Incorporating Slab/Underlying Layer Interaction into the Concrete Pavement Analysis Procedures (2017)

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E-1 APPENDIX E ANALYSIS OF PROFILE DATA USING EMPIRICAL MODE DECOMPOSITION E.1. Introduction It has been hypothesized that JPCP slab profile data can be used to examine the effect of base type (and consequently slab-base interaction) on built-in curl. As built-in curl is accounted for in the MEPDG for rigid pavement projects through the built-in temperature gradient parameter ∆𝑇, it is possible that ∆𝑇 can be also used to characterize PCC slab/base interaction. The study investigated the use of profilometer data to characterizing slab-base interaction This appendix documents that effort and includes an application of the developed profilometer analysis tool to available LTPP project profilometer data from the SPS-2 and GPS-5 experiments. The object of the EMD analysis was to identify if information on built-in curling could be inferred from profilometer data. However, in spite of promising initial results, as briefly discussed in the main body of the final report, the research team was not able to extract conclusive built-in curl information from EMD analysis. E.2. LTPP profilometer data The LTPP database contains pavement performance information, including raw profilometer data, from over 2400 in-field pavement sections in more than 900 locations throughout North America. The profilometer data indicates profile elevation (in millimeters) in both wheel paths of the pavement. Using this profilometer data, FHWA generated IRI analysis, which is also stored in the LTPP database. This study utilized raw profilometer data from the SPS-2 and GPS-5 experiements. E.2. Literature review Previous research has attempted to extend the use of profilometer data past roughness and into slab geometry estimation. Byrum (2000) analysed LTPP pavement section data using an algorithm to estimates slab curvature from a subset of data points within the profilometer data for one slab of one pavement section. Thus, the analysis uses a curated set of profilometer data, and not the direct road profile data. The analysis to estimate slab curvature was later extended using statistics (Byrum, 2009). While the procedure described in Byrum is capable both locally (on a slab-by-slab basis) and globally (in a series of sections considered together), the revised algorithm can be potentially complicated or invalidated by errant data or by exaggerated texture data (i.e. particularly “rough” patches that may obscure slab curl), and thus it cannot be directly applied to road profilometer data. Other literature reviewed, including Chang et al (2008), uses a “pseudo-strain gradient” (PSG) approach to account for the curvature of a slab profile (and for a pavement section in a gross average of all slab profiles). The authors hypothesize the idea that PSG is dependent on the thermal and shrinkage strains in the slab. The challenge of the tool initiated in Chang et al (2008) and later developed by Karamihas and Senn (2012) is that, much like Byrum, the tool involves conditioning of the profilometer data prior to analysis. Furthermore, the PSG analysis imposes joint locations upon the data to then later fit slab deflection profile curves to the conditioned profile data. Thus, the PSG method is nuanced and relies upon time-intensive manipulation of the raw data. However, members of the research team had participated in previous research that had focused on the use of profilometer data to determine slab curl in JPCP. That research developed

E-2 an automated pavement analysis method for real-field profiles that would allow for accurate, consistent analysis of pavement sections or slabs. This method is based on the empirical mode decomposition (EMD) process contained within the Hilbert-Huang Transform (HHT), based in part on previous applications conducted by Adu-Gyamfi et al. (2010) and Attoh-Okine et al. (2006). Furthermore, EMD has been used for similar analysis on LTPP data and reported on in Franta (2012). EMD uses an empirical transformation of signal data, known as a Hilbert-Huang Transform, to decompose raw data into intermediate mode functions, which represent physical artifacts in the data such as texture and slab can profile due to curl. Specific detail on this method of analysis is provided in the following subsection. E.3. Empirical mode decomposition process of the Hilbert-Huang Transform The following subsections summarize the empirical mode decomposition (EMD) process applied to profilometer data in this study to estimate slab curl. E.3.1. Empirical mode decomposition process A sifting process can be applied to profilometer data to filter and identify one or more intrinsic mode functions (IMF) that describe physical features present in the data. The process used in this study is conducted using Hilbert-Huang transformations of the original profile data. Equation 1 from Huang (2005) describes the basic decomposition of any profile 𝑦(𝑥) =∑𝑐𝑗(𝑥) + 𝑟𝑛(𝑥) 𝑛 𝑗=1 1 where y is the profile elevation as a function of position x; cj are IMFs within the data set; and rn is the residue after n total IMFs have been removed. In the case of pavement profile data, some of the IMFs are due to noise and/or surface texture, some are due to slab curl, and the rest correspond to base trends in the pavement.  IMFs associated with noise and surface texture have high frequency (short wavelengths) and small amplitudes. The peaks of these waves tend to appear sharp and pointed.  IMFs associated with slab curl (or slab profile) are characterized by lower frequencies, higher amplitudes, and longer wavelengths.  Base trend IMFs display the lowest frequencies and longest wavelengths of the three general types to result from the filtering process. The process to determine the IMFs from raw profilometer data is automated in a MATLAB program created for this research. The first step toward identifying an IMF is to shift the profilometer data about the y-axis to prepare for further analysis. First a simple linear regression is performed on all data points in the profile using built-in MATLAB functions. This process is illustrated in Figure E-1 using profilometer data obtained from the Minnesota Road Research facility (Franta, 2012).

E-3 (a) (b) Figure E-1. (a) Raw profilometer data and (b) line of best fit for raw data imposed over raw data [from Franta (2012)] Most points in the raw profile, yorig, do not lie along the line of best fit, yfit, and therefore deviate from the line of best fit according to 𝑦𝑠ℎ𝑖𝑓𝑡 = 𝑦𝑜𝑟𝑖𝑔 − 𝑦𝑓𝑖𝑡 2 The deviation, yshift, is shown in Figure E-2b relative to the original profile data. (a) (b) Figure E-2. (a) Original profile data, yorig, and (b) the deviation, yshift, from the linear regression, yfit, for the original profile data [from Franta (2012)] The shifted, zeroed profile, yshift, is then analyzed to identify local extrema (Figure E-3a). The process described in Franta (2012) was modified for this research in two regards:  The endpoints in the raw data set are treated as either a minimum or maximum to ensure that all results were properly interpolated. Doing so reduced errors in the subsequent steps (specifically, extrapolation of the data set using cubic splines). 0 20 40 60 80 100 120 140 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 Profile Length (inches) D e fl e c ti o n ( in c h e s ) 0 20 40 60 80 100 120 140 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 Profile Length (inches) D e fl e c ti o n ( in c h e s ) 0 20 40 60 80 100 120 140 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 Profile Length (inches) D e fl e c ti o n ( in c h e s ) 0 20 40 60 80 100 120 140 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Profile Length (inches) D e fl e c ti o n ( in c h e s )

E-4  The MATLAB procedure to identify local to eliminate errors due to “plateaus” in the data, i.e., local regions in which extrema were repeated for neighboring indices. These plateaus also caused issues in the later creation of cubic splines. The identification of maxima and minima allows for the creation of an upper envelope set that will lead to an upper envelope function, U(x), and a lower envelope set leading to the function, L(x). Given the point-wise envelopes, MATLAB built-in functions are used to determine cubic polynomial splines to describe U(x) and L(x) (Figure E-3b). (a) (b) Figure E-3. (a) Identifying local maxima and minima in yshift and (b) computed U(x) and L(x) in yshift [from Franta (2012)] A running mean, m, is calculated using the upper- and lower-envelopes, where 𝑚1(𝑥) = 𝑈1(𝑥) − 𝐿1(𝑥) 2 3 Once m1(x) has been calculated using the shifted profile, yshift(x), the first component, h1, can be expressed as ℎ1(𝑥) = 𝑦𝑠ℎ𝑖𝑓𝑡(𝑥) − 𝑚1(𝑥) 4 Thus the indices on m, U, L, and h correspond to the calculated component. The first component in this case, h1, is shown in Figure E-4a. For a resulting component hi(x) to be classified as an IMF, ci(x), two criteria must be satisfied: 1. hi(x) must display symmetry of the upper and lower envelopes (Ui and Li, respectively) with respect to zero. More directly, mi(x) must be zero within a certain tolerance value, Ztol. The computational efficiency of the MATLAB program relies upon a reasonable value for Ztol. The analysis conducted in this project varied from Franta (2012) in the use of values of 0.0001 for Ztol. Naturally, larger values of Ztol will result in more IMFs filtered from the profile data, and smaller values of Ztol will result in fewer.) 0 20 40 60 80 100 120 140 -0.1 -0.05 0 0.05 0.1 0.15 Profile Length (inches) D e fl e c ti o n ( in c h e s )

