7. CRACKING MODEL

A similar process was used to develop the cracking model. The dependent variable used was the length of longitudinal cracking per 100 lane meters observed on original flexible pavement structures. The independent variables selected for the first generation longitudinal cracking model are the same than those used in the roughness model. Frost susceptibility of the subgrade soil, freezing index, and precipitation are believed to reflect the aggressiveness of frost action on pavement. The total thickness of the structure is considered as a mitigation factor.

Seven experts were solicited to encode their estimates of crack lengths (at a given time for given conditions). Summaries of lengths of roads affected by longitudinal cracking per 100m and rate of propagation were extracted from Quebec's provincial database and provided for reference to the experts. As before, the expert's responses to the encoding package were combined into a (group prior data set ) containing 756 observations from which the group prior model statistics were subsequently calculated. Reasonableness and coherence of the estimates given by the experts were verified by performing a sensitivity analysis on linear prior models derived for each expert. Prior models were used to assess the variation in roughness predictions. The results of the sensitivity analysis for the cracking model is illustrated in figure 11. The analysis shows that all experts are in relatively good agreement on signs and magnitude (slope of the curves) of the coefficients. There is however a wide variation of opinions concerning the predicted values of cracking for the base cases ((Y) values on the graph).

Sources of field data that met the model requirements were rare. Because of technical problems, SHRP data were impossible to use. Moreover, C­SHRP experiment being focused on rehabilitated (overlaid) pavements, only the observation prior to rehabilitation (on the original pavement surface) for each site was used. Because crack reflection through overlays is believed to be a different mechanism, the inclusion of post­ rehabilitation data would have confounded the analysis. Therefore, only 38 observations on 38 sites were added as new field data to update the prior information. As illustrated in figure 10, there is a reasonable agreement, with respect to the inference space, across thickness, precipitation and frost susceptibility for the two data sources. There is however a significant difference between inference spaces for freezing index and age. The implication of the poor match will have to be assessed.

Cracking of asphalt pavements is fundamentally a two­phase phenomena. The first phase (crack initiation phase) is the period during which pavement resists frost­heave induced stresses. From the time the first crack appears, the pavement structure then enters the crack propagation phase. It is also postulated that the propagation of longitudinal cracks is not a linear function of time. Based on these considerations, the following functional form was postulated:

The probability distribution of regression coefficients for each variable of the prior, data and posterior models is illustrated in Figure 12.

As for the roughness model, all variables have the expected effect on longitudinal cracking. Increasing the total pavement thickness tends to mitigate pavement deterioration while increasing age, precipitation, freezing index and frost susceptibility have the opposite effect. Frost susceptibility is by far the most significant variable (T­value = 16) followed by thickness (­5,4), age (4,3), and freezing index (2,5). The null hypothesis can not be rejected within a 95% level of confidence for precipitation meaning that no significant influence of this variable on linear cracking has been measured within the limits of this project.

The posterior model was tested against the whole data set (expert estimates and field data) and showed a reasonable fit. However, the precision of the model is poor. The standard error, calculated for the transformed Y is equal to 2.14 which translates into a non­normal 68% confidence interval between 0,7 and 49 for a prediction of 6 lane*metres of cracking (all variables being set to their average value). This situation is due to many factors among which the lack of field data and the fact that expert's prior model statistics were also somewhat uncertain are probably the most important. Another probable source of imprecision for the model is the fact that the experts were asked to encode their judgment on a dependent variable format which was not similar to the one of field data. As a matter of fact, since past experience (and data) was based on extent of cracking in terms of length of road affected by 100 m of road, experts were asked to encode their estimates on that basis. In C­SHRP program, which was used as field data source, crack extent was collected in terms of total crack length per section (150 m, one lane). In order to reconcile these two data formats, it was assumed that only one crack could occur per lane width.

It is clear on figure 13 that the structure of the model is not adequate. Basic assumptions of linear regression are not met: Error increases with the extent of cracking and the average error is greater than zero (­6). The functional form therefore needs to be re­evaluated. After revision of the structure of the model, more iterations will be needed to improve the robustness of the model. The first priority is to increase the size and the quality of the field database in order to improve the validity of the Bayesian regression. Other potential improvements include the addition of a factor representing low temperature tensile strength of the asphalt concrete layer.

8. MODELS APPLICATION

As mentioned earlier, the main purpose of the models is to assist pavement designers by allowing them to assess the consequences, in terms of performance, of different design scenarios. Figure 10 illustrates potential design application of the models. In the example, for a given set of environmental conditions (P = 1000 mm, FI = 1250 °C*day and FS = 200 mm/°C*sec *10 ), only a 1000 mm structure would meet an hypothetical design objective of 15 years with an IRI not exceeding 3,0. It is also possible to verify that the 1000 mm structure would probably not be seriously affected by longitudinal cracking during it's 20 years design life with an expected crack length of 6 m/100 lane m of pavement.

