Seismic risk assessment of reticulated shell structures considering multiple uncertainties

Probabilistic seismic performance assessment of aqueduct structures considering different sources of uncertainty

Seismic risk in the form of impending disaster has been seen from past records that moderate-to-large earthquakes have caused the loss of life and property in all parts of Nepal. Despite the availability of new data, and methodological improvements, the available seismic hazard map of Nepal is about two decades old. So an updated seismic hazard model at the country level is imperative and logical. The seismic hazard and risk model constitute important tools for framing public policies toward land-use planning, building regulations, insurance, and emergency preparedness. In fact, the reliable estimation of seismic hazard and risk eventually minimizes social and economic disruption caused by earthquakes. In this frame of reference, the seismic risk assessment at a country level is elementary in reducing potential losses stemming from future earthquakes. Thus, this study investigates structural vulnerability, seismic risk, and the resulting possible economic losses owing to future earthquakes in Nepal. To this end, seismic risk assessment in Nepal is done using an existing probabilistic seismic hazard, a newly developed structural vulnerability, and recently released exposure data. The OpenQuake-engine, the open-source platform for seismic hazard and risk assessment from the Global Earthquake Model initiative, was used to calculate the seismic hazard and risk in Nepal. The seismic hazard and mean economic loss map were formulated for the 1, 2, 5, and 10 % probability of exceedance in 50 years. Finally, the distribution of building damage and corresponding economic losses due to the recurrence of the historical 1934 earthquake was presented in this study.

It is known that the extradosed cable-stayed bridge, a hybrid bridge, possesses the virtues of both classic cable-stayed bridges and girder bridges in mechanical behaviors. In this paper, the sensitivity of seismic fragility demand parameters (SFDP) of a high-speed railway extradosed cable-stayed bridge is studied systematically along with the consideration of structural parameter uncertainty. Based on the probability distribution and correlation of random parameters, the Latin hypercube sampling method is adopted herein. The dynamic 3D finite element model of the employed bridge is established by using powerful and attractive OpenSEES nonlinear software. A nonlinear incremental dynamic analysis is performed to consider the randomness of structural parameters using sampling analysis. Some important conclusions are drawn indicating that the structural design parameter uncertainty predominantly has influence on the SFDP for fragility analysis of bridge structures. The design parameters of extradosed cable-stayed bridges are categorized and identified as primary, secondary and insensitive parameters. The high sensitivity parameters of extradosed cable-stayed bridges for fragility analysis include friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. Additionally, the strength and strain of unconfined concrete cannot be ignored. Furthermore, the uncertainty of structural design parameters fails to be responsible for the cable force responses due to larger girder stiffness. The structural design parameter uncertainty has a significant influence on the responses of extradosed cable-stayed bridges for seismic fragility analysis.

A better seismic design for building and other structures is the most effective way to reduce seismic risk and avoid earthquake disaster. Adoption and implementation of new seismic safety regulations and design standards have caused serious problems in many communities in the New Madrid region, including western Kentucky, however. The main reasons for these problems are (1) misunderstanding of the national seismic hazard maps and (2) confusion between seismic hazard and seismic risk. Both are caused by probabilistic seismic hazard analysis (PSHA). PSHA is a mathematical formulation derived from a probability analysis on the distribution of earthquake magnitudes, locations, and ground-motion attenuation. Some assumptions and distributions associated with PSHA have been found to be invalid in earth science, however. In addition, PSHA contains a mathematical error: equating a dimensionless quantity (the annual probability of exceedance – exceedance probability in one year) to a dimensional quantity (the annual frequency of exceedance with the unit of per year [1/yr]). Thus, PSHA is scientifically flawed and the resulting seismic hazard and seismic risk estimates are artifacts. The national seismic hazard curves and maps are artifacts because they were produced from PSHA, even though the inputs are scientifically sound. Although seismic hazard and seismic risk have often been used interchangeably, they are two fundamentally different concepts. Seismic hazard describes the natural phenomenon or property of an earthquake, whereas seismic risk describes the probability of loss or damage that could be caused by a seismic hazard. Seismic hazard and seismic risk play different roles in engineering design and other policy considerations. Furthermore, measures for seismic hazard mitigation are different from those for seismic risk reduction. The difficulties in the development of design ground motion for NEHRP provisions are caused by the use of the national seismic hazard maps which are neither seismic hazard nor seismic risk. The resulting design ground motions for building codes and other policy considerations are therefore problematic. California’s experience proves that deterministic/scenario seismic hazard analysis is an appropriate approach for seismic hazard assessment, seismic risk assessment, as well as *Kentucky Geological Survey, University of Kentucky, 504 Rose Street, Lexington, KY 40506; phone (859) 323-0564; fax (859)257-1147; e-mail: zmwang@uky.edu. 112 Seismic Hazard Design Issues in the Central United States engineering design and other policy considerations. Deterministic/scenario seismic hazard analysis is also appropriate for engineering design and other policy considerations in the New Madrid region, as well as other regions.

