Further development of a multimodal pushover analysis procedure for seismic assessment of bridges

An improvement is first suggested to the modal pushover analysis (MPA) procedure for bridges initially proposed by the writers (Earthquake Engng Struct. Dyn. 2006; 35 (11):1269–1293), the key idea being that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The proposed MPA procedure is then verified by applying it to two actual bridges. The first structure is the Krystallopigi bridge, a 638 m‐long multi‐span bridge, with significant curvature in plan, unequal pier heights, and different types of pier‐to‐deck connections. The second structure is a 100 m‐long three‐span overpass bridge, typical in modern motorway construction in Europe, which, although ostensibly a regular structure, is found to exhibit a rather unsymmetric response in the transverse direction, mainly due to torsional irregularity. The bridges are assessed using response spectrum, ‘standard’ pushover (SPA), and MPA, and finally using non‐linear response history analysis (NL‐RHA) for a number of spectrum‐compatible motions. The MPA provided a good estimate of the maximum inelastic deck displacement for several earthquake intensities. The SPA on the other hand could not predict well the inelastic deck displacements of bridges wherever the contribution of the first mode to the response of the bridge was relatively low. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic control of flexible rocking structures using inerters

Allowing flexible structures to uplift and rock during earthquakes can significantly reduce the force demands and residual displacements. However, such structures are still susceptible to large deformations and accelerations that can compromise their functionality. In this paper, we examine the dynamic response of elastic rocking oscillators and suggest that their lateral drifts and accelerations can be limited effectively by using inerter devices. To this end, we offer a detailed examination of the effects of structural flexibility on the efficiency of the proposed system. The analytical expressions governing the motion of deformable structures with base uplift are revisited to incorporate the effects of the supplemental rotational inertia. The proposed model is then used to study the structural demands of flexible rocking structures under coherent pulses as well as noncoherent real pulse-like ground motions. Our results show that combining rocking with inerters can be an efficient strategy to control the deformation and acceleration demands in uplifting flexible systems.     

Freestanding block overturning fragilities: Numerical simulation and experimental validation

The overturning fragilities of symmetric and asymmetric freestanding blocks, ranging in height from 0.54 to 3.6 m and with height‐to‐width ratios ranging from 2.1 to 6.6, are determined numerically. A probabilistic formulation regularizes the overturning responses when exposed to earthquake‐like random‐vibration waveforms. The peak amplitude of the forcing excitation (peak ground acceleration or PGA) is parameterized as a function of the block size, block shape, overturning probability, and either the PGA normalized peak ground velocity (PGV/PGA), spectral acceleration at 1 s (S_a(1)/PGA), or spectral acceleration at 2 s (S_a(2)/PGA). These later intensity measures are correlated with the duration of the predominant acceleration pulse. The overturning fragilities are compared with shake table experiments using blocks ranging in height from ～0.2 to 1.2 m and with height‐to‐width ratios ranging from ～2 to 10. Excitations utilized in the shake table experiments include recordings of the 1979 Imperial Valley, 1985 Michoacan, 1999 Duzce, 1999 Chi‐Chi, and 2002 Denali Earthquakes along with synthetic waveforms. The overturning fragilities accurately represent the overturning responses of blocks with simple basal contact conditions. Objects with multiple rocking points, such as precariously balanced rocks, are more fragile than predicted. Nondestructive tilting tests are used to account for blocks with complex basal contact conditions, demonstrating that these blocks overturn similarly to more slender blocks with simple contact conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

Response analysis of rigid structures rocking on viscoelastic foundation

In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

大跨桥梁振动控制的杠杆主动多重调谐质量阻尼器策略

提出了适用于控制大跨桥梁风致振动的杠杆式主动多重调谐质量阻尼器（LT-AMTMD）控制策略.利用建立的LT-AMTMD结构系统的动力放大系数,评价了LT-AMTMD的性能.数值结果表明,驱动器置于质量块处的LT-AMTMD比驱动器置于其它位置的LT-AMTMD更加有效.驱动器置于质量块处的LT-AMTMD可以根据实际需要,通过改变支撑位置来调节弹簧的静伸长,而且保持其性能不变（包括冲程）.数值结果还表明,驱动器置于质量块处的LT-AMTMD可以明显地提高LT-MTMD的性能,而且比单个杠杆式主动调谐质量阻尼器（LT-ATMD）更加有效.     

