Application of the Method of Shooting for the Rapid Determination of the Stressed State Of Underground Parts of Pipelines in the Zone Of Mine Works

We apply the method of shooting for the determination of the state of a pipeline located in the zone of shifts of the Earth surface caused by mine works. The pipeline is split into elementary segments for which, on the basis of the solution of differential equations, we deduce analytic formulas for the relationship between strains and stresses formed at the beginning of the analyzed segment and its end. This enables us to find the values of displacements and forces at all other points according to their at the first point. In this case, we use the analytic relation between these characteristics at the first point. The initial values of displacements are iteratively corrected to guarantee the validity of the boundary conditions at the end of the pipeline. The algorithm of these corrections is based on the method of partition of a segment into two segments with choosing the next segment depending on the sign of the function at the opposite end. By using, as an example, several typical types of displacement of soils (small caused by the elastic interaction of the pipe with the soil, medium caused by mixed elastic and plastic interactions, and large corresponding to the plastic interactions), we estimated the rate and accuracy of the method of shooting as compared with the other numerical procedures and commercial programs. Finally, it is shown that this method is quite efficient for elastic problems, and the presence of physical nonlinearities does not affect the rate and accuracy of calculations.