Shake Table Research Articles

Test and sensitivity analysis of base‐isolated steel frame with low‐friction spherical sliding bearings

AbstractIn Japan, spherical sliding bearings with low friction coefficients are gaining popularity for base‐isolating low‐rise frames that are relatively lightweight. However, the complete dataset of isolators and a base‐isolated frame for evaluating the model sensitivity and response uncertainty are limited. This study first presents the design process, isolation unit‐ and frame‐level testing, and a blind prediction contest conducted on the occasion of full‐scale shaking table testing of a three‐story base‐isolated hospital specimen. The design process utilizes a numerical model that accounts for the velocity and contact pressure dependencies and requires soft‐ and hard‐case simulations with nominal friction coefficients plus and minus standard deviation to consider the uncertainties associated with the bearing behavior. The pre‐shipment isolation unit and frame shake table testing yielded an invaluable dataset for bearings under normal and low contact pressures, low and high velocities, and constant and varying axial loads. The accompanying blind prediction contest provided a valuable dataset for rethinking the impact of modeling uncertainty. In‐depth data analysis and sensitivity analysis were conducted. The sliding coefficient increased under low‐contact pressure and low‐velocity conditions. The static friction coefficient was 1.9 to 4.5 times higher than the dynamic coefficient, but this had little impact on the residual displacement, cumulative travel, and maximum story shear force. The axial force fluctuation, vertical motion, and two‐directional input did not significantly affect the bearing behavior in the test. The test and the following simulations confirmed that the low friction coefficient helped the building contents, that is, medical equipment in this study, remain in order under near‐fault and long‐period ground motions.

Seismic response of a model soil-pile-bridge system in cohesive soil

This paper investigates the dynamic response of a model pile-soil-bridge system subjected to seismic loading using a finite element model (FEM) developed in OpenSees. The numerical model is validated against shake table test data from a companion experimental study, which tested a piles-bridge model fabricated from organic glass. The bridge model comprised four piers, each supported by two-by-two pile groups, with edge piers featuring 60 × 60 mm rubber pads between the pier and deck. Two earthquake ground motions, El Centro and Tianjin, were applied at three intensity levels. The calculated and measured responses show good agreement. The validated FEM reveals that the El Centro earthquake typically induces higher acceleration and moment responses in structural elements compared to the Tianjin earthquake, while the Tianjin earthquake results in greater displacement responses. These findings highlight the impact of earthquake wave characteristics, such as predominant period, on the bridge system's response. Furthermore, the bending moments at the pier top for edge piers remain relatively consistent across different earthquake motions and intensity levels, indicating the role of rubber pads in mitigating seismic forces in the piers.

1-g Shaking Table Test Study on the Influence of Soil–Caisson Dynamic Interaction (SCDI) on the Caisson Foundation Motion

1-g Shaking Table Test Study on the Influence of Soil–Caisson Dynamic Interaction (SCDI) on the Caisson Foundation Motion

Experimental and numerical investigation of the seismic behavior of reinforced concrete frames with restricted ductility

In recent decades, the concept of special ductility has been commonly used to design reinforced concrete frames to resist strong earthquakes. There are numerous situations where strong earthquakes impose restricted ductility demands, e.g., structures governed by gravity loads or wind loads rather than seismic loads, and frames with geometric properties such that the dimensions prevent formation of plastic hinges at the ends of beams. To evaluate performance of such structures, this study has been conducted and emphasis is placed on intermediate reinforced concrete frames with code-conforming details. Shake table tests are conducted on a 3-story intermediate frame under a sequence of 9 incremental excitation records varying from 0.10 g to 0.60 g, representing minor to severe ground motions. A relatively satisfactory performance is observed: the maximum interstory drift ratio does not exceed 1.57 %, cracks are not localized at the ends of members but distributed along the spans of both beams and columns, and joints remain almost uncracked. To examine the effects of different parameters, a numerical model is developed and verified against the test results. Three essential parameters are considered: seismic event profile, span-to-depth ratio of the beam, and joint aspect ratio. The results show that the effects of different factors may be ranked from highest to lowest as follows: seismic event profile, aspect ratio of the beam-column joint, and span-to-depth ratio of the beam. The numerical analyses show that the frame will not exceed life safety limit under far field excitations and for joint aspect ratios larger than 0.9, but it may reach the threshold of collapse prevention limit under near fault earthquakes. Overall, the study sheds some light on seismic response of RC frames with restricted ductility and provides some indications of their feasibility as well as their limits in high seismic zones.

