Determining the minimum pitch for measuring the spatial position of a pipeline when assessing the stress-strain state from the soil surface

In determining the bending radius of an underground pipeline axis from the soil surface, existing methods have some disadvantages associated with a lack of studies on how pipeline depth and equipment errors affect the results of measurement pitch calculations. The purpose of the study is to determine the minimum measuring pitch relative to the spatial position of the pipeline using line locating equipment to assess the stress-strain state from the soil surface. An assumption was made that the pipeline section has a bend in one plane only. Therefore, it is considered as a combination of three axis points that, when interconnected, form a part of a circle. To find the actual values of the bending radii in two borderline cases, some expressions were proposed. Regarding the absolute difference between the maximum bending stresses and the measuring pitch, dependences were obtained for various values of the absolute error attributed to the equipment used with a 1.400 mm diameter pipe. It was established that to limit an error in the absolute difference of the maximum bending stresses to 50 MPa, the minimum measurement pitch should be 20 to 60 meters (this varies depending on the error of the line locating equipment used). Using the MATLAB programming language, a program code was written to construct a three-dimensional graph representing the dependence between the absolute difference of the maximum bending stresses and the measurement pitch for various values of an absolute error attributed to the equipment. It was found that the pipeline bending radius does not affect the value of the minimum pitch for measuring the spatial position of the pipeline.