TECHBRIEF Curl and Warp Analysis of the

LTPP SPS-2 Site in Arizona

FHWA Publication No.: FHWA-HRT-13-040

FHWA Contact: Larry Wiser, HRDI-30, (202) 493-3079, 

larry.wiser@dot.gov

This document is a technical summary of the Federal 

Highway Administration (FHWA) report Curl and 

Warp Analysis of the LTPP SPS-2 Site in Arizona 

(FHWA-HRT-12-068).

Introduction 

Variability in the roughness levels of jointed portland 

cement concrete (PCC) pavements can often be 

observed over short periods of time. This study 

demonstrated specialized analyses for quantifying the 

effect of curl and warp on the roughness of jointed 

PCC pavements using profile data from the LongTerm Pavement Performance (LTPP) Specific Pavement 

Studies (SPS)-2 site in Arizona.

The study sought to quantify and explain changes in 

the International Roughness Index (IRI) observed over 

time on the LTPP SPS-2 site in Arizona using methods 

that were applied to other sites.(1) The study analyzed 

the profiles in detail by calculating their IRI values, 

examining the spatial distribution of roughness 

within them, viewing them with post-processing 

filters, and examining their spectral properties. The 

study also attempted to relate changes in IRI over 

time to design variables, maintenance history, and 

observations of distress.

Traditional profile analyses revealed roughness caused 

by transverse and longitudinal cracking as well as 

some localized roughness caused by built-in defects 

on some test sections. However, the analyses showed 

that curl and warp contributed to, and in some cases 

dominated, the roughness on many test sections. In 

addition, roughness did not increase steadily with time 

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.fhwa.dot.gov/pavement/ltpp

The Long-Term Pavement Performance 

(LTPP) program is a large research 

project for the study of in-service 

pavements across North America. 

Its goal is to extend the life of 

highway pavements through various 

designs of new and rehabilitated 

pavement structures, using different 

materials and under different loads, 

environments, subgrade soil, and 

maintenance practices. LTPP was 

established under the Strategic 

Highway Research Program and is 

now managed by the Federal Highway 

Administration.
2

because of diurnal and seasonal changes 

in slab curl and warp.

Objective 

Using the LTPP SPS-2 site in Arizona for 

a pilot demonstration, this study applied 

objective profile analyses to quantify the 

level of curl and warp on each section and 

distinguish the portion of IRI caused by curl 

and warp from the portion caused by other 

sources of roughness. 

The project team used objective algorithms to estimate the gross strain 

gradient needed to deform each slab 

into the shape present in the measured 

profile and produced a pseudo strain 

gradient (PSG) value. The levels of curl 

and warp within each test section were 

summarized by the average absolute PSG 

value for the slabs within it.

By relating changes in PSG to changes 

in IRI, the portion of roughness change 

associated with PSG could be identified. 

Using these methods, the study examined 

the IRI progression of 21 test sections 

on the LTPP SPS-2 site in Arizona over 

the first 16 years of the experiment. The 

site included 12 test sections from the 

standard experiment and 9 supplemental 

test sections designed by the Arizona 

Department of Transportation. The project 

also sought to diagnose the sources of 

roughness and link the observations to 

records of distress and its development. 

Slab Curvature Index

Analyses performed to distinguish the 

portion of roughness caused by curl and 

warp from the rest of the irregularities 

within each profile used a summary 

index for estimating slab curvature. As in 

previous studies, this quantified the portion 

of IRI linked to slab curl and warp and the 

portion associated with other sources of 

roughness, such as built-in defects and 

surface distress.(2)

The level of curl and warp present within 

each profile was estimated using slab-byslab analysis of local profile segments. An 

automated procedure isolated the profile of 

each slab by seeking the locations where 

negative spikes appeared in the same 

locations within a set of five repeated 

profile measurements. 

The analysis quantified the level of curl 

and warp on each slab using PSG. The 

procedure estimated the PSG value for a 

given slab using an approach proposed 

by Chang et al.(3) In this procedure, an 

idealized profile for a slab with curling and 

warping proposed by Westergaard in the 

classical literature is fit to the measured 

profile of each slab. The shape of the 

idealized profile is fixed by estimating the 

radius of relative stiffness, slab thickness, 

Poisson’s ratio, and slab length. The 

curve fit yields a value of strain gradient 

required to deform a slab into the shape 

that appears within its measured profile 

from a flat baseline.

Figure 1 shows an example curve fit 

for a slab in section 0215. Before the 

curve fit, the segment of profile shown 

was detrended and shifted to a mean 

elevation value of zero. In this case, the 

radius of relative stiffness was estimated 

at 40.7  inches with a slab thickness of 

11 inches and a Poisson’s ratio of 0.15. For 

the slab shown in figure 1, the PSG value 

was 70.57 με/inch.

The analysis produced a summary PSG 

value for a test section by averaging the 
3

absolute PSG values over all the slabs 

within the section.

Relationship to IRI

The study empirically related changes 

in summary PSG over time to changes 

in IRI. Figure 2 shows an example for 

section  0215 (a seasonal monitoring 

section) over several seasonal and diurnal 

visits throughout 3 years. 

Figure 2 shows a useful statistical relationship. Changes in curl and warp exhibit a 

linear relationship to changes in IRI with 

a low standard error of estimate. Using 

extrapolation to a PSG value of zero, an 

empirical estimate of IRI caused by roughness not associated with curl and warp is 

possible. For the example in figure  2, the 

relationship projects to an IRI value of 

66 inches/mi for a PSG of 0 με/inch.

