Accounting for Uncertanties

In CalME, there are two sources of performance variability: within-project variability and between-project variability. Within project variability is the variability of the materials production and construction process within the project for a given contractor and material supplied. Differences in performance-related properties between materials produced by different suppliers are the primary source of between-project variability. Differences in median construction quality between different contractors would also contribute to between-project variability.

Within-Project Variability

Within-project variability comes from variations of the natural subgrade and the variability of materials production and construction using the given set of materials that a contractor brings to a single project. Within-project variability considers the rate of development of distress extent within a project as time and traffic progress. If there was no variability of materials properties in a project due to the natural subgrade and no variability in materials production and construction of the other layers, then theoretically the entire project would fail at exactly the same time. For example, the entire project would go from zero to 100 percent of the wheelpath cracked at the same time. Of course, this does not happen in practice. Within-project variability can be seen in the differences in time/traffic between the first part of a project that fails and the last part that fails.

Here is an example of within-project variability. Suppose there were two contractors, A and B, working with the same materials on the same project, as shown in Figure 1. If both have the same median construction quality but Contractor A’s construction quality variability is higher than Contractor B’s, then the project would reach a typical cracking failure extent threshold extent (such as 25 percent of the wheelpath cracked) earlier if Contractor A built the project than if Contractor B built it. In this case, the within-project variability of the subgrade is included in the within-project variability shown for both contractors.

Figure 1: Two different within-project variabilities.

Between-Project Variability

Between-project variability addresses the uncertainty regarding the materials that a contractor would bring to a project in a low-bid environment, and to potential differences in median construction quality between contractors. Figure 2 shows a situation where Contractor A and Contractor B have the same within-project variability, but Contractor A brings an HMA material with a combination of stiffness and fatigue properties that results in less cracking than if Contractor B won the project.

Figure 2: Between-project variability for two projects.

This can happen because typical construction specifications are method and volumetric based rather than performance based. The materials supplied by the two contractors both meet the method and volumetric requirements but can still have large difference in fatigue cracking performance.

Without performance-related specification (PRS), asphalt materials only need to pass performance-related binder specifications and volumetric mix design requirements that do not fully address mechanical performances such as fatigue and rutting characteristics. The stiffness, fatigue performance, and rutting performance-related properties are not well defined and are unknown to the designer.

Accounting for Within-Project Variabilities

CalME uses Monte Carlo simulation to account for the effects of within-project reliabilities of a given pavement design. Essentially, CalME generates a set of random pavement structures that together provide a representative sample of the as-built structures for a given pavement design. CalME then uses the incremental-recursive procedure to predict the performance of each individual pavement structure and uses the performance statistics to determine the reliability of the given design.

Construction Variabilities

To quantify construction variabilities, the following inputs of each layer are assumed to be random variables:

•Thicknesses: follows normal distribution

•Intact moduli: follows log-normal distribution

•Fatigue resistance: a critical fatigue model parameter is assumed to follow log-normal distribution

•Rutting resistance: a critical rutting model parameter is assumed to follow log-normal distribution

Monte Carlo simulations are run by taking random samples of these inputs. The statistical distribution of these variables are depends on whether it is for an added layer (such as all of the layers in new constructions or the overlays in rehabilitation projects), or an existing layer (such as the old layers of rehabilitation projects). For an added layer, the built-in statistical distribution reflects the stated wide median construction practice and is adjusted as part of the field calibration. For an existing layer, the statistical distribution reflects the in-situ condition determined through site investigation.

For log-normal distributions used in CalME, standard deviation factor (sdf) is used to quantify the variance of a random variable. Specifically, sdf is defined as 10 raised to the standard deviation of the logarithms of the moduli.

Note that for existing layers, the moduli and their sdf values are imported from CalBack, the software program developed by UCPRC for Caltans to do layer moduli backcalculation using FWD. Since layer thicknesses are assumed to be constant during backcalculation, the resulting sdf on the moduli are, in reality, a function of both the thickness and the modulus variability. CalME adds the default variability of layer thicknesses on top of the imported variability of layer moduli, which leads to slightly more conservative designs for rehabilitation projects.

Although currently disabled, it is also possible to include variability on the climate. In this case start of the simulation will be selected randomly from the 30 years of temperature data and the day used during each increment will also be selected randomly.

Accounting for Between-Project Variabilities

CalME uses a shift factor to account for the between-project variability in pavement performances for the same designs (same structure, same traffic, same climate) seen in the PMS calibration data. Specifically, the shift factor acts as a correction factor applied to the median pavement life for a given design to account for the difference in performance between low performing and median performing projects seen in the PMS data.

This shift factor has been determined to correspond to 95% design reliability. This means most (i.e., 95%) of the projects will be able to sustain the design life without cracking or rutting failure.

A more detailed description of this process can be found here.

The adoption of performance related specification (PRS) is likely to reduce the amount of between-project variability and CalME has built-in adjustments to account for that.