Bidirectional Shaking Research Articles

Estimating structural response to bidirectional seismic excitation using spectrum compatible motions: Performance of a pair of companion spectra

AbstractBidirectional analyses covering a range of incidence angles for several records are essential yet challenging for routine design. Recent studies have shown that the response to bidirectional shaking may be estimated per straightforward unidirectional analysis in the most preferred orientation in conjunction with the orthogonal combination rules, and this can also remove the need for various incidence angles. Further, it is well known that the mean response can be estimated with reduced dispersion using fewer spectrum‐compatible records. Combining the advantages of both, a pair of companion spectra independent of period and orientation has recently been developed. While the basis of the companion spectra is established therein from a sound mathematical perspective, the applicability of the proposed spectra to real structures may be revisited, especially to structures sensitive to bidirectional interaction, before recommending the companion spectra for practical design. To achieve this end, following a brief scrutiny of the companion spectra, the performance of the same is critically examined for idealized SDoF analogues and real structures such as bridge piers representative of SDoF systems and buildings with asymmetry using single storey and multistorey models (MDoF systems). The results show that the response of the real structures to bidirectional seismic loading can be reasonably estimated with reduced dispersion using fewer records compatible with the pair of the companion spectra. As such, the critical response parameters may be computed by actual bidirectional analyses or by combining responses to unidirectional analyses under fewer spectrum compatible records. Hence, the pair of companion spectra that can be used as “target” to independently match two components of a chosen record is useful for practical design.

Influence of bidirectional shaking on pore water pressure generation for liquefaction triggering evaluation

Influence of bidirectional shaking on pore water pressure generation for liquefaction triggering evaluation

Seismic safety of RC piers with parameter uncertainties: Assessing dimensionless response using Bayesian linear regression

Both maximum and residual deformations are essential for seismic safety during and following strong earthquakes, especially in the near field. These parameters are often calculated per unidirectional analysis, albeit bidirectional analysis may be carried out for important systems with the availability of growing computational power. However, a pressing challenge in earthquake engineering that continues to exist in the face of several uncertainties is to represent these response statistics – essentially with wide dispersion - in an expressive and effective format. The present paper aims to represent the maximum and residual deformation to unidirectional and bidirectional shaking in a rational format, even when uncertainties in ground motion and structural characteristics are prevalent. To this end, a bridge pier with uncertain material parameters is subjected to a wide range of stochastically simulated near-field motions with forward-directive signature, and the responses are computed to unidirectional and bidirectional shaking. In an attempt to develop predictive models, the responses are regressed first in terms ofprimary parameterscharacterizing structural material and ground motions. Next, by standard principles of mechanics, the response is recast in a dimensionless and orientationally consistent format in terms ofderived parameters. This reduces the number of independent variables yet connotes a sound basis of mechanics. The predictive model in terms of derived dimensionless parameters is further extended in the Bayesian framework to improve the predictive model in a probabilistic sense.

Shaking table test to investigate the size effect on the seismic response of a low-cost friction pendulum system

To enhance the seismic resilience of reinforced concrete (RC) bridge piers, a novel friction pendulum system was developed. It consisted of a friction pendulum and a spherical sliding surface that were constructed from conventional steel and concrete. In comparison to commercial isolators, the complex spherical shape was realised using a three-dimensional printer to fabricate an acrylic glass mold, which allowed a significant cost savings in production. The system was distinguished by stable oscillation and a significant reduction in response accelerations on the flat surface. The inclined part acted as a restoring force that limited the residual displacement. However, these properties were confirmed experimentally using only small specimens. To characterise the fundamental properties of the system, a bidirectional shaking table test was performed in this study to investigate the size effect on the seismic performance of the proposed system. The test results demonstrate that the excellent performance in reducing the response acceleration and residual displacement is independent of the specimen size. In addition to the dependency of the friction coefficient on the sliding velocity and axial pressure, the impact force was observed to increase with the superstructure weight. Furthermore, a simplified method for estimating the maximum and residual displacements of the proposed system is presented.

