Search

The viscous-hysteretic hybrid (HVH) damper system recently introduced by one of the authors has a clear property that, when the hysteretic dampers with gap mechanism become active (stiffness element starts working), the acceleration of building frames with this damper system as a stopper attains large values in spite of the advantageous feature to prevent excessive deformation. It is therefore desired that both the maximum interstory drift and the maximum acceleration exhibit an acceptable value with appropriate compromise. The double impulse as a simplified version of one-cycle sine wave as a representative of the main part of near-fault ground motions can simulate the maximum interstory drifts properly. However, it cannot simulate the maximum accelerations due to its impulsive nature. In this case, the sine wave corresponding to the double impulse can play an important role in the reliable simulation of the maximum accelerations. Even in such circumstance, the analysis using the double impulse is important because it enables to obtain the critical timing of the input, i.e. the nonlinear resonant frequency of the sine wave without repetition. The investigations on the criticality of the sine wave corresponding to the critical double impulse show that the critical timing of the double impulse leads to the nonlinear resonant frequency of the sine wave in view of the maximum interstory drift, the maximum top acceleration and the maximum relative acceleration for the constant input acceleration and the constant input velocity except for some cases. It is demonstrated finally that the index in terms of the maximum interstory drift and the maximum acceleration can be introduced as an appropriate parameter for deriving the optimally compromised gap quantity of hysteretic dampers with gap mechanism for various input velocity levels and various hysteretic damper stiffness ratios.

The optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading is of great concern in the structural design of building structures. The research started around 1980 and many investigations have been conducted. A comprehensive review on this subject is made in this article. After the description of essential features of the optimal design problem of nonlinear building structures under earthquake ground motions, analysis types of optimization problems are explained and the significance of the dynamic pushover analysis is discussed from the viewpoint of analysis of limit states under earthquake ground motions of magnitude larger than the code-specified level. Then, the categorization by the response of frames and dampers was made. In this categorization, several subjects are discussed first: 1) Optimal design of bare nonlinear building frames under seismic loading, 2) Optimal design of nonlinear dampers for elastic building frames under seismic loading, 3) Optimal design of linear dampers for nonlinear building frames under seismic loading, 4) Optimal design of nonlinear building frames with specified nonlinear dampers under seismic loading, 5) Optimal design of nonlinear dampers for specified nonlinear building frames under seismic loading, 6) Simultaneous optimization of elastic-plastic building structures and passive dampers. Finally, the classification of researches in view of solution strategies is conducted for providing another viewpoint.

The critical responses are investigated for a high-rise building with a deformation-concentration seismic control system under double and multi impulses representing pulse-type and long-duration ground motions, respectively. The critical responses were studied for an elastic-plastic multi-degree-of-freedom (MDOF) shear building model under a double impulse and a multi impulse in the previous papers. However, it seems difficult to derive the critical response for a realistic three-dimensional (3-D) nonlinear frame model with a deformation-concentration seismic control system under such double and multi impulses. The criteria on the criticality of the double and multi impulses for the elastic-plastic MDOF shear building model derived in the previous research are extended to this realistic controlled 3-D frame model by regarding the sum of base story shear forces of both main and sub buildings as a key quantity. In the analysis, the concepts of “Double Impulse Pushover (DIP)” and “Multi Impulse Pushover (MIP)” introduced before are used effectively for clarifying the progressive performances for the increasing input level. The analyses of total input energy, frame hysteretic energy and damper dissipation energy are conducted and the criticality of the input derived based on the above-mentioned criteria is investigated in detail.

