Dynamic Time History Analysis Method Research Articles

Study on the Effect of Burial Depth on Selection of Optimal Intensity Measures for Advanced Fragility Analysis of Horseshoe-Shaped Tunnels in Soft Soil

Seismic intensity measures (IMs) can directly affect the seismic risk assessment and the response characteristics of underground structures, especially when considering the key variable of burial depth. This means that the optimal seismic IMs must be selected to match the underground structure under different buried depth conditions. In the field of seismic engineering design, peak ground acceleration (PGA) is widely recognized as the optimal IM, especially in the seismic design code for aboveground structures. However, for the seismic evaluation of underground structures, the applicability and effectiveness still face certain doubts and discussions. In addition, the adverse effects of earthquakes on tunnels in soft soil are particularly prominent. This study aims to determine the optimal IMs applicable to different burial depths for horseshoe-shaped tunnels in soft soil using a nonlinear dynamic time history analysis method, and based on this, establish the seismic fragility curves that can accurately predict the probability of tunnel damage. The nonlinear finite element analysis model for the soil–tunnel interaction system was established. The effects of different burial depths on damage to horseshoe-shaped tunnels in soft soil were systematically studied. By adopting the incremental dynamic analysis (IDA) method and assessing the correlation, efficiency, practicality, and proficiency of the potential IMs, the optimal IMs were determined. The analysis indicates that PGA emerges as the optimal IM for shallow tunnels, whereas peak ground velocity (PGV) stands as the optimal IM for medium-depth tunnels. Furthermore, for deep tunnels, velocity spectral intensity (VSI) emerges as the optimal IM. Finally, the seismic fragility curves for horseshoe-shaped tunnels in soft soil were built. The proposed fragility curves can provide a quantitative tool for evaluating seismic disaster risk, and are of great significance for improving the overall seismic resistance and disaster resilience of society.

Study on the Influence and Optimization Design of Viscous Damper Parameters on the Damping Efficiency of Frame Shear Wall Structure

This study investigates the influence of viscous damper parameters on the damping efficiency of frame shear wall structures. Taking a specific frame shear wall structure as the background, a three-dimensional finite element model is established using a nonlinear dynamic time–history analysis method. The damping ratio, reduction in vertex displacement, reduction in base shear, and inter-story drift utilization rate are selected as the damping performance indicators. Firstly, a sensitivity analysis is conducted to study the influence of different viscous damper parameters on these indicators. Then, the relationship models between the viscous damper parameters and the indicators are fitted using the response surface method, and the fitting effect is evaluated through an F-test and determination coefficient R2. Finally, an objective function based on key damping performance indicators is established to solve for the optimal parameters. The results show that the traditional sensitivity analysis method is unable to comprehensively consider the combined effects of different damping efficiency indicators. The response surface method has high fitting accuracy and good predictability and can serve as an optimization model. Considering the stiffness of supporting components matched with the viscous damper parameters, the feasibility of the optimal damping parameters is demonstrated from an engineering application perspective. A simple and easy-to-operate damping design flowchart is proposed, providing important guidance and reference for designers in frame shear wall structure damping design in the future.

Seismic design and performance analysis of perforated rubber buffer layer in tunnel

Tunnels may be damaged under earthquakes, which has been observed by many earthquake events, and the buffer layer is proposed and widely investigated as a damping measure. The rubber is considered as a qualified buffer layer material because of its small elastic modulus and super elasticity, but its high price makes it difficult to apply in practical engineering. Therefore, four types of rubber buffer layers are proposed in this study, including the common rubber buffer layer and three types of perforated rubber buffer layers (PRBL), which can reduce the seismic damage and cost of tunnels. A pseudo-static method for calculating the seismic response of tunnels under horizontal and vertical earthquake motions is proposed and verified. Based on proposed pseudo-static method, a seismic design method for the buffer layer is present, and the proposed seismic design process is used to study the seismic mitigation performance of buffer layers. The initial design of the buffer layer under earthquake action E1 is carried out by pseudo-static method, and then the seismic mitigation performance is verified through dynamic time history analysis method under earthquake action E2. The earthquake action E1 and earthquake action E2 are the earthquake actions with short and long return periods of the engineering site, respectively. The results show that the common rubber buffer layer has almost no seismic mitigation performance, and the three types of PRBLs have good seismic mitigation performance. The type IV buffer layer is strip-shaped PRBL and the holes are along the longitudinal direction of the tunnel, and it has optimal seismic mitigation performance. The effects of vertical earthquake motion and peak ground acceleration (PGA) on the seismic mitigation performance of the buffer layer are studied. The results show that vertical earthquake motion has little effect on the seismic mitigation performance of different types of buffer layers. For different PGAs, the type IV buffer layer is able to efficiently decrease the peak internal force of secondary lining. The results also prove the validity of design method.

