Peak Lateral Displacement Research Articles

Investigation on the Seismic Damage and Identification of Lateral Stiffness for Ancient Timber Structures

ABSTRACTThis paper investigates the seismic damage and identification of lateral stiffness for ancient timber structures. Based on the shaking table test of a palace‐style timber structure, the lateral displacement responses, interstory equivalent lateral stiffness (IELS), and sensitivity of lateral displacement to degradation of IELS were analyzed to investigate the degradation and identification of IELS. The state and observation equations of a simplified mechanical model of the timber frame considering the friction slipping of the column base were predicted. Considering the noise disturbance in the test, the IELS of the model was identified by the partial least squares–singular value decomposition (PLS‐SVD) and extended Kalman filter (EKF) method. Results shown that the ratio of the IELS of the column frame layer to Ru‐Fu layer decreased as the seismic damage increased, and the peak lateral displacement was more sensitive to the damage of the column frame layer than the Ru‐Fu layer. Under nondamage conditions, the identification error of the IELS was about 10%, while the error ranged from 15% to 20% under damage conditions. Through the identification of the equivalent lateral stiffness of the Xi'an bell tower, it was validated that the hybrid method is effective in monitoring the IELS of ancient timber structures.

Study of the dynamic response of an offshore continuous beam bridge under nonlinear wave and scour

The study highlights the critical factors and findings regarding bridge damage susceptibility during typhoons and hurricanes, primarily due to extreme waves, scour, and storm surges. While existing research has extensively studied bridges' responses to either extreme waves or scour individually, their combined effects have not been sufficiently explored. Experiments were conducted on a scaled two-span bridge to examine its behavior under simultaneous wave and scour conditions. Results from these experiments indicate that as scour depth increases, there is a corresponding escalation in displacement of the bridge pier, acceleration of the bearing platform, and strain along the pile foundation. To further investigate these dynamics, fluid-structure interaction analysis was employed, revealing significant insights. Notably, the study found that wave height exerts a substantial influence on wave load. For instance, at a wave height of 6 m, the average peak horizontal wave load on bridge piers was 2.48 times higher than at 3 m wave height. Moreover, local scour was identified as a critical factor reducing the bearing capacity of pile foundations, thereby significantly impacting the bridge's dynamic response to nonlinear waves. Under identical wave conditions, varying scour depths (3 m, 6 m, 9 m, and 12 m) resulted in increases in peak lateral displacements at the pier top compared to non-scouring conditions. The study concludes by emphasizing the increasing risk posed to pile foundations with deeper scour depths, particularly under stronger wave conditions. Consequently, there is a crucial need to enhance the resilience of offshore bridges against these dual hazards through advanced design and protective measures.

Performance Analysis of Pile Group Installation in Saturated Clay

In offshore pile engineering, the installation of jacked piles generates compaction effects within soil, thus further affecting previously installed adjacent piles. This study proposes a three-dimensional numerical model for pile group installation, soil consolidation, and loading analysis. Subsequently, the effect of pile spacing and pile length-to-diameter ratio on the deformation, internal forces, and vertical bearing capacity of adjacent piles are investigated. The results indicate that with an increase in pile center distance, the peak lateral displacement of the adjacent piles decreases, whereas the peak vertical displacement increases. As the pile length-to-diameter ratio increases, the peak vertical and lateral displacements of the adjacent piles are enhanced. In addition, the peak axial force of the adjacent piles initially decreases and then increases with the penetration depth of the subsequent pile, whereas the peak bending moment initially increases and then decreases. The vertical bearing capacity of the subsequent pile is significantly superior to that of the adjacent piles. Therefore, the effects of pile installation on adjacent piles should be included in pile engineering. The impact of the subsequent pile installation on the bearing capacity of adjacent piles can be significantly reduced by increasing the pile center distance and pile length-to-diameter ratio. The findings provide useful guidance for pile group engineering.

