic demand, and thus can more accurately assess the structural seismic performance. The seismic damage probabilities derived from the fragility curves and surfaces reveal that the seismic damage risk of the shield tunnel in sandwiched liquefiable soil deposit is higher than that of the tunnel structure located in entirely liquefiable or non-liquefiable soil profiles. This finding underscores the importance of carefully evaluating the seismic safety of shield tunnels situated in sandwiched liquefiable soil deposits.

Collapse-based seismic design method

Continuing the structural analysis until the model reaches its ultimate capacity using an incremental nonlinear time history analysis can incorporate all the behavioral complexities of the structure. This approach ensures that all factors influencing the seismic behavior of structures, which can be simulated in numerical modeling, are fully considered in the analysis. This technique addresses many shortcomings in seismic analysis and structural design, using simple criteria for the accurate design of members. With this perspective, this paper explores the collapse-based seismic design method and provides an approach to determine the ultimate tolerable seismic intensity for a structure, or an appropriate collapse seismic intensity. It also establishes design criteria based on the maximum capacity of structural members under maximum loading and utilizes the endurance time method to perform incremental nonlinear time history analysis quickly and easily. Evaluations show that models designed using this method achieve the desired performance level at different seismic hazard levels, provide sufficient seismic capacity, meet all minimum requirements of the seismic code and standards, and are optimized. Therefore, the procedure presented in this paper is introduced for the analysis, design, evaluation, and retrofitting of structures with simple, accurate, and uniform principles.

Utilizing tuned mass damper for reduction of seismic pounding between two adjacent buildings with different dynamic characteristics

Today, population growth and the need for constructing adjacent buildings have raised the likelihood of pounding between adjacent buildings with different dynamic characteristics. The pounding force applied to adjacent buildings during an earthquake is intensive and may cause total or partial damage to structural elements, leading to collapse. It disturbs and complicates the functioning of buildings during and after an earthquake. Therefore, the main aim of this paper is to minimize and, if possible, eliminate the pounding force between two adjacent structures by considering three objective functions. For this aim, the tuned mass damper is utilized here. Also, this paper aims to reduce the number of collisions between different stories of adjacent buildings through a tuned mass damper system. For this purpose, two adjacent steel moment frames with six and ten stories are nonlinearly modeled and validated using the concentrated plasticity model in OpenSees. Moreover, the pounding element is nonlinearly modeled and validated. Then, tuned mass dampers (TMDs) are used on the roofs of the structures. They are optimized in stiffness, mass, and damping coefficient using the grey wolf optimization (GWO) algorithm. Nonlinear time history analysis (NLTHA) is performed under nine far- and near-field earthquakes. The pounding force and structural responses are analyzed, including maximum story acceleration, maximum inter-story drift, and base shear in the TMD-controlled and uncontrolled adjacent buildings. Finally, the Park-Ang damage index is evaluated for the structures with and without the TMD system. It has been found that the maximum pounding force, the maximum acceleration of the stories, the base shear, the drift ratio, and the number of collisions significantly reduce (or omit) in the presence of TMDs when the objective function is considered to be the minimization of the maximum pounding force. It is shown that the maximum pounding force generally declines to zero for this objective function.

Optimized evaluation of ground motion intensity measures for the prefabricated cantilevered roadbed structure in mountainous areas

The prefabricated cantilevered roadbed structure (PCRS) is a novel design that addresses the significant excavation and embankment volume associated with traditional mountainous roadbeds. The seismic performance of it has not yet been fully investigated. Seismic fragility analysis is one of the main methods for assessing the damage pattern of a structure, and the ground motion intensity measure (IM) is a key parameter affecting the damage assessment results. To this end, a finite element model is first conducted based on structural load-bearing capacity verification experiments, relying on a prefabricated cantilevered roadbed structure in a mountainous region. Then, the nonlinear time-history analysis of the structure was carried out, and 20 common IMs were selected and compared from the perspectives of practicality, efficiency, proficiency, and sufficiency. Finally, the seismic fragility analysis of the structure is conducted based on the optimal IM. The analysis results indicate that the peak ground acceleration of response spectrum (PSA) is the optimal IM for such structures. Quadratic fitting exhibits higher accuracy compared to linear fitting. Among all components, fixed-end foundations are identified as the most vulnerable. Anchored reinforcement remains elastic throughout the seismic response calculations and suffers little damage.

