Seismic Analysis Model Research Articles

Engineering model for seismic analysis of flexible rail‐bound structures with uplift

AbstractIn this paper, a highly simplified two‐dimensional three‐mass oscillator model is presented, which reproduces the typical behaviour of flexible structures of large mobile equipment transverse to the rail under seismic excitation. The typical rocking motion of the machine found in previous investigations, which is reproduced in the simplified analytical model, is taken into account together with the characteristic properties of the load‐bearing structure of the complete model. The three‐mass oscillator model is designed in such a way that it is able to provide information about uplift, rocking and tilting as a function of the model parameters and the excitation. A novel approach for the coefficient of restitution is derived, which takes into account the impact of wheel on rail and at the same time includes the stiffness of the subsoil. Also, a non‐linear ground stiffness could be captured with this approach, and thus the influence of the ground could be investigated. This approach is of generic character, so it may be useful to a wide range of other engineering fields than mobile equipment as well. Structural parameters are determined for a range of bucket wheel machines and stackers, producing rocking and tilting spectra under sinusoidal excitations and generating tilting delimitations under seismic excitations. Using a numerical beam‐mass model corresponding to the engineering model, the simplified multi‐mass model can be validated.

Surrogate models for seismic response analysis of flexible rocking structures

AbstractSeismic design tools are based on surrogate models of the designed structure and the responses of those surrogates to earthquake ground motions. To design symmetric flexible rocking structures, a surrogate model that includes rocking and flexure is needed. In this paper, we derive the equation of motion of a flexible multi‐degree‐of‐freedom (MDOF) structure rocking on its base in modal coordinates. Then, we introduce a set of two‐degree‐of‐freedom (2DOF) surrogate models that accounts only for the first elastic vibration mode of the multimass structure and its rotation about the base pivot points. We investigate the surrogates' ability to represent the dynamics of an elastic MDOF structure that uplifts and rocks and the interaction between rocking and flexure. Therein, we detail the simplifications for the equations of motion of the 2DOF surrogate models and the adopted rocking impact model, and develop and check the sliding initiation condition. We show that the simplified 2DOF surrogate model responses compare well to experimental results. Then we assess the 2DOF surrogate model accuracy in representing the earthquake response of the MDOF model using Cloud Analysis and the coefficient of determination approach. We find that simplified 2DOF surrogate of the MDOF model is quite accurate () in estimating its maximum relative top displacement and acceptably accurate () in estimating its maximum base rotation based on a thousand randomly generated flexible rocking structure earthquake response analyses. Lastly, we discuss using the simplified 2DOF surrogate model of symmetric flexible rocking structures in preliminary seismic design, and give examples featuring a continuous elastic hollow semi‐conical chimney and an inelastic flexible MDOF structure, both with a base that may uplift.

Study on Seismic Performance of RC Frame Structures Considering the Effect of Infilled Walls

This paper studies the impact of half-height infilled walls on the failure modes of frame columns through quasi-static tests of both frame models and half-height infilled wall frame models. Based on the experimental results, a seismic analysis model of reinforced concrete (RC) frame structures is established, and parametric studies are carried out to analyze the effects of masonry materials and masonry heights on the seismic performance of structures. The results show that the load-bearing capacity and stiffness of the structure are improved, while the ductility of the structure is reduced because of the existence of infilled walls. As the height of infilled walls increases, there is a notable decrease in the free height of frame columns. At a wall-to-column height ratio of 0.2, the masonry walls exert a negligible effect on the frame structure’s seismic performance. In contrast, at a ratio of 0.6, there is a transition in column failure modes from bending to shearing. When evaluated at consistent masonry heights, aerated concrete block-infilled walls demonstrate the least impact on the seismic performance of RC frame structures. Thus, in the absence of additional structural enhancements, the use of aerated concrete blocks is recommended to mitigate the negative implications of infilled walls on the seismic integrity of RC frames.

