Performance Prediction Models for Flexible Pavements. NordFoU- Calibration to the Norwegian Reality

Transcription

1 Performance Prediction Models for Flexible Pavements NordFoU- Calibration to the Norwegian Reality

2 Table of contents 1 Preface 4 2 Model Roads: Historical Data E39 HP 14 Sogn og Fjordan County E 8 4Tromsø County 2.3 E6 HP 12 Sør Trondelag County R5 HP19 Sogn og Fjordan County 15 3 Modification of the Calibration Factors 18 4 Calibration of the actual model for the Norwegian Case E8 Tromsø County E39 HP 14 Sogn Fjordan County E6 HP 12 Sør Trondelag County R5 HP 19 Sogn og Fjordan County 46 5 Calibration Factors: Proposal E8 Tromsø County E39 HP 14 Sogn Fjordan County E6 HP 12 Sør Trondelag County R5 HP 19 Sogn og Fjordan County 57 6 Conclusions and Suggestions 59 7 References 85 1

3 Table of Appendices Appendix 1: Pavements Structure and other important data 67 Appendix 2: Nomenclature 70 Appendix 3: User Guide to MATLAB 72 Appendix 4: HDM-4 Rutting Model 77 Appendix 5: Importance of input parameter Initial Rut Depth 80 Appendix 6: New designs for the E39 HP 14 Sogn og Fjordan County 82 Appendix 7: Calibration Factors Proposal: Choice 84 2

4 Performance prediction models represent a key element of road infrastructure asset management systems or pavement management systems. Thus successful implementation of these systems depend heavily on the performance prediction model used, as the accuracy of the predictions determines the reasonableness of the decisions (Nordic Website) 3

5 1. Preface This study was developed to achieve a main objective which is related to the applicability of the NordFoU Program to calculate and predict the future conditions of the flexible pavements in Norway. This Program is based on a MATLAB tool 1 that allows to predict the development of distress types on a given road network based in parameters such as traffic level, pavement structure or climate. Although, in the scope of the study, there are only two parameters that are important to follow with special attention during the time, when it comes to the Norwegian roads: rutting 2 and roughness 3. But, it s the rutting the one that will be more conditioning for the present study, since it is the main cause of maintenance and reparation of the Norwegian roads. So, this study consists in comparing the data given by the MATLAB tool, i.e., the theoretical or predicted data, to the data that results of the measures that were done on the field during the time. This comparison is fundamental to calibrate the referred application; in order to it allows predicting in a reliable way the future behaviour of the roads on Norway. Before proceeding it is important to state that the NordFoU cooperation program was developed by Denmark, Iceland, Norway and Sweden. As it was already said it is based on HDM-4 model (MATLAB tool) and the reason for choosing this model is that it has been used in other countries all over the world, especially in tropic countries or undeveloped ones. But, according with previous studies, such as the report Development of performance measures, modelling and calibration it is known that the referred model could be calibrated, so that it could be applied into the Nordic reality. So, in other to calibrate the program was necessary to change the calibration factors. So the main objective of the present study was to find a group of calibration factors that would be able to be applied without restrictions in all roads in Norway. Therefore, to obtain values through the program that were more similar to the real ones, it has necessary during the study to change some of the calibration factors, in order to the NordFoU program deliver data that is more framed with the reality of the Norwegian roads, and through such is possible to make forecasts more accurate and agreed with the road s behaviour. 1 HDM-4 Deterioration models 2 Rutting is characterized by permanent deformation of the pavement. It generally develops during the hot seasons, when the asphalt is softer. It can be identified by ruts on the wheel path. 3 It is defined as irregularities in the pavement surface that adversely affect the ride quality of a vehicle (and thus the user). It is an important pavement characteristic because it affects not only ride quality but also vehicle delay costs, fuel consumption and maintenance costs 4

6 But the challenges of this study weren t only to search for the best group calibration factors, in order to find the one that will fit better into the Norwegian reality. As the study was evaluating it was possible to find some more problems in the MATLAB application, that weren t allow getting congruent results, particularly the nomenclature used in the program. Thus, the worked developed will be present following the format stated below: Part 1 - Model Roads: Historical Data Part 2 - Calibration factors- Brief considerations Part 3 - Tests Part 4 Conclusions. It s never too much to say that the conclusions of this study are only a proposal of what should be modified in the MATLAB tool and they are also only um begging point to some more deep studies. 5

7 2. Model Roads: Historical Data This chapter has as main objective the function of presenting a brief description of the model roads and also to show some historical data that were considered fundamental to develop this study. The data from the field measurements that will be presented and analysed during this study was collected from the Norwegian Data Bank (NVDB Program) and it results of measures that have been constantly done during the time, on field. However, for some roads in study it will be necessary to do some comments or even some minor corrections in the data obtained by Data Bank, but that will be done at an opportune time. In the scope of the present study it is believed that themes as measuring equipment and its techniques aren t relevant, so they won t be described. But, it is never too much to referred that they have an important role in the study, since some errors during the measurements may occur so that it is relevant that the reader is aware of that negative effect on measure data and its negative effect on the study developed here, since that bad data from the measures may lead to wrong conclusions. As this section wants to present an overview of the historical data for each section of each road used as a model, in order to evaluate the changes that should be done in the NordFoU Program, so that it could be applied in the Norwegian reality, is important to refer what parameters should be analyse. The two essential distress types evaluated that influence more the behaviour of the Norwegian roads are the roughness and the rutting. Although, it s important to refer, again, that the rutting has a more active effect on the deterioration of the Norwegian roads, being the main cause of the need to reparation. It should also be added that all the information related with the pavement structure, such as layers thickness and materials, road network, traffic and mean mouthy precipitation are available in the Appendix 1. 6

8 2.1 E39 HP 14 Sogn og Fjordan County E39 is the designation of a 1330 km long north-south road in Norway and Denmark. E39 is mostly a two-lane undivided road, only relatively short sections near Stavanger, Trondheim and Bergen are motorways or semi-motorways. The road was built in 2001 and during its serving period didn t get any new wearing course, i.e., it wasn t overlayed. The section of the road used as a model is form 3200m to 3750m, as the reader could see in the picture below. This section is located in a city in the Southern part of Norway, in Sogn og Fjordan County. Figure 2-1 E39, Section under analyse Next, in the graphs below, is possible to observe the evolution during the time of the most relevant parameters for the present study. It should be remembered to the lector that this measuring data comes from the Norwegian Data Bank. 7

9 Mean Roughness [m/km] 1,95 1,75 1,55 1,35 1,15 0,95 0,75 Mean Roughness [m/km] Both Lanes Mean Roughness [m/km] Graph 2-1 E39, Section under analyse IRI [m/km] Mean Rut Depth 12,0 11,0,0 9,0 8,0 7,0 6,0 5,0 Mean Rut Depth Both Lanes Mean Rut Depth Mean Rut Depth correction Graph 2-2 E39, Section under analyse Mean Depth Rut It s believed that some comments should now be done referring to the measuring data. As the reader can see in the graph above, the one that refers to the mean rut depth, in 2007 the rut depth achieves a peak, and in the following year decreases approximately 3mm. So, it is thought that such peak results from some kind of an error during the measurement. So, in further analysis, the measuring data used concerning to the mean rut depth will be different, since that the value for the parameter used for the year 2007 will be changed. In another words, such means that this value will be replaced by the average of the previous and following year, i.e., the average of the year 2006 and 2008, as it can also be seen in the graph above (red line). Although, there is another problem with the rutting data. As can be seen above and if the reader is now focused on the fixed graph (the red line) it is possible to observe that from 2006 onwards the rutting is not increasing, reaching a constant value surrounding mm. According with experience it s known that as time progresses, the value of this parameters 8

10 increases. Therefore, the lector is already aware that in further analysis the study period will be shortened, and it s going to be between *2003;2006+, otherwise the study wouldn t be developed in solid pillars. 9

11 2.2 E 8 HP4 Tromsø County This European route goes from Tromsø to Turku in Finland and has a length of 1,4 km. The road was built in The section which has interest for the study goes from 16km to the 16,5 km. It s also important to add that in this section no new wearing course was added during the service period of the road. This section of the model road is located in the Northern part of the country, in the Tromsø County. In the following picture is possible to see the section that contributes for the present study. Figure 2-1 E39, Section under analyse In the next two graphs is possible for the reader to observe the evolution of the measuring data of this section under analyse.