The same models could also be used as pavement management tools. For instance, if roughness and longitudinal cracking are used to calculate a composite condition index, the latter can be estimated as a function of pavement age (if models are available for all distresses included in the index) and maintenance can thus be planned accordingly.

9. CONCLUSION

In the absence of large quantities of data needed for classical regression, Bayesian analysis has helped to resolve a very specific pavement performance modeling problem. It is clear that the models developed during the first part of the project are not sufficiently robust to be implemented in current design practice, but subsequent iterations with larger performance data bases should yield satisfactory empirical performance models. The addition of two models predicting deterioration associated with spring thaw will complete the first generation model group.

Subsequent work includes the adaptation of the models to a (mechanistic ­empirical environment and finally, the calibration of the models to the Quebec provincial road network. The models will then be integrated into the new pavement design procedure.

The joint application program was an excellent opportunity to get familiar with model development and more specifically with Bayesian regression. The whole program offered by C­SHRP including the training session, the model development template, the technical support and the mid­course workshop was very helpful and contributed to the successful transfer of Bayesian technology to participating agencies.

ACKNOWLEDGMENT

We wish to express appreciation to many people whose effort contributed to this paper. This research was accomplished in cooperation with C­SHRP and assistance from Luc Frechette, project coordinator as well as Lyle Kajner, Mark Nickeson (VEMAX Management Inc.) and Dale Nesbitt (Decision Focus Inc.), Project consultants was greatly appreciated. The support provided by Guy Bergeron, Pierre Desrochers, Jean Pierre Leroux, Claude Lupien, Nelson Rioux, Marius Roy, Yves Savard and Denis St.Laurent, involved as experts in the project was also greatly appreciated.

REFERENCES

[1] Haas R., Hudson W.R., Zaniewski J. (1994); Modern Pavement Management; Krieger Publishing Company, Malabar, Florida.

[2] Kajner L., Sparks G., Jorgenson J. (1994); Bayesian Roughness Model: Developing the Regression Model (Working Paper); Canadian Strategic Highway Program.

[3] Kajner L., Sparks G. (1994); Bayesian Reflective Cracking Model: Developing the Regression Model (Working Paper); Canadian Strategic Highway Program.

[4] Rauhut B. Et al. (1993); Early analysis of the LTPP General Pavement Studies Data

[5] Queiroz C., Coelho P., Magalhaes J. and Robertson N.(1987); An Optimal Design Method to Rehabilitate Low­Volume Asphaltic Roads; Transportation Research Record 1106; pp244­251

[6] Watanatada T., Harral C., Paterson W., Dhareshwar A., Bhandari A. And Tsunokawa K.(1987); The Highway Design and Maintenance Standards Model Volume 1 ­ Description of the HDM­3 Model; The International Bank for Reconstruction and Development/World Bank; Washington, DC.

[7] Paterson W., and Attah­Okine B. (1992); Simplified Models of Paved Road Deterioration Based on HDM­3; Unknown source.

[8] Bein P., Cox J., Chursinoff R., Heiman G. And Huber G.(1989) Application of the HDM­3 Pavement Deterioration Model in Saskatchewan Pavement Management System; Transportation Research record 1215, pp60­69.

[9] White T.D., Coree B.J.(1990); Threshold Pavement Thickness to Survive Spring Thaw; Third International Conference on Bearing Capacity of Roads and Airfields; Trondheim, Norway.

[10] Esch D.C., McHattie R.L., Connor B.; Frost Susceptibility Rating and Pavement Structure Performance; Transportation Research Record no.809

[11] Allen W., Berg R., Bigl S. (1990); Prediction of Damage to Flexible Pavements in Seasonal Frost Areas; Transportation Research Record No.1286

[12] AASHTO (1985); Design of Pavement Structures

[13] Richter C.A.(1991); Seasonal monitoring of pavements; A whole lot more; Proceedings of the Conference on Road and Airport Pavement Response Monitoring Systems, West Lebanon, NH

[14] Konrad J.M., Morgernstern N.R. (1980); A Mechanistic Theory of Ice Formation in Fine Grained Soils; Canadian Geotechnical Journal 17(4), pp.473­486

[15] Dysli M.(1991) Le gel et son action sur les sols et les fondations; Complement au Traite de Genie Civil de l'Ecole Polytechnique Federale de Lausanne; Presses Polytechniques et Universitaires Romandes.

Return to Table to Contents

Return to Main Page