A NEW METHOD FOR ALIGNING AND SYNCHRONISING ROAD PROFILE DATA FOR BETTER ROAD ROUGHNESS GROWTH ANALYSIS. Robert P. Evans 1* and Arul Arulrajah 1

Transcription

1 A NEW METHOD FOR ALIGNING AND SYNCHRONISING ROAD PROFILE DATA FOR BETTER ROAD ROUGHNESS GROWTH ANALYSIS Robert P. Evans 1* and Arul Arulrajah 1 1 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Australia * Corresponding Author s robertevans@swin.edu.au ABSTRACT Highway-speed laser road profilometer devices have been in use for nearly twenty years and have virtually replaced the older response type measuring systems. However, even with the inclusion of multiple lasers, GPS and hi-tech digital cameras, errors in the captured longitudinal road profile still exist. This paper examines possible causes of longitudinal road profile errors and examines current practice in Australia to treat such errors. More importantly, this paper presents a new and simple methodology to manipulate road profile data files to reduce these errors and better align such data files to allow an improved analysis of road profiles over time, especially at project level. A series of procedural flowcharts have been presented to accurately align and synchronise road profile data at regular intervals. The key to this new technique is the use of a simple road profile adjustment spreadsheet to calculate the realignment and synchronisation of the data points versus chainage once offset values are determined. The spreadsheet then uses this information to generate MATLAB computer code, which is then used to very quickly extract relevant data and build a potential library of multiple new road profile data files, all with unique reconfigured headers. It is these new road profile data files that are then used for the roughness analysis, producing better synchronised roughness data. A statistical comparison has been made between current roughness data available in the State of Victoria (Australia) versus properly aligned and synchronised road profile data using this new method. KEY WORDS: longitudinal road profile, methodology, MATLAB INTRODUCTION Highway-speed laser road profilometer devices have been in use for nearly twenty years and have virtually replaced the older response type measuring systems. Furthermore, multiple lasers, GPS devices and hi-tech digital cameras have been slowly incorporated into the data collection. These cameras typically capture front, side and rear views simultaneously at intervals of between 10 m and 20 m, as well as detailed images of the pavement seal in the wheel paths. With the aid of computer software, such images can be merged and approximate distances measured on the computer screen to provide a very realistic and useful desktop tool. However, with all this new added technology to road profile data collection, longitudinal position errors are still an issue with road profile data, especially when examining pavements for project level maintenance works. The findings in this paper were a by-product of doctoral studies based on evaluating the growth of long wavelength roughness characteristics of low volume rural highways in Victoria, Australia. Most rural highways in North Western Victoria (Australia) are low-volume, two-lane,

2 Evans and Arulrajah flexible pavements with a thin wearing course (i.e. chipseal). Road profile data collection is typically performed once every two years for such pavements. Although these pavements are considered low-volume based on Annual Average Daily Traffic (AADT) counts, they provide a vital link for agricultural freight movements and usually have a high percentage of commercial vehicle use. It is not uncommon for these rural highways to stretch more than 100 km uninterrupted between townships, which typically leads to the collection of very long single continuous road profile data files. LONGITUDINAL PROFILE ERRORS ASSOCIATED WITH COLLECTING ROAD PROFILE DATA Overall, the inaccuracy of collecting road profile data can be divided into two main components. These are due to: (i) the profilometer operator approximating start and end points, and (ii) lateral tracking errors due to the profilometer vehicle continuously deviating from the ideal wheel path. Inaccuracies of Road Profile Data due to Approximating Start and End Points In rural areas, there are far less specific reference markers that contribute to the State Road Referencing System (SRRS) of Victoria. Hence, most road profile data files start and end at highway intersections. Ideally, these key reference points should be clearly marked and easily recognisable by the profilometer data collection team. However, these intersections often include merging entry and exit lanes (sweeping lanes) separated by traffic islands that make locating the true apex (or centre) of the intersection difficult, especially whilst travelling at highway speed. This requires the driver to use substantial judgement in order to locate a highway intersection reference marker according to the SRRS. Thus, errors are inevitable when using such invisible markers. This research consistently noted variations in the order of 20 m to 30 m at the start and end of raw profilometer data files and occasional errors greater than 100 m (i.e. likely due to mistaken SRRS chainage points). Sayers (1) also reported similar start and end of file inaccuracies of between 15 m to 30 m in the United States. Nevertheless, correcting road profile data files by shifting files back or forward to match an existing profile is relatively easy. One method is to compare (by plotting) the profile against a known accurate reference profile and use the offset function in the RoadRuf software (2) to manually adjust the profile until an acceptable visual match is found. Another method is to use the cross correlation technique developed by Karamihas (3), which is available in the latest ProVAL software package (4). Correcting this type of error in a road profile data file is often said to be rubber banding the data file. This essentially involves locating the true start and end locations of the data file, removing unwanted data, and adjusting the sample interval to match the SRRS chainage (i.e. stretching or compressing the original data file to match the chainages). In Victoria (Australia), the maximum rubber banding correction that can be applied to raw road data files is one percent (i.e. 1 m per 100 m) of collected data. This limit of error correction was derived from allowing the International Roughness Index (IRI) values to be reported at either 99 m or 101 m intervals instead of the uniform 100 m intervals. Inaccuracies due to Lateral Tracking and Deviations of the Profilometer Vehicle

