Reliability assessment of the system “structure – multilayer foundation” taking into account stiffness, capacity and configuration of layers

Introduction. Modern studies on the quantitative assessment of the reliability of structures during earthquakes generally do not consider wave effects, the spatial heterogeneity of soil foundations, and the reverse impact of the structure on ground motion. The purpose of this work is to evaluate the reliability of the “structure – multilayer foundation” system, considering factors such as stiffness of the structure, the thickness and density of soil layers, the propagation speed of the transverse seismic wave, and the dominant frequency of seismic action. The reliability measure of the system is taken as the probability of the dynamic coefficient exceeding a specified value.

Materials and methods. A computational model of a horizontally layered medium is used. The structure is considered an element of the layered system with equivalent rigidity characteristics. Seismic loading in the form of a vertically propagating shear wave is modelled as a stationary random process. The output characteristics of the system include the spectral density of acceleration, the amplitude — frequency response, and the dynamic coefficient at any level of each layer and the structure. Based on a series of calculations, the dynamic coefficient is formulated as a nonlinear function of six random arguments. The function is linearized using the experimental design method, and the reliability function is constructed.

Results. Analytical dependencies of the dynamic coefficient function were obtained for two types of foundations with increased and decreased stiffness values of layers, with different orders of their alternation. An assessment of the adequacy of the adopted linear model was conducted. The probabilities of exceeding the normative value of the dynamic coefficient were determined for buildings of varying rigidity, considering the influence of the thickness of the soil foundation layers.

Conclusions. The dynamic coefficient adopted in the standards, which does not exceed 2.5 for all soil categories, cannot ensure the required reliability level of earthquake — resistant buildings and should be determined based on calculations that account for the rigidity of the structure and the characteristics of the multilayer foundation.

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