We revisit a unique building system including a base-isolation, building-connection hybrid control system. The base-isolation system withstands pulse-type earthquake ground motions effectively and the building-connection system resists long-duration earthquake ground motions efficiently. A simple smart critical response evaluation method without nonlinear time-history response analysis is proposed for this hybrid building system under near-fault ground motions. An analytical expression of the maximum elastic-plastic deformation of a damped bilinear hysteretic single-degree-of-freedom (SDOF) model under critical double impulse as a representative of pulse-type ground motions derived in our previous paper plays an important role in the development of the simple critical response evaluation method. A two-step transformation procedure into an SDOF model is proposed. The first step is the transformation of the main base-isolated building into an SDOF system and the second step is the reduction of the connecting dampers supported on a sub building to a damper with a sophisticated compensation factor on an assumed rigid wall. The evaluation of damping coefficients with the consideration of yielding of the base-isolation story is a key step in this paper. Different from the previous work, the equivalent damping coefficient is derived depending on the response range before and after yielding of the base-isolation story. This treatment enhances the accuracy of the proposed method. The accuracy and reliability of the proposed response evaluation method is demonstrated by the time-history response analysis of the multi-degree-of-freedom (MDOF) model.

This paper aims to develop a hysteretic–viscous hybrid (HVH) damper system for long-period pulse-type earthquake ground motions of large amplitude. Long-period pulse-type earthquake ground motions of large amplitude have been recorded recently (Northridge, 1994; Kumamoto, 2016). It is well-known that these ground motions could cause severe damage to high-rise and base-isolated buildings with long natural period. To mitigate the damage caused by such ground motion, a new viscous–hysteretic hybrid damper system is proposed here, which consists of a viscous damper with large stroke and a hysteretic damper including a gap mechanism. A double impulse is employed as a representative of long-period pulse-type earthquake ground motions of large amplitude and a closed-form maximum response to this double impulse is derived for an elastic–plastic SDOF system including the proposed HVH system. To reveal the effectiveness of the proposed HVH system, time-history response analyses are performed for an amplitude modulated double impulse and a recorded ground motion at Kumamoto (2016). The performance comparison with the previous dual hysteretic damper (DHD) system consisting of small-amplitude and large-amplitude hysteretic dampers in parallel is also conducted to investigate the effectiveness of the proposed HVH system.

A dynamic collapse criterion for elastic–plastic structures under near-fault ground motions is derived analytically by approximately transforming near-fault ground motions into double impulse and using an energy balance law. A negative post-yield stiffness is introduced to treat the P-delta effect in the single-degree-of-freedom (SDOF) model. The principal part of fling-step near-fault ground motions is modeled by a one-cycle sine wave and then a double impulse. The double impulse enables the efficient use of the energy approach in the derivation of compact expressions of complicated elastic–plastic responses of structures with the negative post-yield stiffness. In contrast to the previous work (Kojima and Takewaki, 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse. It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations. It is shown that discussions on several patterns of dynamic collapse behaviors introduced in the previous critical case are useful for deriving a boundary between the collapse and the non-collapse in the plane of the input velocity and the input frequency. The most important point to be remarked is that the critical state (Kojima and Takewaki, 2016b) corresponding to the non-linear resonance does not necessarily provide the minimum input velocity level with respect to arbitrary impulse timing. The validity of the proposed dynamic collapse criterion is examined by the numerical response analysis for structures under double impulses with collapse or non-collapse parameters.

While linear system identification (SI) has been developed extensively, research advancement in the field of non-linear hysteretic SI is not satisfactory. An innovative method is proposed in this paper for identification of hysteretic restoring-force characteristics of three-dimensional (3D) building structures with in-plane flexible floors. The hysteretic restoring-force characteristics of vertical structural frames in the 3D building structure are identified from the measured floor horizontal accelerations together with the hysteretic restoring-force characteristics of floors without the assumption of hysteresis types or a priori knowledge of restoring force characteristics. Fourier expansion is applied to the time-history responses of story shear forces in vertical frames and in-plane shear forces in horizontal frames (floors). A batch processing least-squares estimation method for measured data is shown to be applicable to the identification of the Fourier coefficients on the story shear forces in vertical structural frames and those on the in-plane shear forces in floors. The proposed method is simple and direct because only Fourier expansion and batch processing least-squares estimation are required. Numerical simulations with and without noise are conducted for investigating the accuracy and reliability of the proposed method. It is demonstrated that the proposed method can identify successfully the hysteretic restoring-force characteristics of plane frames in 3D building structures with in-plane flexible floors.

