Pipe repair 2

[sam031973]

Hi,
we had a large diameter steel gas-pipe that was installed in potentially unstable slope area. Our ILI geo pigging inspection data indicated that pipe may have deformed and experienced bending (that results in high stress close to yield) due to ground movement . We decided to mitigate the situation by cutting the pipe to remove the excessive stresses. After unpressuering the pipe and exposing it, we cut the pipe at the segment under concern to releif the excessive stress. Upon cutting the pipe we noticed that the differential movement at the cut section close to 180 mm occurred immediately. The question why such large magnitude-movement occurs..? Given this movement, can one back-calculate the stress existing in the pipe at that section before cutting.

Thanks for your thoughts

 

[BigInch]

The movement occcured because you released the internal restraining stress. You turned it into a Free Body. Shear, tension and bending stresses holding the metal together, all of a sudden were cut off and made zero.

You don't say how or in which direction the pipe moved. Did it move to the side (primarily bending stress), or was that the movement of each half of pipe in the axial direction, ie 180mm farther apart (axial tension stress), or did it move in both directions?

You may be able to assume that the stresses now are minimal and figure out what forces are required to pull the pipe back together again. That can give you an idea of the stresses that existed prior to the cut. Some knowledge, or good guessing, of the pipe being subjected to elongation and lateral displacement must be had, or made. If such movement was due to axial stress over a pulled length of about 100m that would be at yield strength of an API 5L X60 pipe material. If you estimated that 180mm elongation occurred over 200m, then it would have been at roughly 1/2 yield stress.

If it was due to a combination of bending and elongation, it's a bit more complicated as estimate of beam lengths become involved, but theoretically you can deduce approximate stresses from the resolved tranverse shear and axial tension forces required to rejoin the segments.

 

[zdas04]

You say "large diameter", but that means different things to different people. A person building houses would call 100 DN "large diameter". In gas gathering system it is common to call 250 DN "large diameter". In transmission piping "large diameter" often starts around 750 DN. The displacement value is only relevant when talking about pipe diameter.

Generally if the displacement is less than half the nominal diameter of the pipe then it is not noteworthy. This means that if your "large diameter" pipe is 400 DN or bigger then the displacement was trivial and a person should just realign the cut sections and reweld it. If the pipe is smaller then I would cut out a whole joint and replace it with a compound overbend.

As to calculating the stresses that resulted in the observed displacement, you would have to know the pipe's spring constant, which you don't know since that is not a parameter that is controlled in pipe fabrication. When we do field bends we find that nearly every joint of pipe requires a different amount of force to permanently deform. The force required is always more than SMYS, but there is so much safety factor in SMYS that the amount you have to go over is quite variable.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

While D may appear to have some direct relationship to stress, it isn't much, apart from being a secondary parameter used to calculate the direcctly related section properties, such as section modulus, moment of inertia and cross-sectional area. When calculating bending stress as the result of lateral displacement, it means far, far less than the length over which bending occured, which increases stress by the square of that length. A lateral displacement of D means nothing, unless bending length is also measured in D. A far more accurate indication of the magnitude of bending stress is given by the lateral displacement divided by the bending (span) length.

Spring constants of the soil or environment in which the pipe will be embedded are needed only to estimate the stresses and displacements that the pipe will reach, once under operational loading conditions. But if you already know the final positions of the pipe, you do not have to know the spring constant of anything. It's exactly like you can estimate how long it will take you to get from Houston to Dallas, if you know the speed limit, but if your watch said it took you four hours, you don't need to know the speed limit.

The differential stress story of pipe can be reconstructed with only,
1) The original position of the pipe (to estimate initial stress)
2) The final position of the pipe (to determine final stress)
3) The properties of the cross-section, section modulus, area of material and moment of inertia
4) Young's Modulus of elasticity of the pipe; steel is about 30,000,000 psi

Using beam analysis theory in reverse, i.e. instead of knowing load, lengths and properties and integrating those to determing shear and bending stresses, curvature and bending deflection, by knowing bending deflections and section properties, you can do each respective derivative in stead;the derivative of curvature is bending stress, the derivative of bending stress is shear and the derivative of shear is load. What more is there? Spline curves can be used to great advantage for this type of analysis, as beams naturally assume spline curves under bending stresses. Spline curves have a constantly varying curvature between known points of displacement. Once you have the equation for the spline curve, you can hire a mathematician to do the rest. Or just give him/her the two curves and say that the final curve is a spline and ask for the second derivative.
y = f(Displacement),
dy/dx = curvature,
d2y/dx2 = moment,
d3y/dx3 = bending stress,
d4y/dx4 = shear,
d5y/dx5 = load causing the displacement.

 

[zdas04]

Cool, how do you estimate the length that the stress is applied over? "Just" knowing length is adequate, but I really don't know a way to estimate length that is stressed.

"Hire a mathematician"? Isn't that another way of saying "you really have no way of knowing"?

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

Yes. It really is cool if I do say so myself. I don't know of anybody else using this method for pipelines, so I don't have any direct references for it. I did quite a bit of research using this spline curve method a couple of years ago and it can give surprisingly good stress estimates and very reasonable results even for the estimated loads required to reach the deflected position, although it requires some sketching of nonuniform load distributions if you do the derivatives to that level. I haven't had time to do any paper on it yet, but it may be in the cards for this coming year. Anyway the method is easy enough to prove for a simply supported structural beams. Assume a beam shape and span length and do the usual structural calculations for shear = integral Load dx, moment = integral of Shear dx, curvature = integral of moment dx/E/I and deflection = integral of curvature dx. Then reverse the procedure using derivatives.

