Earthquake Engineering and Structural Dynamics

Voyagaki, Elia; Kloukinas, Panos; Dietz, Matt; Dihoru, Luiza; Horseman, Tony; Oddbjornsson, Olafur; Crewe, Adam J.; Taylor, Colin A.; Steer, Alan

doi: 10.1002/eqe.3100pmid: N/A

The complex dynamics of a quarter‐scale model of a graphite nuclear reactor core, representative of the second generation of British advanced gas‐cooled nuclear reactors, is investigated numerically and experimentally. Advanced gas‐cooled nuclear reactor cores are polygonal, multilayer, arrays of graphite bricks, with each brick allowed to rock by design relative to each other in accordance with the boundary conditions. A 35 000 DOF, nonlinear finite element model of the core created by Atkins Nuclear, was analysed on a high performance computing facility at the University of Bristol, and a corresponding 8 t physical model, equipped with 3200 data acquisition channels, was built and tested on the University of Bristol 6‐DOF shaking table. In this paper, the two models are subjected to a series of (1) synthetic earthquake and (2) idealised harmonic input motions. The experimental data are used to compare and verify the two models and explore the dynamics of the core. A kinematic model of the response is also developed based solely on geometric constraints. The results are presented in the form of response maps and graphs. Important conclusions are drawn as to the dynamics and earthquake response of such systems, which inform numerical model validation. It is found that contrary to the case of a small number of rocking blocks that exhibit highly complex response patterns, the behaviour of the model at hand is both smooth and repeatable. An analogy between the response of the core and that of dense granular matter exhibiting particle interlocking and dilatancy is highlighted.

Calvi, Gian Michele

doi: 10.1002/eqe.3101pmid: N/A

For several decades, seismologists and engineers have been struggling to perfect the shape of design spectra, analyzing recorded signals, and speculating on probabilities. This research effort produced several improvements, for example, suggesting to adopt more than one period to define a spectral shape or proposing different spectral shapes as a function of the return period of the design ground motion. The spectral shapes recommended in most modern codes are driven by considerations on uniform hazard; however, the basic assumption of adopting essentially three fundamental criteria, ie, constant acceleration at low periods, constant displacement at long periods, and constant velocity in an intermediate period range, has never been really questioned.

Calvi, G. Michele; Rodrigues, Daniela; Silva, Vitor

doi: 10.1002/eqe.3102pmid: N/A

The shape of design spectra, traditionally based on regions characterized by constant displacement, constant velocity, and constant acceleration, has been discussed from a conceptual point of view by Calvi (2018). In the same study, a formulation for the definition of the design spectra relying on four parameters was proposed. Predictive models are proposed herein to calculate these four parameters, conditional on magnitude and distance. These models were developed using a large number of recorded ground motions in Italy, and they allow defining combined spectral acceleration versus spectral displacement plots. Such design spectra are shown to reasonably interpolate the experimental data, resulting in acceleration and displacement demand that approximate the response spectra resulting from +1σ results obtained from recorded ground motions.

Mehrotra, Anjali; DeJong, Matthew J.

doi: 10.1002/eqe.3103pmid: N/A

Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.

Barbagallo, Francesca; Bosco, Melina; Marino, Edoardo M.; Rossi, Pier Paolo

doi: 10.1002/eqe.3105pmid: N/A

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.

Lu, Xinzheng; Tian, Yuan; Wang, Gang; Huang, Duruo

doi: 10.1002/eqe.3108pmid: N/A

Seismic damage simulation of buildings on a regional scale is important for loss estimation and disaster mitigation of cities. However, the interaction among densely distributed buildings in a city and the site, ie, the “site‐city interaction (SCI) effects,” is often neglected in most regional simulations. Yet, many studies have found that the SCI effects are very important in regional simulations containing a large number of tall buildings and underground structures. Therefore, this work proposed a numerical coupling scheme for nonlinear time history analysis of buildings on a regional scale considering the SCI effects. In this study, multiple‐degree‐of‐freedom models are used to represent different buildings above the ground, while an open source spectral element program, SPEED, is used for simulating wave propagation in underlying soil layers. The proposed numerical scheme is firstly validated through a shaking table test. Then, a detailed discussion on the SCI effects in a 3D basin is performed. Finally, a nonlinear time history analysis of buildings on a regional scale is performed using the Tsinghua University campus in Beijing as a case study. The Tsinghua University campus case results show that the SCI effects will reduce the seismic responses of most buildings. However, some buildings will suffer much more severe damage when the SCI effects are considered, which may depend on the input motions, site characteristics, and building configurations.

Ruiz‐García, Jorge; Miranda, Eduardo

doi: 10.1002/eqe.3107pmid: N/A

This short communication presents the assessment of seismic inelastic and elastic displacement demands computed from earthquake ground motions (EQGMs) recorded in Mexico City during the intermediate‐depth intraslab Puebla‐Morelos earthquake on 19 September 2017 (Mw = 7.1). Evaluation is conducted by means of peak elastic and inelastic displacement demand spectra, inelastic displacement ratio, CR, spectra, and generalized interstory drift spectra computed for selected recording stations located in different soil sites of Mexico City, including those located in areas of reported collapsed buildings. Results of this study confirm previous observations made from interplate (subduction) EQGMs that peak inelastic displacement demands are greater than corresponding elastic counterparts for short‐to‐medium period structures, while the opposite is true for medium‐to‐long period structures. Possible basin site effects were identified from generalized interstory drift spectra. It is also shown that an equation introduced in the literature to obtain estimates of CR developed from interplate EQGMs provides also a good estimate for mean CR computed from the intermediate‐depth intraslab EQGMs.