Effects of site response on ground motion directionality based on KiK-net records and numerical analysis

The orientation variability of earthquake ground motions (i.e., GM directionality) is an important engineering characteristic in the seismic design of structures. The GM directionality is believed to be mainly related to source and site contributions. This paper investigated the effect of site response on the change of GM directionality from the borehole depth to the ground surface. Distribution of the range for orientation variability level at both borehole and surface was presented for different intensity measures of 3006 records from downhole arrays in the KiK-net database. It was observed that both the maximum direction orientation of intensity measures and the ratio at various orientations may change significantly from depth to surface, and it is dependent on the specific intensity measures and site class. The numerical analysis of soil column considering bi-directional shaking was demonstrated to have a good ability to capture the influence of site response on the GM directionality. Thereafter, some preliminary insights into the linear and nonlinear site response effects on the GM directionality were provided. The azimuthal variation associated with the predominant period of the input borehole motion is an important factor that results in the change of GM directionality at the surface.

Bond-slip at anchorage under unidirectional and bidirectional seismic excitation: Search for an efficient mathematical model

Reinforcement anchorage slip can significantly contribute to the seismic response of bridge columns, especially to residual deformation. For a reliable numerical model of slip action, the present study evaluates three advanced models, each founded on distinct principles: (a) a macroscopic model (M−I), (b) a microscopic model (M−II), and (c) a mixed model that employed micro-model material properties derived from a macro-model (M−III). The performance of each model under unidirectional shaking has been first validated. The M−I cannot account for bidirectional loading, and as such, the performance of the M−II and M−III has, for the first time, been rigorously examined against the two-component shake table test results. Beginning with the simplified pulses, the responses of representative bridge columns are computed to unidirectional and bidirectional shaking for several near-fault motions. The M−I, M−II, and M−III are fairly similar in mimicking the slip action for unidirectional loading. Also, the M−II and M−III can closely represent the responses to bidirectional shaking. A simple extension of the M−I is proposed to capture the effects of bidirectional loading. The performance of the M−I (extended), M−II, and M−III are shown similar from the viewpoint of representing (i) the seismic fragilities, (ii) the uncertainties of the influential parameters, and (iii) the consequences of a sequence of motions. The detailed scrutiny of a range of models helps select the most appropriate scheme in a specific design context. On the other hand, the less-rigourous model, viz., M−I with the proposed extension, can be used within the limitations of commercial software and can prove useful in routine design for bidirectional seismic action.

Response analysis of single pile embedded in saturated sand under bidirectional cyclic loading

In this study, the dynamic responses of a single pile in liquefiable sand under bidirectional loading are investigated using fully coupled three-dimensional nonlinear finite element analyses. A multi-surface plasticity model is adopted to simulate the liquefiable sand behaviour. The analysis procedures elaborate the bidirectional shaking patterns of 2-D linear, circular, and oval shape simultaneously. Results reveal that compared to the unidirectional loading, the bidirectional loading reduces the soil liquefaction resistance and increases the depth of liquefied soil layer. The results also showed that the phase difference between orthogonal components of base excitation and the frequency content of the input motion have a significant impact on the dynamic responses of soil and pile. In addition, an increase in the phase difference reduces the excess pore water pressure and the thickness of liquefied layer, and delays the liquefaction occurrence. Moreover, the maximum pile bending moment and its location correspond to the dominance of either inertia or kinematic interaction forces, which are primarily influenced by the frequency content of input motion.

