Conference PaperPDF Available

Prediction of Longitudinal Fatigue Cracking in Rigid Pavements Using RadiCAL

  • California Department of Transportation
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 561
Prediction of Longitudinal Fatigue Cracking in Rigid
Pavements using RadiCAL
Jacob E. Hiller, Ph.D.1, James M. Signore, Ph.D., P.E.2, Venkata Kannekanti3,
Imad Basheer, Ph.D., P.E.4, and John T. Harvey, Ph.D., P.E.5
The capability of the software program RadiCAL to predict longitudinal fatigue cracking
in jointed plain concrete pavements (JPCP) was studied to assess several sections in
multiple climatic regions in California. RadiCAL fatigue cracking predictions were
compared against measured distresses using the Caltrans’ pavement management system.
Using this approach, RadiCAL was able to correctly predict zero or near-zero longitudinal
cracking in newer JPCPs. The predictive performance for older JPCPs was variable and
dependent upon defining proper input variables, including built-in curl and the concrete’s
flexural strength. Issues such as random joint spacing and skewed joints complicated
analyses for some sections as well. The challenges and solutions to using an existing
pavement management system database for verification and eventual calibration are also
described. This design verification stage of RadiCAL will help develop future versions of
the software, as transfer functions between stress, damage, and cracking will be further
enhanced to align with measured distresses in the state.
The pavement design methods used in California and most of the U.S. for the past fifty
years have been empirical in nature. While these empirical methods have generally
served pavement designs well, they are severely limited in their ability to effectively
consider increased traffic volumes, increased, axle weights, different axle configurations,
climatic influences, and the development of new pavement materials.
As part of the ongoing development of mechanistic-empirical design procedures
for the state of California, the California Department of Transportation (Caltrans) has
evaluated the Mechanistic-Empirical Pavement Design Guide (MEPDG) (MEPDG 2007)
jointed plain concrete pavement (JPCP) design program and is using California-specific
data to validate the results it produces to calibrate where necessary. One important
capability that the MEPDG currently lacks is the ability to predict longitudinal cracking
in JPCP pavements. Longitudinal cracking is common in California and other western
states, while it is less prevalent in much of the rest of the United States. Climate is the
1 ISCP Director, Assistant Professor, Michigan Technological University, 1400 Townsend Drive,
Houghton, Michigan, USA, 49931,, phone: 906-487-3053, fax: 906-487-1620
2 University of California Pavement Research Center, 1353 S. 46th Street, Bldg 480, Richmond, California,
USA 94804,, phone: 510-665-3669, fax: 510-665-3484
3 T.Y. Lin International, 2010 Crow Canyon Place, Suite 350, San Ramon, California, USA 94583,, phone: 925-365-3960, fax: 925-275-0117
4 Division of Pavement Management, California Department of Transportation (Caltrans), 2389 Gateway
Oaks Dr., Suite 200, Sacramento, California, USA 95833,, phone: 916-274-
6176, fax: 916-274-6213
5 ISCP Member, Professor, University of California Pavement Research Center, Department of Civil and
Environmental Engineering, University of California, Davis, One Shields Avenue, Davis, California,
USA, 95616,, phone: 530-754-6409, fax: 530-752-9603
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 562
primary reason for this difference. Western states have climates that are arid during the
hottest times of the year in comparison with mid-western and eastern states that are more
humid during this season. Even within California, the same JPCP designs will perform
differently depending on the climatic region in which they are constructed. In some areas
of California, the extent of longitudinal cracking is similar to that of transverse cracking
(Harvey et al. 2000). However, some studies have shown that while longitudinal
cracking exists, transverse cracking is predominant in the state (Smith et al. 1998).