If you know the initial and final position, length doesn't enter into the equation for bending stress because you only need the length to estimate a curvature by [Δ]y/(L/2). If you have the actual position of the pipe for 3 linearly adjacent points, 2 intervals of some [Δ]x, you can calculate the curvature directly at the central point, after calculating the relative lateral deflection to the adjacent two points.

To do the same with axial stress you'd need to know the elongations between given intervals of length. Calculating [Δ]x / L. That might be difficult, unless you knew the original and final positions of two or more girth welds. Axial stress would equal [Δ]x/L * E. A rather severe relative axial displacement of 1" elogation between girth welds 40ft apart = 1"/40'/12"/' x E = 0.002083 in/in x 30,000,000 = 62,500 psi tension. If it was at operating temperature, you would have to adjust for the expansion or contraction stress at that temperature as well.

 

[sam031973]

Thank you very much for your thoughtful replies. Unfortunately we did not have intial profile of the pipe since the pipe was installed long time ago so we wanted to make sure of the out-of-straightness observed from geopigging when the pipe was exposed was not from initial installation but it was due to pipe movement under ground-movement. actually the Pipe Diameter was 700 mm and differential movement (around 180 mm) was vertical (in the direction of the suspected dominant displacement of the pipe segment)and there was some lateral movement of around there 100 mm). But given the movement in the vertical and lateral direction, I guess at least we can conclude upon observing these movements that the pipe had significant elastic bending stresses ( rather than elongation stresses since the movement did not occur in the axial direction).. is that correct..?
.Given the fact that pipe had no pressure and exposed for around 20 m, I don't think this movement is due to pipe own weight because the pipe segments are stiff enough to hold themselves after cutting
BigInch you are saying "The movement occurred because you released the internal restraining stress. You turned it into a Free Body. Shear, tension and bending stresses holding the metal together, all of a sudden were cut off and made zero"
Where these internal stresses coming from if the pipe has no pressure : Own weigh of the pipe or the boundary conditions at the end of the exposed segments ( around several meters far from the cut section). I thought that (given the differential movement is vertical) that they all due to bending loading that existed in the pipe before cutting..do you agree with me..?

Thanks alot for your thoughts

 

[BigInch]

Any time something accelerates and moves, there was a presumed force that caused it. The forces that caused the internal stresses are those same forces that caused the movement of the pipe into a new position. Force applied outside = stress inside => displacement if it insufficiently restrained to prevent that movement. When you cut the pipe, you cut the continuity of internal stress, that's what allowed the movement of the pipe, as it tried to return to it's initial zero-stress position. If there are displacements in a pipe that is not pressured, there are stresses resulting only from those displacements. If it is then pressured up, the pressure stresses simply add to those initial displacement stresses.

The vertical and horizontal directional displacements 90degrees apart can be seen as resolved components of one total bending moment in a principal plane. Much the same as the hypotenuse is equal to the square root of the sum of the squares of its component sides. If you had 30mm deflection in the horizontal direction and 40mm in the vertical, then total displacement in the principal plane of bending moment was 50mm. (30^2+40^2)^0.5 = 50mm. The bending stress is related to curvature, so it is important to estimate the span over which that 50mm of bending deflection occurred. Once you have that, then you can estimate the curvature and arrive at the bending stress that caused that curvature.

 

[sam031973]

Thanks BigInch, but at least one can conclude that the pipe out-of-straightness (which we saw when we exposing the pipe prior to cutting) was due to physical pipe bending/beam bending (not that the original pipe profile was installed in that manner). In other words
If the pipe was not under bending loading, it should not have experienced these differential movements. ..?
Given the section modulus ( steel pipe diameter of 700 mm and wall thickness of 5 m , exposed span of 20 m), this bending should not be due to pipe own weight. It is rather due to pipe movement (which we believe caused by ground displacement). I am not sure if you second this..?

 

[austsa]

My calc using DN700 x 5mm WT x 20m cantilever gives 119mm deflection by self weight. Cantilever deflection is sensitive to span (21m span gives 145mm). Deflection is dependent on the type of soil on the end of the excavated hole (i.e. cantilever assumption under estimates deflection; worse if you have soft sandy soil).

 

[sam031973]

Thanks Austsa, To large extent, the pipe was supported on the ground ( it was not fully unsupported for the total length of 20 m) and I guess to assume cantilever case (fixed end) is not realistic.

 

[LittleInch]

Sorry, 700mm (28") 5mm wallthickness?? D/t of 140?

Are you serious? I'm amazed anyone managed to build it, but that is a seriously thin walled pipe.

Is the variance vertical or horizontal when you cut it?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[sam031973]

sorry guys I just got the corrected/exact information: the daiamter of pipe segment in question was 25 inches and wall thickness was 0.30 in

 

[BigInch]

The pipe became subject to bending loads immediately when the moving soil forcibly moved the pipe.

A cantilever might be used to represent each of the cut pipe ends.

You now have to pull both cantilevers back together and rotate each facing end with an applied moment so that the two ends meet straight on, i.e. without any miter angle. The moment needed to make the rotation will be the bending moment present just before the cut was made. The lateral force necessary to move the two ends together in the lateral, or vertical direction will be the shear at the cut point. If you have to stretch each end to get them to meet, the amount of force required to do so will be the axial tension force.