Hi all.
Relatively new to Caesar and am trying to incorporate the bi-linear spring restraints for my pipe/soil interaction in the model. I want a negative yield stiffness (K2), which the user guides says is possible, but whenever I enter a minus sign, the model error check comes back with an error. If I remove the minus sign, all is fine. Am I missing something?
Many thanks
Matt

You can't have a negative stiffness. A negative stiffness would mean that if you pushed to the right (on some object), that object would move to the left.

Exactly where did you see this in the User's Guide?

But ... The next time a politician tries to push you to the right, see which way you go !!

This thread breaks new ground... pipe flex analysis as it relates to politics!

It's in the applications guide under bi-linear restraints (page 3-41) and if you hit F1(help) when inputing the K2 parameter.
I quote from the CII applications guide:
'Both the yield stiffness (K2) and the yield load (Fy) are required entries. The initial stiffness (K1) may be left blank, and a
rigid initial stiffness assumed. The yield stiffness may be negative if necessary. Some subsea pipeline resistance tests have
shown that load carrying capacity drops after the “ultimate” load is reached, and displacement continues.'
And, no, a negative yield stiffness would mean that the stiffness reduces once the yield force was reached, not that it would start to move the element in the opposite direction to force application in some way.
Thanks for the help so far.
Matt

The "yield stiffness" can not be negative. I'll see that this is changed in the documentation for Version 5.10.

This is very strange indeed and doesn't make sense. How this got into the manual I don't know, but it has been there since the DOS version of the program. We will definitely take this out of the documentation. How could you imagine a situation, subsea or otherwise, where if you push something to the right, it moves to the left? Instead, if you want the displacement to continue once the ultimate load is reached, use 1.00 for K2 and it will do exactly that. A negative stiffness would not allow the displacement to continue, but would reverse it.

I wonder if you're looking at a negative stiffness to be summed with a larger positive stiffness, to provide an inflection point. For instance, the common model for carbon steel - stiffness up to the yield point is our old friend Young's modulus. Above the yield point, the stiffness is much lower (but not zero, as a quick glance at any stress-strain curve will show). The stiffness for the portion of the curve may be modeled either as a (lower) value of stiffness, or by superposing a negative stiffness on top of the existing stiffness value for the elastic portion of the curve. It all depends how CAESAR II is coded; from the wording of the manual it may be that the superposition model is in effect.

This problem is unsolveable statically because for any given force you would have two possible displacement values, one prior to breakaway, and one after breakaway. Which one is correct?

This is an interesting topic, and I would like to share the following information on how the non-linear behavior of soil restraint has been addressed in the past, and has been generally accepted by the soil-structure interaction community.

It well documented that the soil load-displacement response to beam-on- elastic foundation types of structural movements is highly non-linear. The soil response or the general shape of the soil load-displacement curve can exhibit two distinct types of behavior which can be described as either "soft" or "brittle".

The "soft" behavior is characterized by a hyperbolic smooth strain hardening type of load-diplacement soil response where the soil load smoothly increases at a decreasing rate where the ultimate soil response becomes asymptotic to a constant value at large structureal (pipeline) displacements. This type of behavior is generally associated with "loose" to medium dense granular soils (i.e. sands or silty sands).

The "brittle" behavior is characterized by an initially "stiff" response to increasing structural displacements where the soil load increases to an ultimate value, and then drops off to a lower residual or mobilized soil response and becomes asymptotic to a constant value at continued increased structural displacements. This type of behavior is generally associated with dense granular soils and/or cohesive fine grained clayey materials. This characterisic is also associated with frictional load-displacment behavior and pipeline sea bottom resistance against lateral loads as mentioned above by a previous respondee.

For either case, the question is, how to mathmatically characterize these types of non-linear soil response using the bi-linear soil model available in CAESAR II? A bi-linear soil model is restricted to characterizing soil behavior using two straight lines. The accepted way of using a bi-linear soil model to approximate non-linear soil response involves an iteritive trial and error type procedure to match the soil response (soil force) and corresponding displacment from the CAESAR output with the predicted "actual" non-linear soil displacement funtion by changing the slope or stiffness of the bilinear CAESAR II soil model at different segments along the buried pipeline.

This is very much considered to be an advanced analysis approach, is not necessarily for "beginners", and implies that the the user be very familiar with the technical literiture that addresses how to generate non-linear soil-load displacement functions, and the he or she has a good working knowledge of soil mechanics focusing on soil-structure interation problems.

