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Publication Number: FHWA-HRT-12-068
Date: December 2012


Curl and Warp Analysis of The LTPP SPS-2 Site in Arizona


The slab-by-slab analysis required careful synchronization of repeat profile measurements and identification of joint locations within a tight tolerance. The joint-finding strategy depended on the following properties of the profile data from each test section:

The strategy for assembling a list of joint positions exploited the repeated presence of negative spikes at the same location. Each group of five profile measurements from a given visit of a given section formed a set, including both the left- and right-side profiles. For each set of 10 profiles, a list of joint positions for the entire set was found using the steps described in this chapter.


High-pass filter each profile with an anti-smoothing moving average filter using a base length of 0.82 ft.


Normalize each filtered profile by its standard deviation. Figure 71 provides an example trace that has been high-pass filtered and normalized. The figure shows the trace produced after application of steps 1 and 2 to a profile from visit 15 of section 0215.

This figure shows a profile after application of steps 1 and 2 over the first 200 ft of the section. The vertical scale shows normalized left elevation from –15 to 5. The horizontal scale shows distance 0 to 200 ft. Most of the trace includes content between 2.5 and -2.5, such that the trace crosses through 0 many times. Narrow dips appear in several locations about 15 ft apart, which are 3–11 units deep on the plot. Four additional narrow dips appear on the plot between 3 and 4 units deep that are not part of the 15-ft spacing pattern. All of the dips are less than 2 ft wide. A horizontal reference line at a normalized left elevation value of -3 shows which dips would be identified in step 3. The line is labeled “threshold.”

Figure 71. Graph. High-Pass Filtered, Normalized Profile.



Search the normalized trace. List the longitudinal position of points with a value below -3. This criterion produces a list of longitudinal positions with regular spacing for the trace in figure 71, with some extraneous locations. Extraneous locations often appeared in the list at transverse joints and in multiple locations along distressed slabs.

The threshold value of -3 was used throughout the experiment. The appropriate threshold value for other experiments depends on the length and depth of the gaps at the joints and on the profiler height-sensor footprint, low-pass filtering, and recording interval.


Eliminate any spike within 0.82 ft of a deeper spike.


Assemble the negative spikes for the left and right profiles of all five repeat measurements into a single list. For sections with skewed joints, offset values of longitudinal position for the left side by 0.919 ft. Sections 0262–0265 included skewed joints.


Sort the list of negative spikes in ascending order of longitudinal position.


Consolidate any set of closely spaced spike positions into a group. Merge spike positions for which no gap larger than 1.97 inches exists between consecutive values. For each group, record the range of longitudinal position values and the number of spikes included in the group. To do this, apply the following steps:

This procedure often produces groups that cover a greater longitudinal distance than 1.97 inches but without any gaps within the group greater than that.

Besides the range, record the average value of longitudinal position within each group. These values provide a basis for calculating the actual slab length in subsequent analyses.

On visit 04 of section 0264, the threshold gap value was adjusted to 3.15 inches.


Eliminate all groups with a count below a given threshold. The threshold value that produced the proper results varied from 2 to 6. Because the joint locations were derived using sets of 10 profiles, this meant retaining groups for which 20–60 percent of the profiles contributed spikes. The most common threshold value was 20 percent. Table 31 provides sample output of step 8 for visit 15 of section 0215.

Table 31. Negative Spike Groups from Visit 15 of Section 0215.