Incremental dynamic analysis (IDA) has been extended by introducing a set of structural models in addition to the set of ground motion records which is employed in IDA analysis in order to capture record‐to‐record variability. The set of structural models reflects epistemic (modeling) uncertainties, and is determined by utilizing the latin hypercube sampling (LHS) method. The effects of both aleatory and epistemic uncertainty on seismic response parameters are therefore considered in extended IDA analysis. The proposed method has been applied to an example of the four‐storey‐reinforced concrete frame, for which pseudo‐dynamic tests were performed at the ELSA Laboratory, Ispra. The influence of epistemic uncertainty on the seismic response parameters is presented in terms of summarized IDA curves and dispersion measures. The results of extended IDA analysis are compared with the results of IDA analysis, and the sensitivity of the seismic response parameters to the input random variable using the LHS method is discussed. It is shown that epistemic uncertainty does not have significant influence on the seismic response parameters in the range far from collapse, but could have a significant influence on collapse capacity. Copyright © 2008 John Wiley & Sons, Ltd.

Fragility analysis constitutes the basis in seismic risk assessment and performance-based earthquake engineering during which the probability of a structure response exceeding a certain limit state at a given seismic intensity is sought to relate seismic intensity and structural vulnerability. In this article, the seismic vulnerability assessment of a subway station structure is investigated using a probabilistic method. The Daikai subway station was selected as an example structure and its seismic responses are modeled according to the nonlinear incremental dynamic analysis procedure. The limit states are defined in terms of the deformation and waterproof performance of the subway station structure based on the central column drift angle and the structural tension damage distribution obtained from the incremental dynamic analysis. Fragility curves were developed at those limit states and the probability of exceedance at the limit states of operational, slight damage, life safety, and collapse prevention was determined for the two seismic hazard levels. Results reveal that the proposed fragility analysis implementation procedure to the subway station structure provides an effective and reliable seismic vulnerability analysis method, which is essential for these underground structural systems considering their high potential risk during seismic events.

Seismic risk assessment in Montenegro has been a critical concern since the devastating earthquake of 1979, which spurred initial studies for the country's spatial planning. In response, significant efforts were made to mitigate seismic risks and regulate the construction of earthquake-resistant structures. Early vulnerability studies were based on damage observations from the 1979 earthquake. However, since then, seismic risk in Montenegro has risen considerably due to rapid urbanization and increased building construction, particularly in coastal zones with high seismic hazard levels. Unfortunately, Montenegro's seismic risk assessment remained outdated until 2021, when a comprehensive study was conducted as part of a European Commission-funded project to develop a National Risk Assessment (NRA), led by the Department of Civil Protection. This recent seismic risk assessment was carried out in accordance with EU guidelines, ensuring consistency and comparability in terms of prevention, preparedness, and planning with EU member states. The development of the NRA encountered several challenges, primarily due to data gaps, especially in the building exposure modelling. In this paper, the methodology used for the seismic risk assessment is presented, with a focus on the main uncertainties in the available existing exposure model from literature. It introduces a refined exposure model tailored for building typologies in northern Montenegro. Finally, ongoing and future research efforts aimed at continually improving the exposure model are discussed.