Axial compressive performance of CFRP-steel composite tube confined seawater sea-sand concrete intermediate slender columns

To alleviate the scarcity of river sand resources and fully utilize the advantages of Carbon Fiber Reinforced Polymer (CFRP), a new type of CFRP-steel composite tube was developed to confine seawater-sea sand concrete (FCTSSC) column structures. This study conducted experimental research on FCTSSC intermediate slender columns for the first time, analyzing their failure modes and working mechanisms. The investigation explored the effects of outer CFRP layers and slenderness ratios on the mechanical performance. The results indicate that the FCTSSC intermediate slender column specimens exhibited global buckling accompanied by local bulging of steel tubes as their failure mode. The load-displacement curves can be divided into strong confinement and weak confinement models. Specimens confined by CFRP exhibited a 12.51–31 % increase in ultimate bearing capacity. The ultimate bearing capacity and its enhancement rate were positively correlated with the outer CFRP layers and negatively correlated with the slenderness ratio. Peak lateral displacements were positively correlated with both parameters. Finally, the model for calculating the axial compression ultimate bearing capacity of FCTSSC intermediate slender columns was proposed, providing a reference for future practical applications in offshore engineering.

Dynamic responses of concrete-filled steel tubes impacted horizontally by a rigid vehicle: Experimental study and numerical modelling

Concrete-filled steel tubes (CFSTs), composed of an outer tube made of steel as the confining material and an inner concrete core, have been popularly utilised as high-rise building columns and urban bridge piers owing to their superior structural behaviour. Since the invention of CFSTs, their mechanical performance under static and seismic loading conditions have been extensively studied, while the investigation on their dynamic behaviour under impact loading is relatively limited. Of these limited studies about CFSTs under impact loading conditions, most experiments were completed using a drop-hammer testing facility or a pendulum-hammer testing device. Against this background, this study investigated six large CFSTs being impacted horizontally by a rigid vehicle to analysis their dynamic response. All specimens were vertically placed with the bottom pedestal fixed on the lab floor and the top end free. The main parameters of these CFSTs included the impact velocity (i.e., vi = 3.16–7.18 m/s), the CFST section size (i.e., D = 180–300 mm), as well as the CFST column height (i.e., hc = 1500–2100 mm). Test results revealed that, (1) all CFSTs experienced a bending-dominant failure when impacted horizontally by a rigid vehicle; (2) the impact velocity had a positive correlative trend with the peak impact force Fpeak and the peak lateral displacement δpeak of the CFST column; (3) a larger section size of the CFST column resulted in a higher flexural stiffness and a larger flexural capacity, thus leading to a higher Fpeak, a smaller time duration T and a smaller δpeak; (4) the column height would affect the inertial response of the CFST column; a larger column height led to a larger Fpeak caused by the larger inertia effect of the CFST segment above the impact point. Finite-element model was established on the platform of LS-DYNA to simulate these CFSTs under horizontal impact loading, which was able to predict both impact force–time history curves and lateral displacement–time history curves with reasonably accuracy.

Experimental and numerical evaluation of seismic behavior of coupled walls connected by post-tensioned, unbonded, precast concrete coupling beams

To investigate the seismic performance of coupled shear walls, which are connected by post-tensioned, unbonded, precast concrete coupling beams (PCCB), two 1/7-scale experiments with 8-story coupled shear walls under cyclic lateral loadings were conducted. Coupling of concrete shear walls is achieved by post-tensioning concrete beams to the wall piers using unbonded post-tensioning tendons (UPT) at the floor and roof levels. Experimental results show that little damage occurs in the coupling beams and the wall regions when the specimen undergoes large nonlinear displacements. The residual displacements of the specimen are small because of the restoring effect of the post-tensioning force. The seismic performance of three systems including CW-RC (coupled wall systems that use traditional RC coupling beams), CW-UP (coupled wall systems which use only post-tensioning tendons without steel reinforcement through the beam-wall joints), and CW-HUP (shear walls and PCCB that use combinations of steel reinforcement and post-tensioning tendons) are evaluated by means of nonlinear dynamic analysis. The calculation results indicate that the inter-story drift and peak lateral displacements of CW-HUP and CW-UP are greater than that of CW-RC, whereas the residual deformations are reduced because of the self-centering effect of the post-tensioning tendons.