Anecdotally, it also appears that longitudinal cracking may appear before transverse
cracking in dry regions of California (most of the state). Therefore, it is important to have
the capability to model and predict the effects of design and construction practices on
longitudinal cracking performance of JPCPs. This capability also provides information
for prediction of future maintenance needs for the state’s pavement management system
(PMS). The University of Illinois, with partial funding from Caltrans through the
University of California Pavement Research Center (UCPRC), developed a mechanistic-
empirical analysis model to help researchers and designers understand the particular
material, environmental, construction, traffic, and design factors causing longitudinal
cracking in JPCP. The model was based in part on Caltrans-funded original research at
the UCPRC (Heath et al. 2003). The model was incorporated into a software program
called RadiCAL (Rigid Pavement Analysis for Design in California) (Hiller and Roesler
2005) to predict longitudinal and transverse fatigue cracking in JPCP under a variety of
design features, environmental, and loading conditions.
To provide data necessary for the calibration of MEPDG and the field verification
of RadiCAL, as well as to better understand the current condition of the rigid pavements
in California, materials samples and structural data on JPCP and crack, seat, and asphalt
overlay (CSOL) sections throughout California were collected. A total of 50 concrete
sections and 43 CSOL sections were sampled. Additionally, the UCPRC extracted and
analyzed cracking performance data to combine with the field data for the
validation/calibration exercise.
The field verification process required measurement, collection or estimation of
the following data for each of the existing sections: joint spacing, slab thickness, climate
region, coefficient of thermal expansion, percent slabs cracked, load spectra, truck
configurations, and slab flexural strength. Once these data were collected, it was used
with RadiCAL to compare between the predicted fatigue damage and the cracking data
from the PMS. Correlations were then developed relating damage to actual field
performance. Details of this process are presented in (Signore et al. 2008). This process
was also used for calibration of the MEPDG rigid pavement models for transverse fatigue
cracking and faulting as described in (Kannekanti and Harvey 2007a).
This paper will briefly discuss the longitudinal cracking mechanism in JPCP and
the use of RadiCAL to verify measured field performance. RadiCAL’s capabilities to
predict longitudinal cracking in JPCP and specifically how RadiCAL can predict varying
longitudinal cracking performance under multiple environmental conditions will also be
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10th International Conference on Concrete Pavements 563
Longitudinal fatigue cracking mechanism
The mechanics of longitudinal fatigue cracking of JPCPs, specific to the western United
States and other dry climates, have eluded pavement engineering researchers and
practitioners for many years. Longitudinal cracking is caused by a combination of
environmental, material, and traffic factors in conjunction with geometry and restraint of
slabs. As a JPCP slab’s top surface becomes warmer or wetter than its lower surface it
expands and slab corners bend downwards. Conversely, as the JPCP slab’s top surface
cools or becomes drier than its lower surface, it contracts, bending the slab corners
upwards. This bending is commonly called warping if due to changes in slab moisture
and curling if due to changes in slab temperature.
A JPCP slab possesses considerable self-weight that counteracts these
curling/warping tendencies, which results in bending stresses within the slab. When a
slab curls/warps downward, its center is unsupported, creating tensile stresses at the
bottom center of the slab where its weight pulls downward. When a slab curls/warps
upward, tensile stresses occur at the top of the slab as the weight of the slab edges pull
down. This stress-reversal process continues throughout the life of a slab as it is exposed
to cycles of temperature and moisture change.
After placement, JPCP slabs start to dry and shrink due to the environment and
the formation of cementing products that are of smaller volume than their constituent
parts (autogenous shrinkage), affecting the entire slab thickness.
As shrinkage causes slabs to crack at their respective joint-relief cuts, they
become freer to curl and warp. Due to this phenomenon, undowelled slabs are freer to
move than those restrained by dowels. Asymmetric bending can occur if one transverse
edge of a slab is more restrained than another. This can be due to late cracking at one
saw joint compared to another or to different levels of joint restraint from load transfer
devices or aggregate interlock.
The magnitude of total curl varies with cyclical temperature and moisture
gradients in the slab, but a certain level of permanent built-in curl always remains (Hiller
2007). The hot dry summer conditions in the arid western states cause greater shrinkage
on the top of JPCP slabs than on the bottom, which results in upward curling of the slab
corners. Irreversible shrinkage in the top 50-100mm of the concrete slab, as well as the
built-in temperature gradients during the setting of concrete, causes a majority of
pavements to curl permanently upward regardless of the cyclical temperature gradient
(Hiller 2007).