Metoda poboljšanja potresno izoliranih mostova novim V-MG uređajima: dinamička ispitivanja modela

A method for enhancing the seismic performance of isolated bridges was developed using innovative vertical multigap (V-MG) devices based on extensive experimental and analytical research. Significant improvements in seismic performance were achieved by creating a unique type of uniform V-MG energy-dissipation device for a vertical-gaped bridge protection system (VG bridge system) that included double spherical rolling seismic bearings for seismic isolation as a complete set. Seismic shaking table tests on large-scale bridge models, which simulated real earthquake conditions, confirmed that the VG bridge system could significantly modify seismic response and enhance the seismic safety of isolated bridges under very strong earthquakes.

Analytical solution of seismic power-based equation of motion

This research proposes an innovative power-based equation of motion (PBEM) for the single degree of freedom (SDOF) system considering seismic excitation. The external or input frequency function, solution of time, relation between external and kinetic powers, and equation of strain-power (SP) are obtained by solving the power balance equation (PBE). The external frequency function is related to both the particular and total solutions of the PBEM. The particular solution of PBEM is applied on the shake table test of the tunnel-soil-pile interaction (TSPI) model, real-scale test of 2-storied reinforced concrete frame structure, and case study of Bolu tunnel for the verification purpose. The differences in verification (PBEM and previous works) results are found to be 21.6 % for the real-scale test and 19.5 % for the case study. These differences may represent a reasonable agreement with verification. Also, the relationship between the kinetic and external powers is verified with the previous shake table test of steel cantilever column, whereas the difference in results is found to be 5 %. Finally, a design chart is proposed for predicting the input frequency function for various frequency ratios and damping.

A self-powered and self-sensing hybrid energy harvester for freight trains

Freight trains, being crucial for economic development, often face challenges due to the lack of electrical infrastructure. In this study, a self-powered and self-sensing hybrid energy harvester system (SS-HEH) is proposed, it consists of an electromagnetic generator (EMG), a piezoelectric energy harvester (PEH), and an energy input module. The proposed EMG utilizes a rolling magnet to intersect the square coil, thereby better adapting to the operational conditions of freight trains and producing higher electrical energy output. Additionally, the PEH converts bogie vibration signals into electrical signals to detect bogie operations. The EMG acts on the PEH, inducing bending and generating electrical signals. Conversely, the PEH acts on the EMG to maintain it horizontally, enhancing its ability to absorb the vibration energy of the bogie and forming a bistable system. Furthermore, at a speed of 40 km/h, the EMG voltage with PEH increased by 43.75 % compared to the scenario without PEH. The electrical performance of the SS-HEH was assessed through shake table experiments, yielding an RMS voltage of 11.5 V and output power of 74.1 mW. In addition, combined with deep learning, SS-HEH has an accuracy of 97.41 % in detecting the operating status of bogie.

A rigid‐flexible coupled rocking structure with nonlinear stress distribution along its base: Analytical modeling, validation and parametric investigation

AbstractStructures allowing their bases to uplift and rock during an earthquake event usually experience less damage; thus, they are more resilient to seismic hazards. Accurate simulation is critical to design and seismic performance evaluation of these flexible rocking structures. Motivated from this, this article presents a new rigid‐flexible coupled rocking model for numerical evaluation of flexible rocking structures under both cyclic and dynamic loadings. The key idea in the model formulation is that the total motion of flexible rocking structure can be decomposed into a rigid‐body motion and an associated flexible deformation. The flexible deformation of the rocking body is described using displacement field of classical Timoshenko beam. Using this approach and appropriate degrees‐of‐freedom (DOFs), the governing equations‐of‐motion for flexible rocking structures are formulated using the variational principle. Multiple springs with appropriate constitutive model are distributed along rocking base to represent the inelastic behavior of rocking body. Potential post‐tensioned tendons are also considered in this model. In addition, nonlinear stress distribution along the rocking base, which cannot be considered in existing flexible rocking model, is also incorporated in the developed model. The proposed model is subsequently validated against published experimental data through quasi‐static and shake table tests, showing good accuracy when the rocking structure is relatively stockier. Finally, a parametric investigation on the effect of flexibility, nonlinear stress distribution and yield stress of rocking body on the rocking response is performed. This preliminary investigation shows that influence of flexibility and yield stress is significant while impact of nonlinear stress distribution is minor.

