Modal Analysis of Nonlinear Hysteretic Structures for Seismic Motions

Characteristics of the strong ground motions from the 6 April 2009 L’Aquila earthquake, Italy

A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element (SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space. To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built on unbounded soil.

On January 1, 2024, a Mw 7.6 earthquake occurred on the Noto Peninsula in Japan, with a focal depth of 9.6 kilometers. To validate the effectiveness of using a finite fault hybrid slip model to simulate strong ground motion events, this study utilized strong motion records from the KiK-net station network of the National Research Institute for Earth Science and Disaster Resilience (NIED) in Japan. Initially, 29 fundamental stations were selected, and 13 of these stations were chosen for further study using the finite fault method. Constrained by the geometric parameters of the initial model from the strong motion inversion, a hybrid slip distribution model (HSM) was established based on the stochastic finite fault model and semi-empirical relationships between source parameters. This model accurately reflects the spatial and temporal characteristics of the source rupture, and its results are comparable to those obtained by the United States Geological Survey (USGS) using GNSS and other long-period effect data. Additionally, using the dynamic corner frequency-based stochastic ground motion synthesis method (EXSIM), a comparative study was conducted on the pseudo-acceleration response spectra (PSA) of the hybrid slip model, the strong motion inversion model, and the source rupture model provided by USGS at the selected stations. These were then compared with the response spectra of actual station records. It was found that all three models showed good fitting results, and in the short-period range, the simulated values of the HSM were closer to the actual records. Finally, the relative error mean and variance between the HSM and actual records’ PSA at different frequencies were calculated for 29 stations. It reveals that they still had good fitting results. Overall, the findings demonstrate that even without relying on extensive station data, the hybrid slip model efficiently and accurately simulated high-frequency strong ground motions near the fault with a damping ratio of 5%, verifying the reliability and applicability of this method.

Numerical simulations of earthquake damage on buildings require the definition of a reliable and appropriate seismic input (e.g., acceleration time histories and/or response spectra) in order to validate the accuracy of structural models in reproducing the observed level of damage – or no damage – associated with a particular earthquake. However, for sites that are not located close to active seismic stations, the definition of the ground motion that would have likely been recorded during an earthquake is not a trivial task.In this paper, we present the results of a case study where the seismic input at the sites of construction of three modern unreinforced masonry buildings caused by the Emilia May 29, 2012 M6.0 earthquake has been recreated following three different methods involving natural, artificial, and deconvolved accelerograms. The differences in the results are compared and contrasted highlighting the intrinsic limitations of the three different approaches while addressing an appropriate use of the seismic input when assessing the seismic performance of the three buildings.

Seismically induced stresses and stability of soil media

The earthquake of April 6th, 2009 in the L’Aquila area is one of the largest seismic events of the last years in Italy. The event, that caused significant damage in a large area of the Abruzzo region (cental Italy) and site amplification phenomena which were recorded even at large distances from the epicentre. After the emergency period, a detailed study of the surface effects was necessary for the post-earthquake reconstruction, but in a way it should be carried out rapidly enough to give instructions to urban planners, codes to public administrators and information to engineers. A team of surveyors were trained to collect field information such as geologic and geomorphologic features and geotechnical or geophysical information. The seismic inputs, for the numerical analyses, were provided, and the collected information were analyzed with the aid of dynamic codes to calculate the possible local site effects. The results are presented as acceleration response spectra, amplification coefficients (FA, FV and FH) and microzonation maps, aimed to urban planning and project design. In particular the more dangerous areas, affected by the higher amplification effects, were identified. Finally a comparison between the results obtained by the numerical analyses and the results derived from an experimental field analysis, measuring both earthquake weak motion and ambient noise, were performed. In this paper we present the results for one of the most severely damaged area (up to IX-X MCS), the Paganica–Tempera–Onna-San Gregorio area, located 6 to 10 km east of the April 6th main shock.

