Stochastic Seismic Response Analysis Research Articles

Stochastic seismic dynamic response analysis for coupled transmission tower-insulator-line systems considering soil-structure interaction

The conventional seismic analysis and design of transmission tower-insulator-line systems usually ignore the effects of soil-structure interaction (SSI) and the randomness of ground motions, which might lead to an unreasonable estimation of the system's seismic performance. In addressing this issue, this paper proposes two effective simplified models of coupled transmission tower-insulator-line systems considering soil-structure interaction (CTILSs-SSI), for stochastic seismic dynamic response analysis. In these models, the foundation and tower are simulated by single and multiple degree of freedom models, respectively; meanwhile, the insulator is simulated by a single pendulum model, and the effect of SSI is considered using the swing-rocking (S-R) model. Specifically, for the in-plane vibration, the transmission line is simulated by a multiple degree of freedom rigid-bar assemblage with lumped masses; for the out-of-plane vibration, the transmission line is simulated by a multiple pendulum model. On this basis, the equations of motion for CTILSs-SSI under both in-plane and out-of-plane vibrations are derived utilizing the Euler-Lagrange equation. Subsequently, a non-stationary stochastic seismic dynamic response analysis framework for CTILSs-SSI is proposed by incorporating the proposed simplified models with the probability density evolution method (PDEM). An ultra-high voltage (UHV) transmission tower-insulator-line system is taken as an example. The simplified models of this exemplar system are established and validated using ANSYS software. In addition, the deterministic and stochastic seismic dynamic response analyses of this exemplar system are conducted. The analysis results demonstrate that the dynamic response amplitudes of the tower top and the tower's natural periods increase considering the effect of SSI, and the impact of SSI increases as the subsoil softens. Furthermore, the probability density function (PDF) of the tower top displacement of the CTILS-SSI exhibits distinct shapes at various moments. The mean value of the tower top displacement of the CTILS-SSI fluctuates around zero over time, while the standard deviation increases within approximately 0s–10s and then decreases.

Probabilistic analysis of seismic mitigation of base‐isolated structure with sliding hydromagnetic bearings based on finite element simulations

AbstractBase isolation is one of the most efficient methods for seismic mitigation of building and bridge structures in high‐intensity areas. However, the base‐isolated structure designed according to current codes based on the local seismic hazard and a few station records might not guarantee the performance of the base isolation system and ensure the safety of the structure. Carrying out a probabilistic analysis of seismic mitigation of base‐isolated structures, considering the randomness associated with earthquake ground motions, is thus necessary. To this end, the stochastic seismic response and reliability analysis of base‐isolated structures subjected to stochastic ground motions are conducted in this study, in conjunction with the probability density evolution method and the principle of equivalent extreme value event. The recently developed sliding hydromagnetic bearing is employed to constitute the base isolation layer of the base‐isolated structure. A refined finite element analysis is carried out to accurately reveal the dynamic characteristics of the base‐isolated structure. It is shown that the base‐isolated structure can be well simulated by the finite element model, which is verified through a comparative study with the results of shaking‐table tests. The base‐isolated structure gains a sound seismic mitigation compared to the base‐fixed structure in a probabilistic sense, and can ensure the safety of the structure by deploying a moderately designed base isolation system.

Effects of response spectrum of pulse-like ground motion on stochastic seismic response of tunnel

It is widely accepted that near-fault pulse-like ground motions potentially cause more severe damage to structures than ordinary ground motions. However, the effects of stochastic pulse-like ground motions on underground structures are not effectively considered. The impacts of response spectra of pulse-like ground motions on seismic response are also unclear. Hence, this study utilizes an underground tunnel to investigate the effects of response spectra of pulse-like ground motions on the stochastic seismic response by combining a pulse-like ground motion simulation method and a finite element method. The combination procedure enables stochastic seismic response analysis under spectrum-compatible pulse-like/ordinary ground motions. The finite element model considers the nonlinear dynamic properties of soil and soil–structure interaction. Monte Carlo simulations are carried out to quantify uncertainties of stochastic tunnel response. Results show that pulse-like ground motions cause larger bending moments for tunnel lining even when they match the same target spectrum of ordinary ground motions. Furthermore, the bending moment of tunnel lining is significantly amplified when the spectral acceleration of pulse-like ground motion contains bulges or multiple peaks in the ranges of 1 s–6 s. Therefore, the seismic risk of tunnels may be significantly underestimated in the near-fault regions without considering pulse-like ground motions and their spectral acceleration characteristics.

