Keywords: dents, gouges, contact, pipelines, external interference, internal pressure, structural integrity.

Motivation for this paper comes from the frequent occurrence of external damage to existing pipelines which are being caused by external forces, e.g. by excavation equipment. It transpires that in many instances a local dent can be formed in a pipeline conveying pressurised liquid or gas. During the damage process the pipe can also be gouged. Hence in addition to shape distortion one is faced with presence of gouges in the dented area. Practical needs have stimulated both experimental and numerical studies in this area in order to assess various aspects of structural integrity of dented pipes.

This contribution is based entirely on numerical work and it complements a concurrently run experimental programme on laboratory scale pipes. In the current study, dents were formed by pressing an indenter of given profile into a circular pipe. In the finite element (FE) simulation the indenter was modelled as a rigid surface. Contact interaction between indenter and the pipe was simulated using a master-slave approach. The coefficient of friction between contacting surfaces was assumed to be, 0.3 (as a result of previous work). Several different shapes of the indenter are considered and their shape varies from prolate elliptical, through hemispherical, to oblate elliptical profiles.

One of initial considerations concentrated on modelling the pipe's support. In real situations pipelines are embedded in soil, sand, etc. In the FE modelling one needs to simulate the effects of such support. In preliminary calculations three types of pipe support were considered, i.e., support by a flat rigid plate, by a rigid saddle, and by a set of linear springs modelling a Winkler foundation. The latter two supports extended by 120^o in the hoop direction of the pipe. The pipe itself was modelled using 20-node brick elements with several layers through the wall thickness in the vicinity of the dent or gouge and with two layers away from that area. Details about meshing are provided in the paper. The FE process of denting was carried out either for an empty pipe, or for a pressurised pipe to the level of design pressure.

The numerical simulation of denting was carried out for the depth-to-pipe-diameter ratio, , varying from 0.06 to 0.36. As mentioned earlier, two types of analyses were performed. Firstly, after reaching a prescribed depth, , the indenter was removed and after unloading some re-rounding took place for most cases of internally pressurised pipe. On the other hand, in the case of non-pressurised pipe, no appreciable re-rounding was recorded.

The resulting permanent dent reduces the magnitude of the circular cross-section of the pipe. The percentage reduction of the cross-section has been calculated for all analysed cases. Calculations have shown that initially circular cross-section area can be reduced by 20%. The permanent distortion of the circular cross-section also extends along the length of the pipe. Again, the length of distorted pipe has been evaluated and its maximum magnitude can be as high as 10 times pipe's diameter.

Comparison of results obtained for three types of pipe support show that there is little difference between loading and denting and unloading response curves. Results obtained for a rigid saddle are bracketed by results corresponding to a rigid plate and by results corresponding to elastic springs. The latter were chosen to model saturated sand and/or stiff clay. As a result of the above observation the remaining calculations were performed for a pipe supported by a rigid saddle.

Another aspect of detailed numerical investigations concentrated on contact pressure and the shape and magnitude of contact area between indenter and pipe as well as between the pipe and the saddle support. Typical illustrations how these variables vary during the denting path and unloading path are given in the paper for shallow, hemispherical and sharp profiles of the indenter.

The ultimate load carrying capacity has also been examined for a number of indenter geometries. Two failure mechanisms have been identified here, and primarily they depend on the shape of the indenter. For example, for a hemispherical indenter the ultimate denting force corresponded to pipe's squashing whilst for prolate elliptical indenter the failure occurred through excessive plastic strains associated with 'puncture-type' deformations.

Prior to the introduction of gouges some calculations were performed for cracked pipes (through 'node release' modelling mechanism and with full, through the wall thickness penetration). Cracks were introduced at the centre of the indenter and/or at the perimeter/flank of anticipated dent. Once crack has been introduced, the denting process followed. Results have been obtained for a range of crack length, crack depth, and its positioning.

In reality gouges would have certain width, depth and length. They might not have regular shape and depth - as recent in-situ measurements have shown. Gouges with a regular shape, only - have been adopted in the current paper. They were positioned either at the centre of the dent and/or at its perimeter. Once gouges were modelled the denting/loading process begun. Parametric studies have included different values of gouge length, depth and width as well as varied positioning. Comparison of results between non-gouged and gouged pipes is provided in the paper. In all cases cracks and gouges are parallel to pipe's length.

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