E-5 2. The number of critical points and zero crossings must be the same or differ by one (Huang, 2005). Although Figure E-4a exhibits the correct number of extreme points and zero crossings, the symmetry of the upper and lower envelopes has not been met as shown in Figure 2.6. Consequently, the sifting process continues for this example to develop a new component that satisfies the two conditions and qualifies as the first IMF, c1(x). The process is iterative; thus, the above maxima/minima and spline operations performed on yshift are performed on h1 to obtain m1,1(x), the difference of the envelopes on the h1(x) set, and eventually one recovers ℎ1,1(𝑥) = ℎ1(𝑥) − 𝑚1,1(𝑥) 5 This process is repeated as many times as required to obtain a component that satisfies the criteria for an IMF. For example, for this example 149 iterations were required to obtain c1(x), where 𝑐1(𝑥) ≡ ℎ1,149(𝑥) = ℎ1,148(𝑥) − 𝑚1,149(𝑥) 6 The first IMF, c1, is shown in Figure E-4b. Within the domain, c1 has twenty-seven zero crossings and twenty eight critical points. Furthermore, c1 displays symmetry of the upper and lower envelopes with respect to zero. (a) (b) Figure E-4. (a) First component, h1, and (b) first IMF, c1, of the example data set [from Franta (2012)] Once the first IMF, c1(x), is recovered, the first residue, r1(x), can be calculated, where 𝑟1(𝑥) = 𝑦𝑠ℎ𝑖𝑓𝑡(𝑥) − 𝑐1(𝑥) 7 As alluded to above, the residue will possess characteristics of the original profile but will carry less information, or be “smoother,” than the original due to the removal of the first IMF, c1, in the signal. The first residue, r1(x), for this example is shown in Figure E-5a. The process outlined above will now be repeated using r1(x) in place of yshift(x) from the original profilometer data. 0 20 40 60 80 100 120 140 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Profile Length (inches) D e fl e c ti o n ( in c h e s )

E-6 (a) (b) Figure E-5. (a) First residue, r1, and (b) fourth residue, r4, of the example data set [from Franta (2012)] The iterative sifting process of calculating components, identifying IMFs, and determining residues a given profile data set varies based on factors such as the profile length, the magnitude of elevations in profile, and natural noise levels present within the data. The sifting process continues to extract IMFs until a residue is uncovered that has three or fewer critical points. On this basis, in this example the sifting process was terminated after the fourth residual (illustrated in Figure E-5b). Finally, the identified IMFs and the final residue can combined to verify that the sifting calculations were performed correctly. The original profile, shown in Figure E-6, should be obtained when the IMFs and final residue are added together. Figure E-6. Sum of all IMFs and final residue from the original profile data set [from Franta (2012)] 0 20 40 60 80 100 120 140 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Profile Length (inches) D e fl e c ti o n ( in c h e s )

E-7 E.3.2. Modifications to software used to process profilometer data While minor modifications to the EMD analysis process were made, larger modifications were made to the MATLAB program to analyze profilometer data. The version described by Franta (2012) was used on a case-by-case basis (one profile pass analyzed at a time). To address the project needs, case-by-case analysis is too burdensome. Thus, the MATLAB program was automated to process profilometer data specified in an input file. Thus the program is more suitable for the analysis of LTPP profilometer data. Tables summarizing all outputs from the MATLAB program for all LTPP sections analyzed are presented in E.9. Summary tables of EMD analysis of SPS-2 and GPS-5 sections Table E-6 (SPS-2) and Table E-7 (GPS-5). E.4. Processing profilometer data to recover slab profile The following steps illustrate the analytical process applied to raw LTPP profilometer data using the MATLAB program developed by Franta (2012). E.4.1. Step One: Apply EMD to the raw data for a given profilometer pass To begin, the raw profilometer data is prepared for each date and the runs associated with each date for a given section. The application of the EMD process requires only the LTPP profilometer data in its raw, unformatted state; no pre-processing is required. Figure E-7 illustrates the raw data associated with three passes of the profilometer on LTPP Section 37-0201 on March 30, 1994. Figure E-7. Raw, uninterrupted elevation data for LTPP Section 37-0201 from three concurrent passes of the profilometer for the same location The raw data (illustrated in Figure E-7) is queried from the LTPP database for all relevant sections and passes into an Excel data file, where each raw dataset is represented columnwise

E-8 and given a unique identifier for convenience. A screenshot of the MATLAB program, as applied to a single profilometer pass dataset, is presented in Figure E-8 to illustrate the automated process. Figure E-8. User interface for the EMD program As noted above, the IMFs recovered from EMD analysis can have physical analogues that represent pavement texture or slab curl. The next step of the process is to analyze the IMFs for the input profilometer data, where the output file in an Excel file. E.4.2. Step Two: Select an IMF of interest from the EMD results After applying EMD to raw data from a profilometer pass, one will find that the initial profilometer signal has been decomposed into a series of IMF and associated residues (which, taken in sum, would allow one to recover the original signal). The objective at this stage of the analysis is to determine which IMF represents the slab profile. This determination is made using analysis of each IMF and properties of the pavement associated with the given profilometer dataset:  The MATLAB software automatically produces summary analysis data of each IMF. The most important product of this analysis is an estimate of the periodicity of the data; in this case, the value represents the average distance between so-called peaks (local maxima) in the data set.  The joint spacing of the LTPP section associated with each section/pass subset is included in a separate Excel worksheet. The selection of IMFs that might potentially resemble slab profile is then automated using a Visual Basic macro that is embedded in the Excel worksheet with the section particulars (including joint spacing, as mentioned previously). This macro uses the output set of IMFs for each section and pass, the periodicity of each IMF within the section/pass subset of the results, and the joint spacing to identify an IMF for each section that may correspond with slab profile.

E-9 The identification itself is based upon an arbitrary difference between the LTPP section joint spacing and the average period for a given IMF: for this analysis, a tolerance of 15 inches is used (meaning, IMFs whose average period is within 15 inches of the joint spacing are identified as being of interest). For some section/pass combinations, it may be than no IMF has periodicity similar to the section joint spacing, in which case that dataset is excluded from further analysis. Thus, for a section with joint spacing of 15 feet, the selection process would attempt to locate an IMF with a mean period of between 165 and 195 inches. Figure E-9 illustrates three selected IMFs for three passes that could potentially represent slab profile. Figure E-9. Interpreted profile (from IMF) for three passes of LTPP Section 37-0201 using EMD program There are a few important notes on the selection process. First, it is clear that the selection process is interpretative and based upon the assumption that the IMF represents some physical feature of the pavement. As has been discussed in previous reporting, the authors feel this assumption is valid given existing literature on the topic. However, it is true that in some cases, the slab profile may not be identifiable in the decomposed profilometer signal. Another important note, then, is that it is much easier to identify an IMF corresponding to slab profile in those sections that have exaggerated curl/warp. This observation is in keeping with sentiments expressed in other research on recovering slab profile from profilometer data using other methods, including Karamihas and Senn (2013). If the slab is not particularly deformed in curl or warp, then it will be difficult to detect the slab profile in the decomposed profilometer data. E.4.3. Step Three: Generate statistics based on the identified IMF After the second step in the process, the combination of the MATLAB program and the Visual Basic macro to select IMFs will generate a number of slab profiles. As noted previously, this may not necessarily result in a selected IMF for each section/pass combination; in some cases, a

