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1 QUT Digital Repository: This is the accepted version of this journal article: Piyatrapoomi, Noppadol and Kumar, Arun and Weligamage, Justin and Robertson, Neil (26) Probability based data analysis for road asset management. Queensland Roads, 1(3). Copyright 26 Please consult the authors.

3 Optimising costs for data collection for network analysis probability-based analysis method Road pavement condition information is expensive and time consuming to collect. Pavement strength data based on the falling weight deflectometer is one of them. Until new equipment is developed that will reduce collection costs there is a need to reduce costs by other means. Using a different mathematical method of analysis it is possible to reduce collection costs by extending the testing interval distance. Deterministic analysis of data is used widely as it is taught in a broad range of tertiary studies and it is relatively easy to understand and manipulate data. However, when the data does not fit tightly around a specific function, analysis is often difficult and there is often a low level of confidence in the outputs of such analysis (ie. R 2 is low.). For example, the R 2 value in the following data set (Figure 1) is low; hence there is less confidence in using the regressed function. Figure 1 Analysis of data in x y scale B R 2 = A Figure 1 Analysis of data in x-y scale Cumulative Probability (Fx) Data (A/B) Figure 2 Analysis of data using Probability methods A probability analysis of the same data reveals the following graph Figure 2. Because the data fits well with the probability distribution, it confirms that the data set is valid. Additionally, the data set may be more easily modelled by the use of probability distribution. Probabilistic analysis is another methodology which may be used to view and analyse data. Because of the variable nature of the data collected for road asset management, the use of a probabilistic analysis has been found to be the most effective. This paper will discuss how probabilistic analysis may be applied to data collection for road asset management. Applying the probability based analysis The probability based method has been used to assess optimal intervals of pavement strength data collection for network application [1]. It was hypothesized in the analysis that if the statistical characteristics (i.e. mean, standard deviation and probability distribution) of data sets were quantifiable, and if different sets of data possessed similar means, standard deviations and probability distributions, these data sets would produce similar prediction outcomes. To illustrate the concept, Figure 3 shows the probability distribution of pavement deflection tests at 2 metre intervals for the outer and inner wheel paths of a 92 km section of road network located in wet and non reactive soil condition situated south of Townsville. The means and standard deviations for the outer and inner wheel paths deflections (microns) are given as Ln outer = N (6.5,.85) and Ln inner = N(5.95,.817). Since the statistical means, standard deviations and the probability distributions of the original pavement deflection data sets for outer and inner wheel paths were similar in values, the pavement deflection sample data of the outer wheel path were used for the optimisation analysis. Figure 4 shows the probability distribution of pavement defection data at 1 metre intervals. The mean and standard deviation are Ln Outer = N(5.95,.817). The mean and standard deviation of the 1 metre interval pavement deflection data are similar to the mean and standard deviation of the 2 metre interval pavement deflection data. The two data sets are log-normally distributed.

4 Cumulative Distribution of Deflection Data F(x) Outer Wheel Path Inner Wheel Path Deflection, Ln(micron) Figure 3. Cumulative distribution of deflection data set for 2 metre intervals Cumulative Distribution of 1-metre Interval Data F(x) metre Interval Data Lognormal Deflection, Ln(microns) Figure 4. Cumulative distribution of deflection data set for 1 metre intervals for outer wheel path A reliability assessment was conducted to assess the prediction outcomes using two sets of deflection data of similar statistical characteristics. The reliability is tested by comparing cost estimates calculated from the 1 metre interval deflection data and the 95 th percentile cost estimates calculated from the 2 metre interval data. Details of the reliability analysis are given in Piyatrapoomi et al 24 [2]. Figure 5 shows the differences in the cost estimates. The difference in five year cost estimates is approximately 12 per cent, while the differences in cost estimates for 1, 15, 2 and 25 years are less than 4 per cent. The analysis method can be repeated to assess optimal intervals for network analysis for other types of soil and climatic conditions. While the analysis indicates that pavement strength data for network studies could be collected at larger intervals than currently occurs, the strength data intervals required for project work would remain at the same closely spaced intervals.

7 2 Cumulative Cost Estimates (A\$) Years Figure 6. Mean cumulative costs for maintaining road pavement of a 45 km road network in Queensland for a 25-year life-cycle period beginning from Cost Variation of One Standard Deviation (A\$) Years Figure 7. The variation in cost estimates of one standard deviation

8 Conclusions This paper presented probability-based methods for road network pavement management investment analysis. The probability-based methods allow us to understand the relationships among asset data items that describe any road network. The methods have already begun to improve understanding of road asset performance characteristics. The methods also allow us to understand the relationship among the variability of asset conditions, variation in budget/cost estimates and the degree of uncertainties in budgeting for investment. The application of the probability-based methods for road network investment analysis presented in this paper include optimising test intervals for pavement strength data collection for network application, calibrating pavement deterioration prediction models and assessing variation and uncertainties for life-cycle cost estimates. As illustrated in this paper probability-based methods have greater applications in solving engineering problems involving uncertainties and large variation in engineering data. This paper presented some applications that used probability-based methods to solve engineering problems for road asset management investment References 1 Piyatrapoomi N, Kumar A, Robertson N, Weligamage J. Assessment of calibration factors for road deterioration models, CRC CI Report No C/9, The Cooperative Research Centre for Construction Innovation, Queensland University of Technology, Brisbane, Queensland, Australia. June Piyatrapoomi N, Kumar A, Robertson N, Weligamage J. Reliability of optimal intervals for pavement strength data collection at the network level. Proceedings of the 6 th International Conference on Managing Pavements, Brisbane, Queensland, Australia. October Piyatrapoomi N, Kumar A, Robertson N, Weligamage J. Assessment of calibration factors for road deterioration models, CRC CI Report No C/9, The Cooperative Research Centre for Construction Innovation, Queensland University of Technology, Brisbane, Queensland, Australia. June The International Study of Highway Development and Management (ISOHDM), Highway Development Management (HDM4) version 1.3, University of Birmingham, UK Piyatrapoomi N, Kumar A, Robertson N, Weligamage J. A probability method for assessing variability in budget estimates for highway asset management. Proceedings 5 th International Conference on Road and Airfield Pavement Technology, Seoul, South Korea. May Rhode G. Determining pavement structural number from FWD Testing. Transport Research Record 1448, TRB, National Research Council, Washington, D.C Rhode G, Hartman A. Comparison of procedures to determine structural number from FWD deflections. Combined 18 th ARRB Transport Research Conference and Transit New Zealand Land Transport Symposium, New Zealand Salt G, David S. Pavement performance prediction: determination and calibration of structural capacity (SNP). 2 th ARRB Transport Research Conference, Victoria, Australia. 21. Acknowledgements The authors wish to acknowledge the cooperation of the Cooperative Research Centre for Construction Innovation. The views expressed in this paper are those of the authors and do not necessarily represent the views of other organisations.

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