A practical framework for assessing the effect of cyclic softening of clays on the lateral response of single piles

Single pile foundation has been widely used for the most offshore wind turbines to resist the cyclic loading resulted from the wind and wave. The cyclic loading can result in the degradation of the shear strength and the stiffness of clays surrounding piles. This study proposed a practical framework for assessing the effect of cyclic softening of clays on the lateral response of piles. A 3D finite difference model was developed for the pile – soil interaction under cyclic loading and then verified by full-scale monotonic and cyclic lateral load tests conducted on the single pile in clay. The cyclic softening behavior of undrained clays was described by a nonlinear dynamic softening constitutive model developed by the authors. The effect of the loading type (i.e., one-way and two-way loading) and the loading amplitude on the cyclic lateral response of piles was investigated. Moreover, a prediction function was proposed and was demonstrated to be effective in estimating the evolution of cumulative peak lateral displacement of cyclically loaded single piles in clays. The proposed practical framework provides an alternative for predicting the cyclic response of single piles in clays based on the monotonic lateral load test of piles.

Numerical Simulation of a Barge Impact on Bridges with Different Configurations of Pile Group Foundations

Three-dimensional finite element dynamic analyses were conducted to evaluate the effect of barge impact of different speeds on the lateral performance of three pile group (PG) configurations (vertical, battered, mixed) in terms of peak lateral displacement, peak shear force, lateral stiffness of PGs, and contribution of piles and pier columns to the total resisting force. The concrete material was modeled using the Concrete Damaged Plasticity model. The clay behavior was described using the Modified Cam Clay model; while the sand was modeled using the Drucker Prager model. The results showed that the vertical PG had the lowest lateral stiffness; while the battered and mixed PGs had closely larger stiffness, which allowed the development of larger impact force and pile cap displacement in vertical PG as compared to other PGs. The results of shear force showed that the foundation contributed up to 82% of the total lateral force in battered and mixed PGs. The results also showed that in vertical PG, the first row had slightly higher percentage of lateral force compared to other rows; while in battered PG, the load percentage was evenly distributed between rows. A contrast performance was observed for mixed PG. The results of bending moment (BM) showed that the piles in vertical PG had notably higher BM than the piles in other PGs due to larger pile cap displacement. In all PGs, the piles in the edge column had higher BM ratio, with the leading row (L) had the highest BM ratio (69–72%) in all PGs.

Effects of axial loading on dynamic response of laterally loaded single piles in liquefiable layered soil of Kolkata city considering nonlinearity of soil

In the present study, an advanced nonlinear finite-element based 3D numerical study has been carried out to investigate the effects of axial loading on dynamic response of soil-pile system in liquefiable layered soil deposits of Kolkata city. An advanced soil constitutive law based on multi-yield surface plasticity model implemented in fully-coupled u-p formulation is adopted for soil-fluid interaction and pore water pressure development reasonably. The present model is validated with the past experimental results. Then, a detailed systematic parametric study is performed for numerical simulation of pile failures in layered soil deposit under axial loading by taking into account various soil conditions, pile and ground motion parameters. It is seen that the depth of liquefaction (DL) is decreased from 11.5 to 1.5 m adjacent to the pile when the axial load on pile increases from 0 to 1327 kN. Parametric studies also reveal that the bending moment response of pile under axial loading can be higher in non-liquefiable condition, with reference to the liquefiable condition. The peak lateral displacement decreases by 83.2% in non-liquefiable condition and 60.71% in liquefiable condition due to decrease of axial load from 1327 to 0 kN. Also, peak bending moment developed in the pile decreases by 97.2% in non-liquefiable condition and 82.7% in liquefiable condition when the axial load reduces from 1327 to 0 kN. So, the designer should be considered both extreme scenarios for safe and economical design. Also, it is noticed that the buckling capacity of pile is improved significantly by using larger diameter pile and the bending capacity is increased by selecting higher grade of concrete. It is concluded that the bending and buckling failure mode may be avoided by selecting a suitable combination of material strength and pile geometry.

