Calibration of Transfer Function

 

There are two parameters in the fatigue cracking transfer function: the critical damage w50 and shape parameter bcrk. Each needs to be determined as part of the field calibration process.

 

Calibration of Critical Damage w50

 

To understand how to determine w50, imagine dividing a project into 100 individual segments. Each segment has a set of M-E inputs that are uniform within itself. There is one segment that has the median M-E inputs and refer to it as the median segment. The median segment will have the median performance among all segments, because fatigue cracking performance is a monotonic function of M-E inputs such as thickness, fatigue cracking resistance, etc. This is referred to as the monotonic property and is true for most M-E systems.

 

An example of the performance of the individual segments as well as the overall median and average performance is shown in Figure 1.

Figure 1: Cracking histories for individual segments segments and the project overall average and median

 

The overall average shown in Figure 1 is the performance data typically collected in pavement condition surveys. Figure 1 indicates that the shape of the cracking history curve for individual segments is very different from the shape of the overall average curve: the overall average curve is much flatter than the curves for individual segments.

 

Figure 1 shows a striking feature: the overall average and overall median reach 50% simultaneously, which is not a coincidence and is the result of the monotonic property. This feature can be used to determine . Specifically, we can find the median M-E inputs and use them to define the median segment. The damage in the median segment will reach  when the project reaches 50% cracking.

 

This concept can be extended to whole highway network. The difference is that the median segment becomes a median project within a given type of pavement and given design and traffic level, and potentially other sensitive M-E variables.

 

Note that there is no need to know what exact material is used in which specific project. It is however required that one knows enough about the performance of historical materials so that the median project can be determined.

 

Calibration of the Shape Parameter bcrk

 

The effect of WPV on the expected pavement performance is illustrated in Figure 2 as an example, which shows five projects with different M-E inputs in terms of fatigue parameter A and HMA stiffness E. The five projects have the same mean/median inputs but different WPV. While all going through the same  (number of load repetitions to 50% cracking), the overall average cracking curves change shape with the amount of WPV. The higher the WPV, indicated by the larger values for standard deviation, the more spread out the pavement performance is, as indicated by the flatter slope of the middle portion of the overall average cracking curves. In other words, the steepest slope of the mid-portion of the observed overall average cracking curves provides an upper bound estimate of the shaper parameter  of the transfer function (since the share parameter is always negative, the lower the value the steeper the slope).

 

Figure 2: Effect of within project variability on observed cracking histories (LN(u,s) indicates log-normal distribution with mean u and standard deviation s) (fatigue parameter A and HMA stiffness E are two critical M-E inputs)

 

An example of the cumulative distribution functions of the shape parameters is shown in Figure 3 for the sub-network of new flexible pavements with aggregate base (AB). According to this figure, the upper bound of shape parameter bcrk  is between -20 and -30. A value of -30 was chosen in CalME for this sub-network.

Figure 3: Cumulative distribution functions of shape parameters for the sub-network of new flexible pavements with aggregate base (hAC is the combined thickness of AC layers)