Engineering Demand Parameters Research Articles

A codifiable methodology for estimating pallet sliding displacements on steel racking systems

AbstractTo facilitate the logistic processes within a modern warehouse, the contents of steel racking systems are not mechanically connected to the supporting beams, allowing a content‐sliding mechanism to develop when static friction is exceeded. Given that the mass of contents is dominant, this is beneficial for limiting the apparent inertia. On the other hand, pallet fall‐off may occur during strong seismic excitations, which is a failure mode that is not addressed by current seismic design processes and guidelines for racks. Along these lines, a codifiable methodology is proposed for estimating sliding displacements on steel racking systems, based on the statistical interpretation of a large set of response history analyses, using different rack configurations and ground motions. Firstly, a multi‐parametric analysis is conducted using simplified rack models to (i) select the intensity measure and engineering demand parameter that can best describe the problem of pallet sliding and (ii) identify the salient rack characteristics that dominate sliding behavior. Thereafter, a series of multi‐stripe analyses are performed using 180 rack realizations with different feature combinations to derive a so‐called, Empirical Sliding Prediction Equation (ESPE) by following a three‐step procedure: (a) perform regression on maximum sliding, (b) perform regression on the normalized sliding profile, and (c) combine steps a‐b to derive the denormalized profile at a given confidence level. The proposed empirical relationships are then validated through a comparison between the observed and fitted sliding displacements in three rack case studies.

Life Prediction and Reliability Evaluation of Reinforced Concrete Frame Structures Considering the Collision Response Under Earthquake Conditions

Firstly, in this study, we utilize the high-order element model (truss link model) simulation method in OpenSees (3.7.0) software and verify the feasibility of this method by comparing it with the shaking table test. Secondly, the structural dynamic response of adjacent structures with different performance levels, spacing, and layout forms under large earthquakes is analyzed, and the corresponding structural failure probability is studied. Furthermore, the life distribution within the design service life of the structure is predicted according to the nonparametric Kaplan–Meier estimation model. Finally, the reliability of adjacent structures is evaluated by using the joint engineering demand parameters. The analysis method of replacing the theoretical analysis based on engineering experience and certainty in the current specification with probability analysis is proposed, which provides a more reliable theoretical basis for decision-making regarding the reinforcement, maintenance, or demolition of structures in the later stage.

Simplified calculation models for evaluating the post-earthquake axial load-carrying capacity of RC bridge piers

This study aims to develop simplified calculation models of the post-earthquake axial load-carrying capacity of reinforced concrete columns to determine the post-earthquake traffic flow capacity of the bridges for the evaluation and design process. To this end, the maximum and residual drift ratios are first determined as the engineering demand parameters for the simplified calculation model for the evaluation and design process, respectively. Then, the optimal models describing the relationships between the maximum/residual drift ratio and the post-earthquake axial load-carrying capacity are selected. The analysis results show the normal cumulative model in the coordinate system of ln(x)-y is the optimal relationship model. On this basis, the effects of high-sensitivity parameters (i.e. the axial compressive ratio and shear span ratio) on the post-earthquake axial load-carrying capacity are investigated. Results indicate that the axial compressive ratio negatively affects, while the shear span ratio positively affects the post-earthquake axial load-carrying capacity. Finally, the simplified calculation models of the post-earthquake axial load-carrying capacity are developed from the optimal model and the effects of the high-sensitivity parameters, and with validated high accuracy. The simplified calculation models provide engineers and policymakers with a tool to predict the post-earthquake traffic flow capacity of bridges.

