Computational Methods For Non-stationary Stochastic Seismic Responses And Overturning-resistant Fragility Of Isolated Structures

Seismic isolation is one of the most promising techniques for reducing the destructive effects of strong earthquakes on structures. It is widely used in new constructions, e.g., residential buildings, government office buildings, hospitals and schools, et al. Additionally it is an attractive technology for retrofitting strategies needed to improve the seismic performance of existing bridges and monumental historic buildings. Since the1995Hyogoken-nanbu earthquake, the number of seismic isolated buildings has been increasing remarkably. In recent decades, several complex forms of isolation structures have appeared, including high-rise isolation buildings isolation, composite isolation and inter-storey, which brings some new challenges to the design of the isolation structures.Because of the uncertainty of earthquakes, stochastic seismic analysis is a powerful and an attractive tool in earthquake engineering. In this paper, based on the pseudo excitation method (PEM) and equivalent linearization method (ELM), the computation procedure of several special isolation systems subjected to the uniformly modulated non-stationary or fully non-stationary seismic excitations is presented, and the overturning-resistant fragility curves for base-isolated high-rise buildings is obtained. The detailed work can be listed as follows:1. Non-stationary stochastic responses analysis for hysteretic MDOF base-isolated structuresBy combining the PEM and ELM, this paper evaluates the seismic responses of hysteretic MDOF base-isolated buildings under uniformly modulated non-stationary or fully non-stationary earthquake excitations. The solution of the stochastic seismic responses of a base-isolated structure considering hysteretic nonlinear behavior is transformed to a deterministic time history analysis by using the PEM. The mixed type precise integration method (PIM) is adopted when the isolation system subjected to uniformly modulated non-stationary seismic excitation, and the Runge-Kutta method is employed when the isolation system subjected to fully non-stationary seismic excitation. The responses of an isolation system evaluated by PEM agree well with those obtained by the Monte Carlo method, thus the accuracy of the PEM is verified.2. Computational method for non-stationary stochastic responses of base-isolated buildings based on3D FE models Based on3D FE models, this paper deduces the governing equations of motion of non-stationary responses for large complex base-isolated buildings, particularly for those with zero or a small amount of eccentricity, it presents an efficient approximation method for the computation of the stochastic non-stationary response based on condensation of the hysteretic components and static correction procedure. The stiffness of the base raft of an isolated structure is much larger than that of the isolators, so it is assumed that the displacements of the isolators in the same direction are equal to each other for buildings with a small amount of eccentricity or none. Note that the number of reduced equivalent linearization differential equations depends on the type of isolator but not upon how many of them are employed, which greatly reduces the number of equivalent differential equations and improves the computation efficiency; meanwhile the static correction procedure is employed to consider the contributions of the higher modes of the structure, with minimal increase in computation effort. Finally, the stochastic response of a simple base-isolated frame structure is obtained by the presented method, and its accuracy is verified by the Monte Carlo method.3. Computational method for seismic responses of inter-storey isolation structures considering P-A effectBy introducing the geometric stiffness of the inter-storey isolation structures, this paper presents a method to evaluate the seismic responses considering P-△effect for such buildings. Large deformation concentrated in the isolation layer when subjected to major earthquakes will yield huge supplemental moment at both ends of isolators. The additional moments formed by axis-forces are replaced by equivalent horizontal force couples. Consequently, geometric stiffness matrix is obtained, thus the seismic responses considering P-△effect can be evaluated by step-by-step integration method after initial stiffness plus the geometric stiffness of the isolation structures. Finally, the iteration is avoided, which improves the computation efficiency. The seismic response of the inter-storey isolation structure subjected to uniformly modulated non-stationary excitation is obtained by PEM, and influence of the P-△effect on the responses of first storey column isolation structures in various soil conditions and classification of design earthquake is studied; the seismic response of the inter-storey isolation structures under near-fault earthquakes is evaluated by time history analysis, and the influence of the P-△effect on the responses of first storey column isolation structures under near-fault earthquakes and far-fault earthquakes is discussed. The results shows that P-△effect will bring security problem to inter-storey isolation structures, particulaly when subjected to near-fault ground motions since those consist of lots of long period components. 4. Computational method for overturning-resistant fragility of base-isolated high-rise buildingsBased on the first excursion failure, this paper presents a method to evaluate the failure probability by overturning-resistant of each isolator of the base-isolated high-rise buildings modelled by3D finite elements. The influences of the direction of the input excitations, fundamental period after isolation, pressure stress limit, supplemental damping ratio, soil conditions and classification of design earthquake on the overturning-resistant fragility curves are investigated, respectively.