The degree of permanent upward slab curl caused by differential drying shrinkage,
built-in construction curl, and other factors can be described in terms of an equivalent
temperature differential (top to bottom) that would cause a plane/flat slab to curl to the
same extent; hence the term effective built-in temperature differential (EBITD). The
more negative the EBITD value, the greater the permanent upward curl at the corners of
the slabs, and hence the greater surface temperature increase required to flatten the slab.
Backcalculations from full-scale test results from the desert climate of Palmdale,
California suggest that the levels of permanent curl in terms of a linear EBITD can
exceed -22ºC for undoweled slabs (Rao and Roesler 2005a), although those values are an
extreme case. During the course of a day, curling stresses working in a typical slab force
its corners to curl both upward and downward. However, in some environments and for
slabs with highly negative EBITD values (corners curled up as if the slab’s top is colder
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 564
than its bottom), downward curling never occurs, leaving these slabs with permanent
upward curl. Interaction between EBITD and a number of other factors, including slab
thickness, traffic load spectra, environment, joint load transfer, and other variables, can
lead to longitudinal cracking. Slabs in these upward curled conditions or slabs with
shorter joint spacing are more prone to longitudinal cracking and corner cracking (Hiller
2007) due to the unsupported corners and reduced bending stress at the mid-slab edge
The traditional mechanics model (Westergaard 1948) states that the underside of
the longitudinal mid-slab edge has the highest stresses due to wheel loading with the
wheel at the mid-slab edge and daytime temperature gradients (warmer on top than
bottom). While this model is correct for mid-slab edge loading situations, it is incomplete,
particularly for slabs that possess a degree of residual curling. It thus becomes difficult to
determine the exact location of highest slab stress (Hiller 2007). The highest-stress
location is highly dependent upon axle configuration and degree of slab curvature, which
contribute to the presence of significant longitudinal cracking in dry environments. The
mid-slab, bottom-up cracking model must be supplemented by additional factors that
account for slab curling and various axle load configurations, which lead to multiple high
stress locations on a JPCP slab. For slabs with upward curled corners that are
unsupported, a corner wheel loading may be the highest stress location, thereby causing
top-down longitudinal fatigue cracking between loaded areas of an axle.
Overview of RadiCAL. RadiCAL was developed as a response to the current
understanding that concrete fatigue failure is a far more complex process than that
described by the classic Westergaard cracking mechanism. In developing RadiCAL,
Hiller and Roesler (Hiller and Roesler 2008b) first computed stresses in JPCP using finite
element analysis (FEA) ISLAB2000 (ERES-Consultants 1999) using a wide range of
physical, environmental, and loading conditions typically found in California and other
western states. RadiCAL uses these FEA solutions in conjunction with statistical
distributions of inputs such as traffic classifications, load spectra, axle spacing
distributions, and climatic influences as well as direct design parameters such as traffic
counts, built-in curl level, slab geometry, load transfer level, etc., to determine fatigue
damage for numerous locations within the concrete slab. RadiCAL also has the ability to
analyze pavements using several fatigue transfer functions with linear or multiple non-
linear temperature profile options.
RadiCAL is programmed to simulate the movement of a vehicle’s wheels as it
travels across a slab for a given axle load or combination of axle loads, while performing
a series of static calculations for each load location (or node) along the slab. Damage is
computed for up to 89 nodes along each slab edge, with the spacing between nodes
dependent on the geometry of the slab. A typical output from RadiCAL is shown in
Figure 1 showing predicted damage accumulated along the transverse joint. Critical
damage locations are indicated by the maximum damage levels along either the
transverse joint (indicating longitudinal cracking potential) or the longitudinal edge of a
slab (indicating transverse cracking) for both top-down and bottom-up fatigue cracking
mechanisms. By examining the level and location of these critical stresses, the likelihood
of longitudinal and transverse fatigue cracking can be determined at locations and by
causes not predicted using traditional theories involving mid-slab edge/bottom-up fatigue.
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10th International Conference on Concrete Pavements 565
Figure 1. RadiCAL output screen showing relative damage values
and locations (1 inch = 2.54cm).