Some literiture that is helpful to understand the soil mechanics side of the problem are as follows:

Nyman, K. J., "Thaw Settlement Analysis For Buried Pipelines In Permafrost", Preocedings, Pipelines In Adverse Environments II, ASCE, San Diego 14-16 Nov. 1983, pp 300-325

Audibert, J.M.E., Nyman, K.J., "Soil Restraint Against the Horizontal Motion of Pipes, Journ. Geotechnical Eng. Div., ASCE, GT10, Oct 1977, pp 1119-1142

"Guidelines for the Design of Buried Pipe", July 2001, American Lifelines Alliance (avialable for free on the Web...look it up)

kjn, excellent information! I would add that for pipelines with moderate temperature differential, typical of gas or oil gathering lines, the simple approach using the ASCE Guideline and a geotech report is "good enough". We can run a lower and upper bound analysis to ensure we are conservative with a simplified approach.

For other pipelines, we not only would use a more comprehensive model of the soil properties but also be concerned with non-linear geometry and non-linear pipeline material curves and use either a general FEA program or that program developed specifically for pipelines. I have collegues that specialize in that type of analysis and have learned it's a whole different field of engineering.

Paul,

You are correct in stating that for the typical buried pipeline applications, characterizing the soil restraint using a bi-linear soil model in accordance with the ASCE guidelines along with representative soil strength parameters from the site specific geotechnical report is usually adequate. I would also venture to say that more detailed pipline stress analyses which have been performed using other more rigorous finite element softwares for plastic analysis (non-linear) of buried or seabottom supported piplines subjected to large displacements also have characterized the soil response using bi-linear soil models, and have achieved reasonable results.

There have been some major advances in research during the 1980's to date regarding how to better characterize soil restraint functions for buried pipline movement problems using bi-linear soil models as previously referenced in the ASCE publications for example. The main point here is that present CAESAR II software (and operating Manual equation descriptions) generate soil response models that are based on somewhat dated information referenced to Dr. Peng's May 1978, Part 2 publication appearing in Pipeline Industry magazine. In addition, Dr. Peng's paper only provides sufficient information to completely define the bi-linear soil model characteristics for the transverse-lateral direction of pipline movement only.

The information required to completely describe the bi-linear soil response curves for the remaining important directions of buried pipeline movement (vertical uplift, vertical bearing and longitudinal-axial directions)are not provided in Dr. Peng's paper. Although these other directions of pipeline movement are generally mentioned in his paper, only an equation for estimating the soil response against longitudinal-axial movement is further suggested with no corresponding equation for the soil-pipeline diplacement at which this soil response is mobilized. In addition, Dr. Peng's paper does not provide any information on how to quantitatively define the bi-linear soil model the vertical uplift and vertical bearing directions of buried pipline displacments. Make no mistake, Dr. Peng's paper was an excellent contribution to the Industry at the time, but the information was somewhat limited, did not completley address all important directions of buried pipline movement, and the technology and research has moved on from there.

The subsequent research summarized in the more recent ASCE technical publications do provide all the information that is needed to properly generate the bi-linear soil models for all directions of pipline movement. Therefore it is recommended that these procedures (equations) be followed, and the bi-linear soil model parameters be user-defined (i.e. user specified) in CAESAR II accordingly as opposed to CAESAR II autimatic generating the bi-linear soil models especially for the vertical uplift, vertical bearing, and longitudinal-axial directions of pipeline displacements.

For buried pipline problems involving lateral pipline movements (i.e. sidebends or pipeline exposed to lateral movement due to earthquake loadings or mud slides for example), if the user desires CEASAR II automaticly generate the parameters for the lateral restraint soil springs on either side of the pipeline, the user should be cautious in the selection of the "overburden compaction factor" (OCR)to be used. It is understood (based on CAESAR II output)that when CEASAR II automatically generates the ultimate lateral soil restraint in accordance with the equation given by Dr. Peng's paper, the results are then multiplied by the OCR. This can lead to very unrealiticly high values of lateral pipline restraint. If one is studying movement of sidebends for example, it is conservative to underetimate the lateral soil restraint rather than to overestimate it by many fold.

If it is desired to provide a reasonably "high" estimate of soil response, this is conventionally accommodated by using reasonably high etimates of soil density and soil strength (soil friction angle for granular soils or shear strength for cohesive soils)in the constitutive equations to predict ultimate soil restraint rather than to mutiply the end result by some general factor.

Paul,

I forgot to mention an additional reference that presents a comprehensive assessment and discussion regarding past collective research on soil restraint of buried pipelines is presented in the ASCE publication:

"Guidelines for the Seismic Design of Oil and Gas Pipeline Systems", Committee on Gas and Liquid Fuel Pipelines, ASCE, 1984.

The previously mentiond "Guidelines for the Design of Buried Steel Pipe", July 2001, summarizes much of this information with some further refinements, but the original 1984 publication provides more historical background and further insight.

Has anyone heard the rumour that the next B31.3 will be recommending some sort of soil response guidelines, following the Peng method?

Paul,

I know of no B31.3 action on buried pipe evaluation or soil response guidance.

We just had our Code Committee meeting last week.