Enhancing resilience of highway bridges through seismic retrofit

The present study evaluates seismic resilience of highway bridges that are important components of highway transportation systems. To mitigate losses incurred from bridge damage during seismic events, bridge retrofit strategies are selected such that the retrofit not only enhances bridge seismic performance but also improves resilience of the system consisting of these bridges. To obtain results specific to a bridge, a reinforced concrete bridge in the Los Angeles region is analyzed. This bridge was severely damaged during the Northridge earthquake because of shear failure of one bridge pier. Seismic vulnerability model of the bridge is developed through finite element analysis under a suite of time histories that represent regional seismic hazard. Obtained bridge vulnerability model is combined with appropriate loss and recovery models to calculate seismic resilience of the bridge. Impact of retrofit on seismic resilience is observed by applying suitable retrofit strategy to the bridge assuming its undamaged condition prior to the Northridge event. Difference in resilience observed before and after bridge retrofit signified the effectiveness of seismic retrofit. The applied retrofit technique is also found to be cost‐effective through a cost‐benefit analysis. First order second moment reliability analysis is performed, and a tornado diagram is developed to identify major uncertain input parameters to which seismic resilience is most sensitive. Statistical analysis of resilience obtained through random sampling of major uncertain input parameters revealed that the uncertain nature of seismic resilience can be characterized with a normal distribution, the standard deviation of which represents the uncertainty in seismic resilience. Copyright © 2013 John Wiley & Sons, Ltd.     

Centrifuge modeling of rocking‐isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil‐footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking‐isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self‐centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

Shake table tests of unattached,asymmetric, dual‐body systems

Systems of unattached, or freestanding, structures are highly vulnerable to damage and/or collapse during an earthquake, as evidenced during numerous past events. This class of structural system includes statue–pedestal systems, multidrum columns, radiation shields, unreinforced masonry walls, and other mechanical and electrical equipment. While a number of studies have analyzed the response of the single rocking block, very few have tested the response of multiple block systems subjected to earthquakes. Therefore, this paper details an extensive shake table testing campaign in which the seismic response of a pair of stiff, unattached blocks, herein referred to as a dual‐body system, was evaluated. Experimental variables include the geometry, including asymmetry, of both top (tower) and bottom (pedestal) bodies, input motion, and the coefficient of friction beneath the system. Furthermore, the tower structures were tested both in dual‐body configurations as well as in single‐body configurations allowing an understanding of the effect of the pedestal. The tests indicate that the presence of a pedestal increases the likelihood of collapse and amplitude of rocking demands, in general. However, certain geometric and interface combinations yield a more stable tower in a dual‐body configuration compared to a single‐body configuration, because of the dependence of the pedestal response on the geometry of the tower. Furthermore, a low‐friction interface beneath the pedestal reduces demands on the tower. However, this low‐friction interface may still transfer long‐period contributions of the input motion to the tower, which may be detrimental to its response. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamics of rocking podium structures

A rocking podium structure is a class of structures consisting of a superstructure placed on top of a rigid slab supported by free‐standing columns. The free‐standing columns respond to sufficiently strong ground motion excitation by uplifting and rocking. Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements. Such ‘soft‐story’ system runs counter to the modern seismic design philosophy but has been used to construct several hundred buildings in countries of the former USSR following Polyakov's rule‐of‐thumb guidelines: (i) that the superstructure behave as a rigid body and (ii) that the maximum lateral displacement of the rocking podium frame be estimated using elastic earthquake displacement response spectra. The objectives of this paper are to present a dynamic model for analysis of the in‐plane seismic response of rocking podium structures and to investigate if Polyakov's rule‐of‐thumb guidelines are adequate for the design of such structures. Examination of the rocking podium structure response to analytical pulse and recorded ground motion excitations shows that the rocking podium structures are stable and that Polyakov's rule‐of‐thumb guidelines produce generally conservative designs. Copyright © 2017 John Wiley & Sons, Ltd.