E-10 slab profile may not be evident in the dataset. Thus, at this point a user could examine the data on a pass-by-pass basis. As noted earlier, the method was developed for the analysis of large sets of data, given that it is not feasible to examine by-hand each decomposition of profilometer datasets when one section alone may have ten passes per date over as many as 18 years of regular monitoring. Thus, the modification of the EMD process included the creation of statistics for the IMFs associated with each section/pass combination (i.e., profilometer dataset) and finally a summary statistic for each SPS-2 section and its associated decomposed profilometer data. The developed statistics to examine EMD analysis in aggregate use the standard deviation of the amplitude of the IMF of interest by section. To summarize:  Assuming the section joint spacing and a tolerance value for joint spacing, the MATLAB program evaluates all profilometer passes for the section and determines the IMF with periodicity corresponding to joint spacing.  The analysis uses the standard deviation of the identified IMF to capture the exaggeration in the profile. This value is averaged across all passes on a given date to provide a rough estimate of the slab profile. The estimate of slab profile is by no means ideal. The use of standard deviation to represent the profile, whether for a single profilometer pass or as an “average” of multiple passes, is not optimal. However it is convenient for processing thousands of raw profilometer files and is adopted for this effort. E.5. Example application of EMD analysis to a single LTPP section The analysis initially focused on profilometer data from LTPP SPS-2 sections in Arizona, after Karamihas and Senn (2012). These sections are summarized in Table E-1, with the initial column indicating the corresponding profile analysis in Figure E-10. The section data was processed using EMD to develop slab profiles for each section. Note that each of the subfigures of Figure E-10 also contain raw data from one of the three passes shown on each figure. The raw data is indicated in a dotted line and whose abscissa values for elevation are indicated at right. In all subfigures, the ordinate axis refers to distance in inches from the origin of the profilometer pass (where the origin is identical for each pass). Table E-1. LTPP SPS-2 sections in Arizona with profilometer data used for EMD analysis Figure SHRP ID DATE TIME RUNS PCC THICK (mm) BASE TYPE LANE WIDTH (m) JOINT SPACING (ft) 4a 04-0214 03/05/1995 11:21:01 2, 5, 6 203 AGG 3.66 15 4b 04-0214 01/25/2010 16:17:16 2, 6, 8 203 AGG 3.66 15 4c 04-0223 03/05/1995 11:21:01 5, 8, 9 279 PATB 3.66 15 4d 04-0223 01/25/2010 17:37:01 1, 3, 5 279 PATB 3.66 15 Analysis of the subfigures in Figure E-10 show that the MATLAB program, in applying the EMD analysis to the profilometer data, is capable of extracting profile characteristics functions having periods close to the joint spacing of the evaluated pavement. These functions are relatively repeatable from run to run, especially if the amplitude is significant. Therefore, it is reasonable to assume that these functions characterize the curling profile. On the other hand, comparisons of Subfigures a and c and Subfigures b and d in Figure E-10 show that that although

E-11 Section 04-0214 exhibited slightly higher amplitudes for the same day of testing, it is not clear if a significant difference can be attributed to base type. This initial analysis motivated the research team to analyze profiles from the entire SPS-2 experiment to enable a comparison of the profiles of the pavements whose design differs only in base type.

E-12 (a) (b) (c) (d) Figure E-10. EMD analysis of two Arizona SPS-2 sections on two dates

E-13 E.6. EMD analysis of LTPP profilometer data from the SPS-2 experiment The discrepancy between observed and predicted MEPDG cracking for LTPP SPS-2 sections prompted the research team to conduct its initial analysis of profilometer data from LTPP SPS-2 sections. This study focuses on a special subset of the LTPP database: the SPS-2 experiment, which was established by FHWA to investigate the performance of new rigid pavements under a controlled number of design variables, including climate, slab thickness, base type, and lane width. The original SPS-2 sites were constructed between 1992 and 1997 (Jiang and Darter, 2005). These sections were to be regularly monitored, and pavement data were stored in the LTPP database for later analysis. In addition to the original experimental SPS-2 sections, supplemental new construction rigid pavements were created by states for inclusion in SPS-2, and these sections were also monitored as a part of LTPP. In addition, the analysis utilized the FHWA report produced by Jiang and Darter (2005) on the SPS-2 construction and performance to eliminate any sections with questionable construction or early performance issues. This was to ensure that, to the best extent possible, the LTPP SPS-2 profilometer data and subsequent analysis was focused on sections where slab profile could be recovered, if it was present in the data. As of 2012, the experimental and supplemental SPS-2 sections accounted for more than 7360 profilometer observations (conducted between 1992 and 2012) in the LTPP database. The authors subjected all available profilometer data to analysis using the EMD method described above. For each section, in addition to developing an average of standard deviations for each date, additional summary statistics on the average standard deviation over the first year, the last year, and for the entire duration of observations was determined. Given this analysis, global perspectives on the SPS-2 profiles can be obtained. For instance, Figure E-11 illustrates the change in profile over the life of the SPS-2 sections evaluated, where the first profile is plotted against the last for each section. A line of parity is included in the figure to show that for the majority of sections, the profile became more exaggerated over time. Figure E-11. Slab profile change over time, in terms of average standard deviation from flat-slab condition, for SPS-2 sections

E-14 The slab profile information resulting from the EMD analysis can be more beneficial when considered with performance data from the LTPP database. E.6.1. Slab Profile and the Performance of SPS-2 pavements The application of the EMD method to the full SPS-2 profilometer data resulted in an extensive database. A first step to restricting this dataset, to improve further analysis, was to restrict the research focus to SPS-2 sections that had at least 10 profilometer observations over a minimum of 6 years. In addition, the authors eliminated from consideration any sections with questionable construction or early performance issues as reported by FHWA [16]. The imposed restrictions focused the discussion on 142 SPS-2 sections, which had an average of 47.0 observations over 13.8 years per section. (The 61 SPS-2 sections not considered for discussion had an average of only 10.1 observations over 1.8 years.) To evaluate the performance of the sections under discussion in terms of slab curvature, the IRI analysis in the LTPP database was consulted. After reviewing the IRI analysis, a few sections (26-215 and 4-262) were excluded from consideration as outliers due to the extremity of their measured IRI relative to that of other sections. An initial, global view of the slab profile and IRI data is shown in Figure E-12. For the first and last dates of profilometer observation, the standard deviation of the slab profile on that date is plotted against the measured IRI for that date in the LTPP database for all SPS-2 sections considered. The scatter of the data from the first measurement to the last in Figure E-12 suggests first that both the measured IRI increased, as would be expected, and the slab profile became more extreme, as was illustrated in Figure E-11. In addition, a linear regression equation for both datasets (the equation for which is included in each subfigure), suggests that the increase in both IRI and slab curvature trends similarly, as the slope, intercept, and R-squared values for the line of fitness have similar values. Figure E-12. Slab profile and IRI observations for all SPS-2 sections with six or more years of profilometer monitoring for first observation (at left) and last observation (at right) Given the design of the SPS-2 experiment, however, the relationship between slab profile and performance can be investigated more closely. The major focuses of the SPS-2 experimental

E-15 design are investigated in terms of the slab profile information obtained through the use of EMD analysis. Those focuses are as follows, with parenthetical abbreviations corresponding to figure legends. Base type: Granular (AGG), cement-stabilized (LCB), or asphalt-stabilized (PTAB) PCC slab thickness: 8 or 11 inches Climate: DF (dry, freeze), DNF (dry, no freeze), WF (wet, freeze), WNF (wet, no freeze) Lane width: 12 or 14 feet Lane width is important in this particular study as it has an obvious effect on slab profile. Thus the ride performance of each of the other factors (base type, slab thickness, and climate) is considered for sections with either 12-foot or 14-foot lane width. E.6.2. Performance of SPS-2 sections by base type relative to slab profile Figure E-13 illustrates the effect of slab profile on pavement performance by base type. The slab profile is represented by the average standard deviation for all calculated profiles from the LTPP profilometer data per section. Thus it provides a general estimate of the severity of curvature for a given slab. The performance is represented along the y-axis in Figure E-13 by the increase in roughness from the first to last observation for a given section. Thus the figure is designed to investigate the possibility that severity in slab profile can be correlated with an increase in IRI over service life. Figure E-13 focuses on this investigation for the three general base types used in the SPS-2 sections, and each subfigure includes linear regression equations to summarize each possible correlation for performance and slab curvature.

