Non-uniform Seismic Excitation Research Articles

Seismic Response Analysis of Hydraulic Tunnels Under the Combined Effects of Fault Dislocation and Non-Uniform Seismic Excitation

Hydraulic tunnels are prone to pass through faults and high-intensity earthquake areas, which will cause serious damage under fault dislocation and earthquake action. Fault dislocation and seismic excitation are often considered separately in previous studies. For tectonic earthquakes with higher frequency in seismic phenomena, fault dislocation and ground motion are often associated, and fault dislocation is usually the cause of earthquake occurrence, so it is limiting to consider the two separately. Moreover, strong earthquake records show that there will be significant differences in the mainland vibration within 50 m. The uniform ground motion inputs in previous studies are not suitable for long hydraulic tunnels. This paper begins with the simulation of non-uniform stochastic seismic excitations that consider spatial correlation. Based on stochastic vibration theory, multiple multi-point acceleration time-history curves that can reflect traveling wave effects, coherence effects, attenuation effects, and non-stationary characteristics are synthesized. Furthermore, a fault velocity function is introduced to account for the velocity effect of fault dislocation. Finally, numerical analyses of the response patterns of the tunnel lining under four different conditions are conducted based on an actual engineering project. The results indicate the following: (a) the maximum lining response values occur under the combined effects of fault dislocation and non-uniform seismic excitation, indicating its importance in the seismic resistance of the tunnel. (b) Compared to uniform seismic excitation, the peak displacement of the tunnel under non-uniform seismic excitation increases by up to 6.42%, and the peak maximum principal stress increases by up to 28%. Additionally, longer tunnels exhibit a noticeable delay effect in axial deformation during an earthquake. (c) Under non-uniform seismic excitation, the larger the fault dislocation magnitude, the greater the peak displacement and peak maximum principal stress at the monitoring points of the lining. The simulation results show that the extreme response values primarily occur at the crown and haunches of the tunnel, which require special attention. The research can provide valuable references for the seismic design of cross-fault tunnels.

A new equivalent acceleration-based non-uniform response spectrum method for efficient seismic SSI analysis

A complex multiple-support response spectrum (CMSRS) method with a concise and universal expression is required to estimate the seismic responses of soil–structure interaction (SSI) systems under non-uniform seismic excitations to replace existing complex methods. This paper introduces and defines a new concept called equivalent acceleration of boundary load (EABL) that converts widely used equivalent loads into equivalent accelerations, and further develops an efficient CMSRS-EABL method for the seismic analysis of the SSI system. First, EABL offers three main benefits: it simplifies the expressions without sacrificing precision, extends the applicable scope of viscous-spring artificial boundary (VSAB) to all stress-type artificial boundaries, and presents dynamic equations in a familiar form. Subsequently, the CMSRS–EABL formula was successfully deduced based on the equivalent simplified dynamic equations. This formula significantly simplifies the traditional method by reducing the effective modal participation factors, mean-square-roots, and cross-correlation coefficients by 4, 5 and 15 items, respectively. Finally, a rectangular construction surrounded by a VSAB–soil combination was used as an example to illustrate the convenience of the developed CMSRS–EABL method and verify its precision. The results indicate that the proposed method is characterized by greater simplicity and ingenuity, and it is capable of high precision similar to that of the conventional methods. We believe this method will be of significant benefit in evaluating the anti-seismic performance of deeply buried and long-standing structures.

Study of Non-uniform Seismic Response of Intercity Tunnels with Defective Shields

Based on the structural viscoelastic boundary theory, considering the geological changes of the soil layer and depth of tunnel crossing, the dynamic time course analysis is carried out for the defective lined tube sheet structure under non-uniform seismic excitation, to obtain the force and deformation law of the whole tunnel structure as well as the defective section. Analyze the dynamic response of shield tunnel structure under non-consistent seismic excitation under the influence of tube sheet misalignment factors, summarize the intrinsic mechanism of the dynamic response of defective tunnel tube lining structure, identify the phenomena affecting lining junction damage, and refine the seismic safety evaluation method of defective lining structure.

