Stuctural Analysis Of Pipe in Ground That Has Locally Heaved 1

[FinnB]

I have been asked to look at what happens structurally to HDPE pipes buried in ground subject to heave.

The concern is that a leak in a pipe or from another source could cause the earth around the pipe to heave. The expansive heaving ground is 'Black Cotton Soil' which in this case can heave up to 18 inches exerting upward heave forces of 6500 pounds/foot^2. If the pipe were to heave locally by 12inch it would obviously deform the pipe causing it to deflect, bend, shear and elongate.

I am trying to work out how to analyse this problem. Here's my thoughts so far.

1. While the pipe is deforming as the the ground heaves/moves the pipe is not subject to bending moments as it always supported continouosly by the ground. The pipe never has to span even though it is bent and deformed.

2. I tried placing the pipe on soft springs in a computer model and applied the upward heave force. I was hoping to demonstrate that the pipe would stretch and become longer as the ground heaved. Demonstrating stetching (strain) of the pipe, I was hoping, would result in an axial force/stress that I could compare to the yield stress of HDPE pipe.

3. The software I am using (ROBOT) does not appear to calculate the strains and resulting stresses due to deformations/deflections. Analysing the pipe on elastic springs supports I have let the deflections of the supports in a 20ft length of a 100ft pipe to increase to a point where there is a deformation/delection of 12 inches. Allowing a max vertical deformation of 12 inches in the computer model is not producing axial forces in the pipe and I do think this is realistic.

I'm scratching my head with this one. Has anybody got any views on what happens structurally to a pipe in heaving ground and how the pipe should be analysed. My feeling is that the pipe will be subjected to more than axial forces due to strain but I do not know how to look at this.

I know there will be practical constructions solutions to this problem and I welcome any there are but it is how these pipes should be structurally analysed is the task I have been given to do.

 

[ishvaaag]

In my view the pipe is mostly bending, only that in large deformations. If you keep analyzing the pipe (in spite of the large deformation) as if small deformations, it is no surprise that the results do not show significanta axial stress. On this regard, within the small deflections field, a beam with imposed transversal deflections at inner points is all you need to derive the flexural action. But since so large, you need include the large deflection itself and a material model complete in the inelastic range to rupture to see if such thing is possible (were not because it is the cause already of the large deflection, it is assumed).

 

[a2mfk]

I have no expertise in pipelines, but I think this is your main problem:


1. While the pipe is deforming as the the ground heaves/moves the pipe is not subject to bending moments as it always supported continouosly by the ground. The pipe never has to span even though it is bent and deformed.


The pipe definitely has bending stresses, imposed by soil uplift pressure. This happens all of the time on structures on plastic soils that expand when they absorb moisture, causes all kinds of structural damage to foundations and walls.

I would think that if you could determine approximately where the pipe's inflection points are your problem becomes pretty conventional.

 

[ishvaaag]

In my view if some geotech program is able to model how heave happens on some kind of water aport, that surely thre is, but I am not aware of, what a22mfk stands. That is, you will be able to exact the actual deformation and if the model encompasses large deformations and material nonlinearity you would have the deformation and stresses. Even then, for that, you will need to model the kind of water apport.

For the other cases, we are stell able to do 1D or 3D analyses on surmised imposed deformations that may describe the differential heave behaviour between points; not such rare methods since we adapt prescribed deformations in bucklin problems, in dynamic analysis, and to local elements in FEM. That was my approach quoted above.

I am remarking this because in my view for properly buried HDPE pipes they (most times) will accompany the heave that prescribe their deformation, and to proceed from (differential along the length) heave pressures would be as adventurous as to prescribe the upwards deformation itself.

 

[BAretired]

The pipe, as stated by others is indeed subjected to bending stress. The problem is that the curvature of the pipe is largely guesswork.

If heaving of the pipe occurs at the point of leakage, it may be reasonable to assume a point load acting upward on the pipe. If the span is deemed to be 20' with both ends fixed, the central deflection is PL³/192EI. Knowing E and I of the pipe, a value of P can be found.

The bending moment at each end and at the middle of the 20' span is PL/8 from which bending stresses may be found. The main problem is, the span, L was a guess to begin with so the final answer is also a guess.

You also state in your sketch that max. radius of pipe bend = 25 x diameter or 25 x 8" = 200". I think you meant to say minimum radius, correct? Knowing that M/EI = 1/R, you can solve for M = EI/R and again you can compute the flexural stress in the pipe.

Having these two values may provide some insight into the possible behaviour of the pipe, but there is no certainty that either result is correct.

You may find some help on the internet respecting Black Cotton Soil:

http://www.google.ca/search?hl=&q=b...BCA404CA404&ie=UTF-8&aq=9&oq=Black+Cotton+Soi

BA

 

[BAretired]

FinnB,

The 20' dimension on your sketch is an assumed value. Its magnitude depends on the weight of soil lying over the pipe, i.e. depth of burial.

If the pipe is lying on the surface and a 12" heave occurs over a length L, there is no bending over that length, but there is bending at each end beyond L. A uniformly loaded beam fixed at one end, free but guided at the other deflects wL⁴/24EI where w is the weight of pipe plus contents per unit of length. Equating this expression to 12" results in L = (12*24EI/w)^1/4.

If the pipe is buried, w would need to include the weight of soil above it.

BA

 

[BAretired]

What happened to this thread? I thought it could provoke some interesting debate, but even the OP seems to have abandoned the discussion, perhaps never to be heard from again.

If a pipeline heaves locally as suggested in the thread, it is wrong to state that it has no bending moment or that it is continuously supported by the ground. If it has curvature then by definition, it has bending moment and if it heaves locally, it is unsupported by the soil immediately adjacent to the portion which heaved.