Seismic response analysis of subway station structure under random excitation based on probability density evolution method

The subway station structure mainly faces the uncertainty of ground motion and surrounding soil mass. Comprehensive analysis of the seismic response of subway station structures under random excitation is the key to ensuring the safety of urban people's lives and property. In this paper, the random shear wave velocity profile model and the random ground motion model characterizing uncertainty are established. Using a high-dimensional space optimization point selection strategy significantly reduces the number of sample points and computational costs of nonlinear time history analysis (NLTHA). Combining the probability density evolution method (PDEM) with finite element analysis, the stochastic seismic response analysis of the subway station structure under dual random excitations is realized. In addition, statistical methods are used to analyze the distribution characteristics of the most unfavorable seismic responses of the subway station structure. The research results show that when random excitation is not considered, the adverse seismic damage risk of subway station structures will be ignored. The evolution of the seismic dynamic response of subway station structures is mainly controlled by the amplitude of random ground motion acceleration. Additional random shear wave velocities can increase the lateral deformation range of the subway station structure, leading to a decrease in the dynamic reliability of the structure. PDEM can conduct stochastic seismic response analysis of the subway station structure from both time and response dimensions. The proposed method provides strong support for a comprehensive analysis of the seismic response of underground structures.

Nonlinear Stochastic Seismic Response Analysis of Three-Dimensional Reinforced Concrete Piles

A reliable assessment and design of engineering structures requires appropriate estimation and consideration of different sources of uncertainty. The randomness of seismic ground motion is one major uncertainty that needs to be considered from the perspective of performance-based earthquake engineering. To properly account for this uncertainty and its corresponding effect on pile foundations, a stochastic seismic response analytical framework based on a probability density evolution method and a stochastic ground motion model is proposed for the nonlinear stochastic seismic response analysis of pile foundations. A three-dimensional finite element model of a reinforced concrete pile with a large diameter embedded in the soil foundation is firstly established and calibrated using the full-scale lateral load test results from the literature, in which the nonlinear behavior of soil, the soil–pile interaction, the concrete damaged plasticity, and the steel yielding of the pile are properly modeled. Then, the calibrated three-dimensional numerical model is employed as an illustrative example for the stochastic seismic response analysis using the proposed framework. The mean, standard deviation, and probability density function of pile settlement and the dynamic reliabilities of the pile concerning various performance requirements are obtained in the present study. The settlements of the pile show great variability under the excitation of various stochastic ground motions, and the maximum mean value of the pile settlements is about 8 mm. The changing shape of the settlement probability density functions in every moment demonstrates that it is unreasonable to use assumed probabilistic distribution models to characterize the seismic responses of pile foundations during a seismic reliability analysis. Based on the proposed method, it is found that the dynamic reliabilities of the selected reinforced concrete pile concerning four different performance levels are 0, 0.1293, 0.8247, and 1, respectively. The proposed stochastic seismic response analytical method in the present study can provide a proper and comprehensive way to quantify various uncertainties and their corresponding effects on the seismic performance of pile foundations. It can also be used to estimate the actual reliability level of pile foundations that are designed by the current codes when they are subjected to seismic loads.