E-16 (a) (b) Figure E-13. Effect of slab profile on smoothness in the SPS-2 experiment by base type for (a) 12-foot lane widths or (b) 14-foot lane widths Figure E-13a shows that for sections with a 12-foot lane width, there is a fairly strong correlation between the performance of sections with granular bases and the slab profiles of those sections (R-squared of 0.6084). For the 12-foot granular sections, an increase in slab profile correlates strongly with an increase in pavement roughness. This relationship also holds for 14-foot granular sections, although the correlation is less strong (R-squared of 0.2146). For other combinations of lane width and base type, there are no other apparent relationships. A possible explanation is that for the same conditions, either the contribution of the slab profile to performance is less severe for stabilized bases or the profile itself is less extreme for stabilized bases.

E-17 E.6.3. Performance of SPS-2 sections by slab thickness relative to slab profile Figure E-14 illustrates the effect of slab profile on pavement performance by slab thickness, where the y- and x-axes are identical to those of Figure E-13. In both subfigures of Figure E-14, one can identify in thin 12-foot and 14-foot wide sections a correlation between pavement performance and slab profile (R-squared of 0.3232 and 0.3358, respectively). For thick sections this correlation is not present. (a) (b) Figure E-14. Effect of slab profile on smoothness in the SPS-2 experiment by PCC thickness for (a) 12-foot lane widths or (b) 14-foot lane widths E.6.4. Performance of SPS-2 sections by climate relative to slab profile Figure E-15 illustrates the effect of slab profile on pavement performance by climate, where the y- and x-axes are identical to those of Figure E-13. In both subfigures of Figure E-14, one can

E-18 observe that for 12-foot and 14-foot wide sections located in wet, freeze conditions, there exists a correlation between pavement performance and slab profile (R-squared of 0.3288 and 0.2478, respectively). For other climates and lane widths no other meaningful correlations exist. The observed relationship in the wet-freeze climate may be related, in part, to the presence of frost heave and other freeze-thaw effects not observed elsewhere. (a) (b) Figure E-15. Effect of slab profile on smoothness in the SPS-2 experiment by climate for (a) 12-foot lane widths or (b) 14-foot lane widths E.6.5. Identifying performance trends in SPS-2 data While the correlation of slab profiles (as determined using EMD analysis) and pavement performance in the LTPP database did not uncover any large, overwhelming performance trends by each experimental variable in the SPS-2 experiment, the correlation of performance and slab

E-19 profile did point to some trends that were supported by non-trivial statistical measures. For pavements with aggregate bases, it was found that the severity of slab curl was strongly correlated with an increase in roughness over the pavement life. Likewise, a mild correlation between curl and performance was observed for both thinner pavements (8 inches) and pavements in wet-freeze climates. The identification of these relationships is a first step to better quantifying the effects of slab curl on pavement performance on a large scale; previous efforts in this regard were restricted to a case-by-case basis, which, although valuable, has limits. Finally, there exist many possibilities for the continuation of this research. As noted previously, the standard deviation of the intrinsic mode function of interest is an admittedly dense metric to quantify slab profile. Its limitations were accepted in this research in exchange for the ability to examine thousands of datasets relatively quickly. However, future work might develop a new metric that better characterizes the amplitude of the IMF associated with slab profile and the regularity of the profile within the IMF. In addition, the application of the EMD analysis was limited to LTPP SPS-2 profilometer data no later than 2012. Future work might include new profilometer data; in so doing, new or previously latent trends may be identified. E.6.6. Case study: Inferring design properties from profilometer data Given the design assumptions of the NCHRP 20-07 Task 327 study, discussed in the main body of the final report, one aspect of the research effort focused on examining the permanent curl/warp effective temperature difference parameter (T) assumed by T327 for its Pavement ME simulations. The motivation for this investigation was to determine if the comprehensive EMD analysis conducted in the 1-51 project work on LTPP profile data could be used to identify sections where T could be varied from its default AASHTO value for design purposes. Table E- 2 through Table E-5 present a comparison of the EMD results for LTPP SPS-2 sections assumed by T327 to have either default values of T (summarized in Table E-3 and Table E-5 for 12- and 14-foot lane width sections respectively) or non-default values of T (whose 12- and 14-foot sections are summarized individually in Table E-2 and Table E-4, respectively). A comparison of statistics for the standard deviation in elevation for the IMF of interest – the parameter associated in this analysis with the slab profile, as detailed in previous reporting – suggests that those sections which were judged to require a modified T in T327 did not, in aggregate, have a profile any more deformed (i.e. curled/warped) than those profiles associated with sections that T327 assigned the default T. This observation is in keeping with previous EMD profile analysis in the 1-51 reporting, which found that, with few exceptions, similar slab geometries occurred in SPS-2 sections regardless of base type or other design properties. This analysis casts further light on the difficulty of associating the slab profile, and actual field data depicting that profile, with the design parameter T. Later analysis of MEPDG simulations under Subtask 5.3 examines other complications in T, particularly the sensitivity of the MEPDG performance predictions to changes in T relative to the sensitivity of the MEPDG to changes in parameters characterizing slab-base interaction.

E-20 Table E-2. IMF profile results for the six EMD-analyzed SPS-2 sections with 12-foot lane width that are assumed to have either non-default built-in curl/warp temperature in NCHRP 20-07 study LTPP_ID LANE BASE T # OBS INCR_STDEV MIN_STDEV MAX_STDEV AVG_STDEV STDEV_STDEV 04_0218 12 CTB -28 50 -3.2% 0.236 0.729 0.396 0.126 04_0219 12 CTB -16 73 72.9% 0.205 0.780 0.462 0.091 08_0214 12 AGG 0 59 172.8% 0.270 0.744 0.483 0.135 08_0218 12 CTB -21 34 -35.3% 0.487 1.190 0.832 0.183 37_0205 12 CTB -2 70 5.4% 0.436 1.243 0.894 0.167 39_0212 12 PSAB -15 40 15.6% 0.258 0.523 0.401 0.058 AVG 54 38.0% 0.315 0.868 0.578 0.127 Table E-3. Summary of IMF profile results for 42 EMD-analyzed SPS-2 sections with 12- foot lane width that are assumed to have AASHTO default built-in curl/warp temperature in NCHRP 20-07 study # of Sections LANE BASE T AVG # OBS AVG INCR_STDEV AVG MIN_STDEV AVG MAX_STDEV AVG AVG_STDEV AVG STDEV_STDEV 42 12 Varies -10 46 44.1% 0.358 1.186 0.604 0.176 Table E-4. IMF profile results for the four EMD-analyzed SPS-2 sections with 14-foot lane width that are assumed to have either non-default built-in curl/warp temperature in NCHRP 20-07 study LTPP_ID LANE BASE T # OBS INCR_STDEV MIN_STDEV MAX_STDEV AVG_STDEV STDEV_STDEV 04_0217 14 LCB -18 51 -23.8% 0.315 0.733 0.461 0.087 19_0217 14 LCB -25 34 35.5% 0.463 0.884 0.650 0.107 39_0203 14 AGG -16 41 27.7% 0.324 0.994 0.512 0.132 39_0211 14 PSAB -15 55 202.9% 0.377 1.317 0.612 0.156 AVG 45 60.6% 0.370 0.982 0.559 0.121 Table E-5. Summary of IMF profile results for 42 EMD-analyzed SPS-2 sections with 14- foot lane width that are assumed to have AASHTO default built-in curl/warp temperature in NCHRP 20-07 study # of Sections LANE BASE T AVG of # OBS AVG of INCR_STDEV AVG of MIN_STDEV AVG of MAX_STDEV AVG of AVG_STDEV AVG of STDEV_STDEV 42 14 Varies -10 47 33.3% 0.334 0.964 0.545 0.138 E.7. EMD analysis of LTPP profilometer data from the GPS-5 experiment EMD analysis was applied to profilometer data from GPS-5 sections, which are experimental CRCP sections. For this analysis, the profiles from the first and last dates of observation for each section were analyzed using EMD. The results are reported in Table E-7, where each column contains an abbreviated label referring to:  State code  LTPP section ID

