Nicos Makris

Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures

In this paper the efficiency of various dissipative mechanisms to protect structures from pulse-type and near-source ground motions is examined. Physically realizable cycloidal pulses are introduced, and their resemblance to recorded near-source ground motions is illustrated. The study uncovers the coherent component of some near-source acceleration records, and the shaking potential of these records is examined. It is found that the response of structures with relatively low isolation periods is substantially affected by the high-frequency fluctuations that override the long duration pulse. Therefore, the concept of seismic isolation is beneficial even for motions that contain a long duration pulse which generates most of the unusually large recorded displacements and velocities. Dissipation forces of the plastic (friction) type are very efficient in reducing displacement demands although occasionally they are responsible for substantial permanent displacements. It is found that the benefits by hysteretic dissipation are nearly indifferent to the level of the yield displacement of the hysteretic mechanism and that they depend primarily on the level of the plastic (friction) force. The study concludes that a combination of relatively low friction and viscous forces is attractive since base displacements are substantially reduced without appreciably increasing base shears and superstructure accelerations. Copyright

Nonlinear response of single piles under lateral inertial and seismic loads

Abstract A macroscopic model that consists of distributed hysteretic springs and frequency dependent -pots is utilized to model the lateral soil reaction and a practical method based on one-dimensional finite element formulation is developed to compute the nonlinear response of single piles under dynamic lateral loads. The model is physically motivated, adequate for cohesive and cohesionless soils, and involves standard geotechnical parameters. Only two parameters have to be calibrated by fitting experimental data. Hysteretic and radiation damping are modeled realistically within the practical range of amplitudes and frequencies. The model is calibrated and validated against five well instrumented full-scale experiments and typical values for the range of the model-parameters are provided. Subsequently, the developed model is utilized to study the nonlinear seismic response of single piles. Finally, the developed method and the calibrated model are used to predict the inertial and seismic response of one of the piles used in the foundation of the Ohba bridge near Tokyo, Japan.

Estimating Time Scales and Length Scales in Pulselike Earthquake Acceleration Records with Wavelet Analysis

This paper is motivated from the need to extract the characteristic time and length scales of strong pulselike ground motions with a mathematically formal, objective, and easily reproducible procedure. The investigation uses wavelet analysis to identify and extract energetic acceleration pulses (not velocity pulses) together with their associated frequency and amplitude. The processing of acceleration records with wavelet analysis is capable of extracting pulses that are not detected visually in the acceleration records, yet they become coherent and distinguishable in the velocity records. Most importantly, the proposed analysis is capable of extracting shorter dura- tion distinguishable pulses (not necessarily of random character) that override the longer near-source pulses that are of significant engineering interest. The study ela- borates on the role of the weighting function in the definition of the wavelet transform and concludes that longer pulses are captured when less suppressive weighting func- tions are implemented in the wavelet transform. We examine the capability of several popular symmetric and antisymmetric wavelets to locally match the energetic accel- eration pulse. We conclude that the exercise to identify the best-matching wavelet shall incorporate, in addition to the standard translation and dilation-contraction of the wavelet transform, a phase modulation together with a manipulation of the oscil- latory character (addition of cycles) of the wavelet. This need leads to the extension of the wavelet transform to a more general wavelet transform during which the mother wavelet is subjected to the four above-mentioned modulations. The mathematical de- finition and effectiveness of this extended wavelet transform is presented in this paper. The objective identification of the pulse period, amplitude, phase, and oscillatory character of pulselike ground motions with the extended wavelet transform introduced in this paper makes possible the immediate use of closed-form expressions published by other investigators to estimate the peak response of elastic and inelastic systems. Online Material: Parameters that maximize the extended wavelet transform of 183 selected records.

Time‐domain viscoelastic analysis of earth structures

In this paper two causal models that approximate the nearly frequency-independent cyclic behaviour of soils are analysed in detail. The study was motivated by the need to conduct time-domain viscoelastic analysis on soil structures without adopting the ad hoc assumption of Rayleigh damping. First, the causal hysteretic model is introduced in which its imaginary part is frequency independent the same way that is the imaginary part of the popular non-causal constant hysteretic model. The adoption of an imaginary part that is frequency independent even at the zero-frequency limit, in conjunction with the condition that the proposed model should be causal, yields a real part that is frequency dependent and singular at zero frequency. The paper shows that the causal hysteretic model, although pathological at the static limit, is the mathematical connection between the non-causal constant hysteretic model and the physically realizable Biot model. The mathematical structure of the two causal models is examined and it is shown that the causal hysteretic model is precisely the high-frequency limit of the Biot model. Although both models have a closed-form time-domain representation, only the Biot model is suitable for a time-domain viscoelastic analysis with commercially available computer software. The paper demonstrates that the simplest, causal and physically realizable linear hysteretic model that can approximate the cyclic behaviour of soil is the Biot model. The proposed study elucidates how the dynamic analysis of soil structures can be conducted rigorously in terms of the viscoelastic properties of the soil material and not with the ad hoc Rayleigh damping approach which occasionally has been criticized that tends to overdamp the higher vibration modes. The study concludes that under pulse-type motions the Rayleigh damping approximation tends to overestimate displacements because of the inappropriate viscous type of dissipation that is imposed. Under longer motions that induce several cycles, the concept of equivalent viscous damping is more appropriate and the Rayleigh damping approximation results to a response that is comparable to the response computed with a rigorous time-domain viscoelastic finite element analysis. Copyright