Parameter-normalized probabilistic seismic demand model considering the structural design strength for structural response assessment

The Probabilistic Seismic Demand Model (PSDM) is a crucial component of the performance-based seismic design framework when establishing the relationship between the ground motion intensity measure (IM) and the engineering demand parameter (EDP). The definitions of IMs and EDPs introduce varying degrees of uncertainty into the PSDM and notes different fragility or hazard analysis results. In accordance with the elastic limit state of the structural seismic response, this study normalizes two key parameters, the IM and EDP, within the PSDM. Normalized EDP (EDPN) is the ratio of the structural response to the elastic limit state of the structure, as defined by the onset of the strength yielding of the main structural element. Similarly, the IM (IMN) is normalized based on corresponding ground motions (scaled) that cause the structure to offer an elastic limit state response. This means that structural design strength is considered in IMN following the construction of a parameter-normalized PSDM. The study examined two typical isolated bridges presented their hazard curves with IMN. The results show that IMN can unify the efficiency and sufficiency of different IMs and reduce uncertainty in the PSDM. The assessment error of the structural elastic limit state for its design strength had little effect on the parameter-normalized PSDM, so the model is robust. Additionally, the IMN outperformed traditional IMs for efficiency and sufficiency in most instances.

Random‐positioned‐sampling effect on probabilistic seismic demand modeling of modularized suspended buildings with free‐standing objects and architectural function regioning

AbstractThe definition of the targeted engineering demand parameters (EDPs) is important to probabilistic seismic demand modeling (PSDM), which produces probability density functions of EDPs conditioned on seismic intensity measure (IM). The targeted EDPs are usually defined at the group level to account for multiple components/units. Thus, they are affected by the considered range of units, i.e., the sample positions. For instance, the maximum peak floor acceleration (PFA) within the whole building differs from the maximum among only the important positions related to seismic loss. Additional uncertainties are induced in the PSDM of PFA if the sample positions vary when architectural function and non‐structural elements change. In this study, the aforementioned influence is termed random‐positioned‐sampling (RPS) effect, and it is investigated by targeting a modularized suspended building, which features the tuning mechanism, multiple major modes, uneven response envelopes, and notable non‐structural‐object‐structure interactions (NSOSI). Results show that the RPS effect lowers the maximum‐based group‐level EDP and increases the dispersion within the EDP sample sets, indicating that conventional PSDMs without considering the RPS effect are biased. The significance of the influence is positively correlated to the position‐wise coefficient of variation of EDP but negatively correlated to the density of sample positions. The combined influence of the NSOSI and the RPS effect is two‐sided for PSDM. The NSOSI amplifies the RPS effect via enlarging position‐wise dispersion of EDP, whereas, the RPS effect waives part of the detrimental scattered contributions from NSOSI. Overall, the IM performance is handicapped, even with IM optimization. However, it can be compensated if architectural function region information is acquired beforehand since the sample positions are restrained.

Serviceability fragility assessment of non-seismically designed railway viaducts in Turkey under near-field and far-field earthquakes

While many railway viaducts still in use in Turkish railway networks are located on active fault zones that produced historical destructive earthquakes, they are not seismically designed in accordance to current standards. This study aims to provide a better understanding about the serviceability fragility of such systems by conducting detailed probability-based seismic assessments under near-field and far-field earthquakes. To achieve this, firstly, 3D finite element models of a range of selected viaducts in Turkey were generated based on their original design drawings. The developed FE models were validated by comparing the analytical modal frequencies with the results of in-situ dynamic tests involving a series of acceleration measurements. Nonlinear time history analyses were then carried out under 25 near-field and 25 far-field real three-component ground motion recordings to obtain the seismic response of each selected viaduct. Subsequently, probabilistic seismic demand models were defined using linear regression analysis to determine relationships between engineering demand parameters (EDPs) and ground motion intensity measures (IMs). Peak ground acceleration (PGA), peak ground velocity (PGV) and spectral acceleration at 1.0 s (Sa (1.0)) were used as the IM parameter, while the maximum lateral displacement of the bridge spans for different service velocities defined in the Eurocode was considered as the EDP at serviceability damage state. Finally, analytical fragility curves for all the selected railway viaducts were developed considering maximum damage probability for the IM levels. The results, in general, demonstrate the seismic vulnerability of the existing viaducts in Turkey. It is shown that while at low speed limits the viaducts exposed to far-field ground motions were more vulnerable than those under near-field ground motions, at high speed limits the viaducts subjected to near-field ground motions were more vulnerable. Also, it is seen that reinforced concrete and masonry viaducts are generally more vulnerable to earthquakes than the steel viaducts. The outcomes of this study should prove useful for the seismic risk assessment, loss estimation and rehabilitation of the railway transportation networks in future studies.

