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Arno Hefer Administrator Posts: 16
4/17/2021
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A question often asked by practitioners is: “What percentage error is acceptable when evaluating backcalculation results?”
Backcalculation requires some skill and experience to perform well. The analyst should understand how changes in different layer properties will affect the deflection bowl and should also have good knowledge of material behaviour. With these basic skills, most engineers should be able to obtain useful results from backcalculation analysis; however, without these basic skills the result of a backcalculation analysis can be highly inaccurate, even when there is a seemingly good match between the measured and calculated deflection bowls. Because of this, it is often said that backcalculation is more an art than an exact science.
In evaluating the results, not only the precision of fit of the deflection bowl (or percentage error per sensor) but also the reasonableness of the backcalculated stiffness values obtained, should be critically evaluated. Stiffness values should be realistic in terms of prior knowledge of materials (e.g. material class, typical stiffness ranges), visual observations in test pits, other indicators such as Dynamic Cone Penetrometer (DCP) results, etc. For granular (unbound) materials, keep an eye on modular ratios – an unbound material cannot have a stiffness that is higher than about 4 times that of its supporting layer.
Whilst the average error per sensor obtained in the bowl matching process is a good indicator of what we are trying to achieve – how effective the pavement model represents the tested pavement structure – proper perspective of the problem should be maintained during the analysis. Ullidtz et al (1987) states:
“It is important to realize, however, that layer elastic theory is only a rather poor approximation of the extremely complex conditions of real pavement structures. Most pavement materials will show viscous, visco-elastic and/or plastic deformation under stress, in addition to the elastic deformations. Pavement materials are often inhomogenous, anisotropic and have non-linear stress-strain (or stress-strain rate) relations. Many materials are even particulate, i.e. consisting of discrete particles. Discontinuities, like edges, joints or cracks, are often present and the conditions at the interfaces (rough or smooth) are not well known.”
The statement above emphasises that discrepancies between the measured pavement and our theoretical layered elastic model is the reason why we often cannot reduce the error per sensor to perceived levels of acceptability. The ease or difficulty of matching the measured deflection using the theoretical model depends greatly on the composition and characteristics of the pavement under consideration. Situations that tend to be difficult to analyse are:
- The influence of thin layers (< 75 mm) on the measured deflection is very small or negligible and in effect impossible to backcalculate. Many thin layers, such as bituminous surfaces composed of several layers of different ages/compositions, are often treated as a single layer during analysis. A thin bituminous layer can also be combined with the base thickness during analysis. Try and build a model with fewer thick layers, as opposed to more thin layers – combine layers with similar properties.
- Thick asphalt layers over strong stabilised (or even concrete) bases, where the asphalt dominates the deflections and it is therefore difficult to determine the effective stiffness of the stabilised subbase.
- Situations where the subgrade is very stress sensitive – the effective stiffness of the material changes vertically and horizontally and the layered elastic model assuming one uniform subgrade is not suitable. The vertical effect can generally be accounted for by subdividing the subgrade into two or more layers (see Online Help/FWD Analysis/Backcalculation: General/Subgrade Characterization)
- Pavements exhibiting very high deflections (thin pavements, often with stress sensitive subgrades) result in highly non-linear deflection bowls that are difficult to fit using linear elastic models. In these situations, the geometry and configuration of the FWD device can affect the measurements (e.g. see Online Help: FWD Analysis/ Deflection Analysis/ Deflection at the 200 mm Offset: Warning)
In evaluating the backcalculation results, a balance between a good fit and reasonable stiffness results needs to be struck. Whilst an average error per sensor below 2% is exceptional, an error of 5% providing reasonable results may be sufficient. For the outer 3 to 4 sensors, it is usually possible to obtain an error of 0. Note that when the error is less than the precision of the measuring device, 0 error is shown. Generally, for pavements that are difficult to analyse, an average error per sensor of less than 10% may still be acceptable.
You should always keep in mind that – in the holistic experienced based approach – that we recommend – the stiffness values obtained from backcalculation are only rough indicators of layer stiffness and condition. We believe that before these stiffnesses are used in design calculations, they should be verified and cross-checked with other test data. Thus, in backcalculation, you should try and establish a habit of focusing on the essential feedback or information that the backcalculation process is giving you. If you can confidently determine the approximate stiffness of each layer, and if you use these to determine if the layer represents the material in question in a very soft, medium stiff, or very stiff condition, then you will have extracted all of the reliable information from your deflection data. (Also see our Online Help/ Design Tools/ DEMAC Materials Classification System)
Bibliography
Jooste, F.J. 2005. Rubicon Toolbox Technical Support Notes. Modelling and Analysis Systems, Pretoria, South Africa.
Rohde, G.T. 1992. Bowler User Guide. Van Wyk & Louw, Pretoria, South Africa.
Ullidtz, P., Battiato, G., Larsen, B.k. and Stubstad, R.N. 1987. Verification of the analytical-empirical method of pavement evaluation based on FWD testing. Proc. 6th Int. Conf. on the structural design of asphalt pavements, Ann Arbor, MI, USA.
edited by on 4/17/2021
edited by on 4/22/2021
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