EBITD is a primary input parameter to RadiCAL, although it is important to note
that EBITD for a given JPCP slab cannot be known with certainty in advance by a
designer. Instead, it must be estimated based on information from previously constructed
pavements using deflection tests with a falling-weight deflectometer. Deflection tests can
be performed to backcalculate EBITD, determine joint load transfer and estimate layer
stiffnesses for an existing pavement slab or series of slabs using the process developed by
Rao and Roesler (2005b). In the EBITD backcalculation process, the pavement structure
is modeled with a FEA using the load transfer efficiencies and moduli backcalculated
previously as inputs. Comparisons are made between the measured slab deflections and
those calculated by FEA at various temperatures for a number of assumed EBITD values.
The EBITD value for a given pavement is the one that produces the best fit to field slab
deflections, as measured by residual sum of squares analysis.
Once appropriate EBITD values are determined, the user can run RadiCAL for
various structural sections and input parameters to calculate damage. The calculated
damage is used with fatigue cracking transfer functions to estimate the performance of
JPCP design sections. In this paper, fatigue cracking factors using cracking
densities/percentages from field surveys will be compared to damage values predicted
from RadiCAL.
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Data Collection and Preparation
For this study, all of the California JPCP sections were undoweled as was typical for past
designs in the state. Slab and base thicknesses and concrete compressive strengths were
determined from cores taken on the sections, which had been in service for many years.
Flexural strengths were estimated from the compressive strengths using American
Concrete Institute correlations (ACI-318 2008).
The coefficient of thermal expansion (CTE) was measured on the cores following
a modified AASHTO TP 60 procedure (AASHTO 2005). Truck traffic data was taken
from Caltrans databases, including truck counts and in some cases Weigh-In-Motion
(WIM) data. Slab lengths were measured in the field for concrete sections or estimated
from historical data for sections that had been overlaid. Details regarding field data
collection are documented in (Kannekanti and Harvey 2007b).
Deflections were measured on many sections. However, lack of sufficient
measurements at different temperatures and uncertainty with regard to the location of
joints under overlaid sections made backcalculation of stiffness and EBITD difficult.
Concrete slab stiffnesses were estimated from compressive strengths, and EBITD values
were assumed for the sections included in this study. Joint load transfer efficiencies were
evaluated using collected deflection data.
Cracking performance data was extracted from historical Caltrans PMS data and
verified by field observations for the sections that had not been overlaid. Specific
information regarding how this data was extracted from the PMS appears in (Kannekanti
et al. 2007).
Within the Caltrans PMS, slab cracking is reported as a percentage of cracked
slabs for the following three types of cracks:
First-stage cracks (FSC) are transverse, longitudinal, or diagonal cracks that do
not intersect and which divide the slab into two or more large pieces.
Third-stage cracks (TSC) are interconnected cracks that divide the slab into three
or more large pieces. Fragmented slabs are characterized by interconnected,
irregular multiple cracks and breaks. By definition first-stage cracking and third-
stage cracking cannot exist in the same slab.
To utilize Caltrans PMS historic performance data for this study, the FSC and
TSC cracking data had to be converted to longitudinal cracking. By definition, an FSC
can be either transverse crack (TC) or longitudinal crack (LC), but cannot be both.
Therefore, there can be two possible scenarios:
Scenario 1: All FSCs are longitudinal cracks. TSC by definition has both
transverse and longitudinal cracks and therefore is added to FSC to get the
percentage of longitudinal cracks. In this case, total longitudinal cracking is equal
to the sum of FSC and TSC.
Scenario 2: All FSCs are transverse cracks. In this case, total longitudinal
cracking is equal to TSC only.
Scenario 1 gives the maximum possible longitudinal cracking (LCmax = FSC +
TSC) and Scenario 2 gives the minimum possible longitudinal cracking (LCmin = TSC).
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 567
In reality, FSC will be a combination of some slabs with transverse cracks and some slabs
with longitudinal cracks. Therefore, the true percentage of slabs with longitudinal
cracking that occurred on the section will always be between this maximum and
minimum. For many sections that had been overlaid, this was the best way to estimate the
previous amount of longitudinal cracking as this value is not expressly recorded in the
Caltrans PMS. Consequently, many of the following figures show both minimum and
maximum cracking measured to demonstrate the target range of longitudinal cracking.