3 The lateral movement of the profilometer vehicle within the lane (i.e. deviation from the ideal wheel path) can accumulate longitudinal distance variations and create a substantial error. These lateral tracking errors can develop from: 1. The profilometer vehicle continuously wandering within the lane and deviating from the ideal path. This causes the vehicle to travel a greater distance between recorded chainage points. This factor naturally becomes more prevalent when travelling at highway speeds over very rough roads due to reduced control of the vehicle. 2. The profilometer vehicle taking curves in the road consistently tighter or wider than the ideal wheel path. This is especially important for large radial curves. As an example, if a road deviated ninety degrees via a 50 m radius, a longitudinal distance error of up to 0.8 m could result from one driver taking a tighter path by one tyre width (approx. 250 mm) of the ideal line versus another driver taking a wider path by one tyre width. 3. The profilometer vehicle overtaking slower traffic via an overtaking lane (when present). This creates a large deviation to the ideal path and a longer data file is recorded. Overtaking or making lane changes during data collection is not recommended, but occasionally the profilometer vehicle can be forced to overtake due to slower traffic or to avoid obstacles in the road. Nevertheless, any overtaking or lane changes should be recorded via an event file during the survey. If the profilometer vehicle wandered consistently during the data collection, the error described above (point no. 1) could easily be reduced by simply adjusting the data interval and spreading this error across the data file (i.e. essentially rubber banding the data). However, when such lateral tracking errors are inconsistent and are non-uniform throughout the data file (i.e. by cornering path errors and overtaking), it would be inaccurate to make this adjustment as isolated local errors should not simply be averaged through the entire road profile data file. These errors ideally need to be corrected at the source location within the profile data file. This research consistently discovered that lateral profile tracking errors in the order of 5 m to 7 m mid profile (after standard rubber banding was applied) when compared to a reference profile. As most road indices in Australia are reported at 100 m intervals, such errors become significant at 5 % to 7 %. These errors are much greater than the accepted tolerances and can lead to misleading roughness and roughness growth rates, which is highlighted in the following section. Sayers (1) measured lateral movement variations of up to 0.6 m (2 ft) in a single wheel path between consecutive road profile data measurements. However, no comment was made how this affected the longitudinal profile length and accuracy of the profile. Impact of Longitudinal Road Profile Data Errors To highlight the importance of properly aligning road profiles, Fig. 1 shows a comparison of standard road roughness data (obtained from the asset management database of VicRoads, the State Road Authority of Victoria, Australia) versus road roughness data that has been aligned and synchronised at 5000 m intervals along the profile. In Fig. 1, plot (a) is the current standard quality of road roughness data available, where IRI is reported for the left (passenger) wheel path at 100 m intervals over an eight year period. This data has been rubber-banded and is supposedly accurate to within 1%. In Fig. 1, plot (b) features the same data, but the raw road profile data has

4 Evans and Arulrajah been aligned at its ends (rubber banded) and then aligned or synchronised at 5000 m intervals using the new method proposed in this paper.

