Random Earthquake Ground Motion Research Articles

Shaking table tests on slope reinforced by anchored piles under random earthquake ground motions

Shaking table tests on slope reinforced by anchored piles under random earthquake ground motions

Stochastic seismic response of a slope based on large-scale shaking-table tests

Slopes should be regarded as stochastic dynamic systems when investigating the uncertainty of ground motions. In engineering, this involves the propagation and spatial evolution of physical quantities (e.g., acceleration) that can be assessed with some probability. More specifically, stochastic stability and amplification effects are important issues under random seismic inputs. In studying the above, a large-scale shaking-table test is carried out to investigate the slope seismic response under random earthquake ground motions, where 144 ground-motion samples are generated using a time-evolution power spectrum model. In this test, acceleration evolves in a way that its PDF changes with time and space. In the time domain, the PDF variability first increases and then decreases with the progression of the earthquake. In the spatial domain, the PDF variability increases upslope, indicating that the mean and standard deviation of amplification factors increase with elevation. Moreover, the stability of the upper part of the slope stochastic dynamic system is poor. Meanwhile, the de-amplification effect of the slope toe is identified under random seismic inputs. Finally, we discuss different amplification factors and consider applications of the research results in slope engineering.

Dynamic failure processes and failure mechanism of soil slope under random earthquake ground motions

Understanding the failure processes and failure mechanism of slopes is essential in the seismic design of slopes. However, the effect of ground motion uncertainty on slope failure is unclear (for example, whether the slope failure processes differ under different ground motions). This study investigated the failure processes and failure mechanism of a soil slope subjected to random earthquake ground motions. Non-stationary random earthquake ground motions were generated based on the improved orthogonal expansion method and dynamic problems were solved using the FLAC3D software. We attempted to determine the slope sliding surface by analyzing the dynamic strain time history of monitoring points. Statistical results obtained using the probability density evolution method revealed that the slip surface extended from the toe to the crest of the slope during the earthquakes and that only one slip surface could be determined under an earthquake scenario. Additionally, the slip surface, time of failure, and failure duration differed under different earthquakes. The strain development patterns also differed and four typical failure modes were identified based on these patterns. The slope risk was assessed based on the sliding mass uncertainty. The proposed framework can be useful in evaluating slope failure processes and for seismic design in the field of slope engineering.

Critical slip surface and landslide volume of a soil slope under random earthquake ground motions

Finding the critical slip surface and estimating the landslide volume are of primary importance for slope seismic design. However, this may be difficult due to the uncertainty of ground motions. To address this problem, a new method for calculating uncertainties is recommended in this paper, especially for the critical slip surface and landslide volume under random earthquake ground motions. Firstly, a series of intensity–frequency nonstationary random earthquake ground motions were generated based on an improved orthogonal expansion method. A given number of potential slip surfaces were set in a soil slope. Subsequently, the factor of safety (FOS) of each slip surface for all ground motions was calculated and the minimum FOS curves were obtained. It was found that the critical slip surfaces and failure times are uncertain under different earthquakes. The Monte Carlo method was used to verify the accuracy of probability density evolution method (PDEM), and the results of the PDEM and the Monte Carlo method are consistent, meaning that the PEDM has higher computational efficiency. Moreover, the distributions of earthquake-triggered landslide volume and landslide depth were analyzed by considering equivalent extreme events. Both landslide volume and depth exhibit a normal distribution for a homogeneous soil slope. The framework of this study is meaningful for slope seismic design in engineering, for example, the location of critical slip surface can be used for slope reinforcement, and the distribution of sliding volume can be used for disaster assessment.

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.

Optimum Design of Lead-Rubber Bearing System Under the Non-Stationary Random Earthquake Ground Motion

Optimum Design of Lead-Rubber Bearing System Under the Non-Stationary Random Earthquake Ground Motion

Sensitivity and Hessian matrix analysis of structural reliability for uniformly modulated random seismic response

This paper presents a numerical method for calculation of the sensitivity and Hessian matrix of the time variant reliability of structures subjected to uniformly modulated evolutionary random seismic excitation. The first three spectral moments, their first and second derivatives are obtained using the auto PSD functions, their sensitivity and Hessian matrix information. The formulas of the first and second derivatives of reliability are derived by direct differentiation based on the reliability formula that assumes the threshold crossings to obey a two-state Markov process. The computational procedure is given in detail for the reliability, its first and second derivatives. Finally, the reliability, its sensitivity and Hessian matrix analysis of a planar frame subjected to the uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method. The accuracy and efficiency of the proposed method in this paper are discussed by comparison with the developed method.