RadiCAL Field Verification
The field verification process consisted of comparing and correlating measured field
performance to damage values calculated by RadiCAL. RadiCAL calculates both top
down (TD) and bottom up (BU) damage at numerous locations. A transfer function was
required to correlate the longitudinal damage calculated by RadiCAL to the percent slabs
cracked in a pavement section. Equation (1) has been taken from the MEPDG (MEPDG
2007), which converts “damage” into a cracking factor (CRK) using the same FEA
program as RadiCAL for development of its stress prediction algorithm. Two CRK values
are computed, one based on top-down (TD) and one on bottom-up (BU) damage.
Equation (2), also from the MEPDG (MEPDG 2007), converts the TD and BU cracking
factors into percent slabs cracked. These formulas were used in this study to determine
percent slabs cracked based on RadiCAL damage calculations, which utilized the same
fatigue transfer function (equation 3) and Miner’s Hypothesis (Miner 1945) for fatigue
damage accumulation as the MEPDG for this analysis. The damage values, DIF,
computed by RadiCAL vary depending on pavement dimensions, traffic, environment,
and other input parameters for each pavement test section included in this study.
CRK (1)
Where: CRK = Predicted amount of bottom-up or top-down slab
cracking (fraction)
DIF = Fatigue damage level after design period using Miner’s
Hypothesis for linear fatigue damage accumulation
Where: CRACK = Total amount of transverse or longitudinal
cracking (%)
CRKBU = Predicted amount of bottom-up cracking (fraction)
CRKTD = Predicted amount of top-down cracking (fraction)
Where: N = Number of repetitions to failure
MOR = Modulus of rupture of the concrete
σ = Applied maximum stress level at particular node
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Longitudinal cracking prediction and analysis
While eight different JPCP sections were analyzed with RadiCAL for this project, the
results from four pavements in three different climate regions are presented.
1. Interstate 80 through Solano County in the central valley climate region
2. Highway 101 through Santa Barbara County in the south coast climate region
3. Highway 58 through Kern County in the central valley climate region
4. Highway 86 through Imperial County in the desert climate region
The basic experimental design and number of RadiCAL runs for each pavement in
addition to RadiCAL input parameter limitations are shown in Table 1. A consistent
process was used to predict longitudinal cracking for each pavement. Input parameters
were selected, RadiCAL was run and the results compared to measured field performance.
RadiCAL currently offers eight different options for fatigue analysis. The results
presented here were obtained using the MEPDG fatigue function with non-linear
temperature profiles using the Non-linear area (NOLA) method (Hiller and Roesler
2008a; Hiller and Roesler 2009). Analysis was performed assuming a constant EBITD
value of -6ºC. Table 1. RadiCAL input parameters.
Input Parameter
(1) Pavement life
(age at time of
analysis) 0, 5, 10, 20, 30, 40 years or yearly As appropriate for age at
(2) Two-way
Year 1 AADTT
Value depends on analysis period Depends on analysis period
(3) Climate
Bay Area
Central Valley
High Desert
Low Mountain
North Coast
South Coast
As appropriate
(4) PCC
thickness 20, 25, or 30 cm
interpolated if different
(5) Lane width
3.8 m
(6) Joint spacing 3.8 m, 4.8 m
closest value to actual is
selected or interpolated with
multiple runs
(7) Shoulder type
Tied PCC or
Asphalt Concrete (AC)
(8) Modulus of
rupture (MOR)
As measured
(9) Transverse
joint load transfer
20, 50, 70, or 90% 20% or 50% due to lack of
dowel bars for load transfer
(10) EBITD
-22ºC to 0ºC
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Due to several issues, Caltrans now promotes the use of dowel bars and less rigid
bases, which will help reduce the level of EBITD in their JPCPs. While many of the
pavement structures analyzed in this study are no longer constructed by Caltrans, the use
of RadiCAL to verify the longitudinal cracking mechanisms from these sections helps
validate the software as a mechanistic tool for all types of fatigue cracking.