Evaluation of seismic response of coupled wall structure with self-centering and viscous damping composite coupling beams

In order to reduce the residual displacement and floor acceleration of coupled wall structures, a novel self-centering and viscous damping composite coupling beam is proposed. The proposed coupling beam consists of the elastic beam segments and the fuse part, which incorporates self-centering friction dampers and viscous dampers. The self-centering friction damper can provide strength and stiffness for the proposed coupling beam and reduce the residual displacement of the coupled wall structure. The viscous damper can add supplemental damping to the system, and this can control the peak lateral displacement demands and floor accelerations of the structure. Moreover, the proposed coupling beam can eliminate the beam elongation effect of the self-centering coupling beam with a rocking behavior. Design methodology and nonlinear numerical model of the proposed coupling beam are developed. The seismic behaviors of the coupled wall structure with the self-centering and viscous damping composite coupling beams (CW-SCVCCB) are assessed and compared with the structure with reinforced concrete coupling beams (CW-RCCB), the structure with steel coupling beams (CW-SCB) and the structure with self-centering coupling beams (CW-SCCB). Analysis results showed that the supplemental viscous damping can effectively reduce the peak interstory drift ratio and floor accelerations of the structure. The residual displacement of the novel coupled wall system is larger than that of the CW-SCCB, however, it is significantly reduced compared with the CW-SCB and the CW-RCCB.

Machine learning-based prediction for maximum displacement of seismic isolation systems

This study developed machine learning (ML) models for predicting the peak lateral displacements of seismic isolation systems subjected to earthquakes. Six ML methods were employed for this purpose: linear, ridge, least absolute shrinkage and selection operator (lasso), artificial neural network (ANN), support vector machine, and random forest (RF). The isolated superstructure was assumed to be rigid, and the base isolation system was assumed to be firmly anchored to a bedrock foundation. A total of 234,360 data points were generated using OpenSees to train and test the predictive models. The input variables included three parameters representing the behavior of isolation systems (i.e., the ratio of the initial to post-yield stiffness, normalized characteristic strength, and post-yield period) and the average spectral accelerations at five selected periods (i.e., 1, 2, 3, 4, and 5 s) for the considered ground motions. The RF model exhibited the best performance among the six models. The coefficients of determination (R2) for the RF model were 0.9930 and 0.9498 for the training and testing datasets, respectively. In addition, the ANN model exhibited the second-best performance. The normalized characteristic strength was found to be the most influential variable in the investigation of the individual input variables for the prediction. Finally, a practical analysis of a hypothetical three-story base-isolated moment frame building was performed to demonstrate the effectiveness and limitations of the developed RF model in predicting the maximum displacements of the isolation systems. The prediction results were compared with those from a previous study and with the equivalent linear force procedure in American Society of Civil Engineers (ASCE) 7–16. A graphical user interface was created for the developed RF model for easy access by engineers. This study represents a pioneering step for the application of ML to the estimation of the responses of seismic isolation systems in practical design.

Effect of unidirectional lateral cyclic load path on hysteretic response of battened steel columns – A numerical investigation

During earthquakes, battened steel columns are subjected to both compressive load in longitudinal direction and cyclic load in lateral direction. The effects of unidirectional lateral cyclic stress on a double channel battened column (DCC) were investigated using ABAQUS software in this paper. Four different unidirectional lateral displacement controlled load paths (U1, U2, U3, and U5) were considered for this study. As per the study, the lateral load carrying capacity (LCC) and peak lateral displacement are significantly affected by the unidirectional lateral cyclic loading path. The results showed that the peak lateral displacement of the columns reduces considerably, with a minor effect on LCC when number of cycles applied for certain deformation level increases.

Predicting the peak structural displacement preventing pounding of buildings during earthquakes

The aim of the present paper is to verify the effectiveness of the artificial neural network (ANN) in predicting the peak lateral displacement of multi-story building during earthquakes, based on the peak ground acceleration (PGA) and building parameters. For the purpose of the study, the lumped-mass multi-degree-of-freedom structural model and different earthquake records have been considered. Firstly, values of stories mass and stories stiffness have been selected and building vibration period has been automatically calculated. The ANN algorithm has been used to determine the limitation of the peak lateral displacement of the multi-story building with different properties (height of stories, number of stories, mass of stories, stiffness of stories and building vibration period) exposed to earthquakes with various PGA. Then, the investigation has been focused on critical distance between two adjacent buildings so as to prevent their pounding during earthquakes. The proposed ANN has logically predicted the limitation of the peak lateral displacement for the five-story building with different properties. The results of the study clearly indicate that the algorithm is also capable to properly predict the peak lateral dis-placements for two buildings so as to prevent their pounding under different earthquakes. Subsequently, calculation of critical distance can also be optimized to save the land and provide the safety space between two adjacent buildings prone to seismic excitations.

