Calibration of the rutting model in HDM 4 on the highway network in Macedonia

The World Bank HDM 4 model is adopted in many countries worldwide. It is consisted of the developed models for almost all types of deformation on the pavement structures, but it can’t be used as it is developed everywhere in the world without proper adjustments to local conditions such as traffic load, climate, construction specificities, maintenance level etc. This paper presents the results of the researches carried out in Macedonia for determining calibration coefficient of the rutting model in HDM 4.


Introduction
This research was carried out in the period from 2010 until 2014 on a number of sections of the highway network in Macedonia, such as Veles-Gradsko, Gradsko-Negotino and Kumanovo-Miladinovci in total length of around 100 km.
The purpose of the research was to provide initial calibration coefficient of the rutting model on the highway network in Macedonia.The data used for the research was provided by regular measurement in the period from 2002 to 2006 and from 2010 to 2014.It should be noted that no significant maintenance activities were taken in the period from 2006 to 2010.The paper presents the results of the calibration of the rutting model in HDM4 [1][2][3][4][5][6][7][8].

Description of rutting development model
According to HDM-4 the rutting model consists of the following components:  Initial thickening  Structural deformation  Plastic deformation  Wear and tear due to use of winter tyres In most cases, only the first three components of the rutting development are taken into account, because there are, usually no data on the influence of winter tyres on the appearance of rutting.

Initial thickening
Initial thickening is given in the following equation: RDO-rutting caused by initial thickening [mm] K rid -calibration coefficient for a certain initial thickening YE4-average annual number of equivalent standard axes [million/lane] DEF-average annual deflection [mm] SNРmodified structural number of the pavement COMP-relative compacting (%) (Table 1) a i -model coefficients What is of special importance is the relation between the advancement of the initial rutting and the standard deviation.Currently, HDM-4 enables for positive linear relation between the rutting and the resulting standard deviation of the rutting depth.It is considered that this trend can be negative in the initial stages of thickening.

Structural information
Rutting is a very good indicator of the pavement structure condition.For example, on the world level, rutting is one of the key indicators of the condition that is used in the road maintenance contracts.It is supposed that the appearance of rutting in the road network shall gain importance in future, receiving increased understanding of the condition.HDM -4 gives two forms of rutting progress on cracked and non-cracked sections:  Structural deformation after the incurrence of cracks

Rutting as a result of wear and tear due to use of winter tyres
The form of the model is given by the following equation: RDW -rutting due to the use of winter tyres in the analyzed year [mm]  PASS -annual number of vehicles with winter tyres per direction S -average velocity of traffic flow [km/h] SALT -variable depending on whether salt is used in winter maintenance ( SALT =1 - no salt used; SALT =2 -salt usef) rsw K -coefficient of calibration of the rutting method due to use of winter tyres The model coefficients are given on the following table.

Overall rutting size
The increase of rutting on annual level is given in the following equations: It must be noted that, as per the HDM recommendations on calibration level 2 it is sufficient to determine the coefficient of calibration of the overall rutting depth, whereas for level 3 of calibration, it is necessary to establish all coefficients of calibration of the individual rutting components (Krid, Krpd, Krst и Krsw)

Measuring of rutting depth
Figure 1 gives the distribution of the increase, that is, the deepening of the rutting in the periods of analysis.The figure includes all rutting measures, except on sections where subsequent measurement indicates errors.The determined precision of rutting measuring is of 1mm.The average annual increase of the rutting is of 4.2 mm (standard deviation = 1, and the changes vary from 0 to 7,4 mm/annually).Remarks from this figure include the following: The annual increase of the rutting depth is within 4mm for all intervals of analysis.

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The maximal annual increase of the rutting is of 11mm, and the minimal one is of 2mm.The format of the HDM-4 rutting model has been adopted within this research fort he establishment of the calibration coefficient.Figure 2 shows the change in the rutting depth for the non-calibrated model (the calibration coefficient being of 1).
Figures 2 and 3 indicate that there is no coincidence between the envisaged and the factual change of the rutting depth.The measured data demonstrate an annual change of 4mm, while the envisaged change of the rutting depth is of 2mm per year.On the other hand, the non-calibrated model demonstrates that the depth of the rutting on the new pavements is of 20mm, which is not appropriate (the line of the envisaged and appeared depths and changes of the rutting begins at 20mm).
The acquired calibration coefficient as pursuant to the data obtained in Macedonia is given in Table 6 (equation 9).  Figure 5 shows that the new calibration coefficient establishes a practically ideal relation between the envisaged and the measured data on the rutting depth.It leads to the conclusion that the rutting development method with the adopted calibration coefficient can be used with high level of certainty. Note: The RMSE error function is obtained as a square root of the difference between the envisaged and the real values of the rutting.

Conclusion
The obtained calibration coefficient yields satisfactory results in comparison with the noncalibrated model.However, it must be noted that the research lacked new data on the rutting depth.
The only available data were the ones obtained in the period of 2002-2006 and 2010-2014.Despite the incompleteness of the measures conducted from 2006-2010, they were sufficient to offer control on the rutting development in the period from 2010 tо 2014.
Nevertheless, more comprehensive analyses are necessary, within the period of at least 10 years as well as possible development of another model, which in fact is calibration of level 3 according to HDM.

2 E3S
Web of Conferences 33, 02023 (2018) https://doi.org/10.1051/e3sconf/20183302023HRC 2017 ΔRDSTgradual increase of the structural deformation in the year of analysis [mm] K rst -coefficient of calibration for a structural deformation YE4-annual number of equivalent standard axes [million/lane] COMP-relative compacting [%] MMP-average monthly precipitations [mm/month] SNС-modified structure number of the pavement ACX-area of non-indexed cracks [% from the total lane of traffic lane] a i model coefficients Ако rutting due to structure deformation on non-cracked pavements [mm] crk RST  -increase of rutting due to structure deformation on cracked pavements [mm]

4
AGE -age of the pavement regarding to the appearance of rutting, in years RDM  -increase of the overall rutting size on annual level pdK -calibration coefficient for all ruttingThe overall rutting size is determined as follows: overall rutting size at the beginning of the analyzed year8 Rutting calibration methodologyCalibration of rutting progressing is a simple process of comparison of the envisaged and the existing rutting depth by establishing the relation between the geometric mean value of the measured rutting depth, ORDM and the geometric mean value of the rutting depth.calibration coefficient can be calculated by the sums of the logarithms of the measured and anticipated value K rp -coefficient of calibration of the rutting depth development PRDM-rutting depth envisaged for the section ORDM-measured rutting depth

Fig. 2 .
Fig. 2. Relation between the predicted and measured change of rutting depth of the noncalibrated HDM model (Default model) Source: Own research Figure 4 demonstrates that the relation between the measured and the real change of the rutting on annual level is already established by the new value of the calibration coefficient, Кpd=0.62.Figure5shows that the new calibration coefficient establishes a practically ideal relation between the envisaged and the measured data on the rutting depth.It leads to the conclusion that the rutting development method with the adopted calibration coefficient can be used with high level of certainty.Note:The RMSE error function is obtained as a square root of the difference between the envisaged and the real values of the rutting.

Fig. 3 . 7 E3SFig. 5 .
Fig. 3. Relation between the envisaged and the measured rutting depth in the non-calibrated HDM model (Default model) Source: Own research

Table 1 .
Recommended values of the relative compacting level COMP

Table 3 .
Values of the coefficients of the structure deformation model

Table 4 .
Values of the plastic deformation model coefficients

Table 5 .
Values of the coefficients of the plastic deformation model

Table 6 .
Calibration coefficient for rutting depth