The Seismic Response of Ultra-High Voltage Gas-Insulated Transmission Lines

As an important part of the substation, the seismic capacity of ultra-high voltage (UHV) electrical equipment is related to the safe and stable operation of the substation and the whole power grid. The UHV gas-insulated transmission lines (GIL) have many structural characteristics, such as long pipeline distance, the large span between supports and the obvious amplification effect of supports. Its natural frequency is close to the predominant frequency of the seismic wave, resulting in its susceptibility to resonance or resonance-like and high seismic susceptibility. In order to analyze the seismic performance of UHV GIL better, the vibration mode decomposition response spectrum method and the dynamic time-history analysis method are used to analyze the seismic response of UHV GIL in this paper. The search for seismic weak positions of GIL is a reference for effectively improving the seismic performance of UHV GIL.

Research on seismic absorption of high-speed railway segmental assembled round-end hollow pier with low yield point steel connection buckle

The research aims to enhance the seismic safety of the segmental assembled round end hollow pier (SAREHP) of high-speed railway in high intensity seismic regions and ensure the repairability of the pier after earthquake. A low yield point steel connection buckle (LYPSCB), which is easy to be installed and to be replaced after earthquake damage, was proposed as a new seismic absorption measure for the pier, and the seismic absorption effect of the LYPSCB was deeply studied. Firstly, the nonlinear numerical model of the SAREHP with energy dissipation bar (SAREHP-EDB) was established according to the pseudo-static test results of the pier completed. Based on the numerical model of the SAREHP-EDB, the SAREHP with the LYPSCB (SAREHP-LYPSCB) was established and corrected. Subsequently, the influence of the LYPSCB on the hysteretic behavior of the SAREHP was studied, and the hysteretic behavior of the SAREHP-LYPSCB was comprehensively compared with a reference to the SAREHP-EDB. Furthermore, considering the far-field seismic wave and the near-field seismic wave with or without pulse, the seismic absorption effect of the LYPSCB was revealed through dynamic time history analysis method. The research results indicated that, by increasing the section contribution rate of the LYPSCB, the horizontal resistance, loading and unloading stiffness as well as energy dissipation capacity of the SAREHP-LYPSCB are significantly improved. However, the residual displacement of the pier is also indirectly increased. Therefore, it is suggested that the section contribution rate of the LYPSCB is controlled and designed in combination with the seismic target displacement and self-centering capacity demand of pier. The hysteretic behavior of the SAREHP-LYPSCB is better than that of the SAREHP-EDB, which indicated that the LYPSCB possesses better seismic absorption effect. Note that the seismic absorption effect of the LYPSCB is more obvious in resisting strong earthquake, in which the seismic absorption rate can reach 80 %. The near-field pulse seismic wave has the greatest impact on the seismic response of the SAREHP-LYPSCB compared with other types of seismic wave, which should be paid special attention.

Influence of spiral anchor composite foundation on seismic vulnerability of raw soil structure

A typical single-layer raw soil structure in villages and towns in China is taken as the research object. In the probabilistic seismic demand analysis, the seismic demand model is obtained by the incremental dynamic time history analysis method. The seismic vulnerability analysis is carried out for the raw soil structure of non-foundation, strip foundation, and spiral anchor composite foundation, respectively. The spiral anchor composite foundation can reduce the seismic response and failure state of raw soil structure, and the performance level of the structure is significantly improved. Structural requirements sample data with the same ground motion intensity are analyzed by linear regression statistics. Compared with the probabilistic seismic demand model under various working conditions, the seismic demand increases gradually with the increase of intensity. The seismic vulnerability curve is summarized for comparative analysis. With the gradual deepening of the limit state, the reduction effect of spiral anchor composite foundation on the exceedance probability becomes more and more obvious, which can reduce the probability of structural failure to a certain extent.