5 (a) (b) FIGURE 1 A sequential time series plot of the International Roughness Index (IRI) vs. SRRS Chainage km to 114 km based on: (a) Actual figures from the Victorian State

6 Evans and Arulrajah Road Authority database, and (b) Recalculated IRI values from fully aligned and synchronised raw road profile data files. Overall, the aligned and synchronised data appears cleaner and sharper with far less fluctuations. For example, between chainage and km (Fig. 1), the aligned and synchronised data clearly shows strong, uniform and unmistakable roughness growth before maintenance was performed sometime between surveys in 2003 and In particular, the 100 m section at chainage km (i.e to km) shows extraordinary roughness growth at approximately at 0.97 m/km per year with a very good coefficient of determination (R 2 ) of Similarly, the aligned and synchronised sections at chainage and km show roughness growth rates of 0.38 and 0.57 m/km per year with R 2 values of 0.87 and When compared to the currently available standard data, the accuracy of the linear regression analysis was much lower with R 2 values of 0.69, 0.79 and 0.83 respectively. Even when the pavement did not experience much deterioration, as was the case between chainage to km, the synchronised data still showed much greater clarity and confirmed this fact with greater confidence. A comparison of linear regression statistics (based on Fig. 1) is better illustrated in Table 1. TABLE 1 Roughness growth rates for section to km, as featured in Fig. 1, including linear regression equations and associated coefficient of determination values. Chainage Type of Data Linear Regression R km Std Data y = 0.457x Aligned and Synchronised Data y = 0.379x km Std Data y = 0.621x Before Maintenance Aligned and Synchronised Data y = 0.570x km Std Data y = 0.211x - After Maintenance Aligned and Synchronised Data y = 0.440x km Std Data y = 0.517x Aligned and Synchronised Data y = 0.972x To further investigate roughness growth and highlight the increased accuracy of the synchronised data, Fig. 2 shows continuous reporting of the IRI (based on a 10 m sliding base) for a 100m section at chainage km (i.e to km). This plot shows two isolated locations where roughness growth was very high with a serious pavement defect at approximate chainage km. It also shows the effect of maintenance performed prior to the last survey. Unfortunately, most senior road asset managers are mainly interested in managing their pavements at a network or corporate level and as a result request only summary profile type indices such as the IRI. At network level, small variations in longitudinal road profiles are negligible as data is summarised and continually averaged to produce general performance indicators. This occurs because road network managers only monitor average performance and are largely preoccupied with modelling the overall required maintenance costs versus improved pavement condition and reducing average roughness levels within the network. However, when it comes to effectively scheduling maintenance activities, better roughness data is needed to confidently examine pavement performance at project level.

7 Summary IRI Values: 1997 = 3.33, 1999 = 5.72, 2001 = 7.26, 2003 = 9.26 and 2005 = 5.26 FIGURE 2 Continuous IRI measurements (Left (passenger) wheel path using a 10 m sliding base) for the 100 m section at chainage km (i.e to km). A SIMPLE METHOD FOR BETTER ALIGNMENT OF ROAD PROFILE DATA Longitudinal road profile data is usually captured in binary form before being converted to a text based ERD file format. The ERD file format was developed within the Engineering Research Division (ERD) at the University of Michigan s Transportation Research Institute (UMTRI). It was originally developed to facilitate automated plotting of experimentally measured and simulated data. An ERD file contains two independent sections, the header and data. The header part contains only text and comprises information used to read the numerical data such as the no. of data channels and recordings present, units, sample interval, a description of the data collected and format of the data. The data part contains only numbers. One advantage of using ERD data files is that they can be easily edited using a word processor. However, as road profile data files are very long (i.e. often comprise of over a million lines of data for a single 50 km survey) manual editing of these files and extracting specific sections of data can be time consuming and fraught with errors. The structure or philosophy behind this new method is to essentially take a large raw road profile ERD data file and build a library of smaller new corrected (aligned and synchronised) ERD files, which are much easier to use, evaluate and compare. The key to this new technique is the use of a simple spreadsheet to calculate realignment or synchronisation of the data points versus chainage once offset values are determined. The spreadsheet then uses this information to generate MATLAB (5) computer code, which is then used to very quickly extract relevant data and build a library of multiple individual new ERD files, all with unique reconfigured headers.