Effect of Frequency Characteristics of Ground Motion on Response of Tuned Mass Damper Controlled Inelastic Concrete Frame

This paper investigates the performance of tuned mass damper (TMD) and dynamic behavior of TMD-controlled concrete structure considering the ground motion (GM) characteristics based on frequency content. The effectiveness of TMD in reducing the structural response and probability of collapse of the building frames are affected by the frequency characteristics of GMs. To attenuate the seismic vibration of the buildings, the TMD controlled building has been designed based on the modal analysis (modal frequencies and modal mass participation ratio). In this study, to investigate the performance of TMD, four different heights (i.e., 3, 5, 10, 20 stories) inelastic concrete moment-resisting frames equipped with TMDs are developed using an open-source finite element software. A series of numerical analyses have been conducted using sixty earthquakes classified into three categories corresponding to low, medium, and high-frequency characteristics of GMs. To evaluate the proposed strategy, peak lateral displacements, inter-story drift, and the probability of collapse using fragility analysis have been investigated through the structures equipped with and without TMD. The results appraise the effect of TMD and compare the seismic responses of earthquake frequency contents and the vibration control system of the inelastic building frames.

Earthquake response of the train–slab ballastless track–subgrade system: A shaking table test study

Earthquake is one of the major factors that provoke train derailment. To investigate dynamic responses of the train–slab ballastless track–subgrade system and derailment features of the train subjected to earthquake, a first large-scale shaking table test on this system was carried out in China. The loaded seismic wave is an earthquake wave of Zhengzhou Yellow River Bridge Site provided by the China Earthquake Administration. It was observed that the elevation of subgrade and embankment could magnify acceleration responses, and the transverse amplification effect of the elevation in soil was more pronounced than the vertical amplification effect. The acceleration response of a track slab was weaker than that of the top subgrade because of integrality and rigidity of the track slab. The bogie shows a shock-absorbing effect in the transverse direction. When the input amplitude was not larger than 0.14 g, the transverse and the vertical acceleration of the rail increased with rising earthquake amplitudes and fluctuated later. Meanwhile, the current stopping threshold for trains is conservative because the derailment factor was less than 0.8 and the peak lateral displacement of wheels was much smaller than the cross-sectional size of the rail model under a 0.12 g earthquake excitation. The current stopping threshold in codes could be reasonable in view of limited quantity and limited types of loaded earthquake in the test. The critical derailment condition of trains was 0.23 g when the Zhengzhou Yellow River Bridge Site earthquake was loaded, and the displacement analysis showed that it would be a great danger for train safety.

Unified Shear-Flexural Model for Vibration Control of Buildings Using Passive Dynamic Absorbers

A unified design model is proposed for various kinds of passive dynamic absorbers (PDAs) attached to buildings with different lateral resisting systems. A total of five different PDAs are considered in this study: (1) tuned mass damper (TMD), (2) circular tuned sloshing damper (C-TSD), (3) rectangular tuned sloshing damper (R-TSD), (4) two-way liquid damper (TWLD), and (5) pendulum tuned mass damper (PTMD). The unified model consists of a coupled shear-flexural (CSF) discrete model with equivalent tuned mass dampers (TMDs), which allows the consideration of intermediate modes of lateral deformation. By modifying the nondimensional lateral stiffness ratio, the CSF model can consider lateral deformations varying from those of a flexural cantilever beam to those of a shear cantilever beam. The unified model was applied to a 144-meter-tall building located in the Valley of Mexico, which was subjected to both seismic and along-wind loads. The building has similar fundamental periods of vibration and different nondimensional lateral stiffness ratios for both translational directions, which shows the importance of considering both bending and shear stiffness in the design of PDAs. The results show a great effectiveness of PDAs in controlling along-wind RMS accelerations of the building; on the contrary, PDAs were ineffective in controlling peak lateral displacements. For a single PDA attached at the rooftop level, the maximum possible value of the PDA mass efficiency index increases as the nondimensional lateral stiffness ratio decreases; therefore, there is an increase in the vibration control effectiveness of PDAs for lateral flexural-type deformations.

