## Uncertainty in highway design (1)

I suspect that one of the differences between engineering and science is that  science tends to claim precision, whilst engineering  involves an element of pragmatism. For example , any highway design manual which quoted friction values to 3 decimal places would probably be suspect. There are so many variables involved that any figure for friction must involve a degree of uncertainty.

Engineers often modify theory to add for a factor of safety to cover this uncertainty. One website (link) defines factor of safety as:

“Factor of safety is a figure used in structural applications that provides a design margin over the theoretical design capacity. Also known as the safety factor, it allows for uncertainty in the design process, such as calculations, strength of materials, duty and quality”.

The question then becomes, how do engineers apply a factor of safety in the geometric design of highways? (if they apply one at all). Possible answers can be seen in examples for the calculation of horizontal radius. This post looks at an example taken from documents for South Africa.

South Africa: Design Domain

This material is based on two documents, (ref. 148 / 2002) and (ref. 1042 / 2003) (see below).

(Ref. 148) says:

“The design domain concept recognizes that there is a range of values, which could be adopted for a particular design parameter within absolute upper and lower limits. Values adopted for a particular design parameter within the design domain would achieve an acceptable though varying, level of performance in averageconditions in terms of safety, operation, and economic and environmental consequences”. (own emphasis)

(Re. 1042) adds that design domain :

“provides an implicit link to the concept of ‘Factor of Safety’ – a concept that is used in other civil engineering design processes where risk and safetyare important”.

The following figure from (Ref. 1042) gives an illustration of “design domain”:

The figure shows four limiting values :

• Absolute lower limit
• Practical lower limit
• Practical upper limit
• Absolute upper limit

(Ref. 148) says that “in some cases, the concept of a design domain with upper and lower bounds, and a continuous range of values in between, may not be practical or desirable. Lane widths provide a good example of such a case“.

and from Ref. 1042:

“If a design involves compromise, it may be more appropriate to compromise severalelements by a small amount than to compromise one element excessively. It is important that a design shouldbe balanced”.

In the normal formula for minimum radius there are 4 variables

R = V2 / [127 (e+f) ]

Where

• R = radius (in metres)
• V = speed (km/hr)
• e = superelevation
• f = side friction

Some notes in (Ref. 148) link this formula to the idea of design domain.  To quote some text from the reference:

“The side friction factor is a function of the condition of the vehicle tyres and the road surface and varies also with speed. For the purposes of design, it is desirable to select a value lower than the limit at which skidding is likely to occur and the international general practice is to select values related to the onset of feelings of discomfort. Canadian practice suggests that theside friction factor be taken as (a function of speed)….

This reduces the formula to one where radius is only a function of superelevation and speed, so that:

“For any given speed, it is thus only necessary to select the maximum rate of superelevation, in order to determine the minimum allowable radius of horizontal curvature for that speed. This selection is based on considerations of the design domain….  In practice, four values of emax are used, being 4, 6, 8, and 10 per cent”(own emphasis).

What seems to be happening here is that:

The original formula (which basically relates minimum radius to safety) is replaced by a constraint related to a sense of discomfort

• a hidden factor of safety is applied (“For the purposes of design, it is desirable to select a value lower than the limit at which skidding is likely to occur”)
• In (Ref. 148) the four quoted values of e max are likely related to the four design domain values
• which of the four quoted values is used can be restricted by practical considerations  (“The spatial constraints in urban areas will very often preclude the development of high values of superelevation“)

The quoted values for minimum horizontal radius (for e = .08) are quite similar to those in the benchmark Swiss values (see the following table and chart):

And

Comment

The design domain concept is interesting. It allows the introduction of flexibility and engineering judgement witin a range of values (the references quoted should be read as they give more extensive explanations of the concept). Not sure however that the quoted application to horizontal radius is a convincing one.

References

148 –  South Africa, “Geometric design guide”, CSIR; 2002

732 –  Switzerland, VSS “VSS 640-080 Projektierung, Grundlagen (basics of road design)”, 1991

1042 – South Africa, “SADC / SATCC Guideline on low volume sealed roads”, SATCC 2003