Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are reached: (i) The viscoelastic behavior of the ground may be simply characterized by performing the creep (or the relaxation) test on a specimen of the ground at the given site; (ii) The number of zero crossing of the absolute acceleration at the free field that for the classical TK model is \(\infty \) for a true white noise acceleration, remains finite for the proposed model.     

A simplified method to determine seismic responses of reinforced concrete moment resisting building frames under influence of soil–structure interaction

As the Iranian seismic code does not address the soil–structure interaction (SSI) explicitly, the effects of SSI on RC-MRFs are studied using the direct method. Four types of structures on three types of soils, with and without the soil interaction, are modeled and subjected to different earthquake records. The results led to a criterion indicating that considering SSI in seismic design, for buildings higher than three and seven stories on soil with V_s<175 m/s and 175<V_s<375 m/s, respectively, is essential. A simplified procedure has been presented, on the basis that lateral displacement increments could be applied to the fixed-base models using simple factors.     

The near-field method for dynamic analysis of structures on soft soils including inelastic soil–structure interaction

The problem of soil–structure interaction analysis with the direct method is studied. The direct method consists of explicitly modeling the surrounding soil to bedrock and the structure resting on the soil. For the soil medium, usually the traditional equivalent linear method with a reduced shear modulus and an increased damping ratio for the soil is used. However, this method does not work in the vicinity of foundation where the soil behavior is highly nonlinear because of presence of large strains. This research proposes a modified equivalent linear method with a further reduction of the soil shear modulus in the near-field of foundation that results in validity of using the equivalent linear method throughout. For regular short, intermediate and tall structures resting on such soft soils, a series of dynamic time-history analysis is implemented using earthquake records scaled to a sample design spectrum and the nonlinear structural responses are compared for different assumptions of soil behavior including the elasto-plastic Mohr–Coulomb, the traditional equivalent linear, and the proposed modified equivalent linear method. This analysis validates the proposed method.     

Ant colony optimization of tuned mass dampers for earthquake oscillations of high-rise structures including soil–structure interaction

This paper investigates the optimized parameters for tuned mass dampers (TMDs) to decrease the earthquake vibrations of tall buildings; involving soil–structure interaction (SSI) effects. The time domain analysis based on Newmark method is employed in this study. To illustrate the results, Tabas and Kobe earthquakes data are applied to the model, and ant colony optimization (ACO) method is utilized to obtain the best parameters for TMD. The TMD mass, damping coefficient and spring stiffness are assumed as design variables, and the objective is to reduce both the maximum displacement and acceleration of stories. It is shown that how the ACO can be effectively applied to design the optimum TMD device. It is also indicated that the soil type greatly affects the TMD optimized parameters and the time response of structures. This study helps the researchers to better understanding of earthquake vibrations, and leads the designers to achieve the optimized TMD for high-rise buildings.     

Idealisation of soil–structure system to determine inelastic seismic response of mid-rise building frames

In this study, a novel and enhanced soil–structure model is developed adopting the direct analysis method using FLAC 2D software to simulate the complex dynamic soil–structure interaction and treat the behaviour of both soil and structure with equal rigour simultaneously. To have a better judgment on the inelastic structural response, three types of mid-rise moment resisting building frames, including 5, 10, and 15 storey buildings are selected in conjunction with three soil types with the shear wave velocities less than 600 m/s, representing soil classes C_e, D_e and E_e, according to Australian Standards. The above mentioned frames have been analysed under two different boundary conditions: (i) fixed-base (no soil–structure interaction) and (ii) flexible-base (considering soil–structure interaction). The results of the analyses in terms of structural displacements and drifts for the above mentioned boundary conditions have been compared and discussed. It is concluded that considering dynamic soil–structure interaction effects in seismic design of moment resisting building frames resting on soil classes D_e and E_e is essential.     

Hybrid simulation of a partial-strength steel–concrete composite moment-resisting frame endowed with hysteretic replaceable beam splices