Improved Park-Ang Two-Parameter Damage Model of Mesh Shell Structures

This research investigates the collapse responses of a concrete moment frame considering modeling uncertainties. These modeling uncertainties are considered for evaluating a collapse response related to the modified Ibarra-Krawinkler moment-rotation parameters for beam and column elements of a given structure. To analyze these uncertainties, the correlations between the model parameters in one component and between two structural components were considered. Latin Hypercube Sampling (LHS) method was employed to produce independent random variables. Moreover, Cholesky decomposition was adopted to produce correlated random variables. Performing 281 simulations for the uncertainties involved considering their inter-correlations, incremental dynamic analysis (IDA) was done using 44 far-field accelerograms to determine structural collapse responses. Collapse responses of each simulation, including mean collapse capacity, mean collapse drift, and mean annual frequency, were obtained. Then, the collapse responses were predicted using the response surface method and artificial neural network. The results show that the Correlation coefficients (R) between the target data resulted from incremental dynamic analysis (IDA), output data resulted from response surface method (RSM), and artificial neural network (ANN) were obtained for the collapse responses above 0.98. The maximum prediction errors for mean collapse capacity and mean collapse drift are less than 5% and for mean annual frequency less than 10% under response surface method (RSM), and artificial neural network (ANN).

Quantitatively modeling and propagating all sources of uncertainty stand at the core of seismic fragility assessment of structures. This paper investigates the effects of various sources of uncertainty on seismic responses and seismic fragility estimates of single-layer reticulated domes. Sensitivity analyses are performed to examine the sensitivity of typical seismic responses to uncertainties in structural modeling parameters, and the results suggest that the variability in structural damping, yielding strength, steel ultimate strain, dead load and snow load has significant effects on the seismic responses, and these five parameters should be taken as random variables in the seismic fragility assessment. Based on this, fragility estimates and fragility curves incorporating different levels of uncertainty are obtained on the basis of the results of incremental dynamic analyses on the corresponding set of 40 sample models generated by Latin Hypercube Sampling method. The comparisons of these fragility curves illustrate that, the inclusion of only ground motion uncertainty is inappropriate and inadequate, and the appropriate way is incorporating the variability in the five identified structural modeling parameters as well into the seismic fragility assessment of single-layer reticulated domes.

The bellows of a vacuum interrupter (VI) become the most vulnerable components when the VI is introduced to comprise a dead-tank fast vacuum circuit breaker (FVCB). However, there is no work revealing the optimal design of VI bellows subjected to high gas pressure and high operating velocity in achieving a high mechanical endurance. The objective of this paper is to confirm the optimum design parameters of bellow structure, which would be subjected to a high gas pressure and high operating velocity. We adopted a transient fluid-structure coupled simulation method, as well as a fatigue failure simulation method, to obtain the dynamic strain-stress distribution and the fatigue life of the bellows. The U-shaped VI bellows used in the simulation were kept the same as those in the FVCB, which was with stainless-steel. The compressed length of the bellows was configured to be 30.00 mm corresponding to the rated contact gap of 30 mm for the VI. The gas pressure was set as 0.50 MPa and the operating velocity was set as 5.00 m/s. The equivalent stress the U-shaped VI bellows' first wave crest being suffered was changed as follows: it was reduced by 27.46% when the thickness was increased from 0.16 mm to 0.18 mm; when the wave height was decreased from 8.34 mm to 7.74 mm, it was reduced by 25.37%; as for the radius of curvature of wave crest and the radius of curvature of wave trough, the equivalent stress was reduced by 16.15%, 19.36% respectively when the first parameter was changed from 2.00 mm to 1.80 mm and the second one was changed from 2.00 mm to 2.20 mm. Excessive reduction of the wave height contributes to higher superimposed frequency of the stress waves, the preferred optimum parameters were as follows: the thickness was 0.18 mm; the wave height was 8.04 mm; the radius of curvature of wave crest was 2.00 mm; the radius of curvature of wave trough was 2.00 mm. Two whole bellow structure models were built to verify the optimum design parameters. The equivalent stress the U-shaped VI bellows' first wave crest being suffered was reduced by 17.13% when the optimum design parameters of the bellow structure were adopted. The fatigue life of the improved model is 942 cycles while the initial model is 720 cycles with the operating speed of 5 m/s under the pressure of 0.50 MPa. The mechanical endurance of the bellows was increased by 30.83% when the optimum design parameters of bellow structure was adopted.

