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

APPENDIX E. JOINT FINDING

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:

• Narrow dips appeared in the profiles at many of the joints.
  
  
• Repeat measurements on a given section were rigorously synchronized, and the repeated presence of a narrow dip at a given location and in the left- and right-side profiles provided evidence of a potential joint instead of a crack or erroneous sensor reading.
  
  
• Narrow dips (i.e., negative spikes) that corresponded to joints appeared in a regular pattern that corresponded to the joint spacing.

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.

STEP 1: FILTER THE PROFILES

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

STEP 2: NORMALIZE

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.

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

STEP 3: SEEK THE NEGATIVE SPIKES

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.

STEP 4: WEED OUT LESSER SPIKES

Eliminate any spike within 0.82 ft of a deeper spike.

STEP 5: AGGREGATE ACROSS THE REPEAT MEASUREMENTS

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.

STEP 6: SORT THE LIST

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

STEP 7: CONSOLIDATE GROUPS OF NEARBY SPIKES

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:

• Step 7a: Establish an open group using the first item in the list.
  
  
• Step 7b: Promote the next item on the list to the current item. If the list is complete, close the final group.
  
  
• Step 7c: If the current item is no more than 1.97 inches downstream of the previous item, add it to the open group and return to step 7b.
  
  
• Step 7d: If the current item is more than 1.97 inches downstream, close out the current group. Open a new group with the current item as the first member. Return to step 7b.

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.

STEP 8: TRIM THE LIST

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.

STEP 9: EVALUATE EACH GROUP ON THE LIST

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.

STEP 10: DESIGNATE ONE OF THE GROUPS AS A JOINT LOCATION

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.

STEP 11: SEEK OTHER JOINTS DOWNSTREAM

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.

STEP 12: SEEK OTHER JOINTS UPSTREAM

Repeat step 11 in the reverse direction.

DISCUSSION

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.