I-80 Solano. Interstate 80 (I-80) was constructed in 1965 with 20 to 25cm JPCP slabs
over a 10cm CTB base. Two-way AADTT varied from approximately 3,500 at 10 years
to 8,000 at 40 years. PCC flexural strength was consistently calculated between 1.45 to
5.0MPa, with one section at 3.52MPa. Joint spacing varies from 4.2m continuous to
5.2m/3.6m alternating. For the RadiCAL analysis, 4.5m joint spacing was used. It should
be noted that joint spacing has a significant non-linear effect on the predicted fatigue
damage for both transverse and longitudinal cracking. While 4.5m is a good
representation of the average joint spacing, smaller (or larger) individual slabs may
perform differently than the average slab dimension.
Figure 2 shows yearly predicted and measured longitudinal percent-cracked-slab
levels versus pavement age for Sections 248 and 255, two of nine examined. There are
two measured cracking values, which were taken from the Caltrans database. Due to
uncertainty about the actual percentage of cracked slabs in the field, minimum and
maximum longitudinal cracking estimates are shown as described previously. Based on
the damage-to-cracking transfer functions (Equations [1] and [2]), for five sections
RadiCAL predicted reasonable percent-slabs-cracked estimates. For the remaining four
sections, an uncalibrated RadiCAL program tended to underpredict longitudinal cracking.
1960 1970 1980 1990 2000 2010
Longitudinal Cracking (%)
Minimum Measured
Maximu m Measured
RadiCAL Predi cted
(a.) I-80 Section 248
Figure 2. Predicted and actual longitudinal percent cracked slabs versus year for
(a.) I-80 Section 248 and (b.) I-80 Section 255.
US-101 Santa Barbara. US-101 through Santa Barbara was constructed in 1958 and
originally consisted of 20 to 22cm JPCP slabs with 4.6m joint spacing. In 1993, this
pavement was cracked, seated, and overlaid with 10 to 13cm of asphalt concrete. The
initial two-way AADTT was approximately 1800 for two sections examined and 900 for
the remaining four sections. Flexural strengths ranged from 4.14 to 4.83MPa.
Coefficient of thermal expansion of the PCC ranged from 10.55 to 10.87*10-6/°C.
Figure 3 presents annual predicted and measured longitudinal percent cracked
slabs versus pavement age for sections 300 and 303. RadiCAL significantly
1960 1970 1980 1990 2000 2010
Minimum Measured
Maximu m Measured
RadiCAL Predi cted
(b.) I-80 Section 255
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overpredicted percent cracked slabs for section 300 due to the reduced flexural strength
found from concrete samples in those sections, while correctly predicting cracking for
section 303. RadiCAL predicted distress consistent with the varying estimated flexural
strength of the sections. The remaining sections generally showed overprediction in
percent cracked slabs when lower flexural strength correlations were used. Better
accuracy of the predictions would be expected using higher strengths in the RadiCAL
1950 1960 1970 1980 1990 2000
Longitudinal Cracking (%)
Minimum Measured
Maximu m Measured
RadiCAL Pred icted
(a.) US-101 Section 300
Figure 3. Predicted and actual longitudinal cracking versus year for (a.) US-101
Section 300 and (b.) US-101 Section 303.
SH-58 Kern. State Highway 58 (SH-58) through Kern County was constructed in 1961 as
21cm thick JPCP slabs with 4.5m joint spacing. It was overlaid with 6cm asphalt concrete
after cracking and seating in 1992, therefore cracking data only exists until this time.
Two-way AADTT ranged from approximately 2600 at ten years to 4700 at thirty years.
Flexural strength calculated from compressive strengths of field cores ranged from
4.0MPa to 4.55MPa.
Figure 4 presents the predicted and measured longitudinal percent slabs cracked
versus pavement age for sections 423 and 427 on SH-58. While RadiCAL predicts
longitudinal cracking within the maximum/minimum band from the available PMS data,
the program overpredicts the amount of longitudinal cracking seen in Section 427 for a
lower flexural strength section. Another major factor that may lead to this overprediction
is the lack of a site-specific EBITD value, which is very sensitive to fatigue cracking
prediction (Hiller and Roesler 2008b).