Bidirectional effect of earthquake on low-rise RC frames with and without the consideration of In-plane effect of unreinforced masonry infill

Low rise RC frames make up the majority of residential structures built in Nepal. They are created in accordance with the requirements outlined in the Nepal Building Code, particularly the mandatory rule of thumb. Only the bare frame model is taken into consideration while analyzing and designing the majority of reinforced concrete structures in Nepal's urban and semi-urban areas. The infill walls' additional impact is often completely disregarded. Furthermore, there are no separate guidelines and standards set by Nepal Building codes for considering the impact of infill masonry during the analysis. Hence, in this study, reinforced concrete frame structures that commonly represent Nepalese low-rise RC frames is subjected to bidirectional (XY) shaking. Four types of models are considered and for each model, two cases are taken: those with and those without taking into account the in-plane effect of unreinforced masonry infill. The infills’ in-plane impact is modeled using a macro modeling approach. The response parameters under investigation are column rebar strain ductility and roof displacement. The results of the analysis clearly indicate that, when the infills’ in-plane effect is taken into account, both the roof displacement and the strain ductility demand of the column are greatly reduced as compared to the situation where it is not. Furthermore, it is obvious from the analytical fragility curves produced for the bare frame and infill models that the structure's vulnerability is exaggerated when the in-plane impact of infill is ignored.

Estimating seismic response to bidirectional excitation per unidirectional analysis: A reevaluation for motions with fling-step using SDOF systems

Within the context of near-fault motions with fling-step signature, the present paper reevaluates the applicability of a straightforward alternative to estimate the response to bidirectional shaking per unidirectional analysis. The method originally evolved for motions with forward-directivity, uses unidirectional analysis in a single incidence angle. The performance of the method is examined using reinforced concrete (RC) bridge piers as the representative single-degree-of-freedom (SDOF) oscillators. Synthetic fling has been introduced to two horizontal components of processed (base-line corrected and filtered) strong motions. It has been shown that the response to bidirectional excitation can be closely estimated by means of a unidirectional analysis using the ground motion components rotated to the most preferred orientation. Existence of the least preferred orientation in which the unidirectional analysis results in the maximum difference from the bidirectional analysis appears to reinforce the development. For a ground motion pair, these orientations can be identified in advance through characteristic ground motion parameters, viz., energetic length and characteristic intensity for peak and cumulative demand, respectively. The usefulness of the said orientations to estimate the Park-Ang damage index is also established. The efficacy of the simple methodology has also been demonstrated through fragility analysis. The straightforward method can hence be used in the near-fault regime regardless of the ground motion characteristics.

Evolution of a 3D model for free-standing rigid blocks and its behavior under base excitations

Highly nonlinear behavior of slender rigid blocks subjected to base excitations is intended to be explored for a 3D prism. To this end, a physical model (PM) capable of handling the intricate dynamics and of viewing the motion of a rigid body during rocking/ overturning has been developed. Limited case studies show satisfactory performance of the PM to represent dynamics of such blocks both in unidirectional and bidirectional excitations. Subsequently, the dynamics of the 3D prism has been studied under trigonometric pulses. Interestingly, it appears that, under bidirectional shaking, the body may rotate about its own longitudinal axis and, due to this spin, the body may ‘walk’ from its original position even when sufficient friction at the interface prevents sliding. This residual displacement of the body under no sliding condition could not be recognized from 2D analysis. Using principles of dimensional analysis, self-similarity in response for complex nonlinear motions of the rocking oscillators has been established. This follows a comparative account on overturning spectra for 2D and 3D motions constructed in non-dimensional formats. A prognosis to chaos is uncovered from a scrutiny of long-term behavior of rocking oscillators in 3D using a set of non-dimensional parameters.