-100 -50 0 50 100

Longitudinal Distance (inches)

-.1

0

.1

.15

Slab Profile (inches)

.05

-.05 model

measurement

Figure 1. Example curve fit for estimation of PSG.

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60

PSG (με/inch)

IRI (in/mi)

IRI = 66.38 + 1.3860•PSG

Standard Error Estimate: 2.14 in/mi

135 samples

R2 = .93

Figure 2. IRI versus PSG for right side of section 0215.
4

Data with this level of historical detail 

were only available for section 0215 on the 

Arizona site. However, data from a recent 

FHWA experiment included seasonal and 

diurnal variations over a 1-year cycle for the 

12 sections in the core experiment.(3) The 

slope of the IRI-PSG relationship was used 

to estimate the portion of IRI associated 

with curl and warp within each profile. The 

balance of the roughness was considered to 

be linked to other sources, such as built-in 

defects and surface distress. The FHWA 

data included a broad enough variety of 

temperature conditions to capture a close 

relationship between IRI and PSG on lowstrength sections, but the change in PSG 

was too small on the high-strength sections 

to provide useful observations.

IRI Trends

Figure 3 shows the results of the analysis 

for the right-side profile of section 0215. The 

circular marks show the IRI values for each 

set of five passes over the section, and the 

cross marks show the portion of IRI associated with sources other than curl and warp. 

IRI increases overall over the first 8 years of 

the experiment, but several seasonal and 

diurnal changes in IRI are evident. When 

the contribution of slab curl and warp is 

removed, the balance of the roughness 

is between 60 and 80  inches/mi throughout the monitoring period. Figure 3 shows 

that curl and warp impose a penalty to the 

roughness of up to 80 inches/mi. The figure 

also shows that other sources of roughness, 

such as distress, did not increase over the 

16-year monitoring period. 

Figure 4 shows the results of the analysis 

for the right-side profile of section 0213. On 

this section, the overall IRI on the right side 

shows a net growth over the monitoring 

period, but diurnal and seasonal variations 

caused IRI to increase inconsistently. When 

the influence of curl and warp is removed, 

the balance of the roughness contributes 

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)

Figure 3. Right IRI progression for section 0215. 
5

50 inches/mi to IRI over the first 11 years of 

the experiment. After 11 years, longitudinal 

cracking caused an increase in roughness.

On both test sections, curl and warp 

contributed up to 80 inches/mi to IRI at 

various times throughout the monitoring 

history. This has important implications to 

the functional performance of each section. However, the influence of structural 

failures such as longitudinal cracking was 

obscured by the inconsistent contributions of curl and warp to roughness.

Results

The study demonstrated the potential for 

isolating the effect of curl and warp from 

other sources of roughness due to the strong 

statistical relationship between changes in 

IRI and changes in PSG on low-strength test 

sections. The study also demonstrated that 

long-term increases in IRI may be caused 

solely by changes in curl and warp and do 

not necessarily indicate structural failure or 

increased surface distress.

The analysis methods applied several 

assumptions that require verification over 

a broader dataset. Further, a method is 

needed to derive the IRI-PSG relationship 

that does not involve as much measurement effort and that can be validated for 

high-strength pavements. However, this 

study clearly demonstrated the potential 

for applying this process and the value in 

further analysis, as being able to quantify 

the curl and warp impacts of jointed PCC 

pavements can greatly inform the most 

appropriate measures to address increases 

in roughness.

References

1. Karamihas, S.M. and Senn, K. (2009).

“Profile Analysis of Arizona Specific 

Pavement Studies 5 Project.” Transportation Research Record 2095, 

pp.  144–152, Transportation Research 

Board, Washington, DC.

0

25

50

75

100

125

150

175

200

225

0 2 4 6 8 10 12 14 16 18

Curl Influence Removed

IRI

Right IRI (in/mi)

Time (years)

Figure 4. Right IRI progression for section 0213.
6

2. Byrum, C.R. (2001). A High Speed 

Profiler Based Slab Curvature Index for 

Jointed Concrete Pavement Curling and 

Warping Analysis, Ph.D. dissertation, 

University of Michigan, Ann Arbor, MI.

3. Chang, G., Rasmussen, R., Merritt, D., 

Garber, S., and Karamihas, S. (2010). 

Impact of Temperature Curling and 

Moisture Warping on Jointed Concrete 

Pavement Performance, TechBrief, 

Publication No. FHWA-HIF-10-010, 

Federal Highway Administration, 

Washington, DC.

Researchers—This study was performed by Nichols Consulting Engineers, Chtd., and the 

University of Michigan Transportation Research Institute, Contract No. DTFH61-06-C-00027.

Distribution—This TechBrief is being distributed according to a standard distribution. 

Direct distribution is being made to the Divisions and Resource Center.

Availability—The publication associated with this TechBrief is Curl and Warp Analysis of 

the LTPP SPS-2 Site in Arizona (FHWA-HRT-12-068). It is available in print and online at 

http://www.fhwa.dot.gov/research.

Key Words—LTPP data, International Roughness Index, Jointed PCC, Curl and warp.

Notice—This document is disseminated under the sponsorship of the U.S. Department of 

Transportation in the interest of information exchange. The U.S. Government assumes no 

liability for the use of the information contained in this document. The U.S. Government 

does not endorse products or manufacturers. Trademarks or manufacturers’ names appear 

in this report only because they are considered essential to the objective of the document.

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May 2013 FHWA-HRT-13-040

HRDI-30/05-13(800)E