Self-centering rocking steel frame with column mid-height uplift: Experimental and numerical investigation

This paper proposes a self-centering rocking steel frame with column mid-height uplift (SCRSF-CMU) that exhibits high post-yield stiffness and energy dissipation capacity. The hysteretic performance of the SCRSF-CMU was investigated through cyclic loading tests. A numerical model of the SCRSF-CMU was established and validated against experimental results. Subsequently, the seismic performance of the SCRSF-CMU was compared with that of the self-centering rocking steel frame with column base uplift (SCRSF-CBU) using nonlinear time history analysis. Finally, the seismic responses of the SCRSF-CMU and SCRSF-CBU under varying earthquake intensities were analyzed using the endurance time analysis. The results indicate that the designed SCRSF-CMU demonstrates excellent lateral force resistance, energy dissipation, and self-centering capabilities. The rocking effect and the restoring force of the post-tensioned steel strands effectively controlled the residual lateral displacement of the specimens. The multi-scale numerical model of the SCRSF-CMU accurately captured its hysteretic behavior and deformation patterns. Compared to the SCRSF-CBU, the SCRSF-CMU exhibited superior rocking deformation capacity, post-yield stiffness, and hysteretic energy dissipation. Under MCE excitation, both SCRSF-CMU and SCRSF-CBU showed uniform inter-story drift distribution with minimal residual deformation, creating a satisfactory condition for the post-earthquake repair work if necessary. The high post-yield stiffness of the SCRSF-CMU was more effective in reducing both maximum and residual displacements. Endurance time analysis revealed that SCRSF-CMU and SCRSF-CBU exhibited relatively uniform inter-story drift distribution under SLE, DBE, and MCE earthquakes. Under FE excitation, the inter-story drift ratio of both structures were nearly identical; however, under DBE and MCE excitations, the maximum roof drift ratio and inter-story drift ratio of the SCRSF-CBU were larger, indicating that the SCRSF-CBU had higher deformation demands than the SCRSF-CMU.

Seismic mitigation of porcelain cylindrical electrical equipment using synergistic concept with base isolation and tuned mass damper

Porcelain cylindrical electrical equipment (PCEEs), such as potential and current transformers, are critical components of electrical substations and essential to power supply networks. Nevertheless, previous strong earthquakes have rendered high vulnerability and poor performance of PCEE during seismic occurrences. To improve seismic performance of PCEE and alleviate adverse seismic impacts, an innovative synergistic mitigation method based on base isolation (BI) and tuned mass damper (TMD) was proposed and subsequently employed to PCEE. Combining BI with TMD allows for a greater utilization of each technology’s capabilities while also circumventing some of the limits of each. While TMD effectiveness is sensitive to input ground motion frequencies, BI could act as a filter to tune input frequency and help TMD fulfill better damping effectiveness. TMD could in return help BI achieve better stability under long-period dominant or pulse-like ground motions. The BI-TMD effectiveness and robustness were investigated using finite element modeling and nonlinear time history analysis. A comprehensive parametric study that considers variable PCEE frequencies, BI periods, TMD mass ratios, and TMD control frequencies was conducted. Results show that the proposed BI-TMD method can significantly enhance the effectiveness and robustness beyond BI single control in mitigating seismic responses of PCEE.

Seismic performance of near-fault girder bridges based on laminated rubber bearings under the impact of sequential earthquakes

Strong aftershocks frequently follow near-fault earthquakes, exacerbating the damage to bridges already impacted by the main shock. However, current seismic design codes worldwide overlook the adverse effects of aftershocks on near-fault bridges. Therefore, it is imperative to conduct research on the seismic performance of near-fault girder bridges under sequential earthquakes. This study proposes a seismic isolation design for near-fault girder bridges subjected to sequential earthquakes, utilizing laminated rubber bearings, sacrificial shear keys, and cable-type unseating prevention devices. Seismic ground motion records from typical stations during the Turkey-Syria earthquakes were collected to assess the seismic safety of bridges. Nonlinear time-history analysis systematically investigated the seismic displacements of the laminated rubber bearings and girder, as well as the seismic damage of shear keys and pier. The results show that the lateral displacement of the girder induced by the sequential earthquake was approximately 1.5 times greater than that caused by a single main shock, while the longitudinal displacement of the girder remained similar. The seismic isolation design proposed in this study not only controlled the relative displacement between the piers and the girder but also effectively protected the pier from severe seismic damage, ensuring the bridge’s functionality after the sequential earthquake.