BA

 

[ishvaaag]

I agree, BAretired, it has moments and even axial forces can have if the pipe is not broken at some section (or at least bond with the soil is not entirely disrupted) and the large deformation asks for some extra length that is so being opposed either by direct standing tensile axial rigidity or on bond attained length of embedment.

In my view since the variation of the heave can vary wildly, if you don't have a program to properly introduce the magnitud of heave, the best way is to study it parametrically for a range of prescribed geometrical deformations. It is a bit a hassle for the problem that likely something to have caused the local heave (for general heave would have scarce interest since a parallel movement to the surface) it is precisely a previous rupture of the pipe at some point or joint; and if general heave on some area there will be more ample length for acommodation of the movement, hence lower stresses.

So I see it difficult to study it without a properly defined set of conditions upon which the heave happens. Having that, then the most scientifical way would be to find some technical procedure that encompasses then all the relevant parameters. Finding a program able to deal well with all these heave effects is paramount, since will define what are precisely the parameters of interest. Then we could use it directly to find the stresses and deformations if as complete, or combine with our knowledge to so produce from the related gained info from the program.

 

[dhengr]

For all my rants about FEA always being the first go-to analysis approach for everything, I think its use here would be quite appropriate. This seems to be a very complex and indeterminate problem, and even a FEA approach will be an approximation to one of a million possibilities.

I would be talking with the HDPE pipe supplier or that industry’s assoc. They brag about how flexible and compliant their pipe is, (not rigid like steel or cast iron) and I would think they would certainly have studied this type problem at some length. I believe that part of what they brag about is how much deformation their pipe can tolerate without failure, its flexibility while remaining intact.

I would be talking with my favorite GeoTech guy, who knows something about frost heaving and soil expansion/contraction deformation as relates to structures. I would expect that one of his FEA programs would deal with soil movement and the forces involved. They are most likely able to model the soil mass movement and forces due to frost heaving, and I would certainly expect these forces and movements to be pushing the pipe around, not the pipe constraining the soil.

I think what you need to do with this problem is treat the pipe and the surrounding soil as a composite system, with very different material properties, but still subject to reasonable interactions btwn. the two materials at their boundaries. The pipe will have bending, axial, shear and maybe internal pressure stresses. The soil will impart shearing stresses (bonding stresses) on the surface of the pipe, and radial forces due to soil confinement of the pipe. Then the soil movement will define the shape of the pipe. This could be a cleaving action is the soil happened to act that way over a very short distance, or it might be a gradual deformed shape as shown in the sketch with the OP. Once some feel for the deformed shape of the pipe is known, I would work backwards asking what stresses and forces would cause this deformation. I wouldn’t know how to do this, but would certainly assume it can be done with some FEA programs. I would use cylindrical shaped plate elements to define the pipe and operate on or with the deformations at the corner nodes of the plate elements. I think this is essentially what Ishvaaag was describing in this last post.

 

[TERIO]

Some reference info for buried pipe is given in this thread:

http://eng-tips.com/viewthread.cfm?qid=264765

 

[BAretired]

The problem is indeterminate. The best we can hope to achieve is to assume various boundary conditions and attempt some sort of analysis of each. In the real world, however, there has to be a better approach. I do not know what that could be. Perhaps someone else does.

BA

 

[FinnB]

Thanks for the responses which were very helpful and apologies for my absense on my own thread.

I have carried out some calculations and this is what I am now thinking:

1) As pointed out by BAretired using the deformed shape to determine the forces is possibly the only way to get meaningful answers to this problem.

2) Using the equation for deflection of a beam gave varying anwsers and seems most dependant on the length of the pipe. Over a distance of say 5.0m the pipe gives very similar bending moments to those using the equation M=EI/R. As the legth of pipe shorteded the deflection equation results diverged away from the M=EI/R equation results.

3) The equation M=EI/R appears to be the most accurate method of establishing bending moments.

4) The manufacturers minimum radius for the pipe can be taken as 15 x Outside Pipe Diameter in warm weather conditions, which is our case.

5) The pipe is flexible enough to accomodate large ground movements based on the properties of the pipe as given by the manufacture. The pipe is not stiff enough to attract a lot of moment when deformed to the minimum allowable radius. My calcs showed that the moment generated from the mimimum allowable bend radius is not great enough to cause tensile yield failure of the pipe.

6) The potential forces acting on the pipe due to heave (300-400 kN/m2 or 6500 pounds/ft2) are far greater than the pipe can resist so I am making the assumtion that the pipe just moves with the ground freely. The bending moments, as noted earlier, are then due to the deformed shape of the pipe.

7) the bigger issue as I see it now is what happens to the pipe at an abrupt change in ground level where there is a signficant heave taking place. The issue here, I feel, is less to do with flexing or bending but more to de with shear.

8) Taking a radius of curvature to find the bending moment then allows the shear force to be worked back based on chosing a lever arm to first find the applied load. With the load and an assumed span length a shear force can be calculated.

9) As is to be expected the shear force from a 4" vertical ground movement over a distance (span) of 3' is verg big (ground movements as suggested by a geotechnical engineer). For this situation I got a shear force of 300kN (67 kip). To my surprise a 225mm (9') pipe has a shear capacity of 150kN (33 kip). The wall thinkness of a 2225mm pipe is approximately 20mm (4/5 inch).

10) Even though the pipe is strong in shear the applied shear force seems too large.

11) I have sent this problem off to a HDPE supplier and I will let you know what they think.

12) For anyone interested the properties of the HDPE pipe I am using are as follows, these are manufacturers figures:

Density: 950 kg/m3
Poissons ratio: 0.4
Tensile strength at yield: 18 MPa
Modulus of Elasticity: 700 MPa
Pipe size: 225mm
Pipe Wall Thickness for SDR11 pipe: 225/11= 20.45mm