On one method of risk evaluating in geotechnical mechanics tasks

To increase the efficiency of the existing labor protection system at industrial enterprises of Ukraine, there was a need for its improvement. It was decided to do it based on systems management of labor protection and risk control. However, it turned out that risks can be identified not in each technical system. Most of the processes in technical applications are deterministic, and therefore the concept of risk is not applicable, since none of the parameters of the system is a random variable. Since it is impossible to determine the degree of risk, then the only possible way out is to assess a degree of influence of this or that parameter on the performance of the entire system. So, for deterministic mathematical models (MM), the influence of the parameters can be determined by the methods of the theory of sensitivity (ST). However, the ST has not yet received widespread use in technical applications due to the significant complexity of research. In order to determine sensitivity, it is proposed to use in technical applications performance criterion approximation, which characterizes the risk of the process going beyond the performance limits, instead of ST. If approximation of a selected criterion is represented in the form of a product of power functions, each of which depends only on one parameter, then, according to the exponents, it is possible to approximately establish its sensitivity to variations in the parameters. The greater is an exponent, the more this parameter influences the criterion. Thus, it is possible not only to carry out an approximate assessment of the influence of the parameters on the criterion itself, but also to make conclusions regarding the risk of the system going beyond the permissible limits. The experience of successful use of the method of sequential approximation (SAM) in applied problems of mechanics allows not only to obtain an analytical form of the criterion at a point, but also to expand a solution of practical problems to the entire domain of function. The errors of such expanding, as a rule, do not exceed 5‑7 %, which is sufficient for most applied problems of geotechnics. The accuracy of determining the criterion can be increased to the required level by narrowing an area of its definition, i.e. parameter change intervals. A hypothesis of existence of representation of functions in the form of a product of functions, each of which depends on one parameter, is formulated. The efficiency of the use of power functions for an approximate assessment of the system risks when it going beyond the limits of operability is shown. Keywords: theory of sensitivity, variation of parameters, approximation of a function, approximate estimate, small error.