Impact of Various High Intensity Earthquake Characteristics on the Inelastic Seismic Response of Irregular Medium-Rise Buildings

In the twenty-first century, the seismic design of buildings seems to have become a fully recognized topic. There are guidelines and standards which should be taken into account by designers in seismic areas. Designers using modern international guidelines have ascertained that the behavior of structures is not as expected. New challenges in the construction industry result in the construction of structures with new, unusual shapes. These are structures that do not meet the assumptions of safe construction in seismic areas. Contemporary buildings are also characterized by their irregular distribution of structural elements. Such solutions are not beneficial from the point of view of seismic engineering and can lead to reduced dynamic resistance and damage in such structures. In this paper, a five-storey, irregular-shaped reinforced concrete (RC) building model was subjected to different earthquakes with varying magnitudes, PGA (peak ground acceleration) and PGV (peak ground velocity) values, and durations of the intense shock phase. Once the model was verified using previous in situ measurements, the building model was subjected to five earthquakes. A numerical nonlinear analysis of the building was performed using a verified FEA (finite element analysis) model in the time domain through non-linear time history analysis with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The building’s dynamic properties were measured using various methods of excitation. The model was influenced, among others, by two far-field representative events caused by the last earthquake in Turkey, which resulted in strong ground motion. The analysis results identified the locations of structural damage and allowed for the assessment of the structure’s dynamic resistance. The results of the calculations prove that the duration of the intensive phase of extortion is one of the reasons for building damage in earthquake-prone areas. Building damage occurs with earthquakes that are characterized by an intensive phase of excitation with a long duration and high values of velocity in the earthquake components. The article highlights the inadequate dynamic resistance of the building, leading to excessive displacements and unfavorable structural solutions. Damage to buildings at this earthquake intensity caused damage to the load-bearing structure, which was not designed for such intensities. This paper is a research report with a specific case study of medium-rise irregular RC buildings.

Seismic evaluation of plan irregular reinforced concrete building equipped with comb teeth metallic passive damper

Active and passive damping devices exhibit significant energy dissipating behavior under seismic loads and are being used to control vibration in buildings worldwide. Comb Teeth Damper (CTD) is one of the most promising recent types of passive dampers which consist of steel plates with multiple teeth designed to dissipate seismic energy by in-plane flexural yielding. In this study, the CTD was modeled and analyzed under lateral cyclic load using the finite element analysis software, ABAQUS. The first phase of this investigation was a comprehensive parametric study on CTD with two different numbers of teeth, namely 4 teeth (4 CTD) and 5 teeth (5 CTD); each model with six different thicknesses, namely 5, 10, 15, 20, 25, and 30 mm. The parametric study showed that by increasing the number of teeth, the load-carrying capacity, initial stiffness, and energy dissipation capacity have increased considerably. A similar trend was observed when the thickness of the damper was increased. From the results of the parametric study, 5CTD with 15 mm thickness damper model was identified as a suitable model for utilizing in Reinforced Concrete (RC) buildings using optimization algorithm. In the second phase, a G + 14 storey plan irregular RC building was modeled in the structural engineering software ETABS and subjected to six different strong earthquake ground motions. The non-linear time history analysis was performed on the building with and without identified CTD and found that the building equipped with dampers reduced 56% top displacement, 60% inter-storey drift, and 33% energy dissipation.

Seismic behavior of base isolated precast frame

The performance of the base-isolated precast frame is examined for both near-field and far-field earthquakes. For comparison, the corresponding base isolated monolithic frame is analyzed. The frames are isolated using a friction pendulum system (FPS), which is appropriately designed to take up the vertical load coming on the frames. The same isolators are provided for the monolithic and precast frames. Two types of precast frames are considered, namely frames with emulated and non-emulated connections. An ensemble of 7 different earthquakes is used for each type of earthquake to obtain the average responses, which include maximum base shear, maximum acceleration, maximum top story displacement, and maximum inter-story drift ratio (MIDR). SAP2000 is used for the non-linear time history analysis of the frames for different earthquakes. The studies are made for three levels of PGA, namely 0.4 g, 0.6 g, and 0.8 g. The study shows that a significant reduction in base shear, top story displacement and MIDR is achieved by base isolating the precast frames. However, the corresponding base isolated monolithic frame offers more reductions in response especially for MIDR. Of the two types of precast frames, the one with emulated connection shows marginally higher reductions of response as compared to the non-emulated connection. Further, the percentage reductions in responses in main shock and after shock remain almost the same for all cases.

