Numerical analysis of the strained state of cellular pipes in inhomogeneous soil
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NUMERICAL ANALYSIS OF THE STRAINED STATE OF CELLULAR PIPES IN INHOMOGENEOUS SOIL M. H. Stashchuk1,2 and M. I. Dorosh1
UDC 539.3
With the help of Fourier series, we propose a method for the evaluation of the strained state of cellular underground pipes with regard for the variations of the reaction coefficient of the surrounding soil. As a result, we write, in recurrent form, the coefficients of Fourier series for the averaged components of the vector of displacements of a cellular structure. On this basis, we find the radial displacements of a polymeric pipe along its contour. Keywords: polymeric cellular pipe, maximum deflection, reaction coefficient of soil, Fourier series.
The importance of application of pipeline transport rapidly grows with time due to its productivity and economic efficiency. Parallel with traditional cast-iron and steel pipes, large- and small-diameter polymeric pipes are now used more and more extensively because their reliability is higher than the reliability of metallic pipes [1, 2]. In this case, it is necessary, on the one hand, to save polymeric materials and reduce the cost of the pipes and, on the other hand, to produce pipes with predicted reliability. Therefore, at present, it is customary to use the so-called cellular (hollow) polyethylene pipes and vessels with cellular structure of the walls. The technology of production of thin-walled structural elements with cellular structure can be described as continuous winding of ordinary water polyethylene tubes 20–110 mm in diameter in special devices (drums) with simultaneous extrusion welding of these tubes between the coils. There are various procedures aimed at increasing the reliability of the pipes: stabilization of their loadcarrying capacity, decrease in the level of in-service loads, and finally, the development of improved methods for the evaluation of their stress-strain state under specific operating conditions. The method of open pipe laying in a trench is used especially extensively. In this case, the main load on the pipe is exerted by the weight of the backfill soil (active pressure). In numerical calculations, the active pressure of soil is, as a rule, regarded as a vertical load [3, 4]:
q = H ,
(1)
where H is the height from the surface of soil to the horizontal diameter of a tubular structural element and is the density of soil. As a result, the pipe suffers deformations depending on the stiffness of the structure and the structure of soil. According to [5], in the design of flexible polymeric pipelines, the maximum shortening of their vertical diameter should not exceed 3% of the outer diameter of the structure. Hence, for the numerical analysis and design of flexible underground pipelines, it is necessary to know the maximum deflection of the pipe. 1 2
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 46, No. 6, pp. 47–50, November–December, 2010. Origi
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