Skip to content

Resistance

As the last piece of the PoF puzzle, an estimate of the component’s resistance against all failure mechanisms is sought. This includes a myriad of issues including manufacturing and construction practices, in-service damage rates, inspection frequencies and capabilities, and the impact of potential defects of varying characteristics. The need for a formal process is readily apparent upon brief contemplation of the possible combinations of strength issues.

Resistance Estimation Process

Few places in the pipeline risk assessment can benefit as much from ‘intelligent simplification’. A screening-type approximation of resistance is often sufficient for general risk assessment. The full, robust solution can usually be reserved for certain specific applications such as incident investigations.

Intelligent simplification first requires an understanding of the full, robust solution. Only then can approximations be considered. The detailed assessment of resistance involves the following steps:

  1. Estimate the defect-free stress carrying capacity available to resist loads
  2. Identify normal loadings applied to the component
  3. Identify stresses generated by the loadings—ie, general structural stresses
  4. Compare to maximum tolerable stress capacity of component.
  5. Adjust stress carrying capacity, based on role of known and suspected defects
  6. Estimate the probability of potential defects in the component
  7. Determine the effect of potential defects—ie, highly localized stresses.
  8. Estimate the potential effects of degradation mechanisms
  9. Estimate the ability of the component to resist additional loads or failure mechanisms
  10. Estimate the amount of stress carrying capacity ‘used up’ by normal loads and potential presence of defects and degradations
  11. Express the remaining stress carrying capacity as effective wall thickness.
  12. Characterize the spectrum of future abnormal loads that may be experienced (for example, from PoD estimates of excavator impacts, landslides, etc).
  13. Estimate the fraction of future loads resisted by the stress carrying capacity implied by the effective wall thickness.

Assessing resistance in this way also ensures that interaction among all threat issues is fully included. Most of the modeled weaknesses are additive, as are most loading scenarios, and all loads and weaknesses should be included. Similarly, delayed failure potential is fully included since weaknesses remain (until repaired) and continue to interact with modeled future loadings, including external forces, pressure surges, corrosion, cracking, etc.

While these steps are well understood, research in most of them continues today. Full models and approximate solutions for some are updated regularly. Applying the latest techniques to specific scenarios of loadings yields the most accurate values but this comes only with substantial–many would say ‘unrealistic’–levels of effort. Safety factors in design guides are normally used to avoid the numerous detailed calculations otherwise required, in addition to maintaining conservatism and dealing with uncertainty.

Background

There is an interesting interplay between exposure and resistance since both are sensitive to the exact definition of ‘failure’. Exposure measurement implicitly involves a theoretical baseline for resistance since an exposure is defined as an event that causes ‘failure’ and resistance is a measure of invulnerability to ‘failure’. So, the definition of ‘failure’ is a component of resistance, just as it is for exposure. This is again best illustrated by examples. If failure = ‘permanent deformation’, then resistance measures the invulnerability to permanent deformation, given the presence of a force (an exposure) that can cause permanent deformation if there is insufficient resistance. If failure = ‘leak/rupture’, then resistance measures the invulnerability to leak/rupture, given the presence of a force (an exposure) that can cause leak/rupture if there is insufficient resistance.

If resistance is to be measured in simple terms of percentage or fraction of mitigated exposure events that do not result in failure, there is a need to define a starting point or baseline. That baseline must be consistent with the definition of the exposure event. If the baseline is to be ‘zero resistance’ then exposure involves imagining that there is no resistance at all. A thin-walled aluminum can or cardboard tube, egg-shell vessel, etc, crushable between two fingers—is the right mental image for almost complete lack of resistance. So, the image of an unprotected beverage can or cardboard tube sitting atop the ground, is the correct image to estimate exposure event frequencies when a ‘zero resistance’ baseline is chosen. If such a can may be broken /crushed/deformed by the event, then it should be counted as an exposure.

There are obviously many more exposure events that could break an aluminum beverage can compared to a steel pipeline. So exposure counts are dramatically increased when zero resistance is assumed. As a matter of fact, the number of potentially damaging events always increases when the threshold for damage is lowered.

If the risk assessment designer feels that zero resistance results in excessive exposure counts, he can define the resistance baseline as something other than zero. For instance, he may set the resistance baseline as the fraction of exposures above ‘normal’, which do not result in failure. Then resistance is the amount of ‘extra’ stress carrying capacity once ‘normal’ loads have been accommodated. This can theoretically lead to negative values. Perhaps failure has not yet occurred in a weakened component only because the upper limits of ‘normal’ have not recently occurred. If there is not only no ‘extra’ resistance, but not even ‘sufficient’ resistance, then a negative value is warranted.