Seismic analysis of free-standing spent-fuel dry storage cask considering soil–concrete pad–cask interaction

This paper presents a seismic analysis method that can evaluate a very large number of cases for the free standing dry storage cask by proposing a methodology that has short analysis time as well as accuracy. This study also performed a seismic analysis of a dry storage facility with multiple casks to show a tip-over phenomenon from earthquake accident conditions. The earthquake accident condition is long-term event that occur during about 20 s long, and lots of seismic analysis cases should be performed to consider various real conditions because the free-standing spent-fuel dry storage cask has many nonlinear responses. The soil–concrete pad–cask interaction was considered in the seismic analysis and finite element model was made using concrete pad, soil and cask models. In the reinforced concrete pad, the rebar was excluded to reduce the analysis time, but the thickness was corrected to maintain the bending rigidity. Additionally, the analysis time reduced by modeling the cask as a rigid body rather than a flexible body. 35-cases of seismic analysis were performed to determine a tip-over phenomenon from each earthquake. The analysis revealed that no tip-over phenomenon of the cask was observed in all analyses from 0.2 g to 0.6 g, however the tip-over of the cask were observed from 0.8 g with friction coefficients of 0.8 and 1.0.

Seismic performance of railway bridges with novel ductile piers under near-fault earthquakes

The destructive force of near-fault earthquakes presents a significant challenge to railway bridges. To enhance the seismic resilience of railway bridges under such conditions, a novelly designed ductile pier is introduced herein, accompanied by a analysis of its stiffness, damping characteristics, and shear capacity. The analysis reveals that the ductile pier exhibits reduced stiffness and increased viscous damping ratio when compared to the traditional pier. Subsequently, a finite element model of a typical railway simply-supported girder bridge is established and verified through shaking table tests. Furthermore, the near-fault seismic wave synthesis method is introduced, and the synthesized near-fault seismic waves are input into the traditional pier model and the ductile pier model for seismic analysis. The findings demonstrate that the ductile pier effectively diminishes girder acceleration and bearing displacement while enhancing pier energy dissipation. Additionally, the ductile pier is proved effective in safeguarding the core concrete during significant seismic events.

Influence of the Seabed Site and Island Structure on Seismic Response of Marine Artificial Islands

Compared with the marine structures such as sea-crossing bridges and offshore wind turbines, the marine artificial islands are bottom sitting structures and particularly sensitive to site conditions. Therefore, the study focuses on determining the effect of seabed site conditions and construction methods on the seismic performance of marine artificial islands. A seismic wave analysis model of seabed-seawater layer–artificial island coupling is developed by combining the self-programmed fluctuation analysis program and the dynamic analysis software. Firstly, the seismic response of marine artificial islands with different site conditions are analyzed by inputting P and SV waves. On that basis, the effects of incidence angles on the seismic response are explored. Then the study further explores the effects of different backfill materials and protective structures on the seismic response of the artificial island. Numerical results show that the silty soft soil layer can amplify the seismic response of seabed sites, and this amplification effect increases with the increase of the depth of silty soft soil layers. Moreover, the coral sand as backfill material can reduce the seismic response of marine artificial islands. The seismic response of marine artificial islands can also be reduced in the model with a protection structure. These results will provide some theoretical references for the site selection and construction method of marine artificial islands.

Longitudinal seismic analysis for underground structures passing through soft-hard strata based on periodic stratum deformation

Poor geological conditions, e.g., soft and hard strata, have a significant impact on the seismic response of underground structures. In this study, a series of longitudinal seismic analysis for underground structures passing through soft-hard strata were conducted based on the concept of periodic stratum deformation. Firstly, the analytical expressions of stratum deformation in soft-hard strata at the oblique incidence of plan P-, and S- wave were obtained via decomposing the stratum deformation into the reflected- and transmitted wave fields. Then, the wave propagation history in soft-hard strata in the time domain was transformed into strata deformation in a period via introducing concept of the periodic stratum deformation. Base on the proposed expressions, a self-developed Python program was implemented into finite element software ABAQUS to establish seismic analysis model and to calculate the longitudinal seismic response of underground structures. Finally, example analyses were conducted to study the influence of plane P- and S- wave, wave velocity ratio of soft and hard media, as well as incident wave angle on the seismic response of underground structures located in soft- hard strata. This study may provide a reference for seismic design of underground structures located in soft- hard strata.

PSHA: Does It Deal with What It Is or What We Want It to Be?