Study on the Response of Staggered Floor Isolated Structures in Mountainous Areas under Three-Dimensional Earthquakes

As coal mines are susceptible to safety accidents due to earthquakes, the requirements for structures in coal mining areas such as fire control centers and hospitals are higher, so base isolated structures, including staggered isolated structures, adapted to mountainous terrain are used in mining areas. The staggered floor isolated structure is a kind of isolated structure in mountainous areas which developed from the base-isolated structure. The theoretical research on staggered isolated structures is relatively few, and the theoretical research lags behind the practical application of engineering. In this paper, three staggered floor isolated structures with different heights of staggered floors are established. The responses of structures under one-dimensional, two-dimensional, and three-dimensional earthquakes are analyzed by the finite element dynamic time-history analysis method. The structural torsion, interstory shear force, maximum axial force, and floor displacement of the structure are compared. Due to the asymmetric characteristics of the staggered floor isolated structure, the center of stiffness of the staggered floor isolated structure deviates from the center of mass, which produces not only horizontal vibration but also obvious torsional vibration. The input of earthquakes in different dimensions also makes a difference in the response of the structure. The location between the upper isolated layer and the first floor above the upper isolated layer is a weak point of the structure. The results obtained in this study are distinguished from traditional basic isolated structures, which supplements the theoretical research of the staggered isolated structure.

Research on seismic ground motion parameters applicable to the safety of rectangular shallow tunnel

The objective of this paper is to optimize the selection of seismic ground motion intensity indexes in the seismic fortification of urban shallow-buried rectangular tunnels. This paper takes a shallow-buried rectangular tunnel in a city as the research object, uses ABAQUS to establish a finite-infinite element coupling model, and selects 70 typical seismic ground motions for dynamic calculation. Using dynamic time history analysis method to study the seismic response of tunnel lining structure in terms of internal force, minimum safety factor and strain energy, and analyze their correlation with 15 seismic ground motion parameters. Selecting the seismic ground motion parameters with strong correlation, good effectiveness, and high credibility for safety evaluation. The research results show that: Peak acceleration (PGA) has a weak correlation with the seismic response of tunnel lining structures, and PGA as an independent seismic ground motion intensity index has greater uncertainty in the seismic fortification of tunnels; Peak displacement (PGD), Root-mean-square velocity (RMSV), Root-mean-square displacement (RMSD), and Specific energy density (SED) can be used as independent seismic ground motion intensity index, The linear regression model is used to evaluate the safety of the lining structure, and finally the evaluation result is verified by the incremental dynamic analysis method (IDA), which shows that the evaluation result is accurate. The research results can provide reference for the preliminary design of seismic fortification of rectangular shallow tunnels.

Seismic response of underground stations with friction pendulum bearings under horizontal and vertical ground motions

The previous earthquake surveys show that central columns are the weak parts in subway stations during the earthquakes. Reducing the seismic responses of central columns can ensure the safety of stations. Setting friction pendulum bearings (FPB) at the top of central columns may be a good strategy. In this paper, based on a subway station in Shanghai, the FPB is simulated detailly. The isolation effect and mechanism of the FPB is studied with the three-dimensional dynamic time history analysis method. The shearing force and bending moment of the station central columns and the inter-layer displacement of the station during the earthquake are analyzed. The vertical ground motion of different amplitudes is considered. It is found that during the earthquake, the FPB can effectively reduce the maximum shearing force of the central columns and slightly reduce the maximum bending moment. At the same time, it will not cause a significant increase in the inter-layer displacement. The vertical ground motion will reduce the isolation effect of the FPB, and the degree of the reduction increases with the increase of the vertical ground motion acceleration amplitude.