Seismic hazard assessment (SHA) and evaluation of seismic risks (SRs) require an adequate understanding of the actual distribution of earthquakes over magnitude, space, and time ranges. The standard probabilistic seismic hazard analysis (PSHA) has never been subjected to unbiased scrutiny before publication of the final maps, which are misleading to unacceptable human and economic losses; this has been proven on many occasions, including the most recent cases – 6 February 2023 (Turkey), 8 September 2023 (Morocco), and 1 January 2024 (Japan).  Neo-deterministic seismic hazard assessment (NDSHA) methodologies have been developed to improve the reliability and accuracy of reproducible seismic hazard maps. In the last decade, the application of NDSHA in many regions of the world has confirmed the availability of reliable and effective input for mitigating earthquake risks (Panza et al., 2021). NDSHA results have passed intensive testing by historical evidence and realistic modelling of scenario earthquakes.We used two agents of the NDSHA synergy, i.e. Unified Scaling Law for Earthquakes (USLE) and anisotropic propagation of seismic effect, to evaluate SRs for the Lake Baikal regional railroad system on the basis of seismic hazard maps of maximum macroseismic intensity expected in 50 years with 10%, 5%, and 1% chance of exceedance. Specifically, we employed the regional layers from the widely used crowdsourced dataset, Open Street Map, which features global coverage. These layers include infrastructure elements such as tracks, bridges, and tunnels.We have extended our analysis of seismic risk assessment for the Lake Baikal Region railway system presented earlier (Nekrasova et al., 2024) and compare our results with the SR evaluations based on the General Seismic Zonation 2016 and Global Earthquake Model 2018 final hazard maps at identical levels of probability of exceedance.A comparison of PSHA and NDSHA approaches in application to the Lake Baikal railway system disclose significant overestimation of the reconstruction costs for expected state of extreme damage (Hazus state standard ds5 - Complete) due to earthquakes, if GSZ2016 or GEM2018 and not USLE modelling is used. In particular, the significant discrepancy in the area of expected ground shaking of macroseismic intensity VIII or higher that may damage the railroad tracks, bridges, and tunnels leads to a dramatic difference in the seismic risk values measured in arbitrary units of currency.Our results are presented for academic purposes only. Evidently, more adequate though significantly more complex procedures involving more complicated procedures of convolution of seismic hazard, exposures, and their vulnerability are required when addressing realistic and practical assessment of seismic risks. Such assessments should involve experts in seismology, earthquake engineering, social sciences, and economics.ReferencesNekrasova A, Kossobokov V, Podolskaia E (2024) Regional seismic risk assessment based on the Unified Scaling Law for Earthquakes: The Lake Baikal railway system. Soil Dynamics and Earthquake Engineering 177, 108402. https://doi.org/10.1016/j.soildyn.2023.108402Panza G, Kossobokov V, De Vivo B, Laor E (Eds) (2021) Earthquakes and Sustainable Infrastructure: neo-deterministic (NDSHA) approach guarantees prevention rather than cure. Elsevier. Paperback ISBN: 9780128235034, eBook ISBN: 9780128235416, xxv, 672 p. https://doi.org/10.1016/C2020-0-00052-