Shaking Table Test on the Seismic Response of Buried Oil and Gas Pipelines under the Bidirectional Nonuniform Seismic Excitation

This paper studies the seismic response of buried oil and gas pipelines under the bidirectional nonuniform excitation. Based on the bidirectional shaking table array test, the loading and testing scheme is designed and developed, analyzing the strain response of the buried oil and gas pipeline under the bidirectional uniform and nonuniform seismic excitation, as well as the acceleration response and displacement response characteristics of the pipeline and the surrounding soil body and their change rule by the test. The test proves to show that the developed bidirectional laminar shear continuum model soil box can meet the requirements of the bidirectional nonuniform seismic excitation and continuous laminar shear deformation of the soil. The peak strains of the pipeline in axial and bending caused by nonuniform excitation are larger than those of the pipeline under uniform excitation, the degree of unevenness in the distribution along the axial direction is greater, and the strain curves are large in the middle and small at both ends along the axial direction of the pipe. The acceleration responses of the pipeline and the soil body under the bidirectional nonuniform excitation are larger than those under the uniform excitation. The acceleration response of both the pipe and the soil under the nonuniform excitation is larger than that under the uniform excitation, and the differences are shown in the transverse and axial directions, the peak acceleration response of the soil body under the nonuniform excitation is about three times that of the transverse direction, and more peak points appear in the axial and transverse acceleration responses of the pipe under the nonuniform excitation as the loading level increases, the peak displacement response of the soil body increases gradually with the height, but the fluctuation range of the peak displacement of the soil body nearby the pipe is larger. The soil displacement curve starts to smooth out when the loading level reaches 1.0 g, and the axial displacement decreases, which indicates that the interaction between the pipe and soil is more intense and the relative motion between the pipe and soil is more obvious under the nonuniform excitation, and the soil is more likely to be damaged and enter the nonlinear stage. Therefore, it is necessary to analyze and design the seismic performance of buried pipes considering the nonuniform seismic excitation.

Characterization of ground motion intensity for the seismic fragility assessment of plan-irregular RC buildings

The identification of ground motion intensity measures (IMs) that are characterized by virtues such as efficiency, sufficiency, scaling robustness and hazard computability, has been the subject of extensive research over the past several years. In the process, there have evolved, numerous non-structure specific as well as structure specific descriptors of ground shaking severity. Most of the studies that investigated the optimality of such descriptors were, however, restricted to the seismic response of single or multi-storey planar frame buildings under unidirectional excitation. The study herein aims to examine, the efficiency and sufficiency of a wide spectrum of IMs, in predicting the maximum interstorey drift demands on plan-irregular RC moment frame buildings subjected to bi-directional ground motion. This is accomplished through a cloud analysis-based framework that integrates nonlinear response history analysis and statistical regression analysis. Further, the use of scalar bi-directional shaking intensity measures (BSIMs) derived from a vector of intensities corresponding to each horizontal component of ground motion using popular combination schemes such as geometric averaging, arithmetic averaging, SRSS and use of envelope values, is examined from the perspective of their ability to predict drift demands. Observations from the study reveal that IMs based on the geometric averaging of spectral ordinates over a range of periods are superior to the other descriptors considered, in terms of the aforementioned attributes and that combining the intensities of the two orthogonal components by geometric averaging leads to an optimal BSIM that could be used in place of vector IMs. The heteroscedasticity in the maximum interstorey drift response under different levels of the BSIM is further investigated using a Multiple Stripe Analysis framework. The optimal BSIM is observed to perform reasonably well at all target intensity levels, making it an excellent candidate to base fragility and vulnerability functions upon.

Estimating Seismic Response of RC Piers under Unidirectional and Bidirectional Shaking: A Mechanics-Based Approach

Estimating seismic response of reinforced concrete (RC) structures under bidirectional excitation covering admissible incidence angles is computationally challenging and time-consuming for routine design. Further, such responses are widely scattered because of inherent variability in the characteristics of real records, especially owing to the degradation of RC members under cyclic loading. Hence, to obviate the complexity and tedium of the task, this paper suggests an approach to making an advance estimate of response under both unidirectional and bidirectional shaking for all incidence angles. To this end, response of a RC bridge pier has been computed under a set of near-fault and far-fault records. Important response indices (peak deformation and hysteretic energy) have been presented in nondimensional Π-terms choosing simple structural parameters (yield force and yield displacement) and ground motion characteristics (peak ground acceleration, root mean square acceleration, and mean period of ground motion). Representation of responses in dimensionless form reveals a shape-similar pattern. A regression model developed using these nondimensional Π-terms has been found to perform reasonably well in the statistical sense and hence can be used in practice.