Sensitivity and Hessian matrix analysis of power spectral density functions for uniformly modulated evolutionary random seismic responses

This paper describes a numerical method for calculation of the sensitivity and Hessian matrix of the response PSD functions of structures subjected to uniformly modulated evolutionary random seismic excitation. The method is formulated based on the pseudo excitation method and Newmark method. The evolutionary non-stationary random response analysis is converted into step-by-step integration computations using the pseudo excitation method. The formulas of the pseudo responses, their first and second derivatives with respect to the structural design variables are derived based on the Newmark method. The PSD functions, their sensitivity and Hessian matrix are calculated using the pseudo responses, their first and second derivatives, respectively. Then the computation procedure of sensitivity and Hessian matrix of PSD functions is given in detail. Finally, the PSD functions’ sensitivity and Hessian matrix analysis of a three-story, two-bay planar frame subjected to the uniformly modulated evolutionary random earthquake ground motion has been studied to elucidate the proposed method.

Fragility of disconnect switch subjected to random earthquake ground motions

A fragility calculation scheme is estabtished in this paper for porcelain-type equipments subjected to random earthquake ground motions. All steps of the method are illustrated by the seismic damage analysis of GW4-110 disconnect switch. The model of the equipment is built applying the finite element method with flexible joints, and the seismic response of the equipment is analyzed using elastic time history method. On the base, according to the strength damage index and Monte-Carlo Method, the seismic damage ratios are counted and the seismic fragility curves are presented. Then the seismic damage of GW4-110 disconnect switch can be predicted.

Optimal instrumentation of structures on flexible base for system identification

A criterion previously developed by Heredia-Zavoni and Esteva for selecting optimal sensor locations is used to analyse the optimal instrumentation of structures on soft soils. The stochastic response of a linear structural system on a flexible base is formulated for use of the criterion. The case of MDOF shear systems on flexible base, with uncertain lateral stiffness and subjected to random earthquake ground motions, is studied. The optimal location of accelerometers, the reduction of prior uncertainty on the lateral stiffness, the effects of the base flexibility, the relative influence of translation and rocking of the base, and the influence of recording noise are assessed and discussed. Copyright © 1999 John Wiley & Sons, Ltd.

Seismic response of offshore structures in random seas

AbstractA study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil‐structure interaction effects and also on the evaluation of non‐linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi‐Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency‐domain random vibration approach.It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil‐structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.

震源過程と伝播体地盤を考慮したランダム地震動モデル

In order to evaluate the reliable earthquake response characteristics of structural systems, it is required to investigate the correspondence between the irregular geological properties of transmission path and the unspecified faulting process of source region and such important physical quantities as peak ground motions, spectral characteristics, duration times and so forth. In this paper, the idealized earthquake ground motion models represened by convolution of the average Green's function of a random medium and the random dislocation time function are analyzed to obtain some indication of the influence these factors may have on aseismic design of structural systems. The vertical, radial and cross-radial components of random earthquake time histories are calculated for Mach numbers M_n=0.6, 0.7, 0.8 and 0.9, rise time t_r=0.03 and the ratios of epicentral distance to focal depth R/H=1 and 5. The observation points of vertical and radial components are assumed to be in the direction of acceleration and deceleration of the fault rupture. The peak ground motions and duration times of vertical and radial components show significant variation with up-and down-Doppler effect associated with the fault movement. They become large and short when the fault propagates toward the observation points of vertical and radial components. On the contrary, they become small and long when the fault propagates in the opposite direction for the observation points. The peak ground motions and duration times of cross-radial component of the earthquake models in the perpendicular direction of the fault movement is insensitive to the variation of Mach number. Then, there is a strong dependence of peak ground motions and duration times at the site in the near field on the rupture direction of dislocation and the relative position between the focus of an earthquake and the observation point. There being some differences in the propagation velocities of P, SP, SV and Rayleigh wave motions, the duration times of earthquake ground motions become inevitably long with the increase of propagation distance unless the fault rupture occurs in the finite source region. The wave form functions, maximum values and their generation times of the earthquake models vary with the ratio of epicentral distance to focal depth since the energies of SV wave motions are transformed into those of SP and Rayleigh wave motions with the increase of the ratio. On the other hand, the wave form functions of cross-radial component of the earthquake models are varied a little with the ratio because there is no such energy transformation for SH wave motion of the component. Since the peak accelerations of random earthquake ground motion models become less sensitive to Mach number with the increase of propagation distance, the stochastic characteristics of them tend to be gradually stationary as the seismic wave motion propagates into the far-field. From the above discussion, it is concluded that Mach number, the ratio of epicentral distance to focal depth and the relative position between the causative fault and the observation point are important parameter and physical quantities for aseismic design of structural systems, which would describe the maximum values, frequency characteristics and duration times of earthquake ground motion.