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Survival probability surfaces of hysteretic fractional order structures exposed to non-stationary code-compliant stochastic seismic excitation

A novel first-passage probability stochastic incremental dynamics analysis (SIDA) methodology tailored for hysteretic fractional order structural systems under a fully non-stationary seismic excitation vector consistently designated with contemporary aseismic codes provisions (e.g., Eurocode 8) is developed. Specifically, the vector of the imposed seismic excitations is characterised by evolutionary power spectra that stochastically align with aseismic codes elastic response acceleration spectra, defined for specified modal damping ratios and scaled ground accelerations. Leveraging the concepts of stochastic averaging and statistical linearization, the approximative non-stationary response displacement joint probability density function (PDF) is derived, retaining the particularly coveted attribute of computational efficacy. Subsequently, the coupling with the survival probability model allows for the efficient determination of the response first-passage time probability density surfaces and the survival probability surfaces across various limit-state rules and scalable intensity measures. The first-passage time probability serves as a robust engineering demand parameter, effectively monitoring structural behaviour by considering both intensity and timing information, while inherently aligned with pertinent limit-state requirements. Notably, the associated low computational cost and the ability to handle a wide range of complex nonlinear/hysteretic structural behaviours, coupled with its compliance with modern aseismic codes, underscore its potential for applications in the fields of structural and earthquake engineering. A nonlinear system endowed with fractional derivative elements is used to exemplify the method’s reliability. The accuracy of the proposed method is validated in a Monte Carlo-based context, conducting nonlinear response time–history analyses with an extensive ensemble of accelerograms compatible with Eurocode 8 response acceleration spectra.

Comprehensive evaluation of seismic fragility in base isolated buildings enhanced with supplemental dampers considering pounding phenomenon

Base isolation is a proven technology effective in minimizing earthquake-induced damage to both the structural and non-structural elements (especially freestanding contents) of buildings. Nevertheless, it has been shown that allowing the flexible isolation layer to endure substantial demand displacements might subject the isolated structure to failure. This vulnerability arises from potential superstructure yielding due to increased deformations and reduced stiffness, such as those occurring through pounding against a moat wall during intense earthquakes. One alternative to controlling these large deformations is to use supplementary dampers at the isolation plane of the building, creating a hybrid base isolation system (HIS), which adds damping to the isolation system. In this research, the seismic performance of base isolated structures with lead-rubber bearing (LRB) are studied in conjunction with linear viscous dampers (LVD). Due to this aim, a base-isolated steel frame with 2 story X-type braces and a surrounding moat wall is modeled with two various configurations: LRB, and LRB with LVD. Fragility curves are developed for an ensemble of near-field (NF) pulse-like ground motions and for the maximum inter-story drift ratio (MIDR) as an engineering demand parameter (EDP). The incremental dynamic analysis (IDA) is conducted to calculate the damage probability of the structure by assuming different threshold values for damage states. It was found that adding viscous dampers to the isolation system balanced the behavior of the structure under near field pulse-type records; resulting in reduced isolation displacement while its adverse effects are insignificant and can be ignored. Moreover, the median spectral acceleration, namely the spectral acceleration associated to a probability of exceedance (POE) equal to 50 %, at the specific limit state, in the hybrid base isolation system is higher compared to the conventional one.