This is a modeling choice. A changing resistance baseline—potentially different for each component under varying ‘normal’ loads—may be confusing to some. On the other hand, the imagineering of a no-resistance component and the associated need to count many seemingly minor exposures might be more troublesome for others.

Exposure Influenced by Resistance

When a resistance baseline other than ‘zero resistance’ is used, exposure varies, as was suggested in the previous section. Exposure rates are sensitive to changing resistance. When material characteristics degrade or are changed, a greater number of exposure scenarios can cause failure. Examples of such material changes include:

  • creation of a HAZ,
  • extreme temperatures effects reducing material stress-carrying capabilities,
  • UV degradation,
  • Hydrogen embrittlement.

Other examples of changing resistance include metal loss by corrosion, crack progression through a component wall, unanticipated or intermittent external loadings such as debris impingement in flowing water or gravity effects when support is lost, and others.

The most robust assessment can provide for a continuous updating of exposure estimates based on changing resistance. That is, if a resistance baseline other than zero has been chosen, then the count of exposures—events that can cause failure—will increase as resistance decreases.

Similarly, when modeling time-dependent failure mechanisms like cracking, the TTF shortens when either the modeled rate of cracking increases or the effective wall thickness is reduced. If material degradation or change (for example, creation of a HAZ) causes the material toughness/brittleness to change, is that better modeled as increased crack propagation rate (ie, more exposure)? or rather as reduced effective wall thickness (ie, less resistance)? Fortunately, the suggested mathematics ensures the same result regardless of chosen approach. While either will work in the proposed PoF model, it may be more intuitive to model this as a change in effective wall thickness. That way, this potential change in a material’s property is readily seen alongside any other potential change in component strength.

As another example of the modeling choices for exposure-resistance interaction, consider the role of an expansion loop in a pipeline. If the expansion loop is present to reduce thermal stresses and fatigue, most would agree that resistance has been improved rather than exposure reduced or mitigation improved. After all, the changes in temperature still occur and the pipe is not protected from those resulting forces. Only the pipe’s reaction, its ability to absorb the forces without damage, have changed. However, a counter could be that each temperature cycle is now no longer imparting the same stresses and, hence, exposure estimates should be reduced. Again, either choice yields the same PoF under the suggested modeling approach.

Aspects such as inclusion of suspect weaknesses will always be necessary in the risk assessment. Other aspects will be discretionary. The risk assessor can decide, in the context of desired PXX and trade-offs between complexity and robustness, the optimum way to handle resistance and resistance-exposure issues such as:

  • Yield vs ultimate stress levels.
  • Inclusion of intermittent loadings.
  • The extent of simultaneous consideration of changing resistance with loadings potentially causing exceedance of stress-carrying capability. See discussions of unanticipated spans and loss of buoyancy control features in .

Resistance as a critical element of PoF

The examination of Resistance triggers many nuances and sometime-complex related topics, including

Resistance Estimation: A Broadcast Solution

Estimating Resistance

The goal is to understand failure fraction even if that understanding is only an approximation. The methodology described here  is not the only way that that understanding can be achieved. The important thing is that, as a last of the three critical elements of failure potential, the risk assessment has the ability to differentiate components that can absorb damage and stresses without failing versus those that will fail.  This is why the independent assessment of resistance is a an essential element in estimating failure frequencies.

Resistance calculations estimate structural integrity against all anticipated loads—internal, external, time-dependent, and random.

Varying levels of rigor are available to the risk assessment designer. The underlying engineering, physics, and material science concepts can be complex. However, approximations often provide sufficient accuracy and will be appropriate for many types of risk assessments. When more precision in pipe resistance estimation is desired, pairings of specific weaknesses with specific potential loadings can be analyzed using solutions up to robust finite element analyses.

Whether a more robust or more modest assessment is desired, the general process is the same. The overall strength of the pipeline segment or component and its stress levels are considered. This includes an assessment of foreseeable loads, stresses, and component strengths. Known and suspected weaknesses due to previous damage or questionable manufacturing/construction processes must also be considered.

The resistance estimation is akin to calculating a safety factor or a margin of safety, comparing what the pipeline can do (design) versus what it is currently being asked to do (operations). The margin provides protection when unanticipated loads or defects appear. This discussion focuses on steel pipe but concepts apply to any component (pump/compressor, tank, valve, etc) of any material (steel, plastics, cast iron, concrete, etc.

m

Concept of ‘Effective’ Wall Thickness

TTF / Remaining Life Estimates

For Full Reading on Resistance, See Chapter 10

Published inRisk AlgorithmsRisk Assessment