Integrating low-cost GNSS and MEMS accelerometer for precise dynamic displacement monitoring

We assess the performance of the self-developed receiver coupling dual-frequency low-cost GNSS chipset and IMU MEMS sensor. The system also comprises software dedicated to vibration monitoring based on relative kinematic positioning in a post-processing mode. The observation assessment reveals high accuracy of low-cost GNSS and MEMS accelerometer data. The Septentrio Mosaic X5 chipset exhibits competitive to high-grade receivers’ phase observation noise, outperformance in code noise level and observation auto-correlation at a level that may be neglected even in high-rate applications. The evaluation of the MEMS accelerometer data proves that the sensor accuracy is adequate for vibration monitoring. With the shake table experiment, we examine the performance of vibration recovery. An advantage of the coupled solution over a GNSS-only one is documented with a 15 % reduction of the amplitude error. The backward smoothing of coupled solutions drives the next 20 % error drop. Finally, the high performance of the coupled solution based on low-cost GNSS & accelerometer is confirmed by a mean amplitude error of 0.4 mm. The frequency analyses indicate that both coupled and single-sensor solutions precisely detect the vibration frequencies; however, they also confirm the outperformance of the former over the latter. The power spectra of the recovered displacement time series accentuate the benefits of GNSS + accelerometer fusion and backward filtering for reducing displacement noise.

Dynamic model of the UC San Diego NHERI six‐degree‐of‐freedom large high‐performance outdoor shake table

AbstractThe UC San Diego large high‐performance outdoor shake table (LHPOST), which was commissioned on October 1, 2004 as a shared‐use experimental facility of the National Science Foundation (NSF) Network for Earthquake Engineering Simulation (NEES) program, was upgraded from its original one degree‐of‐freedom (LHPOST) to a six‐degree‐of‐freedom configuration (LHPOST6) between October 2019 and April 2022. A mechanics‐based numerical model of the LHPOST6 able to capture the dynamics of the upgraded 6‐DOF shake table system under bare table condition is presented in this paper. The model includes: (i) a rigid body kinematic model that relates the platen motion to the motions of the components attached to the platen, (ii) a hydraulic dynamic model that calculates the hydraulic actuator forces based on all fourth‐stage servovalve spool positions, (iii) a hold‐down strut model that determines the pull‐down forces produced by the three hold‐down struts, (iv) Bouc‐Wen models utilized to represent the dissipative forces in the shake table system, and (v) a rigid body dynamic model borrowed from robotic analysis governing the translational and rotational motions of the platen subjected to the forces from the various components attached to the platen. Extensive validation against experimental data shows excellent agreement for tri‐axial and six‐axial earthquake shake table tests. This validated model can be coupled with finite element models of test specimens to study the interaction between the shake table system and the specimens, and it offers potential for enhancing motion tracking performance through off‐line controller tuning or advanced control algorithm development.

Numerical modeling of earthquake-induced landslides using updated Lagrangian nonlocal general particle dynamics method

Developing a robust numerical method to model earthquake-induced landslides has long been a persistent challenge in the field of computational geotechnical engineering. Recently, the meshless methods based on nonlocal theory have piqued the interest of researchers. However, the application of nonlocal theory in seismic analysis is currently limited. This paper proposed a numerical framework based on the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method to analyze earthquake-induced landslide problems. The UL-NGPD method benefiting from the update support domain can capture the whole process of slope run-out induced by earthquakes. To enhance the numerical stability of the proposed method, several optimizing strategies are proposed. In the current framework, the seismic waves are input through the proposed boundary treatments of nonlocal form. Besides, a nonlocal friction model with velocity-weakening is proposed to accurately simulate the movement process of soils on a rocky sliding bed. The proposed framework is validated by the simulations of several classic problems, including the collapse of sand and the shake table test. The performance of the proposed approach is further demonstrated through simulating the landslides induced by earthquakes. The numerical results consistent with recorded data indicate that the UL-NGPD method has an excellent capacity to deal with earthquake-induced landslide problems.

Horizontal shaking table tests on a four-story prototype structure using multi-dimensional earthquake isolation and mitigation devices

Three-dimensional isolation system (3DIS) has been increasingly applied to civil structures with small height-width ratios, but is rarely employed in the multistory and high-rise buildings due to the lack of efficient control strategy for the rocking effect. In this paper, a simplified analysis model of 3DIS was established firstly to bring insights into the coupled motion mode caused by the rocking effect, and the influence of damping ratio and height-width ratio on the modal frequency was revealed. Then, aimed at weakening rocking motion and improving the seismic isolation efficiency, a novel multi-dimensional earthquake isolation and mitigation device (MEIMD) was proposed, and both the design composition and design principle were given in detail. To validate the effectiveness of MEIMDs, a full-scale four-story frame with a height of 13.05 m and a weight of 70 tons was produced for horizontal shaking table tests. The experimental results indicated that after adopting MEIMDs, the first-order modal frequency was 1.7 Hz, with 68% decrease compared with that of the prototype structure, and the first-order modal damping ratio was above 0.23, about eight times that of the prototype structure. Moreover, the horizontal peak acceleration was significantly decreased for each floor with a maximum reduction of 49%, while the maximum horizontal displacement and rocking response were obviously lower than the limit value specified by building codes. Therefore, the MEIMDs can not only efficiently isolate the earthquake energy, but also ensure the sufficient dynamic stability of the system. This study sheds light on the real coupled horizontal-rocking response of the base isolation system with MEIMDs, and can promote the development and application of 3DIS in multistory and high-rise buildings.