Abstract In a recent opinion piece Albarello and Paolucci (2023; hereafter, AP23) provide their view as members of the past Seismic Group of the Commissione Grandi Rischi (CGR-SRS) in Italy, which represents the main scientific consultant for Italian Civil Protection, about the difficulty using probabilistic seismic hazard analysis (PSHA) models for building code purposes. Here, we refer to this specific kind of PSHA modeling as National Seismic Hazard Model (NSHM). We agree with AP23 that the topic is of great and general importance, and here we aim at contributing to this discussion by offering our perspective on two points that are at the heart of the matter, concluding that AP23 is misguided in how to deal with them. First, we assert that the credibility of an NSHM has to be rooted only in the use of the best available science, which includes a rigorous testing phase with observations, independent from the consequences in terms of risk. (PSHA deals with what it is.) Second, we claim that the difficulties in accepting a new NSHM with some major changes with respect to the previous model are mostly due to too rigid building code procedures that do not account for the epistemic uncertainty in the hazard estimates.

Seismic Stability Analysis of Slope Reinforced by Frame Anchors Considering Prestress

Taking the slope reinforced by frame anchors as the research object, it is assumed that the potential sliding surface of the slope is an arc. Based on the limit equilibrium theory, the seismic stability analysis model of frame anchor reinforced slope considering anchor prestress is established. This study considers prestress as uniformly distributed forces acting on the slope surface and calculates the additional stress induced by prestressing within the slope to investigate its reinforcement effect on slopes. Thus, the stability of the slope is analyzed and calculated. On this basis, the functional relationship between the center position coordinates of the potential sliding surface and the safety factor is established. Using the optimization algorithm toolbox in Matlab, the possible center position area is dynamically searched, and the minimum safety factor and its corresponding center position coordinates are obtained. Taking slope engineering as an example, the calculated results are compared with the finite element calculation results. The results show that the calculation result regarding the anchor prestress as the uniformly distributed force is reliable, and the anchor prestress can significantly enhance slope stability. This calculation method applies to slope engineering in homogeneous soil with circular sliding surfaces.

A Distributed Impact Model for Seismic Analysis of Planar Rocking Body

ABSTRACT The problem of a planar rigid rocking block subject to dynamic loading is of significant interest to the earthquake engineering community due to its wide application. Despite its simple configuration, rocking itself is a highly nonlinear phenomenon which exhibits non-smooth dynamic behavior. The non-smoothness in dynamics comes from the sudden impact of the rocking body with ground when the sign of rotation angle reverses. Therefore the impact model used in the simulation for rocking problem has a profound influence on the dynamic behavior. Most of existing impact models assume that the impulse during impact is concentrated at the pivot point of the block, ignoring the potential distribution of impulses. This study proposes a distributed impact model for dynamic analysis of planar rigid rocking body. The distributed impulses are achieved through the integration of normal forces induced by penetration over a dummy time period during impact. The distributed impact model is subsequently used to evaluate the post-impact quantities of interest. Numerical simulations suggest Housner’s impact model is a special case of the proposed model. The developed impact model is also compared with published experimental result, showing good accuracy. Finally, evaluation of overturning spectra under analytical pulse excitations suggests that using the distributed impact model can give substantially different results compared to the classic concentrated impact model for relatively stocky blocks. Similar observations can also be made when evaluating rocking responses under seismic excitations.

Implementing Non-Poissonian Forecasts of Distributed Seismicity into the 2022 Aotearoa New Zealand National Seismic Hazard Model

ABSTRACT Seismicity usually exhibits a non-Poisson spatiotemporal distribution and could undergo nonstationary processes. However, the Poisson assumption is still deeply rooted in current probabilistic seismic hazard analysis models, especially when input catalogs must be declustered to obtain a Poisson background rate. In addition, nonstationary behavior and scarce earthquake records in regions of low seismicity can bias hazard estimates that use stationary or spatially precise forecasts. In this work, we implement hazard formulations using forecasts that trade-off spatial precision to account for overdispersion and nonstationarity of seismicity in the form of uniform rate zones (URZs), which describe rate variability using non-Poisson probabilistic distributions of earthquake numbers. The impact of these forecasts in the hazard space is investigated by implementing a negative-binomial formulation in the OpenQuake hazard software suite, which is adopted by the 2022 Aotearoa New Zealand National Seismic Hazard Model. For a 10% exceedance probability of peak ground acceleration (PGA) in 50 yr, forecasts that only reduce the spatial precision, that is, stationary Poisson URZ models, cause up to a twofold increase in hazard for low-seismicity regions compared to spatially precise forecasts. Furthermore, the inclusion of non-Poisson temporal processes in URZ models increases the expected PGA by up to three times in low-seismicity regions, whereas the effect on high-seismicity is minimal (∼5%). The hazard estimates presented here highlight the relevance, as well as the feasibility, of incorporating analytical formulations of seismicity that go beyond the inadequate stationary Poisson description of seismicity.