12 Mean Rut Depth 24,0 22,0 20,0 18,0 16,0 14,0 12,0,0 8,0 Mean Rut Depth Both Lanes Mean Rut Depth MRD Graph 2-3 E8, Section under analyze IRI [m/km] Roughness [m/km] 1,6 1,5 1,4 1,3 1,2 1,1 1,0 Mean Roughness [m/km] Both Lanes Roughness IRI [m/km] Graph 2-4 E8, Section under analyse Mean Depth Rut There s only going to be done a very brief comment related to the measure data. When the reader looks at the graphs previous presented can observe that for this section is possible to affirm that this measuring data possesses a good quality, once it has a development during the time that is expected, according to the practical experience. 11

13 2.3 E 6 HP 12 Sør Trondelag County European route E6 is the designation for the main north-south road in Norway and the west coast of Sweden and its length is 3,140 Km. It was built in The section of this model road that was used in the study was from 4330m to 5130m. This section is located in Trondheim, in the Sør Trondelag County, a place in the Southern part of the country. This road, in opposite with the others, has 4 lanes, two in each direction. In the following figure, the lector can observe the section in analyse, that has been above described. Figure 2-3 E6, section under analyze Before moving forward, a few comments should be done, since this model road presents some particularities. This road had a new wearing course during it s serving period in both lanes of one its directions. With the two graphs presented in the next page is possible to see that in lane 3 in 2005 there s a big discrease of the rutting and the same happens for the same 4 but in So, such discrease in the rutting means that this lanes have been overlayed. So, below the reader can observe such fact. Also, because of such thing the analisis that are going to be 12

14 done further will be between the years 2001 and 2007, since it isn t possible to compare the two kinds of data, once the fact of the pavement suffer this maintenace work will change the measure results for the following years, so it isn t correct to compare this data with the theortical one. For the other two lanes it has decided not to present the graphs, once this lanes haven t been overlayed, so there s no interest to show them. Mean Rut Depth 19,0 16,0 13,0,0 7,0 4,0 NVDB Data Lane 3 NVDB Data Lane 3 Graph 2-5 E6, Lane 3 Mean Rut Depth 24,0 NVDB Data Lane 4 21,0 Mean Rut Depth 18,0 15,0 12,0 9,0 NVDB Data Lane 4 Graph 2-6 E6, Lane 4 Mean Rut Depth Now, the following graphs referred to the mean roughness and they are grouped in two different directions because only one of the directions was overlayed, and by that the results for each direction are very different, as the reader can see in the graphs. As it is easily understood, the Direction 1 is the one that was a new wearing course, because that the parameter s values have been decreasing. 13

15 Mean Roughness [m/km] 1,5 1,4 1,3 1,2 1,1 Mean Roughness [m/km] Direction Mean Roughness [m/km] Direction 1 Graph 2-7 E6, Lane 4 Mean Roughness Direction 1 Mean Roughness [m/km] 1,4 1,4 1,4 1,4 1,4 1,3 1,3 1,3 Mean Roughness [m/km] Direction Mean Roughness [m/km] Direction 2 Graph 2-8 E6, Lane 4 Mean Roughness Direction 2 14

16 2.4 Sogn Og Fjordan County This is the last model road used in the study, and the section which has interest for the study goes from 9,230km to the km. This section of the model road is located in the Southern part of the country, in the Sogn Fjordan County. In the following picture is possible to see the section that contibutes for the present study. Figure 2-4 R5, Section under analyse The following graphs are representative of the measurements that have been done during the time in this road. As is possible for the reader to see the measuring data is very irregular for both parameters under analyse for this model road. And looking carefully for the mean rut depth graph, the reader can think that the road in 2007 had a new wearing course. Although, such maintenance work didn t happen in this road until the present days. So, it s believed that has been some problems with the measurement procedures, since for the mean rut depth, as it has been said previously, it is expected that it increases during the time, or if it has a huge decrease between two following years, that means that a new wearing course has been laid on the road. 15

17 Mean Roughness [m/km] 2,2 2,0 1,8 1,6 1,4 1,2 1,0 Mean Roughness [m/km] Both Lanes Mean Roughness Both [m/km] Graph 2-9 R5, Section under analyse IRI [m/km] Mean Rut Depth 11,0,5,0 9,5 9,0 8,5 8,0 7,5 7,0 6,5 Mean Rut Depth Both Lanes Mean Rut Depth Both Lanes Graph 2- R5, Section under analyse Mean Depth Rut In the years 2005 and 2007, there s a drop that can be more or less abrupt of the mean rut depth values which is followed by an increase in the next year of the values. So, according to experience such situation does not happen in reality. On the other hand, what has been before explained for the rutting it is also applied to the roughness, and it s more visible such sharp decrease, especially in So, according to what has been previously said it is necessary that the data that results from the measurements should have an expected development during the time, but in this case such thing does not happen. Therefore, to be possible to test this road under normal conditions and to obtain a group of calibration factors that could fit this road, it will be necessary to shorten the analysis period, so that will be possible to achieved reliable results. In this order of ideas, it is shown below the graphs that will be used in further analysis, and as the lector might check the analysis period now will be [2003;2006]. However, it should also be mentioned that the problem with the decrement values of roughness and rutting probably result of errors during the measurement procedure. 16

18 Mean Rut Depth,0 9,5 9,0 8,5 8,0 7,5 7,0 NVDB Data Lane 1 Mean Rut Depth Graph 2-11 R5, Section under analyse Mean Depth Rut Mean Rut Depth Mean Rut Depth 11,0,0 9,0 8,0 7, NVDB Data Lane 2 Graph 2-12 R5, Section under analyse Mean Depth Rut 17

19 3 Modification of the Calibration Factors In the present study is only going to be analyzed the effect of the variation of the calibration factors related with the rutting. Such happens due to the reality of the Norwegian roads. This concern stems from the fact that the rutting is the principal responsible in Norway for the constant maintenance and repair of the roads, unlike the roughness. Although, there s also going to be analyzed the effect on roughness of the changes of the calibration factors related with the mean rut depth. This parameter will be considered during the analysis since it is very sensitive with the variations of the traffic, so it is important that it shall not be forgotten. The rut depth model used in the HDM-4 tool is based in four components of the rutting, such as: - initial densification; - structural deformation; - plastic deformation; - wear from studded tyres. Every of these components depend of specific calibration factors that are respectively: - K rid (calibration factor for the rutting initial densification model) - K rst (calibration factor for the rutting structural deterioration model) - K rpd (calibration factor for the rutting plastic deformation model) - K rsw (calibration factor for the rutting the wear by studded tire model) If the reader has curiosity and wants to see how this factors affect the data given by the MATLAB application, should go to the Appendix 4. The author also thinks that it is relevant to mention in this chapter that there is a direct proportion relationship between each calibration factor and its component of the rut depth model. Now this means that when, for example one of the values of the calibration factors increases also the rutting increases. That means that the curve that results from the MATLAB application is more inclined. But it is emphasize again that for further care, the reader should consult Appendix 4. 18