E-21  First date of observation  Last date of observation  Change in standard deviation of profile amplitude  Average standard deviation of profile amplitude for all observations As was the case for the SPS-2 profile analysis using EMD, the metric of interest is the relative magnitude of the amplitude for a given profile. If this amplitude is large enough, it is possible to observe changes in slab profile using EMD analysis due to non-texture related effects (such as slab curl). Naturally, this analysis is more difficult for CRCP than for JPCP, as the periodicity (joint spacing) of slabs cannot be assumed and IMFs from CRCP profiles must be reviewed more closely. However, the EMD analysis was conducted on CRCP profile data to see if any significant profile could be recovered from the data. In general, no significant profile due to non-texture effects was observed in the data, as supported by Table E-7. For JPCP analysis, deformations of at least 1 mm were required to detect the repeat profile which might naturally occur due to curling between transverse joints. It was anticipated, then, that similar values would be required to observe non-texture effects in CRCP sections. Only one section, Section 18-5043 in Indiana, had multiple observations with an average standard deviation of amplitude greater than 1 mm. These relatively higher values were likely due to significant distress on Section 18-5043; the LTPP database notes high transverse cracking and roughness throughout the observation period. The observation period used for this analysis expired just prior to rehabilitation to remediate the failures noted in the LTPP section data and supported by the EMD analysis. While other sections (e.g. Section 39-5010) had average standard deviations of more than 1 mm, these can be disregarded as they were all associated with sections in which only one observation was made for the LTPP database prior to the rehabilitation of the CRCP section. E.8. Additional References Adu-Gyamfi, Y. O., Attoh-Okine, N. O., and A. Y. Ayenu-Prah (2010). “Critical Analysis of Different Hilbert-Huang Algorithms for Pavement Profile Evaluation.” Journal of Computing in Civil Engineering, Vol. 24, No. 6. Attoh-Okine, N. O., Ayenu-Prah, A. Y. Jr., and S. A. Mensah (2006). “Application of the Empirical Mode Decomposition to Pavement Profile Analysis.” Proceedings of the GeoCongress 2006, Atlanta, GA, pp. 1-6. American Society of Civil Engineers, Reston, VA. Byrum, C. R. (2000). “Analysis by High-Speed Profile of Jointed Concrete Pavement Slab Curvatures.” Transportation Research Record: Journal of the Transportation Research Board, 1730:1–9. Byrum, C. R. (2009). “Measuring Curvature in Concrete Slabs and Connecting the Data to Slab Modeling Theory.” Transportation Research Record: Journal of the Transportation Research Board, 2094:79–88. Ceylan, H., Turner, D.J., Rasmussen, R.O., Chang, G. K., Grove, J., Kim, S., and C. S. Reddy (2005). Impact of Curling, Warping, and Other Early-Age Behavior on Concrete Pavement Smoothness: Early, Frequent, and Detailed (EFD) Study. Report No. FHWA DTFH61-01-X-00042. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C.

E-22 Chang, G. K., Karamihas, S. M, Rasmussen, R.O., Merritt, P.E., and M. Swanlund (2008). “Quantifying the impact of jointed concrete pavement curling and warping on pavement unevenness.” Presented at the 6th Symposium on Pavement Surface Characteristics: SURF 2008, World Road Association-PIARC, October 20-22, 2008, Portoroz, Slovenia. Federal Highway Association (FHWA) (2004). Product Brief: Introducing ProVAL 2.0. Report No. FHWA-HRT-04-154. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C. Franta, D. P. (2012). Computational Analysis of Rigid Pavement Profiles. Master’s Thesis. University Of Minnesota, Minneapolis, MN. Huang, N. E. (2005). Introduction to the Hilbert-Huang Transform and its Related Mathematical Problems. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ Jiang, J. and M. I. Darter (2005). Structural factors of jointed plain concrete pavements: SPS-2, Initial Evaluation and Analysis. Report No. FHWA-RD-01-16. Federal Highway Administration, McLean, VA. Karamihas, S.M. and K. Senn. (2012). Curl and Warp Analysis of the LTPP SPS-2 Site in Arizona. Report FHWA-HRT-12-068. Turner-Fairbank Highway Research Center, Federal Highway Administration, McLean, VA. Wu, M. C., and Hu, C. K. (2006). “Empirical Mode Decomposition and Synchrogram Approach to Cardiorespiratory Synchronization.” Phys. Rev. E 73, 051917.

E-23 E.9. Summary tables of EMD analysis of SPS-2 and GPS-5 sections Table E-6. Summary results of EMD analysis of SPS-2 sections STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 4 213 43 1994 0.604 2007 0.980 62.3% 0.320 1.044 0.755 0.157 4 214 57 1994 0.560 2012 0.497 -11.3% 0.290 0.908 0.503 0.122 4 216 59 1994 0.384 2012 0.497 29.4% 0.300 0.661 0.455 0.090 4 217 51 1994 0.733 2008 0.559 -23.8% 0.315 0.733 0.461 0.087 4 218 50 1994 0.548 2006 0.530 -3.2% 0.236 0.729 0.396 0.126 4 219 73 1995 0.258 2012 0.446 72.9% 0.205 0.780 0.462 0.091 4 220 68 1994 0.502 2012 0.589 17.4% 0.259 0.589 0.400 0.072 4 221 42 1994 0.427 2006 0.621 45.3% 0.375 0.693 0.528 0.083 4 222 70 1994 0.445 2012 0.378 -15.0% 0.214 0.633 0.383 0.070 4 223 68 1995 0.234 2012 0.698 198.1% 0.234 0.874 0.558 0.138 4 224 66 1994 0.330 2012 0.553 67.9% 0.203 0.577 0.340 0.087 4 262 52 1994 0.363 2008 1.638 351.8% 0.329 1.638 0.912 0.322 4 262 52 1994 0.363 2008 1.638 351.8% 0.329 1.638 0.912 0.322 4 263 70 1994 0.666 2012 0.392 -41.2% 0.262 0.670 0.448 0.084 4 264 67 1994 0.640 2012 0.607 -5.1% 0.523 1.375 0.754 0.151 4 265 48 1997 0.756 2012 0.925 22.3% 0.481 1.396 0.812 0.172 4 266 71 1994 0.523 2012 0.713 36.3% 0.352 0.831 0.604 0.114 4 267 40 1994 0.568 2007 0.320 -43.7% 0.320 0.774 0.610 0.093 4 268 43 1994 0.755 2012 0.515 -31.9% 0.281 0.784 0.500 0.115 5 213 8 1997 0.621 2002 0.477 -23.2% 0.355 0.645 0.509 0.098 5 214 26 1997 0.425 2012 1.341 215.8% 0.425 1.341 0.979 0.206 5 215 24 1997 0.332 2012 1.115 235.2% 0.269 1.174 0.644 0.255 5 216 8 1997 0.614 2002 0.720 17.2% 0.565 1.830 0.878 0.403 5 217 11 1997 0.480 2002 0.640 33.2% 0.392 0.894 0.641 0.174 5 218 15 1997 0.490 2002 0.584 19.1% 0.354 0.584 0.472 0.067