Seismic assessments of reinforced concrete (RC) bridges play an important role in the sustainable development of societies and the determination of the critical values of demand measures for various damage limit states is a key issue in seismic assessments. The results of a seismic assessment largely depend on which kind of demand measure is used, but few studies have investigated the nature of the relationships between damage measures in order to avoid inconsistency between seismic assessments. In this study, a finite element model of an RC bridge was constructed to act as a benchmark example. Three parameters, system-equivalent displacement, rotation angle of a plastic hinge, and material strain, were used as the engineering demand parameters (EDPs) to assess the seismic performance of different earthquake levels. Numerical examples demonstrated that the exceedance probabilities significantly depended on the selected EDP and the critical values of the EDPs for the three damage states. To obtain a consistent seismic assessment of the representative bridge for the different EDPs, an iterative probabilistic seismic assessment method was adopted. The EDP critical values could then be determined using the performance-based exceedance probabilities. It was suggested to the exceedance probabilities within 50 years for the three damage limit states (performance-based) at half of the exceedance probability within 50 years for three seismic levels of earthquakes (hazard-based), respectively.

While earthquakes can have a devastating impact on the economic growth and social welfare of earthquake prone regions, probabilistic seismic risk assessment can be employed to assess and mitigate such risks from future destructive events. In a previous study (Sianko et al. in Bull Earthq Eng 18:2523–2555, 2020), a probabilistic seismic hazard analysis (PSHA) tool based on the Monte-Carlo approach, was developed to predict the seismic hazard for high seismicity areas. In this study, a seismic risk assessment framework is developed incorporating the previously developed PSHA tool, with vulnerability functions based on various damage criteria, exposures and casualty models. Epistemic uncertainty is addressed using logic trees and distribution functions. The developed seismic risk assessment framework can estimate human and economic losses for particular return periods using an event-based stochastic procedure. The framework is applied to a case study area, the city of Adapazari in Turkey. Seismic risk assessment is carried out for different return periods to identify the most vulnerable areas of the city. The verification of the developed seismic risk framework is performed by comparing the predicted seismic losses to those observed during the 1999 Kocaeli earthquake that severely affected the city of Adapazari. The results of the study indicate that while overall predictions for extensive and complete damage states demonstrate strong correlation with the observed data, accurate risk predictions at the district level are not achievable without microzonation studies.

지진취약도 분석을 통하여 교량의 지진 위험도를 평가하였다. 지진취약도 분석에서는 교각 하부의 소성힌지의 거동을 주요 손상인자로 분석하였으며, 또한 한반도 지진재해지도를 근거로 하여 지진발생확률을 산정한 후 이들을 이용하여 교량의 성능단계에 따른 손상발생확률을 분석하였다. 이 연구에서는 교각에 직접 전달되는 지진이 아닌 암반노두에서의 지진의 최대지반가속도에 대하여 지진취약도를 분석하였으며, 비선형 지진해석을 위해서는 층상지반의 영향으로 증폭된 지진하중을 고려하였다. 제안된 방법으로 예제교량의 지진위험도를 분석하였으며, 면진받침이 설치된 교량에 대한 지진 위험도의 저감 효과를 정량적으로 분석하였고, 지진재해지도에서의 조건이 다른 지역에 시공되는 경우의 지진위험도를 분석함으로써 현 시방서의 타당성을 간접적으로 검토하였다. Seismic risk assessment of bridge is presented using fragility curves which represent the probability of damage of a structure virsus the peak ground acceleration. In theseismic fragility analysis, the structural damage is defined using the rotational ductility at the base of the bridge pier, which is obtained through nonlinear dynamic analysis for various input earthquakes. For the assessment of seismic risk of bridge, peak ground accelerations are obatined for various return periods from the seismic hazard map of Korea, which enables to calculate the probability density function of peak ground acceleration. Combining the probability density function of peak ground acceleration and the seismic fragility analysis, seismic risk assessment is performed. In this study, seismic fragility analysis is developed as a function of not the surface motion which the bridge actually suffers, but the rock outcrop motion which the aseismic design code is defined on, so that further analysis for the seismic hazard assessment may become available. Besides, the effects of the friction pot bearings and the friction pendulum bearings on the seismic fragility and risk analysis are examined. Lastly, three regions in Korea are considered and compared in the seismic risk assessment.