Seismic response control of shear frame structure using a novel tuned-mass type composite column

Concrete filled steel tube (CFST) column is widely applied in shear frame structure in seismic-prone area owing to its superior earthquake resistant performance. However, CFST column might still suffer damage under a severe earthquake. This paper proposes a novel tuned-mass type column-in-column (CIC) system to improve the seismic behavior of the CFST column and hence protect the structure. The CIC system is formed by splitting the CFST column into a primary column and a secondary column, while the overall cross section area and hence the load-bearing capacity is not changed. By optimally selecting the springs and dashpots to interconnect the two columns, the CIC can act as a non-conventional tuned mass damper (TMD) to reduce seismic vibrations of structures. To demonstrate the proposed CIC concept, a single-story and a five-story frame structure with and without control are designed. Nonlinear time history analyses are performed to study the seismic responses of these structures considering different seismic design levels, earthquake ground motions and CIC control schemes. Numerical results show that the CIC system can effectively reduce the seismic induced story acceleration, displacement and drift ratio of frame structures with the reduction ratios approximately between 21 % and 30 %, and the ratios on reducing the base shear force and bending moment are between 27 % and 31 %, and between 34 % and 49 %, respectively. The proposed CIC control concept is a new solution for mitigations of seismic responses of CFST frame structures.

Parametric study for shear failure of bearing pads due to hurricane-induced wave loadings

The increasing frequency of extreme weather events, such as hurricanes and rising sea levels due to climate change, presents significant challenges to coastal infrastructure. With 42% of bridges in the United States exceeding 50 years of age, which surpasses their intended service life, there is a pressing need to assess their structural integrity, especially in coastal regions. This study focuses on evaluating the structural performance of bearing pads in coastal bridges under hurricane-induced wave loadings. Utilizing a combination of physics-based models (PBM), nonlinear modal time history analysis, and numerical validation, the research examines the hysteresis response of eight distinct bearing pad configurations. The findings indicate that reinforced circular bearing pads exhibit significantly greater shear displacements compared to plain elastomeric pads, underscoring the critical influence of shape factors on shear response. Fragility functions developed in the study illustrate the probability of shear failure, with reinforced circular pads showing a 28% higher likelihood of exceedance compared to rectangular plain pads. These results highlight the necessity for advanced design methodologies specifically for bearing pads to enhance the resilience of coastal infrastructure against severe hydrodynamic forces induced by hurricanes.

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.

Local and global integrative retrofitting of reinforced concrete frames using in‐plane buckling steel braces

AbstractTwo large‐scale, single‐storey, single‐bay reinforced concrete (RC) moment frames, designed as per an outdated seismic code to represent a typical framing detail of a four‐storey building, have been tested under displacement‐controlled quasi‐static loading protocol as per ACI 374.1‐05. The RC frames include a plinth beam with brick infill underneath, a slab monolithically cast with the top beam and provision for applying axial load to the column to simulate real construction scenario. One of the frames has been tested as a bare frame, and the second one has been retrofitted with conventional steel braces designed to undergo in‐plane buckling. The size of the brace has been selected based on the result of a nonlinear time history analysis of representative low‐ to mid‐rise open‐ground storey RC buildings. Post‐installed chemical anchors have been utilized to connect the steel braces to the narrow RC frame members following the outcomes of an experimental investigation by the same authors. Local‐level retrofitting by steel jacketing using adhesives has been designed and utilized on columns and beams to achieve the desired seismic response. The seismic performance of the retrofitted frame has been compared with the bare frame in terms of strength, stiffness, ductility, energy dissipation and hysteretic damping. The tests provide insight into the role of the plinth beam, effect of RC slab on the strong‐column weak‐beam aspect and the achievement of the desirable hinge mechanism through a precise design and detailing of global and local level retrofitting technique.

