## Sapehin V.M. Successive approximation method applying to obtain the transient elastic medium deformations

- Details
- Parent Category: Geo-Technical Mechanics, 2019
- Category: Geo-Technical Mechanics, 2019, № 148

Geoteh. meh. 2019,** 148, **136-143

https://doi.org/10.1051/e3sconf/201910900081

**successive approximation method applying to obtain the transient elastic medium deformations**

^{1}*Sapehin V.M.*

^{1}*Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine*

**UDC** 539.3

**Language:** English

**Abstract****.** In the first part of the article, the well-known sequential approximation method developed at the Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine was used. This method was used to solve the problem of unsteady deformation of an elastic medium under the influence of variable internal pressure in wells. The essence of the method is that the resultant function, according to the results of its numerical research and given in tabular form, can be presented in an analytical form – a product of functions. This method has shown its high efficiency in solving various problems. The objective function, the maximum normal tensile stresses, is represented as the product of power functions, each of which depends on only one parameter. The pattern of changes in maximum tensile stresses from the main mining-technical factors affecting this process is established. Such factors are: the value of the internal pressure of the working agent before discharge, the inner diameter of the well, the speed of the elastic wave in the agent, the decay time of the working agent from the well. The decay time of the working agent is determined by the speed of the elastic wave in the working agent. Thus, it was found that the magnitude of tensile stresses is directly proportional to the pressure of the working agent and the radius of the well and inversely proportional to the speed of the elastic wave in the coal rock mass and the time of pressure relief. Thus, a complex dynamic problem is solved in a relatively simple way. In the second part of the article, a dimension theory method was used to solve this problem. According to the theory, the unknown value of radial stresses on the inner radius of the cylindrical cavity of a well can be represented in the form of the product of power functions. This fully confirms the dependence of the stress change established above. Solving a difficult problem by the method of successive approximation, we can obtain the dependence for any number of initial parameters in the mathematical model as well as the degree of influence of each parameter on the process under study.

**Keywords:** sequential approximation, stresses, dimension.

**References**

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**About the author**

** Sapehin Volodymyr Mykolaiovych**,Candidate of Technical Sciences (Ph.D.), Senior Researcher in Department of Mineral Mining at Great Depths, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine(IGTM, NAS of Ukraine), Dnipro, Ukraine, vladimir
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