Performance Based Design: More Grist to the ‘Limit Analysis’ Mill

How do you Engineer?

One of the most rewarding aspects of my job is working with some really smart people. They come from different parts of Europe and wider afield, and aside from the cultural differences, there are also some really interesting differences in engineering. These tend not to be fundamental, but typically rather subtle differences, that are promoted by the different academic schools of thought in each country.

The various National perspectives on what constitutes an acceptable factor of safety in a design is just one example of the differences in engineering approach.  The basis of these differences tends to be partly philosophical; historical and most significantly: due to the types of problems, soil conditions and quality of survey data encountered in each country.

Another good example is the difference between the UK and Denmark when defining Ultimate Limit State (ULS) conditions. In the UK, there is a school of thought that argues for the collapse ULS should be defined by the point at which the soil body no longer exhibits elastic behavior.  In Denmark, students are taught that collapse occurs once a failure surface has developed and the stress distribution is fully plastic along the failure surface or rupture plane.  Depending on your design approach, both of these are valid points of view.

What Are Partial Factors For? (2.15 mb)

Discussions centered on these sometimes divergent perspectives are entertaining, educational and a good source of inspiration. One of these discussions seems to be making it into consciousness of the wider engineering community.

Performance Based Design, is it New or Nascent?

Professor Malcolm BoltonProfessor Bolton’s most recent public observations on design codes in the Rankine Lecture held at Imperial College in March 2012 were in my view, timely.

In this lecture he made the interesting point that in key design scenarios the ULS requirements against collapse are satisfied, and yet, the structure may still be placed into a condition in which the constraints on displacement (serviceability limit state, or SLS) are not satisfied.    He went on to propose a mobilizable strength design approach in which safety factors are selected to achieve a certain level of “performance”,  defined by serviceability considerations.

The primacy of ULS or SLS conditions in different designs is something we have collectively been aware of for some time.  At my place of work we have developed an approach to design that respects the general principals of mobilizable strength design outlined by Prof. Bolton.  This development occurred based on a collective discussion over several projects and a natural evolution in our thinking with respect to the limitations of design codes.  The outcome is that where we are certain ULS conditions are the dimensioning case, we are quite content to discard our deformation analyses and use the collapse condition as the basis for optimising our design.  The opposite is true for designs controlled by displacements.

Limit State or Stated Limits

The importance of understanding and proving whether a design is driven by the ultimate collapse load or allowable displacements (or a combination!) is not of course to be underestimated.  In the offshore environment we do often have the option of deciding whether a component in the subsea production system is able to accommodate displacements.

This choice is often one between:

  1. Not allowing infrastructure to displace and designing the interfaces between different components to withstand the high forces that develop as a function of this restraint;
  2. Allow infrastructure to displace within defined limits, to reduce the forces on structural interfaces to be within tolerable limits.

We then enter the territory of performance based design, but not however, within the strict limits defined by Prof Bolton: in which the bounds of elastic response are our safety net.  The magnitude of displacement required to satisfy the second point above tends to be in the order of 10’s of centimeters or meters.  This is far in excess of the displacement required to mobilise ultimate resistance, and large enough to be concerned with critical state or residual soil strength and the effects of variable geometry.

Plastic Fantastic

Our ability to predict where a structural component will be situated following a load cycle in which large strains occur is therefore critical in proving that a system will perform within a given envelope and that components within that system are sufficiently robust as to be able to accommodate such displacements.

The point at which a fully plastic yield surface develops is a key step in defining the point at which large displacements will occur.  The upper and lower bound theorems of plasticity become rather relevant in this assessment.  This doesn’t really provide the whole answer though:

The final position of a structural component is very much dependent on the evolution of the critical failure mechanism and any softening or hardening of the soil as this occurs.  The only reliable(?) way of capturing this is with full scale model testing, testing in the centrifuge and correlation with large strain finite element analysis.  Of course, these are all time consuming and expensive tools to use.

Once we have this understanding though, a step-wise analysis using plasticity theory to capture the evolution in geometry and soil properties is an efficient and cost effective way of achieving this.

ULS: The Refuge of the Plastician?

The vast majority of onshore soil structures are designed to remain static, and not only this, they are required to remain static within quite tight tolerances!   The value of the insights provided by Prof Bolton in his Rankine Lecture will hopefully change the way onshore Civil Engineers view material factors and conservatism in design.  The academic school that supports an understanding of the bounds of Elasticity have “new” impetus to push forward their cause .

This might be worrying if we were in a “zero sum” game where one arguments “win” is another’s “loss”.  Fortunately, elasticity and plasticity are complementary and those of us interested in designs controlled by the collapse ULS and large strains have much to be optimistic about.

More on this next time.

NB