20 Although, through the report Development of performance measures, modeling and calibration is known that some calibration factors does not have any effect on the evaluated distress types. And one of this calibration factors is the one related to surface wear (K rsw ). So, that s the reason why in the iterations that have been made for the present study its variation hasn t been considered. In other words, in every iteration it was used its default value, K rsw =1,0. According with the same report, not every coefficient affects the same way the rutting, i.e., in the study that has been used as reference it is said that the K rid is the calibration factor that affects more the rutting values and the K rst is the one that affects less. There s also needed to do small reference to the fact that according to the report that is the base of this study, is possible there to find that the calibration factor for the rutting plastic deformation should increase from 0 to1. That results from the sensitivity analysis of the calibration factors that were done there. Thus, during the realization of the iterations for each section of each model road, it has kept in mind the influence level of each calibration factor. So in order to try to calibrate the MATLAB application is necessary to find out what of these components should be changed and for what value they may change. However, it should be added one more consideration, but now related with the way how the values for the iterations have been chosen. It was believed that in a first approach the values of the calibration factors should have a variation of ±50%, but in some cases another variations, such has ±25% could considered. 19

21 4. Calibration of the actual model for the Norwagian Case In this section all the data from de Matlab application (HDM-4 Model) will be put against to the data obtained through the measures that have been done during the time. First of all, just for the record it must be said that all detailled information related how the program runs and how the input values should be introduced, can be found at the Appendix 3. So, in order to the NordFoU MATLAB tool could be applied without restritions to the Norwigian roads it is necessary to change and to look for new solutions not only at the level of the calibraion factors. Thera are more parameters that might be considerer. One of this parameter is the initial rut depth, i.e., a parameter related with the road network condition, at the begging of the analysis. This parameter is strongly depend of the material of the wearing cours, i.e., the input value for this parameter should be higher when the material of this layer of the pavement is not considerer a good material. Therefore, the lector should have in mind that the type of the wearing course of the pavement, in order to introduce a well thought value for this parameter. So, it is proposed that the interval in which this parameter should be is [2;5]mm. That means, that for each case under study it should be introduce a value that matches with the material of which is made the wearing course, instead of the default value proposed by the MATLAB application 4. Another input values that migh t not be forgotten are the climate parameters. These parameters, accordign with the referred report 5 change according to region climate. So it is important that the lector should not forget the region in which the road or the section of the road that will be under study, in order to adjust the climatic input values, once that the default ones should not be appropriate to that case. These values are availabe in the report that had already been referred 6, and the reader might use the one that fits more to the case under analyse. The values that were adapted to this case are presented in ther Appendix 3. So, it appeared to be that the simplest and most effective way to present the analysis that have been done for each of the road s section should be confronting the actual data 4 0 mm 5 Development of performance measures, modelling and calibration 6 Appendix 5 of the report Development of performance measures, modelling and calibration 20

22 (obtained by the NVDB program by measurements in situ ) with the data provided by the Matlab application, but with the following order: - Without changing the calibration factors (input default values). - Changing the necessary calibration factors. 21

23 4.1 E8 HP4 Tromsø County Knowing that the surface layer of this road is asphalt concrete 7 that can be considered as good material, so the value that was chosen for the initial rut depth was 2mm. As it was said previously, the first iteration will be done with the default values of the calibration factors. So, for the following input values is possible to see further the graphs: - K rid = 0,9 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 Mean Roughness [m/km] Mean Roughness [m/km] 3 2,5 2 1,5 1 0,5 0 NVDB Data Lane 1 Graph 4-13 E8, Lane 1 IRI [m/km] Mean Roughness [m/km] 3 2,5 2 1,5 1 0,5 0 Mean Roughness [m/km] NVDB Data Lane 2 Graph 4-14 E8, Lane 2 IRI [m/km] 7 More detailed information can be found in Chapter 4 22

24 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-15 E8, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-16 E8, Lane 2 Mean Rut Depth It is thought that right now should be done a few considerations before moving forward. As the lector might see in the graphs above, it roughness is possible to conclude that the curve from the MATLAB data is always above the curve from the measuring data. It should be expected since the formula used in the HDM-4 model program depends of coefficients that increase this parameter during the time The opposite occurs when it comes to the rutting. Although, further it will be done a consideration related with the fact of the predicted data being below the curve that results of the measurements. Since the traffic that passes through this road is quite low, and knowing that this parameter is probably the one that most influence has on the increasing of the roughness, is possible to see only with brief look at the mean roughness graph, that the proximity relationship between the theoretical curve (the one the results from the HDM-4 model) and the 23

25 measurements curve is quite good. So that means that when the number of motorized traffic is low, the proximity relationship between the two distinct curves is better. Concerning, now attention in the rut depth parameter is possible to see that, especially for the lane2, the measured data and the theoretical data are distinct. There s an average difference between the two types of data of approximately 7mm, which is too much. Referring to the lane 1, this average difference between the real measures and the predicted ones is 4mm, which is the same a high value. Thus, for the MATLAB model could be applied to the Norwegian roads reality, it is required that these curves are as close as possible in order to the results obtained by the application does not defer too much of the measurements made in the field. Otherwise, it will not be possible to apply the NordFoU program to make predictions of the behavior of the pavements. Therefore, the calibration factors must be changed for such thing to happen. Remembering the lector that given the reality of the Norwegian roads, this study is more focused on changing the calibration factors that affects directly the rutting. This concern stems from the fact that the rutting is the principal responsible in Norway for the constant maintenance and repair of the roads, unlike the roughness. And also reminding the lector that the calibration factor the influences more the rutting is the K rid, so the next iteration will result of only increasing this parameter of 50% and keeping the others as the default values. Thus, for the next iteration the following calibration were used: - K rid = 1,35 - K rpd = 0 - K rst = 4,59 - K rsw =1,0 In the next page there are the graphs with the results. 24

26 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-17 E8, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-18 E8, Lane 2 Mean Rut Depth As is possible to see from the graphs above there s an improvement of the results, since for the new results the average difference from the predict measures and the measurements that were done in field are presented in the table below. Difference Lane 1 Lane 2 3,0 6,1 T able 4-1 Difference between data Looking for better solutions was done a new iteration where were used the following calibration factors: - K rid = 1,35 - K rpd = 1,0 - K rst = 4,59 - K rsw =1,0 25

27 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph4-19 E8, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-20 E8, Lane 2 Mean Rut Depth Using this calibration coefficients the results get better, since that are some points of both curves that are coincident, in case of the lane 1. But also for the lane 2 the proximity relationship of the curve from the NordFoU application and the curve that results from the measure data is better, i.e., the both curves are closer, as it is possible to see in the table below, where are shown the average difference between the predicted data and the measured one. Diference Lane 1 Lane 2 1,6 4,6 T able 4-2 Difference between data 26

28 Since the objective is to find the group of calibration factors that lead the closest relationship between the two types of data, so by improving the calibration factors in order to do iteration is possible to get the results below presented. Bearing in mind that the only calibration factor that has not yet been changed was K rst ; so, this way in the next iteration it will be maintain the values of all calibration factors used in the last iteration, except the K rst that will be increased by 50%, as it is possible to see in the list below. - K rid = 1,35 - K rpd = 1,0 - K rst = 6,9 - K rsw =1,0 Mean Rut Depth Mean Rut Depth MATLAB DATA NVDB Data Lane 1 Graph 4-21 E8, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-22 E8, Lane 2 Mean Rut Depth 27