Derailment Behaviors of the Train-Ballasted Track-Subgrade System Subjected to Earthquake Using Shaking Table

Ballasted track is the most common track model in railway system and earthquake would be a great threaten for train running safety. This study investigates derailment features and lateral displacement response of the train-ballasted track-subgrade system subjected to earthquake using 1-g shaking table. The model was loaded using scaled Zhengzhou Huanghe Qiaozhi (ZHQ) earthquake wave, ALS earthquake and CHY004 earthquake which are with variable-characters. It is observed that current stopping threshold for train is conservative because derailment factor is less than 0.8. The derailment factor of train increase with increasing acceleration amplitude and the critical derailment condition of train under ZHQ earthquake, ALS earthquake and CHY004 earthquake is 0.18 g, 0.15 g and 0.15 g, respectively. The lateral displacement of rail is negligible compared with that of wheel. Lower-frequency earthquake would cause larger derailment factor with derailment analysis and displacement analysis. The maximum peak lateral displacement of wheel under critical derailment condition is significant, which means train safety is under a great danger.

Copula-based seismic fragility assessment of base-isolated structures under near-fault forward-directivity ground motions

The seismic fragility of base-isolated structures subjected to near-fault forward-directivity ground motions is investigated. A general framework for deriving the system-level fragility curve is proposed, where the vulnerability contributions of multiple interrelated components to the overall system are incorporated. In this framework, the joint probabilistic seismic demand model (JPSDM) is established, where the joint probability distribution of multiple engineering demand parameters (EDPs), conditioned on the intensity measure (IM) level, is characterized via copula approach, and the sampling-based JPSDM, along with the capacity models of these components, is employed to generate the overall system fragility curves. This proposed framework is applied in the case study of a typical seismically-isolated RC frame structure, where the peak lateral displacement in the base-isolation layer and the maximum inter-story drift in the superstructure are considered as the two major component EDPs. The analysis results indicate that the combination of t copula, which is quantitatively identified as the best-fit copula function, and the conditional lognormal marginal distribution adequately captures the joint probability distribution of these two EDPs conditioned on the IM level. Moreover, the impact of different copulas selection on the system-level fragility varies depending on the relative fragility contributions of different components in the overall system.

Seismic behavior of pile-supported systems in unsaturated sand

The seismic behavior of pile-supported systems has been an active area of research over the past decades. However, focus has mostly been on evaluating the seismic response of structures embedded in either dry or fully saturated soil conditions. In this study, series of dynamic centrifuge tests were conducted to investigate the effects of soil's degree of saturation on the seismic behavior of pile-supported superstructures. The scaled physical model tests were carried out on two distinct pile-mass systems embedded in uniform sand layers. A steady state infiltration technique was used to control matric suction profiles in the sand layer prior to shaking. The obtained results from these experiments were illustrated in terms of peak accelerations, peak lateral displacements, and frequency content of the structural motion. The observed response showed higher acceleration amplification and lower lateral deformation for the pile-supported systems with foundations embedded in unsaturated sand comparing with those in dry sand. An inverse simple pseudo-static analysis was performed to back-calculate soil modulus values from the pile lateral deformations. The calculated values of soil modulus were higher for unsaturated sands showing consistency with the effect of matric suction on increasing the soil stiffness.

Dynamic lateral response of under-reamed vertical and batter piles

Dynamic lateral response of three under-ream reinforced concrete piles constructed in silty sand {vertical, P1 (β = 0°); and batter piles P2 (β = 10°) and P3 (β = 20°)} having equal length of 2.5 m, shaft diameter 0.2 m and under-ream bulb of diameter 0.5 m were considered for this experimental study. Dynamic loads were generated using an oscillator motor assembly mounted on top of pile cap and the response of these piles were recorded in real time using three accelerometers placed along the depth of the pile cap. These piles were subjected to varying dynamic load by changing the eccentricity setting of the oscillator in the frequency range of 0–40 Hz. The test results show that the resonant frequency of the soil-pile system decreases; and peak lateral displacement increases with increase in the force level. The variation of rotational stiffness and the damping ratio of the soil-pile system with force level did not follow a clear trend. Thus the presence of an under-ream bulb in a batter pile does not have a significant influence on the lateral behaviour of batter piles.