Bidirectional shaking table tests of a low‐cost friction sliding system with flat‐inclined surfaces

SummaryA novel low‐cost friction sliding system for bidirectional excitation is developed to improve the seismic performance of reinforced concrete (RC) bridge piers. The sliding system is a spherical prototype developed by combining a central flat surface with an inclined spherical segment, characterized by stable oscillation and a large reduction in response accelerations on the flat surface. The inclined part provides a restoring force that limits the residual displacements of the system. Conventional steel and concrete are employed to construct a flat‐inclined spherical surface atop an RC pier. The seismic forces are dissipated through the frictions generated during the sliding movements; hence, the seismic resilience of bridges can be ensured with a low‐cost design solution. The proposed system is fabricated utilizing a mold created by a three‐dimensional printer, which facilitates the use of conventional concrete to construct spherical shapes. The concrete surface is lubricated with a resin material to prevent abrasion from multiple input ground motions. To demonstrate the effectiveness of the system, bidirectional shaking table tests are conducted in the longitudinal and transverse directions of a scaled bridge model. The effect of the inclination angle and the flat surface size is investigated. The results demonstrate a large decrease in response acceleration when the system exhibits circular sliding displacement. Furthermore, the inclination angle that generates the smallest residual displacement is identified experimentally.

Developing a laboratory facility to assess friction coefficients of standing samples

The numerical representation of the dynamic response of art works is the most reliable instrument to predict their seismic safety. Their adoption, however, require the knowledge of the effective mechanical properties of the artifacts and their restraint conditions. Namely, the amount of friction arising between standing art works and their supports largely affects the quality of their collapse and, therefore, the choice of the model to adopt in the analysis. In this work a facility for assessing the dynamic contact behaviour of marble sample standing on different supports has been investigated. The facility consists of a dynamic test to perform through the bidirectional shaking table at the Disaster Resilience Simulation Laboratory at the Politecnico di Torino. The friction coefficient has been found from the dynamic test by comparing the acceleration registered at the load cell, which is related to the reaction of the sample, and one measured at the shaking table surface. The obtained values of friction coefficient have been related to the velocity of the adopted input. A preliminary test on a single concrete sample has been performed to check the proposed procedure, by considering three different loading conditions: one of them is the acceleration history of a real ground motion, while the other two have a constant amplitude and a constant frequency, respectively.

Centrifuge shaking table tests on 4 × 4 pile groups in liquefiable ground

A series of centrifuge shaking table model tests are conducted on 4 × 4 pile groups in liquefiable ground in this study, achieving horizontal–vertical bidirectional shaking in centrifuge tests on piles for the first time. The dynamic distribution of forces on piles within the pile groups is analysed, showing the internal piles to be subjected to greater bending moment compared with external piles, the mechanism of which is discussed. The roles of superstructure–pile inertial interaction and soil–pile kinematic interaction in the seismic response of the piles within the pile groups are investigated through cross-correlation analysis between pile bending moment, soil displacement, and structure acceleration time histories and by comparing the test results on pile groups with and without superstructures. Soil–pile kinematic interaction is shown to have a dominant effect on the seismic response of pile groups in liquefiable ground. Comparison of the pile response in two tests with and without vertical input ground motion shows that the vertical ground motion does not significantly influence the pile bending moment in liquefiable ground, as the dynamic vertical total stress increment is mainly carried by the excess pore water pressure. The influence of previous liquefaction history during a sequence of seismic events is also analysed, suggesting that liquefaction history could in certain cases lead to an increase in liquefaction susceptibility of sand and also an increase in dynamic forces on the piles.