29 Diference Lane 1 Lane 2 1,1 3,0 T able 4-3 Difference between data So, as it is possible to conclude the group of calibration factors that lead to the best proximity between the two distinct types of data is the last one. However, there is a particularity that this case should be referred. As you can see during the four iterations that have been done, the data obtained from MATLAB is always lower than measured data in situ. This means that in this case, despite a relatively good relationship of proximity between the two different measurements, the results obtained through analysis of the program are always lower than the real ones. This fact must be taken into consideration when making the prediction about the future behavior of the roads pavement, because such prediction will not be made on a safety way. That is, the forecasts were underestimated and this led to a late intervention in the repair of the pavement, then translating questions either costly or security for passengers. So, for the chosen group of calibration factors will be presented below the results for the mean roughness and also the relationship between the increment of the traffic and rutting. Mena Rut Depth 2,6 2,4 2,2 1,8 2 1,6 1,4 1,2 1 Mean Roughness [m/km] NVDB Data Lane 1 Graph 4-23 E8, Lane 1 IRI [m/km] 28

30 Mean Roughness [m/km] Mean Rut Depth 2,8 2,3 1,8 1,3 0,8 NVDB Data Lane 2 Graph 4-24 E8, Lane 1 IRI [m/km] Mean Rut Depth Mean Rut Depth vs Traffic T= T= T= Graph 4-25 E8, Lane 1 Mean Rut Depth vs Traffic increment It should be added that further in this study the traffic effect on the mean rut depth will be discussed and as well its influence, also, in the mean roughness. Since this was the first model road under analysis it was believed that these two kinds of data should be presented in order to the reader have at least on example of what this type of data will look like. 29

31 4.2 E39 HP 14 Sogn og Fjordan County Knowing that the surface layer of this road is asphalt concrete 8 that can be considered as good material, so the value that was chosen for the initial rut depth was 2mm. Thus, the first iteration results of using the default values for the calibration factors, so for that input values is possible to reach the results that are below presented: - K rid = 0,9 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 Mean Roughness [m/km] Mean Roughness [m/km] 1,6 1,5 1,4 1,3 1,2 1,1 0,9 1 0,8 0, NVDB Data Lane 1 Graph 4-26 E39, Lane 1 Mean Roughness IRI[m/Km] Mean Roughness [m/km] 1,6 1,5 1,4 1,3 1,2 1,1 0,9 1 0,8 Mean Roughness [m/km] NVDB Data Lane 2 Graph 4-27 E39, Lane Mean Roughness IRI [m/km] 8 More detailed information can be found in Chapter 4 30

32 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-28 E39, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth MATLAB DATA NVDB Data Lane 1 Graph 4-29 E39, Lane 2 Mean Rut Depth Diference Lane 1 Lane 2 1,0 1,4 T able 4-4 Difference between data According to the data presented above, it can be concluded that for both lanes the proximity relationship between the measurements made "in situ" and the predicted ones for both parameters that are being analysed, is relatively reasonable, once that the difference between these values around 1 mm for both cases. For the Mean Roughness [m/km] is visible in its graphs that the difference between the two different types of data is sharper. Following the same premise used in the analysis of the model road E8 HP4 Tromsø County, as regards of the relevance of the calibration factors, the next iteration results from the use of calibration factors presented below: 31

33 - K rid = 1,35 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 The results obtained for the fundamental parameter under analysis in this study, are displayed below. Mean Rut Depth Mean Rut Depth Graph 4-30 E39, Lane 1 Mean Rut Depth Diference Lane 1 Lane 2 2,3 0,22 T able 4-5 Difference between data Mean Rut Depth Mean Rut Depth MATLAB DATA NVDB Data Lane 2 Graph 4-31 E3*, Lane 2 Mean Rut Depth 32

34 For this section of the model road is only possible to note that for lane 2 is obtained particularly good results, since the average difference between the data of measurements taken in the field and the data values predicted by the HDM-4, are quite low, 0.2 mm. Although for lane 1 the proximity between the values in analysis less significant, so this means that for this group of calibration factors is not favorable for the desired result. Keeping in mind that the iterations are performed from the knowledge of the fact that the influence of calibration factors affecting the rutting is different, then the next iteration results of application of the following calibration factors: - K rid = 1,35 - K rpd =1, 0 - K rst = 4,59 - K rsw = 1,0 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-32 E39, Lane 1 Mean Rut Depth 11 Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-33 E39, Lane 2 Mean Rut Depth 33

35 Diference Lane 1 Lane 2 2,6 0,17 T able 2-6 Difference between data Watch the results so far obtained, it might be conclude that the results reached for the two lanes have been better for the lane 2 as long as the calibration factors have been being changed. Knowing about what was exposed in the chapter 3, i.e., about the way how the calibration factors affect the growth and the decreased of the values of the mean rut depth, is possible to state that increasing the Krst calibration factor the it will not contribute to achieve better results for the lanes, for the contrary, it will take the opposite path, once the predicted curve will have an inclination that is more accentuated, which will be traduced in a biggest distance between the two types of data that is being analysed. It is also possible to add that the difference between the two kinds of data under analysis for the lane 2 is quite small, so it might be said that this group of calibration is the one that leads to the best proximity relationship between the two kinds of data under study. As it is known, increasing the calibration factors 9 values will contribute to increase the inclination of the MATLAB curve will be more accentuate, which means that the difference between the measures and the predicted data will be larger. And that it is the opposite of the main goal of this study. So, in this order of ideas, the next iteration will result of the application of the calibration factors that are now presented following; which means that to get better results for the lane 1 it will be necessary to reduce the value of the most influence calibration factor: - K rid = 0,6 - K rpd =1, 0 - K rst = 4,59 - K rsw = 1,0 So the iteration with the following calibration factors will not be done, due to what was before exposed. K rid = 1,35, K rsw =1,0; K rpd =1,0 and K rst =6,9 34

36 Mean Rut Depth 8,5 9 7,5 8 6,5 7 5,5 6 5 Mean Rut Depth NVDB Data Lane 1 Graph 4-34 E39, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Deph NVDB Data Lane 2 Graph 4-35 E39, Lane 2 Mean Rut Depth T able 4-7 Diference Lane 1 Lane 2 0,5 2,3 Difference between data So, as it is possible to see this iteration lead to a better relationship between the measures done in situ and the predict data from the MATLAB for the lane 1, since their difference is less the 1 mm. According with the results that were obtained in all iterations is possible to resume the best group of calibration factors for each lane, in the following table. E39 Lane Krid Krpd Krst Krsw 1 0,6 1,0 4,59 1,0 2 1,35 1,0 4,59 1,0 T able 4-8 Best group of calibration factors for each lane 35

37 For each lane is now presented, just for the record, the graphs that referred to the mean roughness. Mean Roughness [m/km] 1,6 1,5 1,4 1,3 1,2 1,1 0,9 1 0,8 0,7 Mean Roughness [m/km] NVDB Data Lane 1 Graph 2-33 E39, Lane 1 IRI [m/km] Mean Roughness [m/km] 1,7 1,6 1,5 1,4 1,3 1,2 1,1 0,9 1 0,8 Mean Roughness [m/km] NVDB Data Lane 2 Graph 4-36 E39, Lane 2 IRI [m/km] 36