Nonlinear stochastic seismic dynamic response analysis of submerged floating tunnel subjected to non-stationary ground motion

Owing to the randomness of seismic excitations, the submerged floating tunnel (SFT), which is a new structure subjected to the combined action of self-weight, buoyancy, and anchorage under seismic excitation, is a nonlinear stochastic dynamic system and the evaluation of its dynamic performance is an issue that must be addressed. In this study, the nonlinear dynamic differential equation of an SFT subjected to seismic dynamic action was systematically derived by considering the wave–structure dynamic coupling interaction, and its numerical solution was obtained based on the Newmark-β integration algorithm. Furthermore, based on the theoretical framework of nonlinear stochastic dynamics and the stochastic seismic model reflecting the characteristics of the site-specific response spectrum, the probability density function (PDF) of the nonlinear seismic dynamic response of the SFT was analyzed, and its seismic dynamic performance was evaluated based on dynamic reliability. Thus, it was found that the randomness of ground motion propagates, fluctuates, evolves, and dissipates in the SFT, and finally reaches the nonlinear seismic dynamic response of the SFT. Additionally, the nonlinear dynamic response of the underwater suspension tunnel is highly sensitive to earthquake excitations. The proposed evaluation framework is an effective tool for evaluating the seismic performance of underwater tunnels.

Stochastic seismic response analysis of engineering site considering correlations of critical soil dynamic parameters

Stochastic seismic response analysis of engineering site considering correlations of critical soil dynamic parameters

GPDEM-based stochastic seismic response analysis of high concrete-faced rockfill dam with spatial variability of rockfill properties based on plastic deformation

The spatial variability of rockfill properties is the key factor affecting stochastic seismic responses. Herein, an efficient probabilistic analysis method for stochastic seismic analysis named the generalized probability density evolution method (GPDEM) is proposed and combined with the random field generated by K-L decomposition to evaluate the stochastic seismic responses of concrete-faced rockfill dams (CFRDs) during earthquakes. The vertical plastic deformation is selected as a significant index to quantify the effect of rockfill spatial variability. First, a series of 2D random fields and a finite element model of the CFRD profile are established. Each realization of random fields is assigned to each grid depending on the coordinates. Then, four working conditions (different constitutive model parameters, cross-correlation coefficients, concrete-faced slab contact positions and earthquake intensities) are investigated and compared in CFRD dynamic calculations. Finally, the GPDEM-based vertical plastic deformation results are obtained, and probabilistic analyses are carried out to evaluate the influence of rockfill property uncertainty on the stochastic seismic responses. Multiple figures of the probability density function (PDF) and cumulative distribution function (CDF) of dynamic calculations are shown as examples to analyze the marked effect of rockfill spatial variability. The results demonstrate that the control parameter (Mf) is the most influential parameter of stochastic seismic responses in the GPDEM. The cross-correlation coefficient increases the probability of large vertical plastic deformation compared to zero. Moreover, the nonfaced-slab side is more sensitive to the effect of rockfill uncertainties. Increasing the seismic motion intensity causes a larger probability beyond the limit.

Stochastic dynamic response and seismic reliability analysis of nuclear power plant’s vertical retaining wall based on plastic failure

Vertical retaining wall is usually built at the water intake in front of the pump station and is widely used in the protection of intake and voidance structures of nuclear power plants (NPPs). It has great practical significance for disaster prevention to gauge the plastic failure of vertical retaining wall accurately. In this paper, a generalized plastic model is introduced to obtain the residual deformation of vertical retaining wall during earthquake and the numerical simulation results based on plastic model reflect the plastic failure mode of the vertical retaining wall, which is consistent with the shaking table test results. In addition, the seismic excitation has great uncertainty, and in order to reflect the uncertainty, a set of fully nonstationary stochastic seismic loading samples are generated with spectral representation random function method. As a recently developed dynamic reliability methodology, the probability density evolution method (PDEM) is incorporated to the generalized plastic model to perform stochastic seismic response analysis of a vertical retaining wall. Plentiful probabilistic results of vertical retaining wall, such as evolution of probability density functions (PDF) and second-order statistics are acquired in this study. Finally, the dynamic reliability of vertical retaining wall under two earthquake levels are obtained based on the dip angle, which can more directly reflect the failure probability and degree of vertical retaining wall. The results of this study indicate that the geotechnical structures can show a more objective failure mode under earthquakes based on the plastic model, and it is more reliable to evaluate the safety of structures from the perspective of probability combined with PDEM.