Seismic behaviour and design of a tall mixed reinforced concrete–steel structure supporting an oil refinery reactor

AbstractThis study investigates the seismic behaviour of a special mixed reinforced concrete-steel structure that supports an oil refinery reactor. The structure is 64.90 m tall and consists of three parts: (a) a reinforced concrete frame basement; (b) a steel braced frame that supports the oil reactor and (c) the steel reactor itself. A three-dimensional model of the structure is created to perform static non-linear (pushover) analyses in order to obtain the capacity curves and understand the overall inelastic behavior of the structure. The results of the pushover analyses reveal that the structure exhibits similar inelastic behavior in both horizontal directions and satisfies the capacity design principles. The structure exhibits limited ductility considering the fact that has been designed with a behavior factor of q = 1.5 and primary damages are expected mainly in concrete members. Subsequently, dynamic non-linear time-history (NLTH) analyses are performed utilizing the three translational components of three seismic motions recorded during past earthquakes. These results involve: (i) the maximum values for displacements, accelerations and base shears; (ii) the maximum stresses at critical points of the oil refining reactor and (iii) the formation of plastic hinges at columns, beams and braces of the structure. Contrary to pushover analyses, NLTH analyses revealed the development of plastic hinges, hence seismic damage, that do not follow the desirable formation pattern. Moreover, the accelerations and displacements observed are expected to cause failure of the piping and mechanical equipment, while local failure of the high-stress areas of the shell of the reactor may be possible. Localized strengthening might be necessary to avoid repair works and downtime after such seismic event.

Estimation of effective damping ratio for cast-in-place tunnel-form system and evaluation of its role in performance point prediction

The extensive time and computational effort are primary challenges in nonlinear dynamic analysis of tunnel-form concrete systems. These challenges lead engineers to resort to simpler, pushover-based analyses, inherently based on estimating the seismic performance point of the system. Technical literature review indicates that no study has yet rigorously evaluated the accuracy of existing methods for estimating the performance point of tunnel-form systems. To eliminate potential ambiguities, in this study, the seismic performance point of the system under design basis earthquake (with a 475-year return period) has been calculated using three different methods (i.e., displacement coefficient, capacity spectrum, and displacement amplification factor), and compared with the results of accurate nonlinear time-history analysis. In the range of 5-, 7-, and 10-story models studied, the results indicate the inefficiency and insufficiency of the mentioned methods. Investigations reveal that while the capacity spectrum method provides better results, but its process is lengthy, and the displacement coefficient method significantly overestimates the performance point (with more than 80 % error). It was also evident that the displacement amplification factor underestimates the performance point and contradicts the direction of confidence. Based on observations, the use of all three methods for the tunnel-form system requires modifications. The calculated values of effective damping ratio for the tunnel-form system explicitly indicate type A behavior according to the ATC-40 classification. By presenting this parameter in a multi-level format, the shortcomings of both capacity spectrum and displacement coefficient methods are easily addressed. Referring to the results, the calculated value of the displacement amplification factor in the system exceeds the recommended value by the seismic design code, and by adjusting it, satisfactory responses can be obtained in the method based on the displacement amplification factor. Finally, introducing the “probable performance interval” parameter, recommending its use instead of the “performance point” parameter in assessments by pushover analysis is suggested. This parameter is applicable with all three mentioned methods and has been introduced in this study as a desirable factor in compensating for inherent uncertainties related to future earthquakes.

Incorporation of machine learning into multiple stripe seismic fragility analysis of reinforced concrete wall structures

This study proposes a novel procedure that incorporates machine learning (ML) into the multiple stripe analysis (MSA) approach to efficiently produce seismic fragility curves for reinforced concrete (R/C) shear walls in building frame systems. The proposed procedure aims to mitigate computational challenges associated with the original MSA approach. In this context, ML models were developed for predicting the failure probability of R/C walls subjected to ground motions based on a specified threshold of maximum interstory drift ratio (MIDR). Specifically, the result of each numerical analysis, taken as the output variable of the ML models, was classified as either “B” (Below) or “E” (Exceeding) to indicate whether the MIDR of R/C walls was below or exceeding the specified threshold. This binary categorization was then used to calculate the failure probability points, which are necessary to derive fragility curves per the MSA approach. Data for training and testing the ML models were generated from nonlinear time history analyses of 46 distinct R/C walls subjected to 1000 ground motions. The R/C walls varied in height from four to 40 stories, and the ground motions included far-field, near-field pulse, and near-field no-pulse types. Four well-established ML methods, including random forest (RF), extreme gradient boosting, light gradient boosting machine, and categorical boosting, were considered. The performances of the ML models were compared using a confusion matrix. Based on this comparison, the RF model was selected and incorporated into the proposed procedure. Subsequently, the proposed approach was demonstrated to create the seismic fragility function of a new R/C wall structure. This study highlights the potential of ML applications in optimization problems within the earthquake engineering domain.