Failure modes-based seismic fragility analysis of concrete gravity dams considering concrete heterogeneity

The heterogeneity of mass concrete often leads to the initiation of micro-cracks in gravity dams, while the accumulation of damage of concrete on the meso-scale leads to the cracking behaviour on the macro-scale. To improve the seismic safety of the dam, a comprehensive study on the effect of heterogeneous properties is crucial in seismic fragility analysis. A novel methodology considering concrete heterogeneity for seismic fragility analysis was developed by combining damage element model for seismic failure analysis, a five-level standard for failure modes-based seismic damage state and a method to generate seismic fragility curves. Then, seismic failure analysis of the Koyna gravity dam was taken as an example to verify the correctness of the damage element model, the damage process of dam from micro-cracks to macro-cracks were simulated. Finally, the seismic fragility of a practical dam in China was studied to verify the effectiveness of the proposed methodology. The results showed that simulated failure modes-based fragility curves were suitable for the target dam and more capable of considering the uncertainty of concrete material parameters. The obtained fragility curve proved valuable in optimizing seismic design, reinforcement and maintenance measures and improve seismic capability of the dam.

An analytical model for seismic response analysis of electrical equipment-steel support structure

Electrical equipment mounted on supporting structures is typical in a substation but vulnerable to earthquakes from previous field investigations. To evaluate the seismic performance of such an electrical equipment-support coupling system, a modal space analytical model was developed using the vibration partial differential equation (PDE) with distributed parameters and joint nodes. In the analytical model, resonant frequencies and mode shapes were obtained through numerical algorithms based on the boundary condition of each segmented beam. Then seismic responses of the coupling system can be attained by the modal decomposition method and superposition principle. A full-scale shaking table test was conducted on a 550 kV bushing-support coupling structure, and the accuracy of the analytical model was verified by the experimental results. Furthermore, a ceramic breakage inside the connecting flange at the base cross-section of the bushing specimen was observed after the seismic qualification test, which means its seismic performance can not meet the demand in the IEC seismic design specifications. To figure out this problem, parametric analysis was carried out using the analytical model to study the influence of parameters of the supporting structure and flange connection on the seismic responses of the equipment. In light of the analytical results, halving the original flange's flexural rigidity can reduce the bottom stress of the bushing by about 20% without over-magnifying its top displacement for this bushing-support coupling system. Application of the presented analytical modelling method can assist in the seismic optimization design of other equipment-support coupling systems in substations.

Nonlinear dynamic response analysis of a hybrid concrete‐filled steel tubular truss lightweight bridge under strong earthquakes

AbstractConcrete‐filled steel tubular (CFST) trusses have seen recent development and application in bridges found in mountainous regions with deep valleys, and especially in seismic zones. In this study, a hybrid CFST truss lightweight bridge was selected as the research object. This bridge is composited of CFST composite truss girders (superstructure) and CFST lattice piers (substructure). Two different finite element models (FEM) for nonlinear seismic response analysis, one is detailed model and the other is simplified model, were established. By comparing with the detailed model, the results of the shaking table test as well as the real bridge test, the simplified model was found to be accurate. Considering the CFST columns' edge strain, the most unfavorable input direction of horizontal ground motion was perpendicular to the connection line of the bearings at both ends of the main girder. Also, the simultaneous influence of vertical ground motion and horizontal ground motion needs to be taken into consideration. By increasing the intensity of input ground motion, the yielding order of CFST lattice piers and its effect on the seismic response were also discussed. Results indicated that the bridge was in the elastic stage for the designed seismic ground motion. After the CFST lattice piers reached the plastic stage, the displacement and in‐plane bending moment had larger amplification coefficients compared to the increase coefficient of the input ground motion, while had a much smaller axial force amplification coefficient. Moreover, the in‐plane bending moment had a larger amplification coefficient in high piers compared to short piers.