An innovative structural control system is proposed for high-rise buildings. A damping layer is provided between a stiff upper core frame suspended from the top of the main building and a stiff lower core frame connected to the building foundation. As the ratio of stiffness of both core frames to that of the main building becomes larger, the relative displacement in the damping layer (damper deformation) approaches to the top floor displacement of the main building. The large displacement of the top floor displacement of the main building is taken full advantage in the proposed control system as most of the total displacement of the main building results from the damper deformation instead of interstory drift. Transformation of the multi-degree-of-freedom (MDOF) model into the single-degree-of-freedom (SDOF) model enables a simplified but rather accurate response evaluation for pulse-type and long-duration earthquake ground motions. The results of the time history response analysis of buildings including this control system are presented for various recorded ground motions. Finally, the effectiveness of the proposed structural control system is discussed from the viewpoint of earthquake input energy.

In most building structures, floors with sufficient in-plane stiffness exist and an assumption of rigid in-plane stiffness is valid. However, in some building structures, an assumption of rigid in-plane stiffness does not hold. A method of system identification (SI) for physical parameters (stiffness, damping) is proposed for three-dimensional (3D) building structures with in-plane flexible floors. The stiffness and damping parameters of each vertical structural frame in the 3D building structure are identified from the measured floor horizontal accelerations together with the stiffness and damping parameters of each floor. It is shown that a batch processing least-squares estimation method for many discrete time-domain measured data enables the direct identification of both the stiffness and damping parameters of each vertical structural frame and the stiffness and damping parameters of each floor. The proposed method possesses an advantage that all stiffness and damping parameters of vertical frames and horizontal frames (floors) can be identified simultaneously without search iteration. The accuracy and reliability of the proposed method are made clear by numerical simulations for measured data without noise and measured data with noise. A method of noise elimination is proposed to enhance the identification accuracy. Finally, experiments using a shaking table are conducted for the accuracy investigation of the proposed identification method. It is confirmed that the proposed identification method possesses a reliable ability to identify the stiffness and damping parameters for 3D building structures with in-plane flexible floors.

The collapse-limit input velocity level of the critical double impulse simulating the principal part of near-fault ground motions is derived for an elastic-plastic structure with viscous damping and P-delta effect. The structural system is modeled by a bilinear hysteretic SDOF system with negative post-yield stiffness reflecting the P-delta effect which plays a key role in the collapse behavior. Since the critical timing of the second impulse in the double impulse has been proven as the zero-restoring force timing after the first impulse for the elastic-plastic SDOF system with viscous damping, that property is used again in this paper. It is shown that the collapse-limit input level of the critical double impulse can be obtained as a function of the post-yield stiffness and the damping ratio by using the energy balance law and the quadratic-function approximation of the damping force-deformation relation. The applicability of the collapse-limit level to actual recorded ground motions is investigated through the time-history response analysis for the stable models and the collapse models under two actual earthquake ground motions.

An equi-spaced consecutive impulse input is treated as a simplified representative for a long-duration earthquake ground motion. The key property of such input can be captured approximately by using harmonic waves. An approximate closed-form solution is derived for the elastic-plastic response of a two-degree-of-freedom (2DOF) system under the “critical multiple impulse input” based on some assumptions. The 2DOF system is assumed to consist of an elastic-perfectly plastic restoring-force characteristic in the first story and a linear elastic restoring-force characteristic in the second story. The fact that only the free vibration emerges under such multiple impulse input enables the utilization of the energy approach in the derivation of the explicit expression for a complicated elastic-plastic response. The critical timing of the impulses is found to correspond to the zero restoring-force timing in the first story. The validation and accuracy check of the proposed theory are conducted by implementing the response analysis to the corresponding sinusoidal input as a representative of the long-duration earthquake ground motion. It is also demonstrated that the proposed theory can be applied to a base-isolated building with hysteretic property in the base-isolation story regardless of the number of stories of superstructures.