E-24 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 5 219 24 1997 0.504 2012 0.639 26.8% 0.393 0.721 0.550 0.091 5 220 12 1997 0.610 2002 0.897 47.0% 0.599 0.964 0.822 0.138 5 221 9 1997 0.349 2002 0.409 17.3% 0.320 0.672 0.452 0.108 5 222 28 1997 0.334 2011 0.757 126.5% 0.299 0.817 0.476 0.151 5 223 16 1997 0.360 2012 0.439 22.0% 0.322 0.497 0.391 0.045 5 224 3 1997 0.337 2000 0.452 34.2% 0.337 0.642 0.477 0.154 6 201 8 2000 0.604 2000 0.488 -19.3% 0.427 0.643 0.568 0.076 6 202 17 2000 0.415 2004 0.451 8.7% 0.349 0.648 0.492 0.081 6 203 4 2000 0.621 2000 0.514 -17.2% 0.514 0.694 0.621 0.077 6 204 22 2000 0.480 2004 0.475 -1.1% 0.443 0.998 0.635 0.130 6 205 5 2000 0.815 2000 0.399 -51.1% 0.292 0.815 0.470 0.201 6 206 14 2000 0.718 2004 0.599 -16.6% 0.410 0.742 0.604 0.092 6 207 13 2000 0.585 2004 0.530 -9.4% 0.446 0.746 0.587 0.071 6 208 7 2000 0.474 2000 0.548 15.6% 0.405 0.673 0.542 0.087 6 209 8 2000 0.498 2000 0.496 -0.4% 0.407 0.626 0.478 0.070 6 210 18 2000 0.392 2004 0.418 6.8% 0.290 0.521 0.407 0.072 6 211 3 2000 0.509 2000 0.853 67.6% 0.509 0.880 0.747 0.207 6 212 17 2000 0.402 2004 0.616 53.4% 0.354 0.790 0.579 0.113 8 213 41 1994 0.497 2012 0.487 -2.0% 0.365 0.935 0.501 0.107 8 214 59 1997 0.273 2012 0.744 172.8% 0.270 0.744 0.483 0.135 8 215 26 1994 0.321 2003 0.769 139.5% 0.318 0.769 0.503 0.123 8 216 31 1994 0.379 2004 0.508 33.8% 0.234 0.754 0.403 0.121 8 217 34 1994 0.630 2004 1.166 85.2% 0.459 1.557 0.664 0.243 8 218 34 1994 1.013 2004 0.656 -35.3% 0.487 1.190 0.832 0.183 8 219 33 1994 0.753 2012 0.896 18.9% 0.557 0.896 0.714 0.087 8 220 58 1994 0.702 2012 0.766 9.1% 0.467 1.014 0.741 0.106 8 221 44 1994 0.754 2012 0.507 -32.7% 0.439 1.210 0.665 0.178

E-25 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 8 222 9 1994 0.398 1998 0.375 -5.8% 0.251 0.466 0.366 0.065 8 223 38 1994 0.845 2012 1.015 20.1% 0.630 1.036 0.840 0.118 8 224 34 1994 0.931 2003 1.113 19.6% 0.527 1.113 0.756 0.165 8 259 66 1994 0.371 2012 0.568 53.1% 0.371 0.844 0.601 0.106 10 201 11 1996 0.379 1998 0.326 -13.8% 0.326 0.631 0.483 0.086 10 202 64 1996 0.267 2012 0.303 13.6% 0.178 0.691 0.333 0.104 10 203 70 1996 0.294 2012 0.513 74.5% 0.234 0.763 0.391 0.087 10 204 22 1996 0.445 1998 0.350 -21.3% 0.301 0.445 0.405 0.035 10 205 10 1996 0.321 1998 0.321 0.0% 0.267 0.363 0.320 0.025 10 206 82 1996 0.384 2012 0.295 -23.2% 0.207 0.469 0.322 0.062 10 207 58 1996 0.354 2005 0.723 104.3% 0.285 0.723 0.466 0.095 10 208 18 1996 0.516 1998 0.507 -1.7% 0.331 0.671 0.530 0.084 10 209 17 1996 0.277 1998 0.257 -7.5% 0.210 1.052 0.329 0.196 10 210 26 1996 0.258 1998 0.361 39.8% 0.212 0.519 0.331 0.078 10 211 56 1996 0.275 2005 0.372 35.3% 0.213 0.597 0.304 0.081 10 212 26 1996 0.746 1998 0.447 -40.1% 0.407 0.759 0.548 0.096 10 259 26 1996 0.292 1998 0.316 8.3% 0.260 0.439 0.338 0.049 10 260 74 1996 0.437 2012 0.943 115.5% 0.305 0.978 0.524 0.153 19 213 39 1995 0.322 2011 0.605 87.8% 0.299 0.605 0.461 0.078 19 214 42 1995 0.476 2011 0.838 76.1% 0.302 1.036 0.670 0.188 19 215 48 1995 0.685 2011 0.620 -9.4% 0.424 0.813 0.627 0.089 19 216 49 1995 0.313 2011 0.709 126.6% 0.262 1.486 0.660 0.257 19 217 34 1995 0.524 2004 0.710 35.5% 0.463 0.884 0.650 0.107 19 218 45 1995 0.426 2011 0.921 116.2% 0.308 1.125 0.586 0.220 19 219 29 1995 0.466 2011 0.572 22.9% 0.325 0.661 0.479 0.081 19 220 51 1995 0.396 2011 0.775 95.5% 0.287 0.898 0.552 0.167 19 221 46 1995 0.528 2011 0.634 20.1% 0.377 0.965 0.559 0.135

E-26 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 19 222 45 1995 0.559 2011 0.649 16.1% 0.331 1.389 0.660 0.223 19 223 42 1995 0.573 2011 0.528 -7.9% 0.396 0.839 0.580 0.086 19 224 52 1995 0.465 2011 0.389 -16.3% 0.319 0.529 0.413 0.048 19 259 49 1995 0.357 2011 0.590 65.2% 0.313 0.801 0.454 0.104 20 201 9 1993 0.292 1995 0.356 21.8% 0.292 0.636 0.451 0.128 20 202 41 1992 0.391 2004 0.432 10.4% 0.217 0.859 0.359 0.131 20 203 29 1992 0.464 2004 0.446 -3.8% 0.399 0.645 0.514 0.068 20 204 4 1993 0.507 1995 0.460 -9.3% 0.453 0.507 0.470 0.025 20 205 41 1992 0.478 2004 0.641 34.2% 0.375 0.734 0.558 0.082 20 206 22 1993 0.561 2004 0.447 -20.3% 0.314 0.977 0.580 0.200 20 207 28 1992 0.522 2004 0.620 18.7% 0.384 0.725 0.544 0.072 20 208 30 1992 0.633 2004 0.566 -10.6% 0.546 1.005 0.750 0.109 20 209 38 1992 0.717 2004 0.444 -38.1% 0.411 0.952 0.615 0.171 20 210 35 1992 0.473 2004 0.464 -1.8% 0.251 0.814 0.480 0.095 20 211 42 1992 0.667 2010 0.371 -44.4% 0.305 0.798 0.426 0.096 20 212 39 1992 0.522 2004 0.390 -25.3% 0.390 0.920 0.608 0.108 20 259 24 1993 0.435 2004 0.434 -0.1% 0.336 0.742 0.460 0.076 26 213 32 1994 0.454 1999 1.152 153.8% 0.395 1.365 0.680 0.263 26 214 33 1994 0.868 2002 1.749 101.4% 0.423 1.785 1.050 0.374 26 215 32 1994 0.557 2000 1.547 177.9% 0.288 1.860 0.567 0.355 26 216 20 1994 0.626 2002 0.877 40.2% 0.331 1.189 0.719 0.243 26 217 33 1994 0.491 1999 0.994 102.5% 0.318 1.371 0.512 0.232 26 218 26 1994 0.669 1997 2.794 317.9% 0.443 3.766 1.239 0.921 26 219 41 1994 0.459 2002 0.470 2.4% 0.371 3.928 0.593 0.537 26 220 40 1994 0.762 2002 0.905 18.8% 0.424 1.167 0.763 0.185 26 221 34 1994 0.781 2002 0.351 -55.1% 0.321 1.802 0.518 0.248 26 222 40 1994 0.566 2002 0.594 4.9% 0.332 3.546 0.626 0.500