38 4.3 E 6HP HP 12 Sør Trondelag County The first consderation that must be done related to the present model road is relatively with the material that composes its wearing course. As the reader might see in Appendix 11, the material used for the referred layer has a low quality( since it is not asphalt conctrete), so for the present model road the value used as an input value for the initial mean rut depth should be higher (comparatively to the roads previuslly analysed 12 ). The adopted value was 4mm. This road has its own peculiarities that must be mentioned before proceeding with the analysis. This particularity is related to the volume of traffic that crosses the road. Since this road is a high-way such amount of traffic is easily understandable to a high value and during the analysis it will be explained how it influences the parameters under analysed. Remember the reader that first iteration corresponds to the default input values, so below it will be visible the results for the each distress types under analysis for each lane. - K rid = 0,9 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 Mean Roughness [m/km] Mean Roughness [m/km] NVDB Data Lane 1 Graph 4-37 E6, Lane 1 IRI [m/km] 11 See Appendix1. 12 To see the explanation the reader should consult the page

39 Mean Roughness [m/km] Mean Roughness [m/km] Graph 4-38 E6, Lane 2 IRI [m/km] NVDB Data Lane 2 Mean Roughness [m/km) Mean Roughness [m/km] 1,9 1,8 1,7 1,6 1,5 1,4 1,3 1, NVDB Data Lane 4 Graph 4-39 E6, Lane 3 IRI [m/km] Mean Roughness [m/km] Mean Roughness [m/km] 3,8 3,3 2,8 2,3 1,8 1,3 0, NVDB Data Lane 4 Graph 4-40 E6, Lane 4 IRI [m/km] 38

40 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-41 E6, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-42 E6, Lane 2 Mean Rut Depth 16 Mean Rut Depth 14 Mean Rut Depth NVDB Lane 3 Graph 4-43 E6, Lane 3 Mean Rut Depth 39

41 Mean Rut Depth Mean Rut Depth NVDB Data Lane 4 Graph 4-44 E6, Lane 4 Mean Rut Depth Difference Lane 1 Lane 2 Lane 3 Lane 4 1,2 3,3 1,4 2,9 T able 4-9 Difference between data For data obtained for the rutting, the difference between the measurements made in the field and those predicted by the MATLAB tool for the lanes 1 and 3 are reasonable, since they are around 1mm. But, the opposite happens for the two other lanes. On the other hand with regarding to results for the mean roughness, the lector might observe through the charts above that the difference between the measurement results and the ones provided by MATLAB in the first 2 or 3 years (depending on the lane under analysis) are nearly coincident, but over time the difference is even more accentuated. The explanation for this disparity is due to the influence of motorized traffic on the average roughness. In other words, it is known that the high motorized traffic affects the roughness in a exponential way, as long as the time passes by the roughness values increases very dramatically. Although, is possible to change the calibration factors to look for better solutions. So, keeping in mind that the K rid is the most influent calibration factor, so the next iteration results of increasing it by 50% and keeping the other with its default values, is possible reach to the following results: - K rid = 1,35 - K rpd =0,0 - K rst = 4,59 - K rsw = 1,0 40

42 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-40 E6, Lane 1 Mean Rut Depth Mean Rut 13 Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-46 E6, Lane 2 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Lane 3 Graph 4-47 E6, Lane 3 Mean Rut Depth 41

43 Mean Rut Depth Mean Rut Depth NVDB Data Lane 4 Graph 4-48 E6, Lane 4 IRI [m/km] Difference Lane 1 Lane 2 Lane 3 Lane 4 2,4 4,7 0,4 1,5 T able 4- Difference between data lane As is might be observed by the data available above, the results for lanes 3 and 4 improve with this iteration, whereas for the third lane may be said that this pair of calibration factors are clearly the ones that lead to an "optimal" close relationship between the two different types of data in the study. Even for the lane 4 is also apparent that with this iteration was possible to obtain a better ratio between the measured field data and forecasts made by the HDM-4 model. And it might be said that for the lane 4 this iteration is the one that also leads to the best results since this difference between the two types of data might be acceptable. Although, for the first two lanes, this iteration turned to be even worse for the proximity relationship of the two distinct types of data. The next iteration that was done, with the calibration factors that are shown below, has more a didactic function for the present study, than scientific. Such state is made, since the results that are achieve with this iteration allows to the author to understand which more sensitive variations should be done in the calibration factors and in what calibration factors should do such variations, in order to look for better solutions for the first two lanes. The results obtained with the following iteration are worse for every lane. So, is possible for the lector to find such facts in the data that is below presented. - K rid = 1,35 42

44 - K rpd =1,0 - K rst = 4,59 - K rsw = 1,0 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-49 E6, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-50 E6, Lane 2 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Lane 3 Graph 4-51 E6, Lane 3 Mean Rut Depth 43

45 Mean Rut Depth Mean Rut Depth NVDB Data Lane 4 Graph 4-52 E6, Lane 4 Mean Rut Depth T able 4-11 Difference between data Now focusing more attention on the lane 1and lane 2, to achieved a better proximity relationship between the data from the measurements that were done on the field and the ones that MATLAB gives, it is necessary to interfere on the K rid calibration factor, but this time decreasing its value, because, what is necessary is reduce the inclination of curve given by the MATLAB tool, in order to it fit better the data from the NVDB Data Bank. So, doing iteration with the following calibration factors is possible to achieve the results below. - K rid = 0,45 - K rpd =0,0 - K rst = 4,59 - K rsw = 1,0 Difference Lane 1 Lane 2 Lane 3 Lane 4 6,8 9,1 2,8 2,4 Difference Lane 1 Lane 2 Lane 3 Lane 4 0,7 2,3 2,85 4,3 T able 4-12 Difference between data 44

46 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-52 E6, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-53 E6, Lane 2 Mean Rut Depth There also visible for the lane 2 that there s an improvement in the results when comparing to the rest of the iterations that were made. Now, it s time to reach some conclusions about the group of calibration factors that are better for each lane. In order to do that there s below a table where is possible to see the group of calibration factors that lead to the best proximity relationship between the measurements in field and the ones that are predicted by the HDM-4 model. E6 Lane K rid K rpd K rst K rsw 1 0,45 0 4, ,45 0 4, ,35 0 4, ,35 0 4,59 1 T able 4-13 Best group of calibration factors for each lane 45

47 4.4 R 5 HP 19 Sogn Og Fjordan County As the reader might find in Appendix 1 the wearing course that constitutes this pavement is made by a material that is thought as a good one, so that means that the values used for the initial rut depth is 2 mm. As is usual in this study, the first iteration results of applying the default values for the calibration factors, so below are the results and as well this default values. - K rid = 0,9 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 Mean Roughness IRI [m/km] Mean Roughness [m/km] 2 1,8 1,6 1,4 1, NVDB Data Lane 1 Graph 4-54 R5, Lane 1 IRI [m/km] Mean Roughness [m/km] 2,4 2,2 2 1,8 1,6 1,4 1,2 1 Mean Roughness IRI [m/km] NVDB Data Lane 2 Graph 4-55 R5, Lane 2 IRI [m/km] 46