Foreword to the special issue “Adjacent Interacting Masonry Structures”

This special issue focuses on the seismic performance of adjacent interacting masonry structures, particularly in historical European city centers. The AIMS project provided unique data on interacting masonry structures through large-scale shake table tests on two adjacent half-scale stone masonry buildings. The experimental campaign was accomapgnied by a blind prediction study where participants modeled the aggregate’s seismic response. Findings highlight challenges in accurately predicting displacement demands and failure modes, providing critical insights for improving future modeling techniques for masonry buildings.

Active Control for Construction Stability of Suspension Arch Rib Segments Based on ARID System

In response to the issues of vibrations affecting the construction safety, speed, and accuracy of suspended structures due to dynamic disturbances during lifting, environmental disturbances, and improper operator actions, this paper investigates the application of the Active Rotary Inertia Driver (ARID) system for double-rope suspended structures, namely analyzes, and applies control to the vibration response of double-rope suspended structures under external excitations. Taking the double-rope suspended structure as an example, a dynamic analytical model of the double-rope suspended structure is established based on D’Alembert’s principle. Through shake table tests, the dynamic response characteristics and vibration control effects of the double-rope suspended structure under various external excitations are studied, and the influence of the twisting radius of the suspended structure on the control effect is analyzed. The experimental results show that the ARID control system achieves significant control effects on the swing and torsional vibrations of the suspended structure, which validates the accuracy of the theoretical model for the ARID control system and demonstrates its feasibility for practical applications.

Comparison of Liquefaction Damage Reduction Performance of Sheet Pile and Grouting Method Applicable to Existing Structures Using 1-G Shaking Table

This study conducted 1-G shaking table tests to compare methods of reducing liquefaction damage during earthquakes. The sheet pile and grouting methods were selected as applicable to existing structures. Model structures were manufactured for two-story buildings. A sine wave with an acceleration of 0.6 g and a frequency of 10 Hz was applied to the input wave. Certain experiments determined the effect of various sheet pile embedded depth ratios and grouting cement mixing ratios on reducing structural damage. The results confirmed that when the sheet pile embedded depth ratio was 0.75, the structure’s settlement decreased by approximately 79% compared to the control model. When the grouting cement mixing ratio was 0.45, the structure’s settlement decreased by approximately 85% compared to the untreated ground. In addition, the sheet pile method suppressed the increase in pore water pressure compared to the grouting method but tended to interfere with the dissipation of pore water pressure after liquefaction occurred. Additionally, comparing the effect of each method on reducing liquefaction damage revealed that the grouting method resulted in less settlement, rotation of the structure, and pore-water-pressure dissipation than the sheet pile method. Overall, the grouting method is more effective in reducing liquefaction damage than the sheet pile method. This study forms a basis for developing a liquefaction-damage reduction method applicable to existing structures in the future.

Educating non-specialized audiences about seismic design principles using videos and physical models

The prevalence of self-construction practices in Türkiye has resulted in a building stock whose earthquake resilience is highly uncertain. To mitigate the potentially devastating impact of anticipated large earthquakes, one viable approach is to increase earthquake awareness among builders themselves. However, these builders lack formal engineering training and are ordinary citizens. Therefore, the challenge lies in devising visual teaching methods, such as short videos, to explain complex seismic phenomena in a comprehensible manner. This paper introduces the use of educational media tailored for non-specialized audiences, encompassing regular citizens and students without engineering backgrounds. These videos are based on experiments conducted with physical models on a homemade shake table. They focus on key factors influencing the seismic response of multi-storey buildings and highlight common design and construction errors that lead to building damage. To assess the effectiveness of this approach, we conducted a workshop with junior architecture students, followed by post-workshop qualitative assessments through knowledge surveys and interviews. The findings indicate that while single-topic videos were effective learning tools for students without prior knowledge of seismic building design, students found models particularly useful for explaining specific concepts such as torsional behavior, the role of diaphragms, and the performance of non-structural components. However, despite positive feedback on the effectiveness of model testing, students generally did not perceive significant knowledge acquisition in model construction. Ultimately, the accessibility of freely available videos, coupled with their enhanced educational value, makes them effective tools for raising seismic awareness in communities vulnerable to future earthquakes.