E-27 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 26 223 42 1994 0.380 2002 0.310 -18.5% 0.270 0.499 0.385 0.051 26 224 34 1994 0.450 2002 0.731 62.4% 0.353 1.048 0.529 0.162 26 259 32 1994 0.423 1999 0.464 9.6% 0.261 0.650 0.450 0.093 32 201 2 1997 0.352 1997 0.467 32.4% 0.352 0.467 0.409 0.081 32 202 6 1996 0.484 1997 1.191 145.9% 0.315 1.191 0.645 0.364 32 203 3 1997 0.308 1997 0.261 -15.3% 0.261 0.308 0.282 0.024 32 204 11 1996 0.421 1997 0.912 116.9% 0.421 0.944 0.722 0.174 32 205 3 1997 0.341 1997 0.299 -12.3% 0.299 0.341 0.317 0.022 32 206 8 1996 0.383 1997 0.534 39.2% 0.281 0.593 0.443 0.101 32 207 6 1996 0.469 1997 0.437 -6.8% 0.334 0.642 0.481 0.101 32 208 5 1997 0.692 1997 0.461 -33.4% 0.461 0.724 0.601 0.109 32 209 41 1996 0.256 2003 0.412 61.4% 0.237 0.591 0.398 0.077 32 210 4 1996 0.253 1997 0.255 0.7% 0.253 0.277 0.261 0.011 32 211 6 1996 0.539 1997 0.242 -55.2% 0.242 0.539 0.395 0.110 32 259 36 1997 0.390 2003 0.630 61.5% 0.390 0.749 0.575 0.096 37 201 111 1994 0.556 2003 0.833 49.8% 0.181 1.625 0.565 0.208 37 202 62 1994 0.570 2003 0.907 59.0% 0.508 1.208 0.847 0.175 37 203 91 1994 0.432 2012 0.510 18.1% 0.359 1.949 0.652 0.253 37 204 80 1994 0.476 2012 0.892 87.6% 0.322 1.019 0.566 0.125 37 205 70 1994 0.938 2003 0.989 5.4% 0.436 1.243 0.894 0.167 37 206 46 1996 0.379 2003 0.306 -19.3% 0.306 0.929 0.586 0.130 37 207 93 1994 0.672 2012 0.952 41.6% 0.404 1.942 0.858 0.275 37 208 58 1996 0.438 2012 0.959 118.9% 0.438 1.167 0.822 0.155 37 209 54 1994 0.830 2003 0.692 -16.6% 0.457 0.961 0.664 0.110 37 210 1 1994 0.420 1994 0.420 0.0% 0.420 0.420 0.420 0.000 37 211 80 1994 0.432 2012 0.514 19.2% 0.432 0.943 0.583 0.097 37 212 48 1994 0.584 2012 0.625 7.1% 0.353 1.320 0.553 0.138

E-28 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 37 259 3 1994 0.737 1994 0.694 -5.9% 0.694 0.755 0.729 0.032 37 260 102 1994 0.613 2012 0.517 -15.6% 0.448 1.290 0.706 0.157 38 213 4 1997 0.500 1997 0.754 50.7% 0.500 0.754 0.589 0.112 38 214 5 1997 0.399 1997 0.608 52.4% 0.399 0.608 0.495 0.092 38 215 1 1997 0.579 1997 0.579 0.0% 0.579 0.579 0.579 0.000 38 216 4 1997 0.857 1997 0.591 -31.0% 0.504 0.857 0.623 0.160 38 217 4 1997 0.448 1997 0.642 43.4% 0.448 1.664 0.968 0.543 38 218 3 1997 0.842 1997 0.554 -34.3% 0.554 1.009 0.801 0.230 38 219 5 1997 1.092 1997 0.496 -54.5% 0.496 1.092 0.653 0.247 38 220 5 1997 0.363 1997 0.251 -30.9% 0.251 0.364 0.332 0.047 38 221 3 1997 0.553 1997 1.057 91.3% 0.553 1.057 0.749 0.270 38 222 2 1997 0.559 1997 0.428 -23.3% 0.428 0.559 0.494 0.092 38 223 3 1997 0.549 1997 0.648 18.1% 0.549 0.811 0.669 0.132 38 224 5 1997 0.625 1997 0.479 -23.4% 0.479 0.625 0.579 0.062 38 259 31 1997 0.903 2007 0.575 -36.3% 0.471 1.453 0.753 0.283 38 260 24 1998 0.422 2007 0.634 50.3% 0.381 0.833 0.529 0.122 38 261 9 1998 0.569 2000 0.452 -20.5% 0.450 0.924 0.606 0.152 38 262 5 1997 0.660 1997 0.591 -10.5% 0.493 0.660 0.574 0.074 38 263 3 1997 0.451 1997 0.572 26.8% 0.359 0.572 0.461 0.107 38 264 37 1997 0.497 2012 0.585 17.5% 0.375 0.745 0.511 0.074 39 201 14 1996 0.410 2006 0.737 79.5% 0.326 0.981 0.590 0.209 39 202 20 1996 0.505 2006 0.722 43.0% 0.486 1.133 0.640 0.164 39 203 41 1996 0.382 2012 0.488 27.7% 0.324 0.994 0.512 0.132 39 204 55 1996 0.381 2006 0.545 42.9% 0.094 1.167 0.466 0.227 39 205 37 1996 0.623 2006 1.168 87.5% 0.393 2.255 0.886 0.458 39 206 25 1996 1.105 2006 1.033 -6.5% 0.397 1.398 0.899 0.289 39 207 68 1996 0.481 2012 1.466 204.6% 0.377 1.851 0.812 0.344

E-29 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 39 208 34 1996 0.566 2006 0.593 4.8% 0.452 0.944 0.609 0.095 39 209 50 1996 0.445 2006 0.666 49.7% 0.288 1.136 0.531 0.163 39 210 42 1996 0.536 2006 1.288 140.5% 0.327 1.288 0.517 0.155 39 211 55 1996 0.435 2012 1.317 202.9% 0.377 1.317 0.612 0.156 39 212 40 1996 0.362 2006 0.419 15.6% 0.258 0.523 0.401 0.058 39 259 16 1996 0.317 2004 0.439 38.3% 0.200 0.454 0.319 0.081 39 260 58 1996 0.416 2012 0.605 45.6% 0.304 0.643 0.474 0.097 39 261 57 1996 0.410 2012 0.419 2.2% 0.337 0.950 0.477 0.102 39 262 50 1996 0.450 2012 0.337 -25.1% 0.244 1.018 0.403 0.117 39 263 51 1996 0.370 2012 0.405 9.6% 0.299 0.746 0.426 0.089 39 264 24 1996 0.524 2005 0.785 49.8% 0.365 1.962 0.750 0.303 39 265 47 1996 0.446 2012 0.636 42.7% 0.391 0.793 0.570 0.091 53 201 58 1995 0.455 2012 0.592 30.0% 0.396 1.279 0.565 0.145 53 202 54 1995 0.737 2012 0.559 -24.1% 0.285 0.830 0.512 0.135 53 203 51 1995 0.621 2012 0.829 33.5% 0.375 0.829 0.576 0.094 53 204 58 1995 0.581 2012 0.547 -5.7% 0.313 0.715 0.487 0.085 53 205 55 1995 0.473 2011 0.541 14.5% 0.362 0.945 0.467 0.108 53 206 57 1995 0.384 2012 0.824 114.7% 0.384 1.260 0.813 0.172 53 207 53 1995 0.565 2012 0.451 -20.2% 0.352 0.821 0.527 0.078 53 208 67 1995 0.391 2012 0.627 60.4% 0.350 0.884 0.614 0.129 53 209 40 1995 0.418 2012 0.744 78.0% 0.394 0.850 0.571 0.121 53 210 69 1995 0.244 2012 0.301 23.3% 0.244 0.640 0.375 0.091 53 211 38 1995 0.495 2012 0.342 -30.8% 0.321 0.792 0.438 0.097 53 212 73 1995 0.479 2012 0.346 -27.7% 0.311 0.659 0.465 0.078 53 259 54 1995 0.336 2011 0.417 24.1% 0.254 0.500 0.385 0.052 55 213 49 1997 0.309 2012 0.643 107.8% 0.304 0.687 0.471 0.104 55 214 51 1997 0.486 2012 0.572 17.6% 0.317 1.020 0.529 0.129