Performance of parallel double pipelines under non-uniform seismic excitation

This paper investigates the structural safety of parallel double-buried pipelines under non-uniform seismic excitation considering the soil-pipeline interaction. A three-dimensional nonlinear numerical model has been established to study the effects of seismic wave propagation and ground motion intensity, as well as the pipeline internal pressure and spacing between the pipelines on their structural safety. The dynamic response of the parallel double buried pipelines was evaluated in terms of the acceleration amplification, settlement of ground surface, and strain, displacement, and elliptical deformation of the pipeline. The results demonstrate that the seismic response of buried pipelines under non-uniform excitation has obvious nonlinear characteristics, especially when the loading intensity is high. It is found that the internal pressure has virtually no effect on the site acceleration response, but it amplifies the settlement of the ground surface. Meawhile, it inhibits the elliptic deformation of the pipeline. Furthermore, the variation of the elliptic deformation of parallel buried pipelines is found to be the same for different pipeline spacings considered in this study. On the other hand, the pipelines spacing has a significant influence on their seismic response as the interaction between the two pipelines gradually decreases with the increase in the spacing.

Numerical Analysis and Experimental Study on Seismic Coupling Response of Pipe-Soil System Under Bidirectional Seismic Excitation

The seismic response of buried pipeline is significantly affected by the soil around the pipeline. In this study, a numerical analysis model of the pipeline and the soil around the pipeline is built, and the finite element numerical analysis of its seismic response law is conducted to address the problem of pipeline soil seismic coupling response. A shaking table test of the seismic response of buried pipeline under two-way seismic excitation is performed based on the developed two-way layered shear continuum model soil box. The peak strain response at the middle section of the pipeline grows fastest, the peak strain of the pipeline under non-uniform seismic excitation constantly exceeds that under uniform excitation, and the axial strain of the pipeline exhibits more sensitivity to earthquake than the bending strain, as indicated by the results of numerical analysis and shaking table test. The peak value of soil acceleration response under non-uniform excitation exceeds under uniform excitation. The displacement of soil increases with the height. The pipeline soil interaction becomes more intense under non-uniform excitation, and the relative movement between pipeline and soil becomes more significant. The seismic excitation more significantly affects the axial displacement of soil. The peak value of soil acceleration response varies from larger along the pipeline to larger along the axis with the increase of the loading grade. A slight difference exists between the peak value of axial and transverse acceleration response of the pipeline. The peak value of pipeline acceleration response declines in the axial direction than the peak value of soil acceleration response, whereas it rises in the transverse direction than the peak value of soil acceleration response, especially under non-uniform excitation. As revealed by the above results, the effect of bidirectional non-uniform seismic excitation on the lateral pipeline soil interaction is enhanced, and soil is more seriously damaged.

Quantification of the effects of the spatial variation of ground motions on the seismic response of highway bridges

The stochastic responses of highway bridges to spatial variation of ground motions (SVGM) are analysed in this paper. A model of spatially varying ground motions is used to investigate the relative importance of the incoherency effect, the wave passage effect and the site effects on the stochastic dynamic response of an asymmetrical R.C box girder highway bridge with variable inertia. In this study, the incoherency effect is investigated using two widely used models while the wave-passage effect is incorporated using various wave velocities. Then, the random vibration theory is applied to study the effect of the non-uniform seismic excitations on the bridge structure. The bridge response is evaluated in terms of the mean values of the maximum displacements and the bending moments. Analyses of both stationary and transient response are performed. The results show that the stochastic dynamic responses related to site effects are mostly much greater than those calculated using uniform, delayed and incoherent seismic excitation assumptions. As a result, analytical models used for the stochastic dynamic analysis of long span highway bridges should take into account all the SVGM components, particularly the site-response effects.