TIME‐DOMAIN ANALYSIS OF LINEAR HYSTERETIC DAMPING

Two linear-hysteretic-damping models that provide energy dissipation independent of the deformation frequency, are studied in this paper: a hysteretic Kelvin element and a hysteretic Maxwell element. Both models use the Hilbert transform and yield integro-differential equations for the equations of motion of structures when real-valued signals are utilized in the formulation. It is shown that the use of analytic (complex-valued) signals allows the transformation of these integro-differential equations into differential equations with analytic input signals and complex-valued coefficients. These differential equations show both stable and unstable poles. A technique for the solution of these differential equations is presented; it consists of a conventional modal decomposition of the state-space equations and the integration of the differential equations forward in time for the modal co-ordinates associated with stable poles, and backwards in time for the modal co-ordinates associated with unstable poles. Some numerical examples are presented to illustrate the characteristics of the models and the proposed analysis technique.

The Role of the Rotational Inertia on the Seismic Resistance of Free‐Standing Rocking Columns and Articulated Frames

Abstract A half century ago, Housner (1963) explained that there is a safety margin between uplifting and overturning of slender, free‐standing columns and that as the size of the column or the frequency of the excitation increases, this safety margin increases appreciably to the extent that large, free‐standing columns enjoy ample seismic stability. This paper revisits the important implications of this postuplift dynamic stability and explains that the enhanced seismic stability originates from the difficulty of mobilizing the rotational inertia of the free‐standing column. As the size of the column increases, the seismic resistance (rotational inertia) increases with the square of the column size, whereas the seismic demand (overturning moment) increases linearly with size. Accordingly, in theory, a slender, free‐standing column can survive any ground shaking provided that the column is sufficiently large, because a quadratic term eventually dominates over a linear term. The same result applies to the articulated rocking frame given that its dynamic rocking response is identical to the rocking response of a single free‐standing column with the same slenderness but larger size.

Dimensional Response Analysis of Multistory Regular Steel MRF Subjected to Pulselike Earthquake Ground Motions

An alternative and efficient procedure to estimate the maximum inelastic roof displacement and the maximum inelastic interstorey drift ratio along the height of regular multi-storey steel MRF subjected to pulse-like ground motions is proposed. The method and the normalized response quantities emerge from formal dimensional analysis which makes use of the distinct time scale and length scale that characterize the most energetic component of the ground shaking. Such time and length scales emerge naturally from the distinguishable pulses which dominate a wide class of strong earthquake records and can be formally extracted with validated mathematical models published in literature. The proposed method is liberated from the maximum displacement of the elastic single-degree-of-freedom structure since the self similar master curve which results from dimensional analysis involves solely the shear strength and yield roof displacement of the inelastic multi-degree-of-freedom system in association with the duration and acceleration amplitude of the dominant pulse. The estimated inelastic response quantities are in superior agreement with the results from nonlinear time history analysis than any inelastic response estimation published previously.

Are Some Top-Heavy Structures More Stable?

AbstractThis technical note investigates the dynamic response and stability of a rocking frame that consists of two identical free-standing slender columns capped with a freely supported rigid beam. Part of the motivation for this study is the emerging seismic design concept of allowing framing systems to uplift and rock along their plane in order to limit bending moments and shear forces— together with the need to stress that the rocking frame is more stable the more heavy is its cap-beam, a finding that may have significant implications in the prefabricated bridge technology. In this technical note, a direct approach is followed after taking dynamic force and moment equilibrium of the components of the rocking frame, and the remarkable results obtained in the past with a variational formulation (by the same authors) is confirmed—that the dynamics response of the rocking frame is identical to the rocking response of a solitary, free-standing column with the same slenderness, yet with larger size, which p...

Electrorheological damper with annular ducts for seismic protection applications

This paper presents the design, analysis, testing and modeling of an electrorheological (ER) fluid damper developed for vibration and seismic protection of civil structures. The damper consists of a main cylinder and a piston rod that pushes an ER fluid through a stationary annular duct. The behavior of the damper can be approximated with Hagen - Poiseuille flow theory. The basic equations that describe the fluid flow across an annular duct are derived. Experimental results on the damper response with and without the presence of electric field are presented. As the rate of deformation increases, viscous stresses prevail over field-induced yield stresses and a smaller fraction of the total damper force can be controlled. Simple physically motivated phenomenological models are considered to approximate the damper response with and without the presence of electric field. Subsequently, the performance of a multilayer neural network constructed and trained by an efficient algorithm known as the Dependence Identification Algorithm is examined to predict the response of the electrorheological damper. A combination of a simple phenomenological model and a neural network is then proposed as a practical tool to approximate the nonlinear and velocity-dependent damper response.

Three-dimensional constitutive viscoelastic laws with fractional order time derivatives

In this article the three-dimensional behavior of constitutive models containing fractional order time derivatives in their strain and stress operators is investigated. Assuming isotropic viscoelastic behavior, it is shown that when the material is incompressible, then the one-dimensional constitutive law calibrated either from shear or elongation tests can be directly extended in three dimensions, and the order of fractional differentiation is the same in all deformation patterns. When the material is viscoelastically compressible, the constitutive law in elongation involves additional orders of fractional differentiation that do not appear in the constitutive law in shear. In the special case where the material is elastically compressible, the constitutive laws during elongation and shear are different; however the order of fractional differentiation remains the same. It is shown that for an elastically compressible material, the four-parameter fractional solid—the rubbery, transition, and glassy model,...