Evaluation of the seismic site response in randomized velocity profiles using a statistical model with Monte Carlo simulations

Abstract Uncertainty associated with the soil properties inevitably affects the seismic ground response, which is unable to be properly assessed using a deterministic seismic site response analysis. In this paper, an attempt has been made to investigate the possible impact of the shear-wave velocity ( V s ) variation on the predicted ground motions using a real site in Italy. A statistically-based randomization model is adopted to describe the uncertainty of the V s profiles for various scenarios. The equivalent-linear method combined with the direct Monte Carlo simulation is employed to perform the stochastic seismic site response analysis. The results are presented in terms of amplification function ( AF ), spectral acceleration ( S a ), fundamental frequency ( f 0 ) and amplification factor ( F a ). The mean and standard deviation of these four factors are evaluated for a wide range of shear-wave velocity variations, interlayer correlations, and input motion intensities. This study also explores the accuracy of adopting truncated bounds as an approximate process of preventing the generation of unrealistic soil profiles. The results show that the variability of the predicted ground motion is significant in some situations and can be decreased by reducing the shear-wave velocity uncertainty.

PDEM-based stochastic seismic response analysis of sites with spatially variable soil properties

The spatial variability of soil properties has a significant effect on the seismic responses of sites. Considering that the probability density evolution method (PDEM), an efficient probabilistic methodology, has not been used in the probabilistic analysis with spatially variable soil properties before, the random field theory is incorporated to the traditional framework of PDEM to perform stochastic seismic response analysis of a soil profile. The stochastic seismic responses, including seismic deformation, surface ground motion, amplification factor and excess pore water pressure ratio, are obtained to quantify the effect of spatially variable soil properties. Probabilistic sensitivity analyses are also carried out to study the influence of spatial variability of different soil parameters and coefficients of variation on the ground motion in terms of probability density function. The results indicate that the random field model of shear modulus has a higher possibility of experiencing higher ground motion intensity than does friction angle.

Stochastic seismic response and stability reliability analysis of a vertical retaining wall in front of the pumping station of a nuclear power plant using the probability density evolution method

Vertical retaining walls are widely used to protect the water intake and drainage structures of nuclear power plants (NPPs); in particular, they are built as the inlet in front of the pumping station pool. It is of great significance to investigate the seismic behavior of the vertical retaining walls considering the uncertain nature of earthquakes according to the nuclear safety design requirements. The probability density evolution method (PDEM), which is a new and efficient methodology, is proposed here to study the stochastic seismic response and stability reliability of a vertical retaining wall in front of the pumping station pool of a NPP. Firstly, a set of representative acceleration time histories of non-stationary earthquake ground motions are generated by the spectral representation random function method according to the RG1.60 spectra for the NPP project design. Then, a series of deterministic stochastic seismic response analysis of a 26-m-high vertical retaining wall are performed. Finally, the probability information and seismic reliability of the vertical retaining wall under two seismic levels (SL-1 (operating-basis earthquake) and SL-2 (safety shutdown earthquake)) are obtained based on two physical parameters: the anti-sliding safety factor and anti-overturning safety factor. The results demonstrate that the proposed method of investigating the stochastic responses and seismic reliability of vertical retaining walls can provide more objective indices to evaluate the seismic safety during SL-1 and SL-2 seismic events. Furthermore, the proposed method can effectively investigate the ultimate seismic capacity of vertical retaining walls and other geo-structures in NPPs.