In seismic engineering, the earthquake-induced ground motion is generally represented in the form of pseudo-acceleration or displacement response spectra. There are, however, situations in which the response spectrum is not considered appropriate, and a fully dynamic analysis is required. In this case, the most effective approach is to define artificial spectrum-compatible stationary accelerograms, which are generated to match the target elastic response spectrum. So a Power Spectral Density (PSD) function is derived from the response spectrum. However, the above approach possesses the drawback that the artificial accelerograms do not manifest the variability in time and in frequency observed from the analysis of real earthquakes. Indeed, the recorded accelerograms can be considered sample of a fully non-stationary process. In this study a procedure based on the analysis of a set of accelerograms recorded in a chosen site to take into account their time and frequency variability is described. In particular the generation of artificial fully non-stationary accelerograms is performed in three steps. In the first step the spectrum-compatible PSD function, in the hypothesis of stationary excitations, is derived. In the second step the spectrum-compatible Evolutionary Power Spectral Density (EPSD) function is obtained by an iterative procedure to improve the match with the target response spectrum starting from the PSD function, once a time-frequency modulating function is chosen. In the third step the artificial accelerograms are generated by the well-known Shinozuka and Jan (J Sound Vib 25:111–128, 1972) formula and deterministic analyses can be performed to evaluate the structural response. Once the EPSD spectrum-compatible function is derived, a method recently proposed by the authors (Muscolino and Alderucci in Probab Eng Mech 40:75–89, 2015), is adopted to evaluate the EPSD response function of linear structural systems subjected to fully non-stationary excitations by very handy explicit closed-form.

Nonlinear seismic response of seabed with terrain variation and seawater-seabed coupling

This paper describes the numerical simulation of two dynamic centrifuge tests on reduced scale models of shallow tunnels in dry sand, carried out using both an advanced bounding surface plasticity constitutive soil model and a simple Mohr–Coulomb elastic-perfectly plastic model with embedded nonlinear and hysteretic behaviour. The predictive capabilities of the two constitutive models are assessed by comparing numerical predictions and experimental data in terms of accelerations at several positions in the model, and bending moment and hoop forces in the lining. Computed and recorded accelerations match well, and a quite good agreement is achieved also in terms of dynamic bending moments in the lining, while numerical and experimental values of the hoop force differ significantly with one another. The influence of the contact assumption between the tunnel and the soil is investigated by comparing the experimental data and the numerical results obtained with different interface conditions with the analytical solutions. The overall performance of the two models is very similar indicating that at least for dry sand, where shear-volumetric coupling is less relevant, even a simple model can provide an adequate representation of soil behaviour under dynamic conditions.

In this paper, new formulations to calculate equivalent damping ratios used in equivalent linear analysis of seismic-isolated structures, specifically isolated with lead-rubber bearings (LRBs), are proposed. These formulations are capable of incorporating the variation in LRB hysteretic behavior due to reduced bearing strength as a function of lead core heating. To quantify the accuracy of the proposed equations in predicting the maximum isolator displacements (MIDs), MIDs obtained from an extensive number of nonlinear time history analyses (NTHAs) were compared with predicted ones. NTHAs were conducted with two sets of near-field ground motions recorded at different soil conditions. It was found that different formulations are needed to calculate the equivalent LRB damping ratios for the two considered ground motion sets. It was also found that the proposed equations result in highly accurate MID estimations, regardless of isolator characteristics, soil properties, or seismicity levels.

We estimate pseudo acceleration response spectra with 5% damping (Sa) for the great Michoacán earthquake at 22 lake bed sites (in addition to five sites where the event was well recorded) in the valley of Mexico. The method used consists of (a) estimation of Fourier acceleration amplitude spectra (FAS) at the sites via observed FAS at Ciudad Universitaria (CU) and compiled spectral ratios of these sites with respect to CU obtained from recorded earthquakes, (b) estimation of the duration of strong ground motion during the Michoacán earthquake at the sites, and (c) application of random vibration theory to predict Sa. A constant duration of 71 sec at all sites is found to be satisfactory. The main uncertainties in estimated Sa come from (a) possible nonlinear behaviour of the clay during the great earthquake (the spectral ratios used in the computation are mostly for moderate earthquakes, when the clay behaves linearly), and (b) variations in site's spectral ratios due to randomness and/or its dependence on earthquake characteristics which are presently unknown. Assuming that the nonlinear behaviour was neglegible and the spectral ratios estimated from one or few recordings are representative, we find (a) Sa ≥ 600 gals over a wide area of the lake bed zone, (b) Sa ≥ 1g at 14 out of the 27 sites, (c) regions of high Sa in the center of the city and east of CU, and (d) a good correlation between severe damage and regions with Sa ≥ 800 gals. Although in general our results agree with reported effects of the earthquake, because of the uncertainties mentioned above direct use of the computed response spectra for code or design purposes is discouraged.