Numerical analysis of buried pipelines response to bidirectional non-uniform seismic excitation

The multi-directional, spatially variable earthquake motion is a primary cause of pipeline damage during earthquakes. A comprehensive finite element model considering soil nonlinearity and pipeline-soil interaction nonlinearity was established and validated based on shaking table tests and then employed to investigate the difference in response of buried pipelines subjected to longitudinal unidirectional (UD) and bidirectional (BD) horizontal non-uniform excitations. The responses were evaluated in terms of the acceleration and axial strain time histories along with the peak axial strain, hoop strain, and radial strain in the pipeline cross-section. The results demonstrate that the strain response and axial force of the pipeline under BD excitation are 50%-70% larger than under UD excitation. The large difference is attributed to the increase in maximum frictional force and the delay of the strain growth inflection point under the BD excitation. It was also observed that the pipeline cross-section experienced only lateral ovalization under the UD excitation. For the BD excitation, the cross-section experienced both lateral ovalization and vertical ovalization. Finally, the existence of the Y-direction seismic component in the BD excitation did not significantly change the X-direction acceleration response of the pipeline but increased the peak values.

Shake table test and numerical analysis of the seismic response of buried long-distance pipeline under longitudinal non-uniform excitation

To investigate the seismic response characteristics of buried pipelines under longitudinal non-uniform seismic excitation, a three-dimensional finite element overall analysis model is established on finite element analysis software based on the shaking table test of buried oil and gas pipelines under longitudinal non-uniform excitation. The calculated results are compared with the experimental analysis results to evaluate the correctness and reliability of the established model. The acceleration response, strain response, and displacement response of buried oil and gas pipelines and surrounding soil under longitudinal traveling wave excitation at different seismic intensities are compared and analyzed using finite element models to supplement the test conditions. The test and analysis results show that the longitudinal displacements at each measurement point under longitudinal non-uniform excitation follow the same pattern except for differences in displacement magnitude and the vibration pattern of the tube and soil when the peak input acceleration reaches 1.00 g. As shown by both experimental and numerical simulation results, the soil acceleration amplification coefficients along the soil height fluctuate between 0.5 and 1.5. The pipe acceleration time curves and Fourier spectrum exhibit the same simulated and experimental pipe acceleration waveforms, and they both show significant amplification in the low to medium frequency band of 5–20 Hz. The testing and numerical simulated pipeline axial strain peak curves are similar and in good agreement, indicating the high reliability of the experimental results.

Application of an integrated nonuniform seismic random excitation method in tunnel engineering in soft soil areas

Nonuniform seismic excitation cannot be neglected in the seismic design of long-span tunnels in soft soil areas, as it might induce tunnel damage. This paper proposes a method that combines an integrated nonuniform seismic random excitation method with the finite element method to solve the problem of nonuniform seismic input for geotechnical tunnel seismic design in soft soil areas. The integrated nonuniform seismic random excitation method of producing multipoint random seismic waves is investigated considering the effects of passage, incoherence, and energy attenuation. Design codes are developed to achieve random seismic ground waves, baseline adjustment and filtering, and inversion of bedrock. The correctness of an integrated nonuniform seismic random excitation is verified by analysis of the differences (5%–10%) between the simulated and theoretical power spectrum functions. Based on this modelling, the dynamic responses of tunnels subjected to longitudinal and lateral seismic excitations are investigated. Nonuniform seismic excitation will cause greater tunnel deformation and internal forces than uniform seismic excitation due to the tunnel consuming more seismic energy under nonuniform seismic excitation. Longitudinal nonuniform seismic excitation induces compressive and tensile states in the tunnel, and the maximum tension is close to the tensile strength of the concrete. Lateral nonuniform seismic excitation can enlarge the bending moment and shear force, and bending moment and shear force distribution ranges are recommended for this case study.

Rapid Seismic Evaluation of Continuous Girder Bridges with Localized Plastic Hinges.