The uncertainties in ground motions may result from several factors, e.g., (i) the fault rupture process, (ii) the wave propagation, (iii) the site amplification from the earthquake bedrock to the ground surface. The uncertainty in the fault rupture slip is taken as a main factor of uncertainties in the present paper and the critical fault rupture slip distribution causing the maximum structural response is found by using the stochastic Green's function method as a generator of ground motions. Then, a multi-degree-of-freedom (MDOF) building structure is introduced as a model structure and an optimal damper placement problem is discussed for the critical ground motion. The main topic in this paper is the simultaneous determination of the critical fault rupture slip distribution and the optimal damper placement. The sequential quadratic programming method is used in the problem of critical fault rupture slip distribution and a sensitivity-based method is introduced in the optimal damper placement problem. Furthermore, the robustness for the maximum interstory drift in MDOF building structures under the uncertainty in fault rupture slip distributions is presented for resilient building design by using the robustness function. Since the critical case leads to the most unfavorable structural response, the proposed method can provide structural designers with a promising tool for resilient building design.

It is known that, while the stochastic Green's function method is suitable for generating ground motions with short periods, the three-dimensional finite difference method (FDM) is appropriate for ground motions with rather long periods. In the previous research, the stochastic Green's function method was used for finding the critical earthquake ground motion for variable fault rupture slip (slip distribution and rupture front). However, it cannot be used for ground with irregularities and for wave component with rather long periods. In responding to this request, the FDM is used in this paper for finding the critical ground motion for structures with rather long natural period. Since the FDM is time-consuming, it seems unfavorable to use it in a simple sensitivity algorithm where an independent response sensitivity is calculated for many design parameters. To overcome this difficulty, the bi-cubic spline interpolation of uncertain parameter distributions (seismic moment distribution in this paper) and the response surface method for predicting the response surface from some sampling points are used effectively in this paper. The uncertainty parameter is the fault rupture slip distribution described in terms of seismic moments. It is found that the critical ground motion for structures with rather long natural period can be found effectively by the proposed method.

A new method for optimal viscous damper placement is proposed for elastic-plastic multi-degree-of-freedom (MDOF) structures subjected to the critical double impulse as a representative of near-fault ground motions. The double impulse consists of two impulses with different directions and the critical interval between those two impulses is characterized by the criterion on the maximum input energy that is expected to lead to the maximum deformation. The critical timing of the second impulse is the timing at which the sum of the restoring force and the damping force in the first story attains zero. The objective function and constraint in terms of the maximum interstory drift along the building height or the sum of the maximum interstory drifts in all stories are selected and the corresponding optimization algorithm based on time-history response analysis and sensitivity analysis is investigated. Since the objective function in terms of the sum of the maximum interstory drifts in all stories is superior to the objective function in terms of the maximum interstory drift along the building height, it is employed in this paper. A new concept of double impulse pushover (DIP) is proposed for determining the input velocity level of the critical double impulse. It is demonstrated that the combination of two algorithms, one for effective reduction of the overflowed maximum interstory drift via the concentrated allocation of dampers and the other for effective allocation of dampers via the use of stable objective function, is effective for finding a stable optimal damper placement.

An evaluation method of robustness of base-isolation building-connection hybrid controlled building structures is developed by introducing a measure for robustness (robustness function) and considering shallow and deep ground uncertainties. The earthquake ground-motion amplitude at the earthquake bedrock is evaluated by the Boore’s stochastic method including the fault rupture and the wave propagation into the earthquake bedrock. Then, the phase angle property at the earthquake bedrock is investigated by introducing the concept of phase difference, which is defined for each earthquake type. The ground-motion amplification in the shallow and deep ground is expressed by the one-dimensional wave propagation theory. The robustness of base-isolation building-connection hybrid controlled building structures is measured by use of the robustness function due to Ben-Haim (2006) and is evaluated by taking full advantage of the updated-reference-point method. It is shown that, as the total quantity of damping coefficients of connection dampers increases, the robustness for the deformation of the base-isolation story becomes larger without the drastic reduction of the robustness for the top acceleration.