48 Mean Rut Depth Graph 4-55 R5, Lane 2 IRI [m/km] Mean Rut Depth 9,5 8,5 7,5 6,5 5,5 4, NVDB Data Lane 1 Graph 4-56 R5, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-57 R5, Lane 2 Mean Rut Depth Difference Lane 1 Lane 2 1,7 1,4 T able 4-14 Difference between data As is possible to understand by the data presented above, the difference between the predicted data and the data that results from the measurements that have been done during the time on the existing road is not that higher for this group of calibration factors. It is possible to state that it might be considered pretty well due to the irregularity of the data from the NVDB Data Bank. Nevertheless, the fact associated to the irregularity of the data that results of the measurements that have been done in situ will make hard for the present model road to look for a very good result, since it will be very difficult to adapt a quality line in that, which will fit perfectly with these measurements made on site. Noting, as mentioned earlier, as long as the rutting is increasing, the values of calibration factors used are, as well have increasing so the results of predictions made by the HDM-4 47

49 model also they suffer an increment. Therefore, if the reader looks at the graphs corresponding to the rutting can see that increasing the value of K rid (the most influential factor calibration) it is possible to obtain a line more inclined line. So, trying to get a smaller difference between the measured data in the field and the data provided by MATLAB program, the next iteration was done. - K rid = 1,35 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 According to these ideas is possible to see below the results that were obtained. Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-58 R5, Lane 1 Mean Rut Depth Mean Rut Depth Mean Rut Depth MATLAB DATA NVDB Data Lane 2 Graph 4-59 R5, Lane 2 Mean Rut Depth 48

50 Difference Lane 1 Lane 2 0,8 0,6 T able 4-15 Difference between data So, looking in a very lightly way for the graphics that are above exposed is possible to the reader to realize that increasing by 50% the calibration factor for the rutting initial densification model (the most influential one that produces more visible alterations in the results) makes the results more close of what is expected, i.e., contributes to the a small difference between the two kinds of f data, which is necessary, Keeping in mind that due to the irregularity of the present data from the NVDB Data it will be very hard do achieved a good correlation between the two distinct types of data under analyze. But, still trying to get to better results, a new iteration was tried. So for the next iteration d the values used were: - K rid = 1,35 - K rpd = 0 - K rst = 4,59 - K rsw = 1,0 Mean Rut Depth Mean Rut Depth NVDB Data Lane 1 Graph 4-60 R5, Lane 2 Mean Rut Depth 49

51 Mean Rut Depth Mean Rut Depth NVDB Data Lane 2 Graph 4-61 R5, Lane 2 Mean Rut Depth Difference Lane 1 Lane 2 1,3 0,7 T able 4-16 Difference between data Trying to improve the calibration factors, i.e., increasing by 50% the two most influents ones, in order to get a less difference between the measurements and the predicted Data, is visible that the opposite path is reached with this iteration. So, according to what has been said in this chapter and also in the Appendix 1, if another iteration will be done, and it will result by increasing the calibration factors, that will mean that the results will be even more worse. Because, just to remind, when the values of the calibration factors are increased, that means too an increment on the values for the rutting. So, if in the last iteration only one of the calibration factors was increased and it lead to worse results, when comparing to the iteration that results of increasing only the K rid calibration factor. So according to the bad quality of the measures and with what was exposed just above, it was decided that anymore iterations will be done. 50

52 5. Calibration Factors: Proposal In this chapter the most important part of the work will be developed, since it will be in this chapter that will be presented and debated the selection of proposal of the calibration factors that should be used when the user wants to predictions of the behaviour of the flexible pavements of the Norwegian Roads. As it was exposed in the last chapter, there it was tried to find the best group of calibration factors for each model road. But, sometimes, due to the specificity of the data from the measurements that have been done in the roads it was found group of calibration factors for each lane. So, now the big challenge is to discover a group of calibration that might be able to fit all the roads and that might lead to results quite good for the predictions of the behaviour of the pavements of roads. That means that a well calibrated group of calibration factors should be determined, so that this MATLAB Tool might be used without restrictions to do predictions about the behaviour of the pavements, in order to define, carefully works of reparation sand maintenance of repair of the pavements. Below, the lector might find a compilation of the results that were achieved for all lanes. E8 Lane Krid Krpd Krst Krsw 1 1,35 1,0 6,9 1,0 2 1,35 1,0 6,9 1,0 T able 5-17 T able 5-18 Best group of calibration factors for each lane E6 Lane Krid Krpd Krst Krsw 1 0,9 0 4, ,13 0 4, ,35 0 4, ,35 0 4,59 1 Best group of calibration factors for each lane E39 Lane Krid Krpd Krst Krsw 1 0,6 1,0 4,59 1,0 2 1,35 1,0 4,59 1,0 T able 5-19 Best group of calibration factors for each lane 51

53 R5 Lane Krid Krpd Krst Krsw 1 1,35 0,0 4,59 1,0 2 1,35 0,0 4,59 1,0 T able 5-20 Best group of calibration factors for each lane So the proposal is presented in the table below. Is possible for the reader to find a brief explanation for this choice in the Appendix7. Krid Krpd Krst Krsw 1,2 0,3 4,7 1,0 T able 5-21 Calibration Factors: Proposal Now, it is necessary to validated this propose, in order to see if this work that was developed has profits. So, for each lane of each model road will be presented the correlation between the measured data, given by the NVDB Data Bank, and the predicted data using the proposed calibration factors. 52

54 5.1 E8 HP4 Tromsø County Predicted vs Measured Data R² = 0, Predicted ,000,000 20,000 30,000 Measured Lane 1 Quality line Graph 5-62 E8, Lane 1 Correlation between data Predicted vs Measured Data R² = 0,9542 Predicted ,000,000 20,000 30,000 Measured Lane 2 Quility line Graph 5-63 E8, Lane 2 Correlation between data As it is possible to see, for both lanes when using the proposed calibration factors, the correlation between the two kinds of data under analysis is good, this means that the difference between the measurements and the predicted data is lower. So, it might be said that this proposal allows doing quite reliable predictions. 53

55 5.2 E39 HP 14 Sogn og Fjordan County Predicted vs Measured Data,5 9,5 9 Predicted 8,5 R² = 0, ,5 7 6,5 5,000 7,000 9,000 11,000 13,000 Lane 1 Measured Quality Line Graph 5-64 E39, Lane 1 Correlation between data Predicted Predicted vs Measured Data,5 R² = 0,7369 9,5 9 8,5 8 7,5 7 6,5 Lane 2,000 5,000,000 Measured Quality Line Graph 5-65 E39, Lane 2 Correlation between data As it is possible to see also for the present road it was possible to find a good correlation between the two types of data under analysis, using the proposed calibration factors. That relationship is particularly good for lane 1, where the R 2 is almost 1. 54

56 5.3 E6 HP 12 Sør Trondelag County Predicted vs Measured Data R² = 0,9587 Predicted ,000 5,000,000 15,000 20,000 Lane 1 Measured Quality Line Graph 5-66 E6, Lane 1 Correlation between data Predicted Predicted vs Measured Data R² = 0, ,000 11,000 Measured Lane2 Quality line Graph 5-67 E6, Lane 2 Correlation between data Predicted vs Measured Data Predicted 24 R² = 0, ,000,000 15,000 Measured Lane 3 Quality line Graph 5-68 E6, Lane3 Correlation between data 55

57 Predicted vs Measured Data Predicted ,000 11,000 16,000 21,000 Measured R² = 0,9842 Lane 4 Quality Line Graph 5-69 E6, Lane 4 Correlation between data As the reader may observe the graphs that were presented above the proximity relationship between the measurements that were made on the pavements during the time and the data predicted by the MATLAB application is actually very good for almost all lanes, since the R 2 is almost 1, except for the lane 3, because it is a little less than 0,9. But even though the result achieved is very good. 56