In seismic assessment of continuous girder bridges, plastic hinges form in bridge piers to dissipate seismic energy through nonlinear restoring forces. Considering temporal and spatial variations of ground motions, seismic evaluation of the bridges involves nonlinear stochastic vibration and expensive computation. This paper presents an approach to significantly increase the efficiency of seismic evaluation for continuous girder bridges with plastic hinges. The proposed approach converts nonlinear motion equations into quasi-linear state equations, solves the equations using an explicit time-domain dimension-reduced iterative method, and incorporates a stochastic sampling method to statistically analyze the seismic response of bridges under earthquake excitation. Taking a 3 × 30 m continuous girder bridge as an example, fiber beam-column elements are used to simulate the elastic–plastic components of the continuous girder bridge, and the elastic–plastic time history analysis of the continuous girder bridge under non-uniform seismic excitation is carried out. Results show that the computation time is only 5% of the time of the nonlinear time history approach while retaining the accuracy. This study advances the capability of rapid seismic assessment and design for bridges with localized nonlinear behaviors such as plastic hinges.

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

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

Modal Identification of a Soil-subway System with Emphasis on Scattering of Seismic Waves Induced by Uniform and Non-uniform Support Excitations

ABSTRACT Subways, as one of the critical structures in urban design for solving traffic problems, require continuous monitoring during operation. Therefore, it is imperative to study the scattering of seismic waves caused by the presence of these underground structures. System identification is one of the most efficient methods for investigating structural behavior during operation and identifying potential problems that may be encountered for an in-service underground structure. In this study, through extending an advanced system identification method called Frequency Response Function Matrix and Singular Value Decomposition (FRFM-SVD) and wavelet transform methods, modal parameters of a soil-subway system were identified. Further, using a random vibration method based on coherence functions, non-uniform accelerations under site condition were generated and the seismic behavior of soil-subway model under uniform and non-uniform seismic excitations were studied. The obtained results indicated that the FRFM-SVD method developed in this study shows a reasonable accuracy for identifying the seismic behavior of underground structures. The maximum amplification of the responses will occur in the proximity of the subway to the amount of 1.75 under non-uniform excitation, which is almost 20% greater than that from uniform excitation. Thus, to increase the accuracy of the estimation of ground surface accelerations, the effect of the presence of underground structures should be accompanied by considering non-uniform excitation in the analysis.

Numerical investigation on behaviour of cylindrical steel tanks during mining tremors and moderate earthquakes

Cylindrical steel tanks are important components of industrial facilities. Their safety becomes a crucial issue since any failure may cause catastrophic consequences. The aim of the paper is to show the results of comprehensive FEM numerical investigation focused on the response of cylindrical steel tanks under mining tremors and moderate earthquakes. The effects of different levels of liquid filling, the influence of non-uniform seismic excitation as well as the aspects of diagnosis of structural damage have been investigated. The results of the modal analysis indicate that the level of liquid filling is really essential in the structural analysis leading to considerable changes in the shapes of vibration modes with a substantial reduction in the natural frequencies when the level of liquid increases. The results of seismic and paraseismic analysis indicate that the filling the tank with liquid leads to the substantial increase in the structural response under ground motions. It has also been observed that the peak structural response values under mining tremors and moderate earthquakes can be comparable to each other. Moreover, the consideration of spatial effects related to seismic wave propagation leads to a considerable decrease in the structural response under non-uniform seismic excitation. Finally, the analysis of damage diagnosis in steel tanks shows that different types of damage may induce changes in the free vibration modes and values of natural frequencies.

