Abstract
The automation of control processes for the stability of geotechnical systems is a great challenge involving the development of methods for multivariate analyzing and forecasting the stability with the subject to the nonlinearity of material stiffness parameters. The aim of the study is to improve the efficiency of automated control systems for geotechnical stability by developing an approach to detect negative changes in bifurcation diagrams of vibration displacement parameters of object structures. The authors present a mathematical model of the dynamic behavior of structural elements of an object as an elementary unit of a geotechnical system that describes a response to an external vibration action. An algorithm of bifurcation analysis is presented, which allows authors to determine the initial transition stage of the object structure to an unstable state by the acceleration values of forced oscillations exceeding the model parameters. A bifurcation diagram of stability changes in the structure of object at the displacement resulting from the load increase under vibration action has been constructed. This diagram, which type of codimension-one bifurcations is merging, enabled to determine the critical load values resulting in an unstable state transition of a system due to the influence of a combination of vibration factors. The efficiency evaluation of the proposed approach was carried out by the comparison with the results of construction stability calculations obtained by the use of the dynamic coefficient. The difference between the values of the maximum object displacement without loss of the stability under vibration action, obtained by the standard calculation method and using the developed model, is 32.5%, and it is significant in the theory of structure stability. When exogenous vibration noise is used as a source of a sounding signal, the application of the developed approach in automated control systems for geotechnical stability enable to change the permissible stability thresholds of objects being exploited depending on the level and combination of influencing factors.
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