58 5.4 R 5 HP 19 Sogn Og Fjordan County Predicted Predicted vs Measured Data R² = 0, ,500 8,00 8,500 9,00 9,500 Lane 1 Measured Quality line Graph 5-70 R5, Lane 1 Correlation between data Predicted Predicted vs Measured Data 12 R² = 0, ,000 5,000,000 15,000 Measured Lane2 Quality line Graph 5-71 R5, Lane 2 Correlation between data As the reader might see for the lane 2 the correlation for the two types of data is quite good, which means that, as it was expected, the proposed calibration factors are able to lead to a quite good results, i.e., the results of the two types of data are quite close. Although, when it comes to the lane 1, the results obtained are bad, since the correlation factor between the two types of data is very low. So, keeping in mind that all the results obtained for the other models roads were particularly good, this lane of the R5 HP 19 Sogn Og Fjordan County should be ignored, once it is not representative. So it is possible to conclude through the results that were achieved above, that the proposed calibration allow getting a bigger proximity relationship between the predicted data and d the measured one. Thus, this means that they should be used when the user is trying to do forecasts of the future behaviour of the flexible pavements to program maintenance and reparation work, 57

59 because it allows getting a good idea how the development of the rutting of will be, for example. However, it is important that the lector realizes that the values proposed here for the rutting calibration factors should still be subject to further testing, as may be necessary that they suffer a few minor adjustments. It is also thought that some more studies related with this subject should be developed, in other to find some calibration factors that might also be changed, for example those related to roughness, so that it is thus possible to still get most realistic overall result. There one more aspect that should not be forgotten about the calibration factors. Thus, for the future forecasts be done on the safety side, i.e., it is necessary that the predicted data is not inferior (or very inferior) from the real one. Such fact could mean that the reparation and maintenance work could be delayed, since the predicted data might suggest that. So, the reparation and maintenance works will be more expensive, since the pavement would be more damage, or there s also the possibility that a non-programmed intervention should be done. 58

60 6. Conclusions and Suggestions Now, in this chapter is going to be presented the behaviour of new designs of pavements that are going to be tried for the model road E 39 HP 14 Sogn og Fjordan County. This aims to look for new solutions of flexible pavements and test using the new calibration factors the behaviour of these new designs and also evaluate the traffic influence on the progressing of the rutting, in order to evaluate and programing works of reparation and maintenance. The new designs were projected for four different traffic scenarios, according with the traffic categories, in order to be possible to see its influence and to look for points in the MATLAB algorithm that also should be improve, in case the results of this part of the analysis would be not expected. In the Appendix 6 the reader might find the new pavements designs and as well the traffic values. So, right now it s going to be presented the results that were obtained. Mean Rut Depth Traffic Category C NVDB Data Lane 1 Graph 5-72 E39, Lane 1 Traffic Category C 21 Traffic Category C Mean Rut Depth NVDB Data Lane 2 Graph 5-73 E39, Lane 2 Traffic Category C 59

61 Mean Rut Depth Traffic Category D NVDB Data Lane 1 Graph 5-74 E39, Lane 1 Traffic Category D Mean Rut Depth Traffic Category D NVDB Data Lane 2 Graph 5-75 E39, Lane 2 Traffic Category D Mean Rut Depth Traffic Category E NVDB Data Lane 1 Graph 5-76 E39, Lane 1 Traffic Category E 60

62 Mean Rut Depth Traffica Category E NVDB Data Lane 2 Graph 5-77 E39, Lane 2 Traffic Category E Mean Rut Depth Trafic Category F NVDB Data Lane 1 Graph 5-78 E39, Lane 1 Traffic Category F Traffic Category F Mean Rut Depth NVDB Data Lane 2 Graph 5-79 E39, Lane 2 Traffic Category F So it is visible through the presentation of the graphs above that the MATLAB algorithm is not sensitive to the increment of the Traffic. As is possible to observe, while the traffic category increases 61

63 the results predicted through the MATLAB increase much faster than the real ones. To the first two low traffic categories 13 there is some proximity between the predicted and measured data, but only in the initial years of the analysis. Then, suddenly the predicted results begin to increase in a very sharply way. So predict the future behaviour of roads that have a high level of traffic, the algorithm of the HDM-4 Model does not allow achieving to congruent results, since the predicted values are overestimated in relation to the reality. Such fact will induce to do maintenance and reparation works too early, which is anti-economic,once this works will be done before the pavement achieve a deterioration level that justify such kind of works. Here is on topic that should be considered in new reach works, since the algorithm should be calibrated to respond in a consistent manner to the traffic increment, in order to be possible to do congruent predictions. The point here developed in this study, was to calibrate the MATLAB tool to do predictions of the behaviour of the flexible s pavements, but to low values of traffic. So, it is thought that here is one more point of improvement that should be considered in future studies. It was also though that should also be presented the graphs that are referred to the mean roughness, because the same problem is also visible, i.e., as the traffic is increasing, the results predicted are very high, when comparing to the real ones. So, beyond of being necessary to calibrate the algorithm for the rut model it is also necessary to do the same for the roughness model, once that the values that are obtained while the traffic is increasing are unreal. Mean Roughness [m/km] Traffic Category C NVDB Data Lane 1 Graph 5-80 E39, Lane 1 Traffic Category C 13 Categories C and D 62

64 Mean Roughness [m/km] 4,5 3,5 4 2,5 3 1,5 2 0,5 1 0 Traffic Category C NVDB Data Lane 2 Graph 5-81 E39, Lane 2 Traffic Category C Mean Roughness [m/km] Traffic Category D NVDB Data Lane 1 Graph 5-82 E39, Lane 1 Traffic Category D 15 Traffic Category D Mean Roughness [m/km) NVDB Data Lane 2 Graph 5-83 E39, Lane 2 Traffic Category D 63

65 Traffica Category E 20 Mean Roughness [m/km] NVDB Data Lane 1 Graph 5-84 E39, Lane 1 Traffic Category E Traffica Category E Mean Roughness [m/km] NVDB Data Lane 2 Graph 5-85 E39, Lane 2 Traffic Category E 20 Trafic Category F Mean Roughness [m/km] NVDB Data Lane 1 Graph 5-86 E39, Lane 1 Traffic Category F 64

66 20 Mean 15 Roughness [m/km] 5 0 Traffic Category F NVDB Data Lane 2 Graph 5-87 E39, Lane 2 Traffic Category F There also some questions related to the way how traffic 14 affects the final results. So, in this topic there s also some reach that should be done. It is believed that there s also more in the MATLAB application that should be review. For example, the MATLAB s algorithm should suffer some alterations to turn the program more interactive with the user. For example, it should be possible to the reader to create their own folders related with the calibration factors and also with the climatic values, so that the user could just define it as defaults values, instead of being, every time changing, one by one the this parameters. However, it is thought that still is another aspect on that might also be subject of future studies that is related with the layer coefficient. In the chapter 5 of the report Development of performance measures, modelling and calibration is possible to find a table where is visible for each kinds of materials which interval of layer coefficient should be considered. A part of the table is below transcript. As the lector may see the intervals for each kind of material are a quite large. Thus, there is some subjectivity associated to their use. So it is here proposed that for each type of material it should be created sub materials with a precise layer coefficient, in order to minimize the subjectivity related with the choice of these coefficients. Because, as it easily understandable, for the same material two different user can pick different layer coefficients. 14 As the case of the input value of the ESALF 65

67 Material a i Asphalt concrete 0,2<a i <0,44 Granular base 0,06<a i <0,20 Granular sub base 0,06<a i <0,20 Bitumen treated base 0,<a i <0,30 Cement treated base 0,<a i <0,28 Broken Portland Cement Concrete 0,<a i <0,44 T able 6-22 Layer coefficients 66