Damage quantification based on drift ratios and axial capacity degradation for RC columns under low-velocity impact loads

Damage determination and quantification are critical issues in conducting damage assessment and performance-based design for RC columns under low-velocity impact loads. An impediment in these issues lies in defining reasonable damage criteria. To this end, a framework inspired by existing experimental results is proposed to quantify the damage of RC columns. The core concept of this framework is to establish the relationship between the engineering demand parameter (i.e., drift ratio) and the damage index based on residual axial capacity and to convert the damage index threshold to the drift ratio threshold using a reliability-based method. According to the proposed framework, damage criteria are developed for RC columns in two typical impact scenarios, including the mid-span and near-base impacts. During this process, linear relationships between the maximum drift and the residual one at the impact location are developed by statistically analyzing the existing experimental data (a total of 212 test samples). Based on experimentally validated numerical models, empirical formulas for estimating the residual axial capacity of RC columns are established. The maximum drift, the residual drift, and the axial capacity degradation are interrelated in the proposed damage criteria, overcoming the limitation that the current deformation-based damage criteria used for low-velocity impact loads lack physical significance.

Suitable engineering demand parameters for acceleration‐sensitive nonstructural components

AbstractEarly earthquake design codes used peak ground accelerations (PGAs) as intensity measures (IMs) to characterize the demands of ground motions on structures, but have since shifted towards using spectral accelerations because they provide a better indication of demand. The design of acceleration‐sensitive nonstructural components has followed a similar approach, with modern codes being based on an estimate of the spectral acceleration at the period of the nonstructural component. However, most fragility curves for loss assessment of acceleration‐sensitive nonstructural components, including the existing FEMA P58 library, continue to be based on peak floor accelerations (PFAs). Similar to PGAs as an IM for buildings, a limitation of PFA as an engineering demand parameter (EDP) for nonstructural components is its lack of dependence on the period of those components. In this study, fifteen alternative EDPs suggested in the literature are evaluated as potential candidates for developing seismic damage fragility curves. Acceleration‐sensitive nonstructural components are simulated by single‐degree‐of‐freedom (SDOF) components with elastic perfectly plastic behavior, with a period range of 0.01 to 1 s, and varying strength levels. Nonlinear response history analyses are conducted for the SDOFs, using floor motions obtained from both the first floor and the roof of buildings designed with four distinct seismic force‐resisting systems. Ductility demands for each SDOF are taken as an indicator of damage and are predicted using a linear regression model developed for each specific EDP. The suitability of candidate EDPs is evaluated based on their efficiency and relative sufficiency. Furthermore, a comparison is made between the expected annual loss calculated using fragility curves derived from the selected EDPs to quantify how the EDP used for a fragility curve can affect the seismic loss assessment. The results reveal that the PFA is a suitable EDP only for nonstructural components with very short periods (i.e., less than 0.1 s). Moreover, although the spectral acceleration at the period of the SDOF nonstructural component is a suitable EDP for components that are nearly elastic and are located on the roof of buildings, the peaks that develop in the floor spectra can grossly overstate the demands on nonstructural components that experience significant nonlinearity in their response. In such situations, an average of the spectral accelerations in a range of periods near the period of the SDOF nonstructural component is more appropriate. Moreover, although the spectral acceleration at the period of the SDOF nonstructural component is a suitable EDP for components that are nearly elastic and are located on the roof of the buildings, an average of the spectral accelerations near the period of the SDOF nonstructural component is more appropriate when the component encounters higher levels of nonlinear behavior or is installed on a lower floor.

Using In-Building Observations of Small-to-Large Earthquakes to Predict the Seismic Response of Structures

ABSTRACT The main goal of this study is to evaluate the potential value of data from weak-to-moderate earthquakes for structural response analysis. Data recorded over 18 yr by the seismic network installed in the 12-stories Grenoble City Hall Building (France) is considered. The building response is analyzed in terms of intensity measures and engineering demand parameters, and then compared with strong earthquake data recorded in Japanese buildings. The uncertainties of structural response prediction are estimated and defined in terms of “within-building” and “between-building” components in the same way as the components of the ground-motion model. Data complementarity in the response model is observed between the weak-to-moderate (France) and the moderate-to-strong (Japan) earthquake datasets, disclosing nonlinear processes (associated with resonance period elongation) that are activated in buildings during low-to-strong motion. For example, fundamental frequency shifts are triggered at low values of both total structural drift amplitudes and equivalent strain rates (i.e., time derivative of structural drift). In addition, strain rate thresholds from 10−11 s−1 to 10−5 s−1 representing different structural conditions from undamaged to severely damaged buildings are observed to activate nonlinearities. This confirms the link between loading rates and structural conditions. Our results highlight the interest in instrumentation in buildings located in regions of weak-to-moderate seismicity, for (1) the development and calibration of realistic models for predicting the seismic response of structures, (2) for improving our understanding of the components of uncertainties in the risk assessment of existing buildings, and (3) to investigate physical processes activated in structures during seismic loading that influence their response.