A double impulse input is used as a substitute for near-fault earthquake ground motions. An explicit expression is derived on the maximum elastic–plastic response of a single-degree-of-freedom damped structure with bilinear hysteresis under the “critical double impulse input” which causes the maximum response for variable impulse interval with the input level kept constant. Owing to the existence of only the free vibration under the double impulse, the approach of energy balance for the kinetic energy, hysteretic and strain energies, and damping energy plays a crucial role for deriving the explicit expression on a complicated damped bilinear hysteretic response. It is shown that the critical elastic–plastic deformation and the critical impulse timing, the interval of two impulses, can be derived depending on the input level. The accuracy and reliability of the proposed simplified but smart methodology are investigated through the comparison with the results by the response analysis to the critical double impulse and the corresponding one-cycle sine wave as a representative for the near-fault earthquake ground motion.

The critical nonlinear response considering soil-structure interaction is investigated for a base-isolated building under a double impulse as a substitute for near-fault earthquake ground motions. The complicated model of the nonlinear base-isolated building considering soil-structure interaction is first modeled as a two-degree-of-freedom (2DOF) system (SDOF superstructure and base-isolation story) on a swaying-rocking spring-dashpot system. Then the 2DOF system on a swaying-rocking spring-dashpot system is transformed into an SDOF system on a swaying-rocking spring-dashpot system by neglecting the mass on the base-isolation story. Finally the SDOF system on a swaying-rocking spring-dashpot system is further transformed into an SDOF system by neglecting the mass and moment of inertia of the base mat. Since an explicit expression had been derived in the previous paper on the maximum elastic-plastic response of an SDOF damped bilinear hysteretic structure subjected to the “critical double impulse input” causing the maximum response for variable interval of impulses with the input level kept constant, this expression is applied to the finally transformed SDOF system. The transformation of structural viscous damping in different elements is another new aspect in this paper. The reliability and accuracy of the proposed simplification methodology are investigated by comparing with the results by the time-history response analysis under the critical double impulse and the one-cycle sine wave as a representative of the main part of the near-fault earthquake ground motion.

An innovative hybrid control building system of base-isolation and building-connection has been proposed in the previous study. This system has two advantages, (i) to resist an impulsive earthquake input through the base-isolation system and (ii) to withstand a long-duration earthquake input through the building-connection system. A simple response evaluation method without the need of non-linear time–history response analysis is proposed here for this hybrid building system under a long-period and long-duration ground motion. An analytical expression is derived in the plastic deformation of an elastic–perfectly plastic single-degree-of-freedom (SDOF) model with viscous damping under the multi-impulse, which is the representative of long-period and long-duration ground motions. A transformation procedure of a base-isolation building-connection hybrid structural system into an SDOF model is proposed by introducing two steps, one is the reduction of the main base-isolated building to an SDOF system, and the other is the reduction of the connecting oil dampers supported on a free-wall to an oil damper with a newly introduced compensation factor on a rigid wall. Application of the analytical expression of the plastic deformation to the reduced SDOF model including the compensation factor on the connecting oil dampers enables the development of a simplified, but rather accurate response evaluation method. The time–history response analysis of the multi-degree-of-freedom model and the comparison with the proposed simplified formula make clear the accuracy and reliability of the proposed simplified response evaluation method.

A system identification problem is investigated for high-rise buildings to identify the story stiffnesses of a shear-bending model (SB model). In the previously proposed stiffness identification method due to the present authors, the shear and bending stiffnesses of the SB model were identified by means of the subspace and inverse-mode methods. The lowest mode of horizontal displacements and floor rotation angles of the objective building was identified first by using measured data of both horizontal and rotational accelerations via the subspace method. Taking into account the resolution in the measurement of floor rotation angles in lower stories, floor rotation angles in all stories were predicted from the floor rotation angle at the top floor. However, it was difficult to obtain the bending stiffnesses reliably in the previous method. In this paper, to overcome the difficulty in the stiffness identification method using the SB model, a statistical model-updating approach is proposed, where the probability distribution of floor rotation angles in the lowest mode is obtained for the identified SB model, and a conditional probability problem is applied by providing additional measured data on floor rotation angle. The proposed stiffness identification method is useful for the structural health monitoring of high-rise buildings. For investigation of the validity of the proposed stiffness identification method, a 10-story plane-building frame is examined under micro-tremor.