A modified simplified analysis method to evaluate seismic responses of subway stations considering the inertial interaction effect of adjacent buildings

A modified simplified analysis method is proposed in this paper to evaluate seismic responses of subway stations in dense urban environments. Based on the dynamic analysis of the underground structure-soil-adjacent building interaction (SSSI) model, the seismic response of subway station was distinguished as the kinematic interaction (KI) effect (induced by the free-field movement) and the inertial interaction (II) effect (induced by the vibration of adjacent building). In order to comprehensively and simply consider the KI and II effects, a modified model was established after simplifying the analytical solution of underground structural seismic response. Owing to acquiring the dynamic response via static modelling and calculation, the method proposed herein requires a shorter analysis time and incurs a lower cost. In addition, a typical subway station-soil-ground building system in an east city in China was selected as the case-history to verify the modified method and further evaluate its computational accuracy. The traditional response displacement method and dynamic time history analysis method were also conducted in simulation as a comparison method and standard method, respectively. The case study demonstrates that referencing the results obtained by the dynamic time history analysis method (D-M), the maximum story drift and maximum internal force (including bending moment, axial force and shear force) errors of the traditional response displacement method (T-M) reached −28% and −48%, respectively. Obviously, this method is dangerous in designing due to its smaller computing results. In contrast, the modified method (M-M) which can accurately reflect the impacts of adjacent buildings, is a more accurate and safer analysis method (two seismic response indexes of the modified method generally exceeded the actual values, and more gratifying is that the errors were less than 12%). Therefore, the modified simplified analysis method proposed is a higher accuracy, safer design, less time consumed, and faster analysis process method, which can be used to substitute the traditional method in the aseismic performance and dynamic response analysis of subway stations in dense urban environments.

A BOUNDARY FORCED RESPONSE DISPLACEMENT METHOD FOR SEISMIC ANALYSIS OF SYMMETRICAL UNDERGROUND STRUCTURES

A boundary forced response displacement method is proposed for the seismic analysis of symmetrical underground structures based on the requirement of quasi-static pushover test of soil-underground structure systems. The implementation procedure and special features of the method are introduced in detail. We took the Daikai subway station which was damaged during the Kobe earthquake in Japan as an example for the analysis, and compared the results of boundary forced response displacement method, the FEM seismic deformation method and the dynamic time-history analysis method. The results show that the accuracy of the new method was much higher than the FEM seismic deformation method when the width of the model was reasonable. The errors of the internal forces and the story drift were less than 15%. The new method is an effective simplified method for seismic response analysis of symmetrical underground structures. The attenuation law of lateral boundary forced displacement was analyzed. It provides references for the quasi-static pushover test of soil-underground structure system.

Seismic response analysis of high-pier long-span continuous rigid-frame bridges under far-field long-period ground motions

The seismic response of a high-pier long-span continuous rigid frame bridge under the action of far-field long-period ground motions is studied. A numerical calculation model of a high-pier long-span continuous rigid frame bridge whose span layout is (95+170+95)m is established by using finite element software. According to the established wave selection criteria, 10 long-period far-field seismic records and 10 ordinary seismic records are selected from the strong earthquake record database. Using the dynamic time history analysis method, the seismic response of the bridge structure under the far-field long-period seismic record and the ordinary seismic record was obtained through calculation, and a comparative analysis was carried out. The results show that the seismic response of a high-pier long-span continuous rigid frame bridge under far-field long-period ground motions is significantly greater than that of ordinary ground motions, the effect of ground motion spectrum characteristics should be considered in seismic design of such Bridges.

Optimal design of a large-span spatial structure based on dynamic elastic-plastic analysis

With the expansion of the urban areas and the rapid growth of the urban population, the disposal of large amounts of domestic waste has become a problem faced by large cities. To solve this problem, many MSW incineration power plants have been continuously built. As a typical large-span spatial structure of waste incineration power plant, how to achieve economic, beautiful, and environmentally friendly design goals under the premise of meeting the requirements of the production process is an important problem currently facing. In this paper, a structural design optimization method based on damage index is proposed. Taking a large-span mixed structure of a MSW incineration power plant as an example, the paper firstly uses the dynamic elastic-plastic time history analysis method to evaluate its seismic performance, and then optimizes the structure according to the damage degree of the structure under small and large earthquakes design. The results show that under the premise of meeting the requirements of the code, this method can ensure that the degree of structural damage under the earthquake remains almost unchanged, while significantly reducing the amount of building materials and reducing the cost. At the same time, this method is more direct, simple, and effective than optimization design methods based on experience and internal forces of structural members.