Estimating seismic response under bi-directional shaking per uni-directional analysis: Identification of preferred angle of incidence

Implications of incidence angle of ground motions on inelastic demand of bridge piers under bi-directional seismic excitation have been studied against the corresponding uni-directional counterparts. Recognizing that the bi-directional analysis is complex and computationally intensive, to improve the use of less-rigorous uni-directional analysis, present study identifies the most and the least preferred orientations for a given pair of horizontal ground motion. We define the most and least preferred orientations, where the difference between bi-directional and uni-directional response is respectively minimized and maximized. These orientations can be uniquely identified for both peak and cumulative demand in terms of appropriate ground motion parameters (energetic length and characteristic intensity respectively for peak and cumulative demand) independent of structural properties. It has been shown that the improved estimate of bi-directional response may be obtained from simplified uni-directional analysis by utilizing these preferred incidence angles in conjunction with appropriate combination rules (30% for peak and 40% for cumulative demand).

Maximum credible damage of RC bridge pier under bi-directional seismic excitation for all incidence angles

Extending conventional Park-Ang damage index, a simple yet rational damage measure applicable for bi-directional seismic shaking has been evolved. Comparing predicted damage states of a bridge pier in terms of the evolved damage index to the component strains, efficacy of the proposed index has been verified. Quantitative assessment of damage of a bridge pier demonstrates substantial magnification in damage due to bi-directional shaking relative to uni-directional companion. This amplification in damage may further vary with incidence angles. Unfortunately, conducting true bi-directional analysis is challenging and implications of incidence angles are elusive yet. Collectively investigating these two crucial issues, present study identifies suitable orientations/ incidence angles in terms of pure ground motion parameters. Maximum credible damage of bridge pier under bi-directional shaking may be estimated by combining damage (30% rule) due to less-rigorous uni-directional analysis conducted in the most preferred orientation defined by the ratio of energetic length of components. The present investigation thus appears to evolve a rational damage index and a novel strategy to quantify the same for bridge pier under bi-directional seismic excitation.

Analysis and Evaluation of the Stochastic Damage for Recycled Aggregate Concrete Frames Under Seismic Action

In this paper, the seismic response of recycled aggregate concrete (RAC) frames was investigated through the bidirectional shaking table test for a three-storey RAC frame model with 1:4 reduced scale. According to test results, the variation regularity of the structural frequency, damping, and the inter-storey displacement angle was analyzed, which illustrated a good seismic behavior of this RAC framework. Furthermore, a damage model of the corresponding RAC integral structure was proposed with a comprehensive consideration of the different frequencies in X and Y directions, damping ratio, stiffness, vibration mode of the structure, variety of structure forms, and test methods for natural frequency. Based on the damage model for the RAC structure, the damage grade was analyzed. Meanwhile, combined with the classification of earthquake damage to buildings and special structures, code for seismic design of buildings (GB50011-2010), and other literature, a standard with five damage grades of the RAC structure was established. At last, to apply for practical engineering, a quick computational formula for RAC structure damage index was fitted. The results obtained from the previous studies indicate that the damage model is basically consistent with the experimental results and is capable of applying into seismic damage quantitative evaluations and analyses for actual RAC structures.

Seismic Behavior of RC Bridge Piers under Bidirectional Excitations: Implications of Site Effects

Seismic demand of structures may be potentially magnified due to bidirectional shaking. This may also be strongly influenced by the amplification and/or attenuation of motions due to local site conditions. Current investigation examines the implications of these two aspects collectively. A code-designed reinforced concrete pier has been analyzed under recorded accelerograms and their derivatives from 1-D site analysis. Magnification in peak and cumulative responses due to bidirectional shaking may be sensitive to record-to-record variability. However, such magnification remains relatively stable across site characteristics. Combination rules are shown adequate to estimate peak deformation and deficient for cumulative demand irrespective of the site conditions.