Longitudinal response of buried pipeline under non-uniform seismic excitation from multi-point shaking table tests

The spatial variability of ground motion has a significant influence on the seismic response of long infrastructure and is considered the primary cause of pipeline damage during earthquakes. In this study, a series of three-dimensional shaking table tests were carried out to investigate the influence of non-uniform seismic excitation on the pipeline response using a scaled pipeline model installed in sand. The pipeline-soil model was enclosed in a suspension continuum soil box situated on three shaking tables that can induce uniform and non-uniform seismic excitations. Accelerometers were distributed along the soil profile, and strain gauges and accelerometers were attached to the pipeline to monitor the dynamic response of the pipeline-soil system during the shaking. The pipeline-soil model was subjected to a series of uniform and non-uniform excitations with gradually increasing intensity. The testing results demonstrated that the pipeline experienced tensile and compressive strains due to the longitudinal seismic excitation because the phase and waveform of the seismic waves were almost the same at the strain measuring points around the pipeline profile. The acceleration response of the pipeline under non-uniform seismic excitation was larger than that of the surrounding soil. The pipeline strain response under non-uniform seismic excitation was approximately twice that under uniform seismic excitation. The soil-pipeline interaction exhibited complex behavior; sliding may occur with the increase of loading intensity, and more likely to occur under non-uniform seismic excitation. These results indicate that the dynamic response of the pipeline-soil system is sensitive to non-uniform ground motion, which should be properly considered in the seismic design of pipeline.

Nonlinear soil response under non-uniform seismic excitation from multi-point shaking table tests

The soil response to large earthquakes is strongly nonlinear, which has a significant influence on the performance of buried infrastructure as well as input motion to superstructures. This paper reports on uniform and non-uniform multi-point shaking table tests to elucidate the effect of soil non-linearity on free-field soil response. Emphasis was placed on investigating the effect of the non-uniform seismic excitation in different directions on the soil response. The tests were conducted on scaled sand deposits enclosed in a suspension continuum soil box using three shaking tables that can induce uniform and non-uniform seismic excitations. Quantitative analyses were performed to study the ground motion response characteristics and variation of free-field soil characteristics underground motions with different intensity, frequency content and directions. The analyses evaluated the soil dynamic characteristics and their variation with strain level, as well as soil acceleration and settlement responses. The results demonstrated that the soil nonlinear behavior is influenced by the ground motion intensity, direction (longitudinal or transverse) and uniformity. Non-uniform ground motion may lead to more pronounced changes of soil structure, which would decrease the soil profile natural frequency and increase its damping ratio. The variation of soil shear modulus with strain also reflected the soil plastic response. The longitudinal excitation had a more pronounced effect on the soil vertical settlement compared with the transverse excitation. However, non-uniform excitation had a minor effect on the soil vertical settlement.

Response spectrum method for seismic analysis of monopile offshore wind turbine

Monopile offshore wind turbines (MOWT) are inserted into sea water and sea bed soil. As the piles are usually embedded into the soil as deep as about 40 m, dynamic pile-water and pile-soil interactions, as well as seismic excitation non-uniformity, often occur under earthquake. In this paper, the response spectrum method (RSM) is developed to calculate the maximum response of MOWT considering the pile-water and pile-soil interactions subjected to the non-uniform seismic excitation. The tower and pile are modeled by Timoshenko beam elements, with both nacelle and rotor including hub and blades integrated as a lumped mass at the top of the tower. The pile-water and pile-soil interactions are considered by added mass and soil spring at their interfaces, respectively. The non-uniform seismic excitation is obtained by the site transfer function from the horizontal earthquake motions or design response spectrum at the water-soil interface. The seismic analysis model is solved by using a multiple-support RSM under design response spectrum. Seismic responses of a case of 5-MW MOWT on two types of soil sites are analyzed. The results indicate that the pile-water and pile-soil interactions and seismic excitation non-uniformity should be considered in analyzing such seismic problems of MOWT, while the RSM can be an effective tool.