Stochastic seismic response analysis of buried onshore and offshore pipelines

Previous studies on the seismic responses of offshore pipelines are not only very limited but also usually use earthquake ground motions recorded at the onshore sites as the inputs in the analyses due to the lack of seafloor earthquake recordings and the difficulty to predict seafloor seismic motions. This application may lead to erroneous predictions of offshore pipeline seismic responses, since it has been revealed that the existence of the seawater can significantly suppress the seafloor vertical motions near the P-wave resonant frequencies of the seawater layer. Moreover, the seawater layer can indirectly influence the seafloor motions by changing the water saturation and pore pressure of subsea soil layers, which in turn may obviously affect the propagation of seismic P-wave at the offshore site and therefore the pipeline seismic responses. This paper investigates the stochastic seismic responses of buried onshore and offshore pipelines. The direct and indirect influences of seawater layer on the seafloor seismic motions are explicitly considered by using the recently derived theoretical local site transfer functions. The mean peak seismic responses of buried onshore and offshore pipelines in the axial and lateral directions are stochastically formulated in the frequency domain. The differences between the onshore and offshore pipeline seismic responses are emphasized and the influences of seawater depth and water saturation level of the subsea site on the offshore pipeline responses are discussed.

Dynamic reliability analysis of slopes based on the probability density evolution method

Earthquake ground motions display random behavior; therefore, it is necessary to investigate the seismic response of engineering structures using stochastic analysis methods. The probability density evolution method (PDEM) is applied in stochastic seismic response analysis and dynamic reliability evaluation of slope stability. Combining PDEM with finite-element dynamic time-series analysis, this study analyses the stochastic seismic response of a slope under random earthquake ground motion. Comparison between the results of the Monte Carlo stochastic simulation and PDEM analysis demonstrates the effectiveness and high precision of the PDEM method. We assess the stability of the slope under earthquake conditions using the safety factor criterion to obtain the stability probability of the slope. Compared with traditional equilibrium methods, the reliability analysis can directly reflect the failure probability and degree of safety of the slope, demonstrating a novel approach to slope stability assessment using a random dynamic method.

A marginal fractional moments based strategy for points selection in seismic response analysis of nonlinear structures with uncertain parameters

The present paper proposes a new strategy for selecting representative points in the probability density evolution method (PDEM) to conduct stochastic seismic response analysis of nonlinear structures with uncertain parameters. In PDEM, the strategy for selecting representative points in random-variate space is of critical importance to the efficiency and accuracy. The proposed strategy is established based on the marginal fractional moments of input random variables, which can be evaluated both analytically and numerically without difficulty before performing stochastic analysis. In this strategy, an optimization problem is actually involved. First, the initial points are generated by a low discrepancy sequence and the corresponding assigned probabilities can be computed accordingly. Then, the initial points are rearranged to minimize the index, which is adopted as the maximum relative error between the estimated marginal moments and the exact ones. The rearranged points are accepted as the representative points in PDEM when the index reaches the prescribed tolerance. Numerical example is investigated, showing that the proposed strategy can achieve the good tradeoff of efficiency and accuracy in PDEM for seismic response analysis of structures with uncertain parameters.

Random function based spectral representation of stationary and non-stationary stochastic processes

In conjunction with the formulation of random functions, a family of renewed spectral representation schemes is proposed. The selected random function serves as a random constraint correlating the random variables included in the spectral representation schemes. The objective stochastic process can thus be completely represented by a dimension-reduced spectral model with just few elementary random variables, through defining the high-dimensional random variables of conventional spectral representation schemes (usually hundreds of random variables) into the low-dimensional orthogonal random functions. To highlight the advantages of this scheme, orthogonal trigonometric functions with one and two random variables are constructed. Representative-point set of the dimension-reduced spectral model is derived by employing the probability-space partition techniques. The complete set with assigned probabilities of points gains a low-number-sample stochastic process. For illustrative purposes, the stochastic modeling of seismic acceleration processes is proceeded, of which the stationary and non-stationary cases are investigated. It is shown that the spectral acceleration of simulated processes matches well with the target spectrum. Stochastic seismic response analysis, moreover, and reliability assessment of a framed structure with Bouc-Wen behaviors are carried out using the probability density evolution method. Numerical results reveal the applicability and efficiency of the proposed simulation technique.