Parametric seismic fragility model for elephant-foot buckling in unanchored steel storage tanks

The parametric seismic fragility model of elephant-foot buckling (EFB) in the tank wall of the unanchored storage tanks is introduced by utilizing the results of a parametric study of eighteen tank-soil configurations. The model can be used to rapidly assess the seismic vulnerability to EFB for a larger number of tanks. The parametric study involved a 1D cloud-based soil response analysis to relate the ground-motion intensity measure at the bedrock with that at the free surface, and a pushover analysis of the refined finite element model of the tank to assess the engineering demand parameter in terms of axial compressive stress in the tank wall and the critical value that triggers EFB. As a consequence, the parametric seismic fragility model can be applied to intensity measures at the bedrock, as it is demonstrated for the spectral acceleration at the tank’s impulsive period, Se,bedrock,EFB, and the peak ground acceleration, PGAbedrock,EFB. The input parameters of the introduced seismic fragility model are the harmonic average shear-wave velocity in the top 30 m of soil, Vs,30, the slenderness ratio of the tank, H/R, the ratio between radius and wall thickness of the tank, R/t, and the standard deviation of log values for the intensity measure causing EFB. The model reliably predicts the median intensity measure causing the onset of EFB in the investigated tank-soil configurations, especially when Se,bedrock,EFB is selected for the intensity measure. However, further investigation is required to enhance the accuracy of predicted intensity measures that trigger EFB by considering the dynamic impact between the base plate and the foundation during an earthquake and accounting for the complete soil-structure interaction effects.

Assessment of the seismic failure of reinforced concrete structures considering the directional effects of ground motions

Seismic intensity measures at different levels significantly impact the seismic damage of building clusters. Reinforced concrete (RC) structures are a type of building widely used in different regions worldwide. A large amount of field seismic damage observation data indicates that within the same seismic intensity zone, the directional effects of varying ground motions lead to significant differences in damage to RC structures on different floors. However, relatively little research has been conducted on estimating the seismic fragility and vulnerability of RC structures considering the directional effects of seismic action. To further study the directional effect of seismic motion on the damage of different floors, this study conducted dynamic time history and spectral analyses on 1472,379 acceleration records in multiple directions obtained from monitoring at nine actual seismic stations during the 2008 Wenchuan earthquake in China. This paper innovatively reports on the actual damage features of RC structures during the Mw6.2 magnitude Jishishan earthquake in Gansu Province, China, on December 18, 2023 (the most severe destructive earthquake in China in 2023) and analyses the influence of earthquake directionality on the damage to different floors of RC structures. A three-dimensional numerical model of a four-story RC frame structure was established using numerical simulation and the finite element method. Different intensity measures were taken to input seismic excitations of different intensities into the RC structure in the 0°, 30°, 60°, and 90° directions, and damage simulation analysis was conducted. The nonlinear dynamic time history curves of structures under multiple directions of seismic excitation in different intensity zones have been developed. Using the interstory stiffness and interstory displacement angle as engineering demand parameters, damage assessment curves and stress clouds for RC structures with 1–4 floors considering different seismic directional effects were generated. The analysis results and major findings indicate that the seismic sequence in the 0° direction has a relatively heavy impact on the first floor of the RC structure in zone IX, which is consistent with the actual field observation results.