Range (ft) Average Position (ft) Number of Spikes Compatibility Score
Start End
-21.04 -20.84 -20.90 10 35
-10.83 -10.70 -10.76 2 2
-6.08 -5.82 -5.92 10 35
8.94 9.13 9.07 7 35
24.02 24.22 24.15 10 35
38.98 39.18 39.08 10 35
54.00 54.20 54.11 8 35
69.02 69.22 69.13 10 35
82.16 82.16 82.16 2 5
83.98 84.17 84.10 8 35
98.93 99.13 99.05 10 35
104.01 104.07 104.04 2 0
113.96 114.15 114.08 9 35
129.04 129.17 129.13 8 35
144.00 144.13 144.08 10 35
158.95 159.15 159.08 8 35
173.98 174.17 174.09 10 35
189.00 189.19 189.10 10 35
204.02 204.08 204.06 5 35
219.04 219.23 219.14 9 36
233.86 234.06 233.97 10 36
248.95 249.08 249.01 9 36
263.78 263.97 263.88 9 36
278.80 278.99 278.91 10 36
293.82 294.01 293.93 7 36
308.77 308.97 308.89 10 36
323.80 323.93 323.88 9 36
338.82 339.01 338.93 10 36
353.84 353.97 353.91 7 36
368.79 368.99 368.92 10 36
383.88 383.94 383.91 8 36
398.84 399.03 398.92 9 36
413.79 413.92 413.86 10 36
420.36 420.42 420.38 3 3
428.81 428.94 428.88 10 36
436.49 436.62 436.53 3 5
443.77 443.90 443.84 10 35
458.85 458.99 458.91 10 36
473.81 473.94 473.86 10 36
479.79 479.79 479.79 2 5
488.77 488.90 488.85 8 36
495.27 495.33 495.29 3 3
503.79 503.98 503.88 9 36
505.41 505.41 505.41 2 2
510.42 510.55 510.49 4 3
512.05 512.24 512.10 5 3
515.17 515.43 515.28 5 2
518.55 518.87 518.74 9 19

Note: Bold row indicates the group designated as joint location. Italic rows indicate the groups left out by steps 11 and 12.



Calculate a compatibility score for each surviving group. To do this, seek other groups that appear at the expected distances from the group under evaluation within an acceptable tolerance, given the expected saw cut spacing. The tolerance for compatibility was set at 2 percent of the average expected saw cut spacing. (This was 0.27 or 0.30 ft, depending on the section.)

The compatibility score is the number of compatible groups found within the rest of the list. For example, the expected saw cut spacing on section 0215 was 15 ft. The first group in table 31 produced a compatibility score of 35, because 35 other groups appeared within the list that were an integer multiple of 15 ft away, to within 0.3 ft.

Sections 0213–0224 included slabs that were all about 15 ft long. However, the saw cuts in sections 0262–0265 appeared in intervals of about 12, 14, 13, and 15 ft, and the saw cuts in sections 0266–0268 appeared in intervals of 15, 13, 15, and 17 ft. Each group was evaluated four times on sections with irregular joint spacing, once for each of the possible starting points within the pattern. The algorithm retained the highest of the four scores.


Designate the group with the highest compatibility score as a joint. If multiple groups share the highest compatibility rating, select the joint that is farthest upstream. For visit 15 of section 0215, a joint was selected that produced negative spikes from 219.04 to 219.23 ft from the start of the profile.


Seek the adjacent joint in the forward direction. Designate the adjacent joint as the group with the highest compatibility score that appears between the shortest expected joint spacing for the section (minus 6 percent of its length) and the longest expected joint spacing for the section (plus 6 percent of its length). Each time a joint is found, seek the next joint using the same criteria until the end of the section is reached.

The search for the next joint location covered a range of 14.1–15.9 ft from the current joint location on sections 0213–0224; the range was 12.72–15.90 ft on sections 0262–0265; and the range was 13.79–18.02 ft on sections 0266–0268.


Repeat step 11 in the reverse direction.


This procedure produced a list of joints for each set of five repeat measurements. However, the locations were expressed as a range rather than a precise value. For example, the joint locations listed in table 31 include spike groups that cover a range of 0.130–0.325 ft (2 to 5 times the profile recording interval). The range for spike groups in this experiment typically covered a distance of less than 0.33 ft.2

The range at each joint proved to be important in the subsequent slab-by-slab curve fitting analysis, where the profile at each end of the slab was masked over the range where the spikes were detected plus a 0.082-ft-long margin of safety. The average position within a group of spikes was used at each joint to provide slab end locations for calculating overall slab length.

The strategy of searching for narrow dips was successful in all of the profiles after visit 02 because profile data were recorded at a short interval (0.77 or 0.98 inches) and measured using a height sensor with a footprint with a longitudinal dimension equal to or less than the gap at the joint.(17) The joint-finding strategy described here is not suited for profiles measured with the K.J. Law Engineers DNC 690. As a result, the joint locations found for visit 03 of each section were also used in the analysis of visit 01 and visit 02. This practice was successful because the synchronization was very consistent between visits and because the longer recording interval (6 inches) in visits 01 and 02 reduced the requirement on precision of the joint locations.

2 Of the 10,539 joints, 10,200 covered a range of 0.33 ft or less.


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