Figure 5 shows the predicted versus measured percent longitudinal slabs cracked
for all sections analyzed over time. RadiCAL accurately predicted the slab cracking for
Sections 423, 424, and 425 (MOR ranging from 5.24 to 5.34MPa), while overpredicting
fatigue cracking for Sections 426 and 427 (MOR ranging from 4.70 to 5.03MPa). In
general, the RadiCAL program predicted longitudinal cracking well for the sections with
higher measured flexural strength in most cases. Further confirmation of concrete
flexural strengths in addition to calibration of the fatigue cracking prediction model may
help remedy these differences between predicted and actual cracking performance.
1950 1960 1970 1980 1990 2000
Minimum Measured
Maximu m Measured
RadiCAL Pred icted
(b.) US-101 Section 303
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1960 1965 1970 1975 1980 1985 1990 1995 2000
Longitudinal Cracking (%)
Minimum Measured
Maximu m Measured
RadiCAL Predi cted
(a.) SH-58 Section 423
Figure 4. Predicted and actual longitudinal cracking versus year for (a.) SH-58
Section 423 and (b.) SH-58 Section 427.
0 20 40 60 80 100
Longitudinal Cracking Predicted from RadiCAL
(% Slabs Cracked)
Longitudinal Cracking Measured from PMS (% Slabs Cracked)
Sections 423, 424, and 425
Sections 426 and 427
Figure 5. Predicted versus actual longitudinal cracking for all SH-58 sections.
SH-86 Imperial. State Highway 86 (SH-86) through Imperial County was constructed in
1994. It consists of 20 to 25 cm thick JPCP slabs with a joint spacing of 4.2m, and a 10 to
15cm asphalt concrete base. Joint spacing of 4.5m was used as an input in RadiCAL.
Initial two-way AADTT was 1750. PCC modulus of rupture calculated from
compressive strengths on field cores varied from 4.0 to 4.4MPa.
1960 1965 1970 1975 1980 1985 1990 1995 2000
Minimum Measured
Maximu m Measured
RadiCAL Predi cted
(b.) SH-58 Section 427
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Figure 6 presents the predicted versus measured longitudinal percent cracked
slabs versus pavement age and various EBITD levels. The upper of the pairs of points
represents 20 percent load transfer, the lower point represents 50 percent as these
pavement were undoweled and typically had low load transfer efficiencies. For lower
EBITD values, RadiCAL correctly predicted the level of longitudinal slabs cracked, while
larger EBITD values lead to poorer predicted values for this section.
0 5 10 15
Longitudinal Cracking (% Slabs Cracked)
Pavement Age (yrs)
Figure 6. Sensitivity analysis of predicted and actual longitudinal cracking
versus age for SH-86 Section 636.
Network-Level EBITD Value
Similar comparisons of measured and calculated cracking performance for different
assumed values of EBITD for other sections were included in (Signore et al. 2008). Due
to variation in predictive performance among the sections studied, it was therefore
intuitive to combine all the data from this study into one group to determine an
“optimum” EBITD value for designers to assume for JPCP pavements in California. Two
issues were readily apparent: (1) in general, RadiCAL tended to overpredict the amount of
longitudinal slab cracking; and (2) the accuracy of the prediction is highly dependent
upon the value of EBITD used for analysis. It must be noted that this consistent
overprediction may in part be due to the fact that these comparisons have been made
against visual field measurements and that no records or account of slab replacement due
to slab cracking were available. Therefore the levels of overprediction may be overstated
and could be rectified through a calibration process of the transfer function in RadiCAL.
