If an indentation is relatively long in the axial direction, the indenter force-deflection behaviour can be accurately assessed using a two-dimensional ring model for the pipe; this greatly simplifies the analysis. The possible modes of failure which must be taken into account as a result of the indentation are the immediate failure by puncturing or by low cycle fatigue which is exacerbated by the significant residual stresses resulting from the indentation. Therefore, to ensure that failure does not occur, it is important to be able to predict the force-deflection behaviour of indented pipes under a wide range of support conditions and indentation depths.

The limit load and force-deflection behaviours of dented rings with symmetrical and non-symmetrical loads and supports, using analytical methods and finite element (FE) analyses has been reported in previous papers [5,6]. The effects of asymmetry of supports, offset loading, internal pressure, types of material and pipe geometry were investigated. The FE meshes, boundary conditions and large deformation FE analysis methods used have been validated by comparing predictions for unpressurised rings with the results of experimental tests.

For underground pipelines, the surrounding soil provides support for the pipelines and produces reaction forces that resist the pipeline deformation or the movements caused by indentation loads. Exact simulation of the support conditions produced by the surrounding soil is difficult and would require many experimental tests and corresponding FE and,or analytical analyses to be performed. Since the soil support around pipes is more likely to be spring-like rather than rigid, this paper is therefore concerned with the prediction of the indenter force-deflection behaviour when the pipes have spring-type supports.

A general analytical formulation, which covers the effects of the spring support and indentation positions on the limit loads of indented rings, is described. FE solutions for pipes indented by a radial rigid indenter with the pipe resting on two types of spring supports are presented. Comparisons of the FE analyses and analytical solutions indicate that the analytical methods are capable of predicting the indenter force-deflection curves with reasonable accuracy. Generally, the analytical solutions are higher than the corresponding FE results.

1

Park T.D. and Kyriakides S., "On the collapse of dented cylinders under external pressure", Int. J. Mech. Sci. 38, 557-578, 1996. doi:10.1016/0020-7403(95)00065-8

2

Corder I. and Chatain P., "EPRG recommendations for the assessment of the resistance of pipelines to external damage", AGA/EPRG Seminar, England, 1995.

3

Doglione, R. and Firrao, D., "Structure Collapse Calculations of Old Pipelines", Int. J. Fatigue, 20, 161-168, 1998. doi:10.1016/S0142-1123(97)00100-X

4

Lancaster, E.R., Palmer, S.C., "Strain Concentrations in Pressured Dented Pipes", Proc Inst Mech. Eng., Part E: J. Process Mechanical Engineering, 210, 29-38, 1996. doi:10.1243/PIME_PROC_1996_210_290_02

5

Hyde, T.H., Luo, R. and Becker, A.A. "Elastic-Plastic Response of Unpressurised Pipes Subjected to Axially-Long Radial Indentation", Int. J. Mech. Sci., 47, 1949-1971, 2005. doi:10.1016/j.ijmecsci.2005.07.004

6

Hyde, T.H., Luo, R. and Becker, A.A., "Prediction of Force-Deflection Behaviour of Pressurised Pipes Subjected to Axially Long Radial Indentation", Int. J. Pressure Vessels and Piping, 82, 625-637, 2005. doi:10.1016/j.ijpvp.2005.02.001

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