Seismic Analysis Model of Partially Concrete-Filled Steel Piers Considering Ultralow-Cycle Fatigue Crack Propagation

ABSTRACT Seismic performance of partially concrete-filled steel tube (PCFST) bridge piers is controlled by the coupled failure of ultralow-cycle fatigue (ULCF) and local instability of steel plates. An empirical formula was established for the plastic fracture displacement on average stress triaxiality of the crack intiation process, and the two-stage prediction model for the ULCF cracking of steel was improved. Furthermore, an empirical formula was established for the plastic strain amplification factor on the element size and the stress triaxiality of the coarse model. A complete modeling method was proposed for the seismic performance analysis model of PCFST piers considering ULCF cracking.

Characterization of Focal Mechanisms for Upper Crustal Distributed Seismicity in Aotearoa New Zealand

AbstractApplying distributed seismicity models for seismic hazard analysis requires postulating the styles of faulting and nodal planes for anticipated earthquakes. Here, we present a model describing focal mechanisms, or more specifically, strike, dip, and rake angles, for the ruptures of shallow (hypocentral depth ≤40 km) crustal earthquakes in Aotearoa New Zealand. This model is based on delineations of neotectonic domains and analysis of pre-existing datasets, including an active fault database, geological map-based fault datasets, the New Zealand Community Fault Model, and a regional moment tensor catalog. We demonstrate that the focal mechanism model is broadly consistent with the regional moment tensor catalog, with respect to spatial distributions of P and T axes and in terms of the Kagan angle. This characterization of focal mechanisms complements the distributed seismicity component of the New Zealand National Seismic Hazard Model 2022.

Analytical solution for seismic response of vertical shaft with primary and secondary linings under SH wave excitation

This paper presents a novel mechanical model for seismic response analysis of vertical shafts. The model is based on elastic foundation beam theory and simplifies the shaft linings as parallel Euler Bernoulli beams. Their interaction is simulated using uniformly distributed springs. The governing differential equation for shaft vibration is derived for SH wave excitation. The seismic input motion is applied to the primary lining by converting the free field displacement into harmonic form. The closed-form solutions for seismic response of both primary and secondary linings are obtained via the transfer function method. The accuracy of analytical solution is validated by comparing with finite element analysis results. Additionally, the impact of foundation stiffness, secondary lining thickness, shaft outer diameter, and relative stiffness between linings on seismic response are investigated in the parametric analysis. The analytical solutions of the seismic response analysis of vertical shafts indicates that the relative stiffness between linings significantly affects the secondary lining's peak bending moment. Furthermore, higher stiffness of the elastic connection layer between the two linings can effectively reduce the peak displacement response of the secondary lining.

A Simplified Finite Element Model for Seismic Analysis of a Single-Layer Reticulated Dome Coupled with an Air Duct System

Damage to nonstructural components, such as air ducts, in buildings during earthquakes, which are more fragile than single-layer reticulated domes, has a significant impact on the sustainability of the building’s functionality. To study the coupling effect and failure mode of a single-layer reticulated dome with an air duct system, then, simplified finite element models of air ducts and flange bolt joints were established and validated against the solid element model. Moreover, the simplified finite element models of support hangers were also built and validated against the existing experiment. Three kinds of support hanger layout schemes were studied to analyze the dynamic characteristics and seismic responses of a single-layer reticulated dome with an air duct system from earthquakes at different intensities. The results showed that the simplified finite element model can effectively simulate the coupling effect and failure mode of the single-layer reticulated dome with an air duct system. The coupling effect of the air duct system reduces the natural vibration frequency in the dome and increases the number of damaged members in the dome by strong earthquakes. The rate of falling air ducts with all the seismic support hangers is the highest compared to the two other support hanger layout schemes.

Stochastic-based vulnerability curves for the out-of-plane seismic safety assessment of URM walls

Earthquakes are a major cause of damage and human losses to the built environment, including cultural heritages, monumental buildings and historical centers. In the last decades, the seismic performance of buildings has received special attention due to the interest in the built heritage conservation and protection of human life, particularly with respect to masonry structures which have shown evidence of poor behavior once subjected to seismic loads. The present work contributes to the seismic safety assessment of the out-of-plane behavior of unreinforced masonry walls through a displacement-based approach, providing the capacity for different out-of-plane geometric indexes and its seismic response in different earthquake-prone regions. The analyses are conducted using a seismic probabilistic framework, considering the most common out-of-plane mechanisms, different material properties, various slenderness ratios, and a wide range of seismicity levels to cover the seismic hazard in Europe. The results presented can be useful for seismic safety assessment and to incorporate vulnerability models for seismic risk analysis.

Seismic fragility analysis of steel moment frames using machine learning models

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