Quantitative evaluation method for post-earthquake functionality loss of pedestrian flow pathways within a complex building using evacuation and rescue simulation

The complex building is a single building, characterized by its large size and complicated structural systems, such as high-rise-buildings, long-span-podium, and large underground space, as well as diverse functions. The pedestrian flow pathways within a complex building play a crucial role in urgent evacuation and rescue following seismic events. This study proposed a quantitative method for evaluating the functionality loss of pedestrian flow pathways within the complex building following seismic events. The method performed the component fragility analysis and constructed the speed reduction models that considered the variations of occupants' motions under different damage states of various nonstructural components. To evaluate the functionality loss of pedestrian flow pathways, the evacuation and rescue scenarios were established by analyzing the maximum speeds and behavioral delays of occupants at different spatial locations within the post-earthquake complex building. Based on the simulation, a quantitative index was constructed. Finally, a process accounting for uncertainties such as component damage was presented by generating the engineering demand parameters. A case study was employed to demonstrate the functionality loss of pedestrian flow pathways on each floor and in different areas within the post-earthquake complex building, which has reference significance for improving the post-earthquake complex building 's evacuation capacity as soon as possible to deal with secondary risk.

Utilization of stochastic ground motion simulations for scenario-based performance assessment of geo-structures

Probabilistic seismic performance assessments of engineered structures can be highly sensitive to the seismic input excitation and its variability. In the present study, the scenario-based performance assessment recommended by Federal Emergency Management Agency (FEMA) P-58 guidelines is adopted to estimate seismic fragility of concrete dams for various seismic hazard scenarios. Due to the scarcity of recorded ground motions and thereby their poor representation of uncertainties, stochastic ground motion simulation methods are utilized to obtain the required input excitations. Moreover, to understand the uncertainty in ground motion simulation models, two broadband stochastic simulation models are used to generate input excitations representing six seismic hazard scenarios defined by earthquake magnitude, source-to-site distance, and soil conditions.Optimal intensity measure parameters for each scenario are identified using a systematic procedure that considers criteria such as efficiency, practicality, proficiency, sufficiency, and hazard compatibility. Fragility curves and surfaces are derived using the cloud analysis technique, taking into account various damage measures and limit state functions. The study finds that the derived fragility curves are particularly sensitive to the selection of earthquake scenarios, the choice of records, and the methods used to calculate fragility curves, with less sensitivity observed to different engineering demand parameters. Given this sensitivity, particularly to ground motion selection, the study highlights the necessity of incorporating both model-to-model variability (epistemic uncertainty) and record-to-record variability (aleatory uncertainty), alongside the established material and modeling uncertainties, in the probabilistic seismic assessment.

Analytical vulnerability functions for assessing fatalities in masonry buildings

AbstractThe assessment of human losses and injuries due to earthquakes is critical for the development of risk reduction measures. Yet, most vulnerability studies have focused on the derivation of fragility functions for structural damage, neglecting the evaluation of the human impact. In this study, we implemented a fatality vulnerability assessment procedure based on advanced structural modelling, with an application to typical limestone and granite masonry buildings in Portugal. We performed nonlinear time‐history analysis on 3D numerical models whose characteristics were sampled from statistical models representing the geometric and mechanical properties of this type of construction. Engineering demand parameters, such as volume of loss and volume of survivable space, were estimated and converted into a fatality rate based on observations from past fatal earthquakes. We compared these vulnerability functions with other proposals from the literature in which conventional fragility functions are directly combined with collapse and fatality rates. Finally, the resulting vulnerability functions were tested for two earthquake scenarios for Portugal. The results from this study indicate that the conventional approach for fatality modelling tends to underestimate human losses for strong ground shaking due to the inability to account for catastrophic structural collapses. The fatality vulnerability functions developed in this work can be directly used in probabilistic seismic risk analysis or the assessment of earthquake scenarios.