Design and Commissioning of Continuous Soil Box Supported on Shake Tables Array for Testing Long Geostructures

The seismic soil response and soil-buried infrastructure interaction are of immense importance for the resilience of urban centres. Shake table testing offers an efficient tool for modeling the seismic soil-structure interaction. This paper presents the design and commissioning of a suspended continuum soil box supported on an array of shake tables to enable simulating homogeneity and inhomogeneity of soil and non-uniform seismic excitation of extended buried structures such as pipelines and tunnels. The large-scale shaking table model involves a steel box 7.3 m × 1.4 m × 1.2 m supported by 3 shake tables. It comprises 3 active rigid boxes (2 end boxes and one middle box) supported on 3 shaking tables and 2 passive (suspended) soft joint boxes to provide continuous soil medium. The continuous box design is modular and allows its expansion to be supported by the available 9 shaking tables for even much longer soil continuum model. The developed test setup was used to investigate the seismic response of free-field soil to verify the performance of the soil continuum box. The sand test model was instrumented with arrays of accelerometers embedded along its height within both rigid and suspended boxes to evaluate the effect of the test setup on the ground motion characteristics in both segments. Dynamic performance of the continuum box is examined by comparing the results of shaking table tests on the box empty and box containing a sand model. The results demonstrat that the soil box did not experience resonance with the sand model, hence it did not affect its response to the shaking. A quantitative analysis is conducted to evaluate the box boundary effects on the soil seismic response in terms of the L2-norm, μ, the acceleration time history waveform and Fourier spectrum characteristics at soil surface and 0.7m below surface. The consistency of surface peak acceleration under different seismic excitations and intensity levels are compared in terms of standard deviation, β. The results demonstrat that the developed suspended continuum model box performed well and can simulate the continuity and boundary conditions of free-field.

Seismic Pounding Between Bridge Segments: A State-of-the-Art Review

Earthquake-induced structural pounding in bridge structures has been observed in several previous seismic events. Collisions occur at the expansion joints provided between adjacent decks or between the deck and abutment. Pounding between the structural elements may lead to severe damages and even to the unseating of the bridge in certain cases. Several investigations have been performed to study pounding in bridges under uniform and non-uniform seismic excitations. Moreover, different mitigation measures have been suggested to overcome the drawbacks of this phenomenon. This work reviews previous research studies concerning earthquake-induced structural pounding in bridge structures, the factors that influence it and the recommended mitigation measures.

Study on the Seismic Response of Long and Large Tunnel under Non-Uniform Excitations

In recent years, the underground tunnel engineering has developed rapidly, moving towards long, large, deep, new and complex structures. The seismic design of the tunnel should consider not only the conventional consistent excitation, but also the response of the non-uniform seismic excitation to the tunnel. Taking the actual Yellow River tunnel project as an example, the non-uniform seismic excitation analysis method is used to study the lateral and longitudinal seismic responses of the super-large tunnel, and the deformation characteristics of the top, bottom and waist of the tunnel are analysed. The study found that the longitudinal deformation and mechanical behavior of long tunnels are characterized by non-uniformity, inhomogeneity and asymmetry. Under the non-uniform excitation, the maximum response displacement of the top, bottom and waist of the tunnel section is larger than the displacement under the uniform action. Therefore, during the design of long tunnels, longitudinal seismic deformation should be emphasized, and the study of non-uniform load effect should be strengthened.

ANALYSIS OF LOCAL SITE EFFECTS ON SEISMIC RESPONSE OF FRAME STRUCTURES SUPPORTED BY FOUNDATIONS AT DIFFERENT ELEVATIONS

Frame structures supported by foundations with different elevations (such as a structure on the slope) undergo different ground motions because of the local site effect. Seismic response of the structure under non-uniform excitation of ground motion is different from that under uniform excitation on upper embedding end or lower embedding end. Sites with the same height difference and different soil conditions were set up in this paper to subject them to ground motions related to different positions and the seismic response of structures built on the sites under uniform and non-uniform strong seismic excitation were compared. The results show that the predominant period and amplitude of ground motions on upper embedding end and lower embedding end are different and affected by soil conditions. The extent and law of amplification of shear force, displacement and storey drift of structures under non-uniform excitation differ from those under uniform excitation when soil changes from soft to medium-hard soil. In addition, the position and degree of plastic hinges change under non-uniform excitation compared to uniform excitation. The uniform excitation using the ground motion on the upper embedding end is not always safe for the frame structure supported by foundations at different elevations.