8 Evans and Arulrajah It s these new ERD files that are then used for the roughness analysis, producing better synchronised roughness data. Procedure for Realignment and Synchronisation of Road Profile Data This new technique involves three distinct stages of data correction. These are known as stages 0, 1 and 2. Stage 0 Acceptance of Road Profile ERD Data File Stage 0 type data refers to the raw road profile ERD data file once it has been accepted based on accuracy tolerances. Basic information is fed into the ERD File Adjustment Spreadsheet including, road name, start SRRS chainage, end SRRS chainage, sample interval, and the number of lines of data present in the raw ERD file. The spreadsheet then very simply calculates the error and accepts the ERD file if this error is within an appropriate tolerance. A flowchart of this procedure is presented in Fig. 3. If the ERD file does not fall within an accepted accuracy range, it may be due to chainage mislabelling. This can occur from two possible errors. The first occurs when the profilometer vehicle stops prematurely during data collection and the chainages in the title of the data file are not adjusted. This can be confirmed by viewing the associated profilometer event file and matching the chainages. If the ERD file is proven to be incorrect, it can easily be adjusted (edited) and the details re-entered into the ERD File Adjustment Spreadsheet. The second occurs when the profilometer vehicle operator simply fails to mark the end of the survey run and records too much profile data. This can be confirmed by viewing (plotting) the full profile and comparing it to the reference profile. Such an error is easily recognisable. To fix this error, simply adjust the end chainage in the ERD file based on the sample interval and re-enter the ERD file details into the ERD File Adjustment Spreadsheet. Once the ERD file has been accepted, it is considered to be at a Stage 0 level of accuracy. Stage 0 type data is essentially raw road profile data with zero alignment corrections applied.

9 START Start STAGE 0 Open ERD File Adjustment Spreadsheet Input Various ERD File Details into Spreadsheet Is longitudinal error in ERD file acceptable? No Input corrected ERD file details into spreadsheet Yes View Profilometer Event Correct ERD file Does event file match contents of ERD file? No Yes No Any valid reason to explain error? Yes Reject ERD file Go to STAGE 1 END FIGURE 3 Procedural flowchart for accepting road profile ERD data files providing stage 0 type data.

10 Evans and Arulrajah Stage 1 Alignment at Ends of Road Profile ERD Data File Stage 1 type data refers to road profile data that has been aligned at each end and linearly rubber banded. This simply means that each end of the road profile ERD data file has been compared to a reference profile and corrected. By the term corrected, the actual or true SRRS chainages at each end have been established and the sample interval adjusted to match these chainages. A flowchart of this procedure is presented in Fig. 4. Start STAGE 1 Input start / end length details of ERD file to extract and evaluate Go to Stage 0 code sheet and copy MATLAB code to a text file Convert text file to a MATLAB m file Run MATLAB m file to create ERD files Input a longer length of ERD file at start / end to extract and evaluate Evaluate ERD files versus equivalent reference profiles and determine the correction offset to be applied at the start and end locations Have acceptable offsets been determined? No Yes Enter start / end offset correction values into ERD File Adjustment Spreadsheet Go to STAGE 2 FIGURE 4 Procedural flowchart to align road profile ERD data files (at their ends) and provide stage 1 type data. First, a suitable length of ERD file is extracted near the start and end of the file. Depending on the method of comparison used, a 300 m to 500 m length of file is recommended. This extraction of data is performed by the ERD File Adjustment Spreadsheet by it generating appropriate MATLAB computer code. This computer code can be copied and pasted into any word processing software and saved as a text file. It is then converted to a MATLAB m file by simply changing the file extension from.txt to.m. An example of this code is presented in Fig. 5.