Real-time seismic damage simulation for urban building portfolio based on basic building information and machine learning

Timely and accurate simulation of seismic damage of the urban building portfolio is essential for pre-earthquake planning and post-earthquake rescue. This study proposes a real-time seismic damage simulation method for the urban building portfolio based on the multiple degree-of-freedom (MDOF) shear and flexural-shear model established by basic building information and machine learning. The formulas for predicting periods of six types of structures are proposed, and the surrogate model-I for predicting the critical inter-story hysteretic parameters are established to optimize the MDOF models. The surrogate model-II is established to rapidly predict the engineering demand parameters and damage states of structures under earthquakes. Regarding the generalization capability, an incremental learning strategy is advised to guarantee the accuracy of the surrogate model-II in predicting the seismic damage of other urban building portfolios. The results in two city-scale cases show that the proposed method can achieve real-time seismic damage simulation of urban building portfolio with acceptable accuracy, and it's not necessary to retrain or only needs minor additional training on the existing surrogate model when applied to other urban building portfolios.

Minimum magnitude boundaries in probabilistic seismic hazard analysis: an insight from structural engineering

In order to systematically advance our understanding of the minimum magnitude limit (Mmin) in the probabilistic seismic hazard analysis (PSHA) calculations, a novel and useful approach utilising a broad range of Single-Degree-of-Freedom oscillators and hazard conditions is being developed and tested. We have determined the most reasonable Mmin value for a variety of structures by examining the impact of Mmin on the mean annual frequency (MAF) of various limit states (LSs) (including the collapse capacity). The originality of the suggested methodology in the current work, known as the MAF saturation strategy, is the recommended Mmin, which is the cut-off value at which lesser magnitude events do add to the hazard but do not significantly change the MAF. The current work is the first to offer the MAF saturation strategy methodology, which searches for the cut-off magnitude at which the MAF value essentially remains constant even when smaller values of this cut-off are utilised as Mmin for hazard assessments. Therefore, given a series of carefully chosen ground motions in each oscillator instance, an incremental dynamic analysis is carried out (by applying the Hunt and Fill algorithm), and the appropriate LS (including the collapse capacity defined as global instability) points are calculated. Thus, the relationship between the distribution of LSs and the Engineering Demand Parameter and intensity measure is found. A simple point source hazard curve is convoluted with this distribution, yielding the structure-specific MAF. In order to find the cut-off lower magnitude (Mmin), this convolution is repeated for several Mmin values. This cut-off is defined as the point at which, when lower values are utilised as Mmin in the PSHA computation, the MAF’s values do not change considerably (with a five per cent threshold). The acquired data were thoroughly discussed in relation to various structural features and seismic input factors. The primary findings showed that each of the structures under consideration requires a Mmin value in the range of 4–4.3. Put otherwise, the suggestions seen in technical literature, which range from 4.5 to 5, are not cautious, at least not when it comes to probabilistic structural limit state frequency. The derived Mmin value is mostly controlled by the natural period of the structure and is largely unaffected by other structural characteristics like ductility, damping ratio and overstrength factor.

Optimal intensity measure for seismic performance assessment of shield tunnels in liquefiable and non-liquefiable soils

Relating the ground motion intensity measure (IM) and the structural engineering demand parameter is a crucial step in the performance-based earthquake engineering framework. This study investigates the selection of IM for development of probabilistic seismic demand model of urban shield tunnels subjected to earthquake ground motions in liquefiable and non-liquefiable soils. Nonlinear dynamic effective stress analyses are conducted to develop a database of the intensity measures and structural seismic responses exposed to ground shaking and soil liquefaction. Two advanced soil constitutive models (i.e., Pressure DependMultiYield03 and PressureIndependMultiYield for liquefiable and non-liquefiable soils, respectively) are employed to capture the nonlinear behavior. A suite of 23ground motion intensity measures is selected and assessed based on the evaluation criteria of correlation, efficiency, practicality and proficiency. Eventually, the multi-level fuzzy comprehensive evaluation method is employed to comprehensively consider the four evaluation criteria and establish the optimal ground motion IM suitable for probabilistic seismic demand analysis of shield tunnel structures. The obtained results show that the sustained maximum acceleration is the optimal IM for evaluating the structural seismic response, followed by the peak ground acceleration in both liquefiable and non-liquefiable soils. Peak pseudo velocity spectrum, displacement square integral and Housner spectral intensity are found to be not suitable for the probabilistic seismic demand analysis of shield tunnel structures.