E-30 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR MIN ST DEV MAX ST DEV AVG ST DEV ST DEV OF ST DEV 55 215 19 1997 0.483 2010 0.614 27.0% 0.396 0.676 0.501 0.076 55 216 59 1997 0.562 2012 0.474 -15.6% 0.407 1.165 0.690 0.199 55 217 60 1997 0.282 2012 0.422 49.7% 0.237 0.522 0.349 0.057 55 218 39 1997 0.469 2012 1.035 120.9% 0.297 1.035 0.448 0.131 55 219 32 1997 0.416 2012 0.680 63.2% 0.316 0.785 0.520 0.110 55 220 62 1997 0.494 2012 0.596 20.7% 0.372 0.980 0.568 0.120 55 221 57 1997 0.457 2012 0.632 38.4% 0.300 0.776 0.488 0.106 55 222 20 1997 0.470 2012 0.412 -12.2% 0.367 0.582 0.477 0.065 55 223 34 1997 0.658 2012 0.507 -22.9% 0.310 0.658 0.455 0.094 55 224 59 1997 0.289 2012 0.439 51.7% 0.265 0.533 0.380 0.069 55 259 34 1997 0.367 2012 0.639 74.2% 0.300 0.716 0.480 0.109 55 260 47 1997 0.540 2012 0.972 79.8% 0.337 1.409 0.731 0.239 55 261 54 1997 0.303 2012 0.351 15.9% 0.182 0.625 0.411 0.091 55 262 26 1997 0.414 2005 0.407 -1.7% 0.337 0.760 0.500 0.101 55 263 46 1997 0.337 2012 0.799 137.3% 0.214 0.799 0.405 0.142 55 264 16 1997 0.437 2012 0.741 69.3% 0.339 1.158 0.532 0.197 55 265 5 1997 0.404 2000 0.395 -2.4% 0.288 0.488 0.395 0.071 55 266 28 1997 0.295 2011 0.608 106.3% 0.295 0.701 0.488 0.136

E-31 Table E-7. EMD analysis of LTPP GPS-5 section profile data STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR AVG ST DEV 1 3998 5 1990 0.29563 1990 0.29563 0% 0.29563 1 5008 34 1990 0.219966 2011 0.225624 3% 0.22007 4 7079 50 1990 0.232815 2004 0.259507 11% 0.263289 5 5803 48 1990 0.359978 2010 0.372985 4% 0.352909 5 5805 47 1990 0.239151 2010 0.226836 -5% 0.248885 6 7455 47 1989 0.22405 2000 0.291892 30% 0.237965 9 5001 47 1989 0.498941 1996 0.543498 9% 0.502493 10 5004 31 1990 0.319531 1994 0.335448 5% 0.300395 10 5005 26 1990 0.357326 1994 0.33513 -6% 0.378105 13 5023 29 1990 0.335855 1998 0.297354 -11% 0.321903 16 5025 36 1989 0.539786 1995 0.581592 8% 0.594414 17 5020 71 1990 0.228497 2010 0.249563 9% 0.262417 17 5151 6 1990 0.451 1990 0.451 0% 0.451 17 5843 30 1990 0.300765 1998 0.446053 48% 0.333409 17 5849 20 1990 0.342546 1994 0.365958 7% 0.329269 17 5854 30 1990 0.511404 1997 0.648535 27% 0.584097 17 5869 36 1990 0.258292 1998 0.320244 24% 0.286921 17 5908 39 1990 0.413101 1999 0.386397 -6% 0.401864 17 9267 30 1990 0.233724 1998 0.220966 -5% 0.25416 18 5022 15 1989 0.58378 1991 0.567371 -3% 0.572841 18 5043 49 1989 0.944737 2001 1.106319 17% 1.304312 18 5518 21 1990 0.310137 1992 0.556142 79% 0.363954 19 5042 52 1990 0.385231 2001 0.395308 3% 0.392358 19 5046 15 1990 0.376821 1992 0.317674 -16% 0.335032 19 9116 15 1992 0.187007 1994 0.223591 20% 0.208145 24 5807 11 1989 0.698186 1990 0.400977 -43% 0.536072 26 5363 25 1989 0.292941 1993 0.332617 14% 0.33419

E-32 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR AVG ST DEV 27 5076 5 1990 0.197441 1990 0.197441 0% 0.197441 28 3099 12 1990 0.259849 1991 0.278015 7% 0.267418 28 5006 19 1990 0.264994 1994 0.3048 15% 0.276798 28 5025 40 1991 0.24984 2011 0.275147 10% 0.278726 28 5803 10 1990 0.322251 1992 0.332497 3% 0.327374 28 5805 27 1990 0.437794 1998 0.458946 5% 0.426517 29 5047 48 1990 0.421743 2002 0.496309 18% 0.464331 31 5052 30 1989 0.210648 1997 0.279581 33% 0.256959 37 5037 42 1990 0.239831 1999 0.295532 23% 0.270714 37 5826 5 1994 0.277665 1994 0.277665 0% 0.277665 37 5827 40 1990 0.261278 1997 0.263329 1% 0.263711 38 5002 36 1989 0.208968 1999 0.292569 40% 0.233879 39 5003 56 1989 0.208104 2004 0.346335 66% 0.269983 39 5010 6 1989 1.996899 1989 1.996899 0% 1.996899 40 4158 45 1991 0.234462 2010 0.370092 58% 0.288376 40 4166 40 1991 0.241972 2010 0.313255 29% 0.282644 40 5021 45 1991 0.186871 2010 0.189871 2% 0.193072 41 5005 77 1989 0.318232 2013 0.278722 -12% 0.300064 41 5006 55 1989 0.316154 2003 0.314589 0% 0.282681 41 5008 55 1989 0.195033 2003 0.211999 9% 0.204695 41 5021 35 1989 0.288125 1998 0.278867 -3% 0.267754 41 5022 75 1989 0.306657 2013 0.271645 -11% 0.290819 41 7081 75 1990 0.165391 2013 0.18832 14% 0.198077 42 1598 47 1989 0.386833 1998 0.450601 16% 0.446034 42 1617 14 1989 0.556635 1990 0.528803 -5% 0.544707 42 5020 57 1989 0.493625 1998 0.427445 -13% 0.452966 45 5017 46 1990 0.449409 2011 0.500714 11% 0.485839 45 5034 35 1990 0.40963 2001 0.361008 -12% 0.392437

E-33 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR AVG ST DEV 45 5035 19 1990 0.271487 1994 0.283405 4% 0.282123 46 5020 10 1989 0.228665 1990 0.239861 5% 0.234263 46 5025 79 1989 0.690403 2011 0.218899 -68% 0.277131 46 5040 55 1989 0.465897 2004 0.42363 -9% 0.448034 48 3719 21 1990 0.557475 1995 0.495427 -11% 0.523905 48 3779 39 1990 0.790485 2010 0.630123 -20% 0.542862 48 5024 51 1990 0.676859 2010 0.716897 6% 0.700769 48 5026 50 1990 0.289082 2011 0.323644 12% 0.358244 48 5035 49 1990 0.315527 2010 0.389971 24% 0.3549 48 5154 4 1990 0.421032 1990 0.421032 0% 0.421032 48 5274 20 1990 0.464356 1994 0.476385 3% 0.459572 48 5278 30 1990 0.232651 1998 0.246064 6% 0.242385 48 5283 52 1990 0.330861 2010 0.345263 4% 0.341169 48 5284 49 1990 0.430775 2010 0.605291 41% 0.74816 48 5287 34 1990 0.318285 2000 0.313337 -2% 0.344237 48 5301 25 1990 0.383905 1998 0.459441 20% 0.432429 48 5310 45 1990 0.476768 2010 0.46717 -2% 0.451214 48 5317 5 1990 0.401173 1990 0.401173 0% 0.401173 48 5323 20 1990 0.334212 1994 0.355759 6% 0.351881 48 5328 52 1990 0.470549 2010 0.361532 -23% 0.400576 48 5334 30 1990 0.257784 2000 0.235943 -8% 0.257035 48 5335 30 1990 0.403723 1999 0.34106 -16% 0.365508 48 5336 50 1990 0.242626 2012 0.306794 26% 0.299994 51 2564 49 1989 0.228514 1997 0.270935 19% 0.257241 51 5008 80 1989 0.578415 2011 0.538905 -7% 0.533669 51 5009 36 1989 0.529333 1997 0.652066 23% 0.566936 51 5010 49 1989 0.390103 2000 0.395199 1% 0.449364 54 5007 18 1989 0.464779 1991 0.67279 45% 0.540342

E-34 STATE SECTION #OBS 1ST DATE 1st ST DEV LAST DATE LAST ST DEV %INCR AVG ST DEV 55 5037 31 1989 0.232985 1997 0.310277 33% 0.258681 55 5040 35 1990 0.345894 1997 0.413927 20% 0.383471