The use of sequential approximation method for risk determination in problems of geotechnical mechanics

Abstract

Most processes in technical improvements are deterministic, therefore, the concept of risk as a product of the probability of an accident occurrence on the financial costs of its elimination, which is proposed in most articles and regulatory documents, is not acceptable, since none of the project parameters is a random variable. In this regard, it is proposed to define risk as a technical system exceeding the values permissible by technical specifications, that is going beyond the operational capability. Before determining the degree of influence of parameters on the risk amount, it is necessary to determine sensitivity to their changing. Sensitivity analysis allows identifying parameters with the greatest influence on the risk of criterion going beyond the operational capability. However, in practice, it is not always possible to determine criterion sensitivity to the change of one or another parameter. In practice, typical situation is a problem to determine risk under conditions of simultaneous change of all parameters. Thus, a relevant method for risk calculation would be a method which allows determining risk sensitivity to the change of parameters and, at the same time, calculating the risk with simultaneous changes in all parameters. The sequential approximation method (SAM) makes it possible to calculate the risk with simultaneous changes of other parameters within a certain range using the information obtained during determining the risk sensitivity to the change of parameters. In the SAM, risk is represented in a multiplicative form, where the components of the product are the functions of one parameter. If the risk approximation is carried out in the form of a product of power functions, each of which depends on only one parameter, then the risk sensitivity to the change of the parameters can be approximately determined by the power indicators. The higher is the power, the greater is the influence of parameter on the risk. In this way, it is possible not only to make an approximate assessment of the influence of parameters on the criterion itself, but also to make conclusions about the importance of the influence of the system exceeding the permissible limits on the risk. In this work, the efficiency of the SAM method for determining the risks of parameters exceeding the permissible limits is demonstrated by the results of solving a classic problem of determining the stress-strain state in the neighborhood of the roadway with a circular cross-section by the finite element method. An algorithm for calculating risks based on specific examples is presented. In order to demonstrate the satisfactory accuracy of the criterion calculations, surfaces of the tangent stress intensity function obtained by the SAM method is compared with the interpolation surfaces obtained by numerical results. Conclusion is made about the ability of the method to determine the risks of the criterion exceeding the permissible limits and to provide satisfactory accuracy of the obtained results. Keywords: risk of loss of operational capacity, multiplicative form of representation, sensitivity of the function, change of parameters, neighborhood of a point, tangential stresses intensity.