Seismic Reduction Effectiveness of Friction Pendulum Bearings in Underground Station Structures

Setting friction pendulum bearings (FPB) at the top of central columns may be a good strategy to reduce the stations’ seismic responses. In this paper, the FPB is simulated in a detailed manner. The seismic reduction effectiveness of the FPB is studied with the three-dimensional dynamic time history analysis method. It is found that FPB can effectively reduce the maximum shearing force of the central columns and slightly reduce the maximum bending moment. It is stated that FPBs are also effective in the underground station structures.

Study on the damping efficiency of continuous beam bridge with constant cross-section applied by lead rubber bearings and fluid viscous dampers

Bridges are the lifelines of disasters in earthquake areas. Therefore, it is very necessary to ensure the safety and traffic function after earthquake. Seismic isolation refers to install external energy dissipation devices or external energy input devices in specific parts of engineering structures. There are certain differences in longitudinal and transverse seismic responses of multi-span continuous beam bridges by changing the seismic dynamic characteristics or dynamic effects of structures. It is difficult to achieve the purpose of seismic isolation in both horizontal directions using isolation devices alone. The rubber deformation ability of lead rubber bearings can effectively insulate, and the yield energy consumption ability of its lead core can effectively consume the seismic energy for damping. The horizontal resistance is very small under the creep load, and the stiffness decreases rapidly after yielding under the strong dynamic earthquake load; meanwhile, the seismic energy is dissipated by the hysteresis of bearing. Fluid viscous damper is a velocity-dependent energy dissipation device, which produces viscous damping force, provides strong restoring force for components, and has a good limit function. This process will also dissipate the seismic energy, so as to reduce the structural earthquake response. Using these two methods together, the horizontal seismic responses of multi-span continuous beam bridges can be effectively controlled at the same time. Based on this idea, this article takes a high-speed multi-span continuous beam bridge with equal section as the engineering background, and uses dynamic time history analysis method to discuss the seismic isolation effect of lead rubber bearings and fluid viscous dampers.

Seismic Effectiveness of Multiple Seismic Measures on a Continuous Girder Bridge

Seismic hazards, such as bridge pounding, unseating, collapse, etc., cause significant economic losses and affect traffic and safety. Research on seismic measures, such as limiting and unseating prevention devices for the bridge, can effectively prevent damage to the bearings, such as excessive displacement, the pounding of the beam end, etc., in an earthquake. In this paper, the dynamic time-history analysis method was used to study the mechanical behaviors of the bridge structure, such as its seismic performance, structural displacement, pier bending moment, etc. We found that different combinations of seismic measures can effectively reduce the displacement at the bridge expansion joint and bearings. The joint application of an expansion device, restrainer, and unseating prevention devices shows the best limiting effect on bridge displacement and expansion joint displacement. The maximum reduction of bridge expansion joint displacement reaches 48% and is within the allowable deformation range of an expansion device in a large earthquake, and the maximum reduction of bearing displacement reaches 34%, which only slightly exceeds the shear deformation of the bearing. The expansion device, restrainer, and unseating prevention devices have smaller internal forces in this case than other cases, without damage. In contrast to the previous studies on single seismic measures of unseating restrainers, this study investigates the combination of multiple seismic measures and earthquakes of various magnitude. It reveals the catastrophe process of the bridge structure and the cooperation law of seismic measures in an earthquake.