MOCS-based optimum design of TMD and FTMD for tall buildings under near-field earthquakes including SSI effects

A probabilistic seismic hazard analysis (PSHA) determines the probability rate of exceeding of various levels of ground motion in a specified period of time, in a given area. On the other hand, the neo-deterministic seismic hazard assessment (NDSHA) is based on modeling techniques, developed from physical knowledge of the seismic source process and of the propagation of seismic waves, which can realistically simulate the ground motion due to an earthquake by means of synthetic seismograms. The NDSHA confirms that peak ground acceleration values are larger than those given by the PSHA in areas where large earthquakes are observed and in areas identified as prone to large earthquakes, such as in the case of the city of Catania (Italy). The city of Catania, located on the eastern part of Sicily, is one of the most seismically active areas of Italy. The Val di Noto earthquake of January 11, 1693 is considered one of the biggest earthquakes which occurred in Italy. Site response analyses have been developed for a group of 3 test sites in the city of Catania (Italy). On the sites are localised some strategic buildings to upgrade against seismic risk. The analysis of seismic ground response at the sites was conducted using a numerical method, which is developed in three main phases: the definition of the geometric, geological and geotechnical model of the subsurface, the definition of the seismic input (synthetic or recorded), the choice of one or more computer codes to use and process the results. The reconstruction of the geological and geotechnical model of the subsurface has highlighted a morphology quite irregular especially with regard to the covers. One-dimensional local site response analyses have been performed assuming that all geologic boundaries are horizontal and the response of soil deposits is predominantly caused by waves propagating vertically from the underlying bedrock. Equivalent linear analysis using EERA code has been performed in this study. One of the targets of the paper is the development of measures for the seismic retrofitting of buildings.Seismic retrofitting and/or improving have to be definitely considered a multidisciplinary subject, which depends in fact on many factors, such as: local site effects and the dynamic interaction between the foundation soil and the structure. The accurate investigation on the structure and the surrounding soil is the first fundamental step for a realistic evaluation of the structure seismic performance.

The determination of Design Ground Motion time history (or response spectra) is the primary and critical step to derive correct Seismic Design Inputs for a Nuclear Power Plant (NPP) design. Historically Design Ground Motion (design SSE input) for a NPP was determined by early version procedure provided in RG 1.60. It was based on a theory of deterministic approach; the resulting ground motion is given in acceleration response spectra located at free surface of a site. As a transition point, 1997 was the year where new procedure was developed and recommended in RG 1.165 based on the new theory of SSE ground motion probabilistic approach. RG 1.165 was authorized for application on all new NPPs’ design after 1997. With the advancing of PSHA approach, RG 1.165 was withdrawn and replaced with new RG 1.208 in 2008. RG 1.208 established an effective way through the similar probabilistic approach used in RG 1.165 by improving PSHA method. Both RG1.165 results and RG 1.208 results are focused on addressing site-specific design, its Ground Motion Response Spectra (GMRS) and Ground Motion Time History (converted from GMRS) are used as design inputs to specific Nuclear Island (NI) seismic design. To accomplish a Standard Design Certification, the RG 1.60 DRS is used to develop the Certified Seismic Design Response Spectra (CSDRS) by modifying control points on original RG 1.60 curves to broaden the spectra in higher frequency range. In reality, CSDRS serves as a good approach to define DRS and Design Ground Motion Time History for standard design of new NPPs in current timeframe, hence envelop the site-specific GMRS given in RG 1.208. In this paper, through the comparison of above US NRC regulatory requirements and Chinese regulatory requirements, gives recommendations on the determination of Design Ground Motion Response Spectra (or Time History), which serves as the basis for deriving seismic design inputs at required specific location (e.g. the bottom of NI foundation level) for potential “GEN III & Plus” plants in China.

A significant research effort has now been devoted towards the development of more complete or rigorously correct nonlinear soil models, appropriate for use in the solution of earthquake or offshore storm wave loading problems. The primary intent of this research has been to establish soil models which correctly account for nonlinear, hysteretic behavior of soil at higher levels of shearing strain or relative shearing stress (ratio of imposed stress to failure stress). Need for the development of these nonlinear soil models arose from the observation that soils subjected to cyclic loading tests in the laboratory behaved in a nonlinear, hysteretic manner (Hardin and Drnevich, 1972a), the realization that equivalent linear analyses sometimes led to inaccurate ground response predictions (Joyner and Chen, 1975; Finn, et al, 1978). the availability of computer codes which efficiently handled, nonlinear ground response problems (Streeter, et al, 1974; Joyner and Chen, 1975; Taylor and Larkin, 1978)