A Statistical Linearization Method For Stochastic Response Of Isolated Structures To Near-fault Earthquakes

Near-fault ground motions are ground motions measured on engineering sites that are very close to the fault(generally less than 30km).In general,there is a clear distinction between near-fault ground motions and far-field ground motions.Among them,the velocity pulse caused by the forward directivity effect is the most significant.Therefore,these ground motions are also called near-fault pulse ground motions.On the other hand,there are many hidden or active seismic fault zones in densely populated areas in China,such as the Longmenshan fault zone,the Tanlu fault zone,etc.In China,a large number of foundation works are constructed near the seismic fault zone,some of which even cross the fault zone.Numerous studies have found that under the action of near-fault pulse-type ground motions,structures(especially flexible structures such as high-rise buildings,long-span bridges,and isolated buildings)may experience greater reciprocating inelastic deformation under far-field earthquakes,resulting in severe structural damage or even collapse.Therefore,it is urgent to develop a prediction method for the stochastic dynamic response of nonlinear structures under near-fault pulsed seismic excitation.In this process,the engineering load model of nearfault pulse ground motion must be developed,and a prediction method of structural dynamic response based on the load model is proposed.The stochastic model of near-fault pulsed ground motions represents the latest research results for this special catastrophic load.This model separates the impulselike low-frequency components from the random broadband components.In this model,the impulse-shaped low-frequency components and random broadband components are described separately.At the same time,under the action of near-fault pulse-type ground motion,the structure often experiences large hysteretic deformation.In this paper,the near-fault seismic excitation is simplified to a combined excitation composed of deterministic harmonic and modulated non-stationary random excitation.And use the Bouc-Wen hysteretic system to simulate the hysteretic behavior of the isolated structure.The external excitation model and the structural model determine which structural response prediction method should be used.Therefore,this paper develops a statistical linearization method for the non-stationary stochastic dynamic response of multidegree-of-freedom hysteretic systems under joint excitation.Therefore,in this paper,a statistical linearization method for nonstationary random dynamic responses of multid OF hysteretic systems under combined excitation is developed.Then,taking the seismically isolated structure under the action of near-fault ground motion as the research object,and using the method proposed in this paper to predict the stochastic dynamic response of the seismically isolated structure.It should be noted that in previous studies,the research on nonlinear random vibration under joint excitation by mechanics researchers and the research on near-fault seismic response of structures by civil engineering researchers are disconnected.The former does not pay attention to the engineering application of the latest research results of random vibration,while the latter only focuses on the deterministic response of the structure to near-field earthquakes.Therefore,the innovation of this paper is obvious: it is the first time to develop a theoretical framework for the random dynamic response of structures under joint excitation based on statistical linearization method,and it is the first time to apply this method to solve the non-stationary dynamic response of isolated structures under near-fault random earthquake.In terms of theoretical research: first,representing the system response into a combination of a deterministic and of a zero-mean random component,the equation of motion is decomposed into a set of two nonlinear differential equations,governing deterministic response and stochastic response,respectively.Next,the statistical linearization method is utilized to treat the non-linear stochastic differential equation,deriving the related Lyapunov differential equation in terms of response variance.The system response can be obtained by solving the Lyapunov differential equation and the deterministic equation of motion,simultaneously using standard numerical method.Finally,pertinent numerical examples demonstrate the applicability and accuracy of the proposed method.In terms of engineering application: first,the low and high frequency bands of near-fault earthquakes were simulated by Gabor wavelets and modulated white noise,respectively.Specifically,three ground motion records of Chi-Chi earthquakes affected by directivity effect are selected from the PEER ground motion database.The Gabor wavelet parameters are obtained by the least square method,and a deterministic velocity pulse time history model is established.Then,statistical linearization method is used to solve the dynamic response of the isolated structure under the combined excitation of the obtained velocity pulse time history and modulated white noise.Finally,the results of the Monte Carlo simulation are compared with the calculation results of the method proposed in this paper,which shows that the method has high accuracy and computational efficiency.