This paper deals with the seismic response assessment of a steel–concrete moment-resisting frame (MRF) equipped with special dissipative replaceable components (DRCs): the dissipative replaceable beam splices (DRBeS), which combine large energy dissipation with ease of replacement. The evaluation of the full potential of DRBeS requires a system-level investigation, that is, a six-story MRF, whereby the hysteretic effects of beam splices partial-strength joints are considered on the global response of the structural system. Therefore, an OpenSees finite element (FE) frame model, based on previous experimental campaigns with cyclic displacements on partial-strength joints, and a Matlab model validated on OpenSees, were used for a more complex experimental activity via hybrid simulation (HS). The aim of the simulations was twofold: (i) to increase knowledge of the non-linear behaviour of steel-concrete composite partial-strength MRFs; and (ii) to study the effectiveness of the DRBeS components for increasing the recovery of functionality after a major seismic event. Therefore, to appreciate the performance of the partial-strength MRF at damage limitation (DL), significant damage (SD) and near collapse (NC) within the performance-based earthquake engineering (PBEE) approach, HSs were carried out. In such instances, the ground floor was physically tested at full scale in the laboratory and the remainder of the structure was numerically simulated. Relevant results showed that the DRBeS were capable of dissipating a significant amount of hysteretic energy and of protecting the non-dissipative parts of partial-strength joints and the overall structure with an ease of replacement.     

Dynamic responses of structure–soil–structure systems with an extension of the equivalent linear soil modeling

A three-dimensional problem of cross interaction of adjacent structures through the underlying soil under seismic ground motion is investigated. The story shears and lateral relative displacements (drifts) are the targets of the computations. These are calculated using a detailed modeling of soil, the foundations and the two adjacent structures. An equivalent linear behavior is assumed for the soil by introducing reduced mechanical properties consistent with the level of ground shaking for the free-field soil. Then a distinctive soil zone (the near-field soil) is recognized in the vicinity of the foundations where the peak shear strain under the combined effect of a severe earthquake and the presence of structures is much larger than the strain threshold up to which the soil can be modeled as an equivalent linear medium. It is shown that it is still possible to use an equivalent linear behavior for the near-field soil if its shear modulus is further reduced with a factor depending on the dynamic properties of the adjacent structures, the near-field soil, and the design earthquake. Variations of the dynamic responses of different adjacent structures with their clear distances are also discussed.     

A parallel finite–infinite element model for two-dimensional soil–structure interaction problems

A parallel soil–structure interaction (SSI) model is presented for applications on distributed computer systems. Substructring method is applied to the SSI system and a coupled finite–infinite element based parallel computer program is developed. In the SSI system, infinite elements are used to represent the soil which extends to infinity. In this case, a large finite element mesh is required to define the near field for reliable predictions. The resulting large-scale problems are solved on distributed computer systems in this study. The domain is represented by separated substructures and an interface. The number of substructures are determined by the available processors in the parallel platform. To avoid the formation of large interface equations, smaller interface equations are distributed to processors while substructure contributions are performed. This saves a lot of memory storage and computational effort. Direct solution techniques are used for the solution of interface and substructure equation systems. The program is investigated through some example problems. The example problems exposed the need for solving large-scale problems in order to reach better results. The results of the example problems demonstrated the benefits of the parallel SSI algorithm.     

A model for the seismic analysis of a periodic viaduct when considering the pile–soil–structure interaction

In this study, a new model is developed for the aseismic design of a periodic viaduct when the pile–soil–structure interaction is considered. To account for the influence of the pile–soil–structure interaction, a wavenumber domain boundary element method (WDBEM) model for the periodic pile row supporting the viaduct is developed using the sequence Fourier transform as well as the boundary element method for the elastic medium. By using the WDBEM model for the pile row, the transfer matrices for the beams and piers, the joint conditions at the beam–beam–pier (BBP) junction as well as the periodicity condition for the viaduct, the wavenumber domain response of the periodic viaduct to spatially harmonic waves is determined. Based on the wavenumber domain response of the viaduct, the space-domain response of the viaduct to an arbitrary seismic wave can be obtained by invoking the inverse sequence Fourier transform method. Numerical results show that when the periodic viaduct is exposed to the spatially harmonic wave, resonances may occur at the bounding frequencies of the passbands of the characteristic waves of the viaduct. Also, it is found that the coincidence between the traveling seismic wave and characteristic waves of the viaduct will generate additional resonant frequencies located in passbands of the characteristic waves.     