11 Line MATLAB Source Code 1 % Opening Road Profile Data Source File 2 fin=fopen('2690t 2A 2007.ERD'); 3 %Creating Output Files 4 fout1=fopen('2690_2a_2007_start_s0_v1.erd','w'); 5 fout2=fopen('2690_2a_2007_end_s0_v1.erd','w'); 6 a = textscan(fin, '%s', 'delimiter', '\n', 'whitespace', ''); 7 lines = a{1}'; 8 H1=11; 9 %Writing Header Line No 1 10 fprintf(fout1,'%s\n',lines{:,1:1}); 11 fprintf(fout2,'%s\n',lines{:,1:1}); 12 %Writing Header Line No 2 13 fprintf(fout1,'%s\n',' 2, 9007, 9007, 1, 5, , -1,'); 14 fprintf(fout2,'%s\n',' 2, 8370, 8370, 1, 5, , -1,'); 15 %Writing Header Line No 3 16 fprintf(fout1,'%s\n','title : '); 17 fprintf(fout2,'%s\n','title : '); 18 %Writing Header Line Nos 4 to fprintf(fout1,'%s\n',lines{:,4:h1}); 20 fprintf(fout2,'%s\n',lines{:,4:h1}); 21 %Assigning Line Numbers 22 LA1=1; 23 LB1=9007; 24 LA2=824025; 25 LB2=832394; 26 %Writing Data to File 27 fprintf(fout1,'%s\n',lines{:,la1+h1:lb1+h1}); 28 fprintf(fout2,'%s\n',lines{:,la2+h1:lb2+h1}); 29 %Closing Files 30 fclose(fout1); 31 fclose(fout2); 32 fclose(fin); FIGURE 5 Spreadsheet generated MATLAB computer code to extract two ERD data files. This code (Fig. 5) is very simplistic as it reads the source ERD data file, creates two new ERD files with individual headers and then extracts the relevant lines of data. Overall, an explanatory commentary of the MATLAB code is as follows: Lines starting with % are comments and allow simple reading of the code. Line 2 opens the source ERD data file. Lines 4 and 5 create and open new ERD files. Lines 6 and 7 provide instruction of how to read the file. Line 8 informs that the header is eleven lines long and data starts from line 12 in the ERD file. Lines 10 and 11 copy the first line of the original header to each of the new ERD files.

12 Evans and Arulrajah Lines13 to 17 write a new second and third line of the header to each of the new ERD files. The components of these lines are formatted and computed from within the ERD File Adjustment Spreadsheet. Lines 19 and 20 copy the remaining eight lines of header information (unchanged) to each of the new ERD files. Lines 22 to 25 assign the start and end line numbers of the sections of road profile data required for the new ERD files. These numbers are calculated from within the ERD File Adjustment Spreadsheet. Lines 27 and 28 write the road profile data required to the each of the new ERD files. Lines 30 to 32 simply close all the files. Once the start and end ERD files have been extracted, they need to be compared against equivalent reference profiles in order to determine the correction offset for each. Two methods available to determine the correction offset are: 1. Plot each ERD file against its equivalent reference profile using the RoadRuf (2) software package, preferably using a suitable Hi-Pass filter to highlight or exaggerate any defects in the pavement s profile and thereby provide a better match. The offset function in RoadRuf can be used to manually shift the profile forward or backward until it becomes visually aligned at the start of the file. 2. Plot each ERD file against its equivalent reference profile using the ProVAL (4) software package and apply the cross correlation function to calculate the optimum offset and correlation percentage. To increase the effectiveness of the cross correlation result, Karaminhas (6) recommended to first run the profiles through the IRI filter. The long wavelength component within the IRI filter helps ensure that the longitudinal positioning is nearly correct, while the short wavelength content of the IRI filter isolates rough spots and fine tunes the optimum offset position. However, when using this cross correlation analysis tool, it is important to remember that the offset is calculated based on the average correlation of the entire selected profile length and not on a single defect in the pavement s profile. This fact should be remembered when comparing very long lengths of road profile. After correct offsets have been determined and entered into the ERD File Adjustment Spreadsheet, the alignment of the road profile data within the spreadsheet is at a level of stage 1 accuracy. This means that the profilometer data has been corrected at its ends and rubber banded by adjusting the sample interval to match the correction offsets. Therefore, the data has had one level of corrective action applied to it. Stage 2 Synchronisation of the Road Profile ERD Data File Stage 2 type data refers to road profile data that has been rubber banded and synchronised at various intervals along the profile. A flowchart of this procedure is presented in Fig. 6. Essentially, it is very similar to the previous data correction flowchart except that corrections (offsets) are made at regular intervals to correct accumulated vehicle wandering errors.