Practice-oriented numerical model for seismic response of cold-formed steel-framed mid-rise buildings

Cold-formed steel (CFS) framed buildings are becoming increasingly common, notably in the high seismic regions of the United States (US). However, research to understand the seismic performance of CFS-framed buildings specifically using large-scale (building-level) specimens has begun only recently. Therefore, efforts to validate and improve numerical modeling of whole building systems have been limited due to this lack of experimental data. A recently completed experimental program, conducted at the Large High-Performance Outdoor Shake Table at the University of California, San Diego, involved earthquake testing of a full-scale 6-story CFS-framed building. The test building adopted an assembly of continuous tie-rod and built-up compression stud pack at the ends of individual shear walls to resist seismic overturning moment and uplift forces within the building. The objective of this paper is to present a practice-oriented phenomenological finite element modeling approach intended for design engineers and compare the predictions from this model against the measured seismic response of the 6-story building. The model aims to provide a robust, yet computationally efficient approach, with minimal degrees-of-freedom, while also capturing the salient features of seismic response of mid-rise CFS-framed buildings suitable for nonlinear time history analyses-based design. The building model, developed within the OpenSeesPy finite element platform, includes the shear walls and gravity walls as well as the lateral strength and stiffness contribution from exterior and interior gypsum sheathing. The continuous tie-rod system is also modeled to capture the cumulative floor displacements caused by the axial elongation in the steel rods. The effect of built-up compression stud packs on the lateral behavior of a shear wall was estimated using available experimental data and a detailed numerical model of an isolated shear wall, then subsequently incorporated in the nonlinear hysteretic material model. The numerical model captured the natural frequencies of the translation modes of the building in its undamaged state with <3% error. It also predicted the peak roof drift ratio within an error of 0.03% drift ratio under the design earthquake event. These results provide confidence in the proposed numerical modeling approach as a tool for seismic response prediction of mid-rise CFS-framed buildings with similar structural detailing features.

Tunable High-Static-Low-Dynamic Stiffness Isolator under Harmonic and Seismic Loads

High-Static-Low-Dynamic Stiffness (HSLDS) mechanisms exploit nonlinear kinematics to improve the effectiveness of isolators, preserving controlled static deflections while maintaining low natural frequencies. Although extensively studied under harmonic base excitation, there are still few applications considering real seismic signals and little experimental evidence of real-world performance. This study experimentally demonstrates the beneficial effects of HSLDS isolators over linear ones in reducing the vibrations transmitted to the suspended mass under near-fault earthquakes. A tripod mechanism isolator is presented, and a lumped parameter model is formulated considering a piecewise nonlinear–linear stiffness, with dissipation taken into account through viscous and dry friction forces. Experimental shake table tests are conducted considering harmonic base motion to evaluate the isolator transmissibility in the vertical direction. Excellent agreement is observed when comparing the model to the experimental measurements. Finally, the behavior of the isolator is investigated under earthquake inputs, and results are presented using vertical acceleration time histories and spectra, demonstrating the vibration reduction provided by the nonlinear isolator.

Experimentally Calibrated Numerical Modeling for Performance-Based Seismic Design of Low-Frequency Rocking Electrical Cabinets

ABSTRACT In this paper, the performances of two electrical cabinet specimens during shake table tests are described in detail in terms of the observed damage and their measured peak transient responses. The measured responses of the specimens are then used to calibrate simplified numerical models of the two specimens. The calibrated numerical models are used to derive fragility functions to illustrate their usefulness in performance-based seismic design applications. The calibration process and the basic concept of the numerical models can be used for calibrating similar numerical models for other typologies of similar floor anchored non-structural elements that have a rocking failure mode.

Structural performance analysis of a new bolt–steel plate connection precast concrete sandwich wall structure

This study proposed a new low-rise bolt–steel plate connection precast concrete sandwich wall structure (PCSWS). Shake table testing was conducted on an experimental model of the bolt–steel plate connection PCSWS with two stories. The experimental phenomenon, failure pattern, displacement response, dynamic characteristics, and global hysteresis were analyzed in detail. The test results revealed that the proposed structure demonstrated excellent seismic performance without any structural cracks when subjected to an excitation intensity level of IX for Model-1. The seismic damage was moderate with no significant structural cracks after an excitation intensity level of IX for Model-2. Cracks in Model-2 occurred in the sequence of the places at the bottoms of the columns, the door corners, window opening corners, and the filled surfaces in the bolt–steel plate connection joint zone on the first floor. The observed damage states were primarily light and moderate, indicating the structure’s ability to withstand seismic events.