Random Response Computational Theory And Application Research Of High Pier Bridges Subjected To Non-Stationary Earthquek Excitations In The Mountains

Construction of railways is under enormous developments in China, many of them have been built or are now being built in the southwestern region of China. Due to mountainous site topopraphies of the southwest China, many railway bridges are constructed and they usually have high pier, large height differentce, long span and small radius of curvature features in those mountainous areas and called irregular bridges beyond the bridge specification requirements. Stochastic vibration method is an inevitable to replace other seismic analysis approaches in the future, but not be fully applied in the actual projects as a result of theoretical complexity and computational inefficiency. Basd on above resons, How to use stochastic vibration theory(SVT) for aseismic analysis of mountainous high pier bridges subjected to multi-dimensional and multi-support stationary or non-stationary random earthquake excitations will be discussed in this paper and SVT is also employed without the restriction of structural style in actual engineering. Therefore highly efficient pseudo excitation method, absolute displacement solving method, precise integration method and a general finit element roftware ANSYS with powerful modeling capability are combined, and then based on APDL language, it is conducted in ANSYS that aseismic analysis of mountainous high pier bridges subjected to multi-dimensional and multi-support stationary or non-stationary random earthquake excitations and this approachis solved conviently without self-developed program and facilitates the applications of SVT in practical engineering.The first section of this paper first reviews the major domestic and foreign development history of long-span and high pier bridges and applications of SVT in seismic analysis of long span and high pier bridges, then describes the role and application of pseudo excitation method in the dynamic calculation of long-span bridges, as well as scholars explore the combination process of pseudo excitation method and general-purpose finite element software. Thereby, it is confirmed the feasibility and inevitability of SVT application in the project.To make stationary stochastic vibration theory used extensively in practical engineering, the second section presents absolute displacement solving response motion equation method of structure under multi-dimensional and multi-support random earthquake loading swiftly extends muti-support excitations input theory from one-dimensional and multi-support to mult-dimensional and multi-support and avoids computing the static influence matrix, which first is implemented in ANSYS at home and abroad. A numerical example is used to testify to the accuracy and precision. This technique will converte stationary excitations into a series of harmonic analyses for detail model of spatially varying ground motions (traveling wave effect, local site effect and coherence effect) acting on mountainous high pier bridges.The third and fourth sections present a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute displacement directly solving scheme of PEM in non-stationary stochastic analysis of structure under tridirectional spatial seismic motions has been proposed to resolve the drawbacks of conventional indirect approach, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions. To apply the proposed theoretical approach readily in stochastic seismic analysis of some complex and significant structures, this scheme has been implemented and verified in the general finite element platform, and then been applied to a high pier railway bridge under spatially varying ground motions considering the local site effect and effect of ground motion non-stationarity. Critical conclusions are drawn and can be applied in the actual seismic design and analysis of the high pier railway bridges under tridirectional non-stationary multiple excitationsTo further improve the computational efficiency of non-stationary stochastic vibration, the approach of the combination of high-precise integration method employed and directly solving method is proposed to compute expediently transient analysis at every deterministic frequency, the structure response will be achieved only according to two transient analyses, and the computational efficiency is updated greatly. Simultaneously, the non-stationary stochastic vibration implemented in general finite element software not only improves computational efficiency but also inherits all merits of the non-stationary stochastic vibration and saves times of self-developed program and calculation, so that this promotes deeply implements of stochastic vibration technique in seismic analysis. Meanwhile, correct analytic solution is first given of which a structure of single degree of freedom subjects to non-uniformly modulated evolutionary non-stationary random excitations and which confirms the precision of calculations for other scholars. Taking a mountain high pier bridge for example, the establishment of the three-dimensional model of high pier bridge is carried on in ANSYS to study the influence of the collision response for non-uniform distributing spatially varying local site condition and topography.