Study on the Seismic Performance of Different Combinations of Rubber Bearings for Continuous Beam Bridges

Rubber isolation bearings have been proven to be effective in reducing the seismic damage of bridges. Due to the different characteristics of isolation bearings, the mechanical properties of bridges with different combinations of rubber bearings are complex under the action of earthquakes. This paper focuses on the application of combinations of rubber isolation bearings on seismic performance of continuous beam bridges with T‐beams. The seismic performances of continuous beam bridges with different combinations of rubber isolation bearings, pier height, and span length were studied by the dynamic time history analysis method. It was found that the bridges with natural rubber bearings (NRBs) have the largest seismic responses compared to the other types of bearings. The continuous beam bridge with isolation bearings, such as lead rubber bearings (LRBs) and high damping rubber bearings (HDRBs), has approximately 20%∼30% smaller seismic response than that with NRBs under the action of earthquakes due to the hysteretic energy of the bearings, indicating that the isolation bearings improve the seismic performance of the bridge. The continuous beam bridges with both NRBs and LRBs or NRBs and HDRBs have larger seismic response of the piers than those with a single type of isolation bearings (LRBs or HDRBs) but smaller seismic response of the piers than those with only NRBs. For a continuous beam bridge with shorter span and lower pier, it is not economical to use LRBs or HDRBs underneath every single girder, but it is more reasonable to use cheaper NRBs underneath some girders. The larger difference in stiffness of the bearings between the side and middle piers leads to the more unbalanced seismic response of each pier of the bridge structure. The results also show that with increasing pier height and span length, the difference in the seismic response value between the cases gradually increases.

Numerical Modeling of Seismic Responses and Seismic Measures of Tunnel Crossing a Fault Zone: A Case Study

The investigation shows that Longxi Tunnel, across a fault zone, was severely damaged during the 2008 Wenchuan earthquake, China. In this paper, the dynamic time history analysis method is used to study the seismic response characteristics of Longxi Tunnel and the aseismic effect of seismic measures. The interfaces of the fault are simulated by bonded interfaces. The results show that high earthquake intensity, high in situ stress, and fault zone are the main reasons for damage of Longxi Tunnel. The inconsistent motion response between the normal surrounding rocks and surrounding rocks within the fault zone resulted in the damage of Longxi Tunnel, and the maximum displacement difference reaches 50 cm. With the seismic measure by setting shake absorb layer and seismic joints, the tunnel has better performance: the maximum peak internal force of the tunnel structure is reduced by about 26% and the acceleration is reduced by 30%. Seismic measures should not only be considered within fault zones but also extend to adjacent surrounding rocks. In this study, the fault seismic measures of Longxi Tunnel should be no less than 4.0 times the tunnel diameter.

Optimisation Design and Damping Effect Analysis of Large Mass Ratio Tuned Mass Dampers

Under harmonic load and random stationary white noise load, the existing fitting formulas are not suitable for calculating the optimal parameters of large mass ratio tuned mass dampers (TMDs). For this reason, the optimal parameters of large mass ratio TMDs are determined by numerical optimisation methods, and a revised fitting formula is proposed herein based on a curve fitting technique. Finally, the dynamic time history analysis method is used to study the control effect of large mass ratio TMDs. The results show that when the mass ratio is large, the error between the existing fitting formula and the actual optimal value is quite large, and the revised fitting formula is applicable to the parameter design of the traditional small mass ratio and large mass ratio (≤1) TMDs. When the ratio of local base soil predominant frequency to structure vibration frequency is greater than 4, the optimal parameters of a TMD under white noise excitation can be calculated according to the revised fitting formula, and the remaining conditions should be determined by numerical optimisation. In addition, a large mass ratio TMD reduces the dynamic response of the main structure effectively compared with a small mass ratio TMD and reduces the relative displacement between the TMD and main structure.

Application research of seismic isolation device in long-span continuous beam bridge

The three-dimensional finite element model of pre-stressed concrete continuous girder bridge with span (76+144+76)m is established by using finite element structural analysis software Ansys in this paper. The dynamic time history analysis method is used to study the influence of viscous dampers and friction pendulums with different parameters on the seismic response of long-span continuous beam bridges, which provides a basis for rational selection of seismic isolation measures. The results show that reasonable seismic isolation measures can effectively reduce the seismic response of long-span continuous beam bridges; both the viscous damper and the friction pendulum can have good seismic isolation effects, but the damping effects are related to their parameter settings.