A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters

In the stochastic dynamic analysis of nonlinear structures, the strategy of point selection plays a critical role in achieving the tradeoffs between the accuracy and efficiency. To this end, cooperated with the concept of the extended F-discrepancy (EF-discrepancy), the Koksma–Hlawka inequality, which bounds the worst error of cubature formulae, is extended to the cases involving non-uniform distributions in the present paper. Further, in order to avoid the computational complexity of EF-discrepancy, the Generalized F-discrepancy (GF-discrepancy) is introduced. In light of the quantitative equivalence between the EF-discrepancy and GF-discrepancy, the extended Koksma–Hlawka inequality could be modified by replacing the EF-discrepancy with the GF-discrepancy. Thereby the rationality of adopting GF-discrepancy as the objective function of point selection is theoretically supported. Thus, by reducing the GF-discrepancy, a new strategy of representative point set determination via rearrangement is proposed. The proposed approach is then applied to stochastic dynamical response analysis of strong nonlinear structures by incorporated into the probability density evolution method, showing its effectiveness for practical applications. Problems to be further studied are outlined.

Ground seismic response analysis based on the probability density evolution method

Based on an overview of pertinent literature, the work presented in this paper focuses on the simulation of non-stationary ground motion processes and the stochastic seismic response analysis of site-specific soils. Using the random process orthogonal expansion method and the concept of random functions, initial earthquake ground motion is expressed as a random process based on only one random variable. Then, by discretizing the random acceleration process, we obtained 628 non-stationary earthquake acceleration time history samples with assigned probabilities. By comparing second-order statistical quantities of the random acceleration process between the sampled ensembles and an initial random targeting process, we demonstrate the advantages and effectiveness of this hybrid approach. The first part of this process also laid a foundation for subsequent stochastic seismic response analysis. Then, during the next part of the procedure, the calculation accuracy of the probability density evolution method (PDEM) was verified for a single-degree-of-freedom system with random excitation. The site-specific stochastic seismic response of the ground was then analyzed using the PDEM with the previously mentioned 628 acceleration time history samples. Abundant information was obtained on the probability of the ground seismic response, and the amplification effect on the target soil was verified from a random viewpoint. According to the performance-based method and PDEM, the reliability of the Shanghai soft engineering site was determined to be 0.7959. Furthermore, this new research introduces the use of PDEM techniques for modern geotechnical engineering problems.

General Laws of Dynamic Responses of the High Slope Construction under Earthquake

Based on stochastic seismic response and time-history seismic response analysis，Dynamic response laws of the high slope constructions by three real seismic waves and a synthetic seismic wave were studied using finite - element method, discussing the differentiation and relation between the high slope constructions and ground constructions. The results show that the dynamic response on high slope constructions are less intensive than ground constructions due to delaying effect of high slope soil acts on the structure, but its internal force stronger than ground constructions as the pile in high slope constructions are anti-sliding and bearing. Results are conducive to the seismic design of high slope constructions.

Stochastic seismic response analysis and reliability assessment of passively damped structures

Viscous dampers have demonstrated their value for vibration control of civil engineering structures subjected to seismic excitations due to their effective energy dissipation capabilities and excellent durability characteristics. In most existing designs of practical applications on structural control with viscous dampers, just several ground motions with different risk levels are included. Logical treatment on the randomness inherent in the occurrence and propagation of earthquakes has still not received sufficient appeal. In this paper, stochastic seismic response analysis and reliability assessment of passively damped structures are carried out through experimental investigations and numerical simulations. Complete shaking-table tests on a framed structure with viscous dampers are involved, where the base excitation is represented by a physical stochastic ground motion model. For the numerical analysis and reliability assessment, the probability density evolution method and the theory of extreme value distribution are employed. Experimental and numerical investigations indicate that the seismic performance of the controlled structure with viscous dampers is significantly improved compared with that of the uncontrolled structure, and the structural safety is essentially enhanced.