68 Appendix 1- Pavements Structure and other important data In this Appendix the reader is able to find information related with: - Pavementes structure - Road network - Traffic data - Climatic data E39 HP 17 Layer Thickness Material Wearing course [2001] 40 Hot-mixed asphalt - Agb 16 85/0 Asphalt layer 50 Precoated chippings - AP /150 Base 180 Crushed rock - FK 0-63 Sub base 140 Crushed rock - FK Subgrade - Stone rich, hard subgrade T able A1-23 Pavement Structure Mean monthly precipitation 180 CBR Number of lanes 2 Width shoulders [m] 0,5 Width carriageway [m] 7,5 elevation difference ADT total Average traffic speed [km/h] 70 T able A1-24 Diverse Data E 8 HP 4 Layer Thickness Material Wearing course [2001] 50 Hot-mixed asphalt - Agb Asphalt layer 70 Hot-mix - Ag Base 0 Crushed rock - Fk Sub base 700 Gravel Subgrade - Clay, silt, moraine T able A1-25 Pavement Structure 67

69 Mean monthly precipitation 0 CBR Number of lanes 2 Width shoulders [m] 0,5 Width carriageway [m] 7,5 elevation difference ADT total Average traffic speed [km/h] 70 T able A1-26 Diverse Data E 6 HP 12 Layer Thickness Material Wearing course [2001] 50 Hot-mixed asphalt - Agb 16 85/0 Asphalt layer 80 Precoated chippings - AP /150 Base 60 Recycled asphalt - Gja Sub base 91 Crushed rock - Fk Subgrade - Stone rich, hard subgrade T able A1-27 Pavement Structure Mean monthly precipitation 50 CBR 5 Number of lanes 4 Width shoulders [m] 0,5 Width carriageway [m] 7,5 elevation difference ADT total Average traffic speed [km/h] 70 T able A1-28 Diverse Data R 5 HP 19 Layer Thickness Material Wearing course [2001] Hot-mixed asphalt - Agb 16 85/0 Asphalt layer Hot-mixed asphalt - Agb 16 85/0 Base 30 Recycled asphalt Sub base 640 Crushed rock - Fk Subgrade - Gravel, sand, moraine, T able A1-29 Pavement Structure 68

70 Mean monthly precipitation 180 CBR 15 Number of lanes 2 Width shoulders [m] 0,5 Width carriageway [m] 7,5 elevation difference ADT total Average traffic speed [km/h] 70 T able A1-30 Diverse Data Road initial mean rut depth E 8 P 4 2 RV 5 HP 19 2 E 6 HP 12 4 E 39 HP 17 2 T able A1-31 Initial Mean Rut Depth Road ADT total 20 AADT Total ANVPST 15 E 8 HP ,5 RV 5 HP ,9 E 6 HP ,4 E 39 HP ,5 T able A1-32 Traffic Data 15 Annual number of vehicles passes with studded tyres in one direction 69

71 Appendix 2 - Nomenclature This appendix wants to clarify the reader about some controversy that may exist in the nomenclature of the program., The first challenge that was presented in the study appeared at the traffic and vehicle data department. The first doubt arose in the input value of the Annual Average Traffic, because in the way that it is identified is should creat some ambiguity, however a conclusion of it s value has been reach. So, it means that this input value refers to the total number vehicles that passes per year on the road. Then, is as also arose a doubt in the Annual Number of Vehicles passes with Studded Tyres in one direction, because this information must be introduced in the program in thousands, otherwise the results given by it will be akward. There is also another factor that has been causing some controversy, which is the ESALF because it s not that quite well known it s leverage in the results. So during the analisys it was kept at 2, which is a default value. It is very important to clarify the reader about this aspects since it is very imporatant to introduce the correct data in the program, otherwise the output data will not be realible, so the user might be aware of this. So just for the record, it will be here given an example of how some of this data is calculated. For this example the model road chosen was: E8 HP 4. For this road it was found in the NVDB data Bank that the ADT total 20 = So in order to calculate the Annual number of vehicles passes with studded tyres in one direction is also needed to know for each road in study the percentage of cars that use in the winter the studded tyres. For E8 HP is known that this percentage is 60%. Just for the record, for the model road E6 HP12, this percentage drops for 20%. Considering that the winter has 180 day is possible to state that: ( ( )) It is important that the user should not forget that this value should be introduced on the in thousand, so that s why it must be divided by 000. When it comes to the Annual average traffic, as definition can be read in the previous page, for the road in analysis, it will be: 70

72 The author also thinks that is important to referred in this appendix that since the MATLAB is a sensitive case, the user might be aware of the difference of using comma or dot. However, for the program to run correctly the dot must use always, never in any case the comma. 71

73 Appendix 3 User Guide to MATLAB application This Appendix aims to present the user the way how the MATLAB applications runs. The firs panel that will pop up is below presented, and in here the user may chose the country, and the default values for the calibration factors will be assumed. Although, since the proposal values for the changes that could be done in the calibration factors lead to better results that the default ones, so the user might use them. However, the user must be aware that every time that uses the program must change the calibration factors, because the algorithm of the program does not allow saving this changes. Figure A2-5 Calibration factors and Climatic Parameters: Input Values 72

74 Now some comments about the climatic parameters shall be done. When running the program the user must be sure about the climatic situation about the area for which the analysis is going to be done, so that the user may be able to choose wisely these parameters. Since the default values that were displayed for Norway were not according to real climatic conditions, according to the author, it was decided to change them, as is possible to see in the figure above, and as well in the table below. It also should be added that for more detailed information about this parameters, the reader shall consult the report that has been being referred during this study. So, for the author Norway fulfil the requirements for the Temperate Freeze- Per Humid 16 climatic zone. Ncteq 20 Teq 7 CCT 0 Roughness environmetal coefficient [m] 0.06 T able A2-33 Climatic parameters Here is one more time presented a transcript part of the table of the report Development, of performance measures, modelling and calibration Material a i Asphalt concrete 0,2<a i <0,44 Granular base 0,06<a i <0,20 Granular sub base 0,06<a i <0,20 Bitumen treated base 0,<a i <0,30 Cement treated base 0,<a i <0,28 Broken Portland Cement Concrete 0,<a i <0,44 T able A2-34 Layers coefficients According to what was in the Appendix 1 presented, for all the four model roads where chosen the same 17 layer coefficients, as is possible to see below. - Surface layer: a i =0,44 - Base layer : a i =0,2 16 Classification according to the report Development of Performance measures, modelling and calibration 17 It was chosen the same layer coefficient for all the roads because the used material is same, according to the definition of the table, although a different sub type is used in each road 73

75 - Sub base layer: a i =0,3 Before, moving forward, to the next panel the user may change the calibration factors. In the figure A2-6 is possible to see the ones that for the present study were changed. Figure A2-6 Road Network input parameters The second panel is related with the road network and pavement data, which may be seen in the following figures. In this panel, the user might insert input data related with the pavement structure in study. When the third panel pop s up it will ask for input data related to the traffic and vehicle, and the at this point the user must now be aware of the fact that the Annual number of vehicles passes with studded tyres in one direction must be introduced in thousand and also of real meaning the Annual average traffic See Appendix 2 to search for more information. 74

76 Figure A2-7 Traffic and vehicle input parameters One last panel will pop up and it will ask for information related with the road network condition. Here, the user might change the mean rut depth input value to one of the others that were proposed during this study See chapter 4 75

77 Figure A2-8 Road network input parameters 76