13 Start STAGE 2 Input SRRS chainages where synchronisation is required Go to Stage 1 Code sheet and copy Matlab code to a text file Convert text file into a Matlab m file Run Matlab m file to extract ERD files for evaluation Let n = no. of ERD files created and i = 1 No Is n I? i = i + 1 Yes Evaluate the i th ERD file vs. equivalent reference profile and determine the correction offset to be applied If an offset cannot be determined due to reconstruction or maintenance, it is recommended that you estimate an offset correction by averaging the previous offset and the next offset values. Acceptable offset able to be determined? No Yes Enter offset correction values into ERD File Adjustment Spreadsheet i = i + 1 End

14 Evans and Arulrajah FIGURE 6 Procedural flowchart to synchronise road profile data and provide stage 2 type data. First, SRRS chainage locations are input into the ERD File Adjustment Spreadsheet where profile synchronisation is required. From experiences gained in this study, it is recommended that synchronisation be performed at approximately 5000 m intervals in order to achieve a 1% error. However, for winding roads or roads with very high roughness levels, this synchronisation interval should be reduced. A series of relevant ERD files are again extracted via the ERD File Adjustment Spreadsheet generated MATLAB code. These are compared against equivalent reference profiles and offsets are determined exactly the same as before, either using manual plotting methods with RoadRuf or by cross-correlation techniques with ProVAL. If reconstruction / rehabilitation or significant maintenance has been conducted since the previous road survey in the vicinity of a synchronisation point and an offset value cannot be established, the length of the ERD file used for comparison should be expanded to beyond the reconstruction length until a portion of the original pavement is present. Hence, allowing a comparison and synchronisation at a different location. If an offset value can be obtained within ten percent either side of the intended location (i.e. with 500 m of the intended synchronisation point for 5000 m intervals), then this offset value should be used. However, if a suitable offset value cannot be determined, the offset should be estimated by taking an average of the previous synchronisation offset value and the next synchronisation offset value. This assumes that the road profile data error is linear over the synchronisation interval. Once all offset values are input into the ERD File Adjustment Spreadsheet, synchronised stage 2 type data is available to be extracted. The spreadsheet can be set up to generate MATLAB code for any interval of ERD file required. For example, the author often uses individual 100 m and 300 m ERD files for evaluating road profiles using Power Spectral Density (PSD) analysis in RoadRuf as well as Wavelet analysis using MATLAB. Furthermore, 1020 m and 5020 m ERD files are used for calculating IRI and profile indices based on the four pole Butterworth filter. The odd 20m is at the start of the file and is used to intialise the filter (not reported) as recommended by Sayers (1, 7). CONCLUSIONS This paper has discussed possible sources of error when collecting longitudinal road profile data, which are largely associated with either (i) the profilometer vehicle operator approximating start and end SRRS chainage locations, and/or (ii) lateral tracking errors due to deviations of the profilometer vehicle from the true path. Furthermore, this paper has demonstrated that misaligned longitudinal road profile data can lead to poor quality road roughness indices where it is difficult to accurately and confidently evaluate roughness growth over time. A new and simple method has been developed to align and synchronise road profile data to better evaluate road roughness growth. A statistical comparison was completed between current roughness data available versus aligned and synchronised road profile data using this new method. Procedural flowcharts and example MATLAB computer code has also been included to help describe this new method.

15 ACKNOWLEDGEMENTS The authors would like to thank Ian Cossens from the Asset Management Group at VicRoads for providing access to the road asset management database for the State of Victoria as well as providing some of the raw road profile ERD data files used in this study. The first author would also like to thank Associate Professor Ali Bab-Hadiashar from Swinburne University of Technology for his assistance with programming in MATLAB. REFERENCES 1. Sayers, M. W. Profiles of Roughness. In Transportation Research Record: Journal of the Transportation Research Board, No. 1260, TRB, National Research Council, Washington, D.C., 1991, pp UMTRI. RoadRuf Software, University of Michigan Transportation Research Institute, Ann Arbor, Michigan, U.S.A., Karamihas, S. M. Development of Cross Correlation for Objective Comparison of Profiles, International Journal of Vehicle Design, Vol. 36, Nos. 2/3, 2004, pp Transtec Group. ProVAL: Profile Viewing and Analysis Software, Version 3, Austin, Texas, U.S.A., The Mathworks Inc. MATLAB: The Language of Technical Computing, Release 2010a, The Mathworks Inc., Massachusetts, U.S.A., Karamihas, S.M. Profile Analysis of the LTPP SPS-1 Site in Arizona, University of Michigan Transportation Research Institute, Report No. UMTRI , Ann Arbor, Michigan, U.S.A., Sayers, M.W. On the Calculation of International Roughness Index from Longitudinal Road Profile. In Transportation Research Board: Journal of the Transportation Research Board, No. 1501, TRB, National Research Council, Washington D.C., 1995, pp