A decision support system for post-earthquake reliability assessment of structures subjected to aftershocks: an application to L��Aquila earthquake, 2009

The post-earthquake assessment of existing structures can be further complicated by the progressive damage induced by the occurrence of a sequence of aftershocks. This work presents a simple methodology for the calculation of the probability of exceeding a certain limit state in a given interval of time. The time-decaying mean daily rate of occurrence of significant aftershock events is modeled by employing a site-specific aftershock model for the L??Aquila 2009 aftershock sequence (central Italy). The number of aftershock events occurring in a given interval of time elapsed after the main event is modeled using a non-homogenous Poisson model. An equivalent single-degree of freedom structure with cyclic stiffness degradation is used in order to evaluate the progressive damage caused by a sequence of aftershock events. Given the time history of the main-shock and the residual damage caused by it, the probability of exceeding a set of discrete limit states in a given interval of time is calculated. Of particular importance is the time-variant probability of exceeding the limit state in a 24-h (a day) interval of time which can be used as a proxy for the life-safety considerations regarding the re-occupancy of the structure and to complement the results of visual inspections for prioritizing the emergency operations. The method presented herein can also be used in an adaptive manner, progressively conditioned on the time-histories of aftershock events following the main-shock and on the corresponding residual damage caused by them.     

Use of global ductility for design of structure–foundation systems

This paper investigates the applicability of global ductility in the conventional design procedure of structure–foundation systems under earthquake excitation. For a bilinear elastoplastic model, an equivalent ductility factor for the combined structure and foundation is derived, which can be used in conjunction with the enlarged period and increased damping due to soil–structure interaction (SSI) to determine the design strength. A geometric transformation rule for predicting the ductility demand developed in the structure alone from that experienced by the interacting system is also derived, without the need of computing the rigid-body motion of the foundation. To validate this practical approach for assessing both inelastic strengths as well as ductility demands, a number of numerical results for different system parameters and earthquake excitations are provided. The effects of principal parameters involved are also examined.     

Translation,torsion, and wave excitation of a building during soil–structure interaction excited by an earthquake SH pulse

A two-dimensional (2-D) model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed. The building, the foundation, and the soil have different physical properties. The building is assumed to be linear, but the soil and the foundation can experience nonlinear deformations. While the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy—and thus less energy is available for the excitation of the building—the nonlinear response in the soil and the foundation does not signficantly alter the nature of excitation of the base of the building. It is noted that the response of a building can be approximated by translation and torsion of the base for excitation by long, strong motion waves.     

Asymptotic behavior of an n-species stochastic Gilpin–Ayala cooperative model

An n-species stochastic Gilpin–Ayala cooperative model was investigated in this study. The Lyapunov function and the M-matrix method were applied to study the stability of the solutions. Sufficient conditions for the existence of a global positive solution of the Gilpin–Ayala cooperative model were established. Certain asymptotically stable results of a global positive solution of the cooperative model and its domain of attraction were estimated. That main objective of this study is to provide corrections for errors in some theorems given in the work of Lian et al. (2007). The errors of Theorems 2, 3, 5, and 6 from the published work appeared in the parameters θ _i and p _ii .     

A simplified 3 D.O.F. model of A FEM model for seismic analysis of a silo containing elastic material accounting for soil–structure interaction

The purpose of this study is the evaluation of dynamic behavior induced by seismic activity on a silo system, containing bulk material, with a soil foundation. The interaction effects between the silo and bulk material, as well as the effects produced between the foundation of the silo and the soil, were taken into account. Proposed simplified approximation, as well as the finite model, were used for analysis. The results, from the presented approximation, were compared with a more rigorous obtainment method. Initially, the produced simplified approximation, with elastic material assumption for the grain, could determine the pressures on the dynamic material along with displacements along the height of the silo wall and base shear force, etc., with remarkable precision. Some comparisons, via a change of soil and/or foundation conditions, were also made regarding the seismic pressure of the dynamic material pressure, displacement and base shear forces for both squat and slender silos. Comparing the analytical predictions to results from the numerical simulations produced good results. It can be concluded that the model can be used effectively to perform a broad suite of parametric studies, not only at the design stage but also as a reliable tool for predicting system behavior under the limit state of the system. The results and comprehensive analysis show that displacement effects and base shear forces generally decreased when soil was softer; however, soil structure interaction (SSI) did not have any considerable effects on squat silos and therefore need not be taken into practice.     

Equivalent linear substructure approximation of soil–foundation–structure interaction: model presentation and validation

An equivalent linear substructure approximation of the soil–foundation–structure interaction is proposed in this paper. Based on the inherent linearity of the approach, the solution of the structural and the soil domain is obtained simultaneously, incorporating the effects of the primary and secondary soil nonlinearities. The proposed approximation is established theoretically and then validated against centrifuge benchmark soil–foundation–structure interaction tests. The equivalent linear substructure approximation is proved to simulate efficiently the effects of the nonlinear soil behavior on the soil–foundation–structure system under a strong earthquake ground motion.     

Seismogenic model of earthquakes in groups in tectonic block and analysis for some features of earthquake precursory field

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