A sum-of-squares analysis was performed to determine the EBITD value for use
with RadiCAL that produces longitudinal cracking performance estimates that most
closely match measured performance, Figure 7 shows a box-and-whisker plot of the
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difference between predicted and measured longitudinal cracking versus EBITD value
used for analysis. The top and bottom of the solid bar represent the 75th and 25th
percentile measurements respectively. Therefore, in general, the larger the solid bar, the
greater the variation in prediction of the middle half of the data. The white bar in the
center of the solid bar is the median (50th percentile) measurement. Therefore, the closer
the center of the solid line is to zero, the more accurate the prediction. The lines above
and below the solid bars, the “whiskers,” represent the extreme values determined from
the data. Based on a review of these four sets of data, it is evident that an EBITD value of
-3°C produced the most accurate prediction of percentage of longitudinal slab cracking
over the course of the pavement lives for these sections studied under the current set of
transfer functions in place in RadiCAL.
EBITD = 0 C EBITD = -5C EBITD = -10C EBITD = -20C
Difference Longitudinal Percent Cracked Slabs
(Predicted – Measured)
EBITD = 0 C EBITD = -5C EBITD = -10C EBITD = -20C
Difference Longitudinal Percent Cracked Slabs
(Predicted – Measured)
EBITD = 0 C EBITD = -5C EBITD = -10C EBITD = -20C
Difference Longitudinal Percent Cracked Slabs
(Predicted – Measured)
EBITD -18C EBITD = -21C EBITD = -21C EBITD = -29C
(0F) (-5F) (-10F) (-20F)
Figure 7. Box plot of accuracy of RadiCAL prediction of longitudinal cracking
percentages versus EBITD.
While this network-level approach may provide a ballpark number for design, the
effects of specific climates, geometries, restraint, curing conditions, and other factors
should be considered when designing a joint concrete pavement for a specific project.
Initial Fatigue Cracking Verification
Using the four JPCP routes noted in the previous sections, the fatigue damage predicted
by RadiCAL was paired with the maximum and minimum longitudinal cracking from the
Caltrans PMS as shown in Figure 8. These data points were compared with the MEPDG
damage to cracking model presented in equation (1) as shown in the black line of Figure
8. While the plotted data demonstrates a great deal of scatter, a clear trend of increasing
longitudinal cracking with damage predicted by RadiCAL can be observed that matches
the sigmoidal curve from equation (1). This initial verification helps start a more in-
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 574
depth look at calibration of the fatigue model and damage-to-cracking model utilized in
RadiCAL for more accurate predictions of longitudinal fatigue cracking in JPCPs.
0.0001 0.001 0.01 0.1 1 10 100 1000
Longitudinal Cracking Measured
(% Slabs Cracked)
Longitudinal Fatigue Damage Predicted by RadiCAL
Minimum Cracking
Maximum Cracking
Figure 8. California longitudinal cracking data fitted with MEPDG fatigue
calibration function.
Conclusions and Recommendations
A study was undertaken to assess the capability of RadiCAL to predict longitudinal
cracking in JPCP structures in different climate regions. Over 3,000 RadiCAL runs were
performed on over forty pavement sections within eight stretches of California highways.
Analysis of the pavement sections presented here has shown that the longitudinal
cracking predictive capabilities of RadiCAL can be accurate. However, the predicted
cracking levels are dependent upon a number of critical input factors. RadiCAL was able
to correctly predict zero or near-zero longitudinal cracking in newer pavements as seen in
Highway 86. With the most accurate EBITD values selected, RadiCAL was able to
predict consistently accurate levels of cracking for periods up to thirty years on I-80, US-
101, and SH-58. The accuracy of the RadiCAL predictions was also improved for
sections with higher concrete flexural strengths, generally above 5MPa. Issues such as
random joint spacing, non site-specific EBITD values, and a PMS that does not clearly
identify cracking by transverse or longitudinal cracking further complicated this effort.
While RadiCAL assesses a broad range of concrete pavement performance
parameters, enhancements to future versions should include capabilities to account for
localized differences in soils, paving times, slab lengths, and coefficients of thermal
expansion. These refinements could address the above mentioned pavement variability
Hiller, Signore, Kannekanti, Basheer, and Harvey
10th International Conference on Concrete Pavements 575
issue and provide insight into the differences in field performance they create. Further
calibration and refinement of the program could then be made to enhance its usefulness
for predicting longitudinal cracking.
Finally, the authors believe that RadiCAL can be used in its present form to
supplement designs based upon MEPDG. The latter could be run to find a design that
does not fail in transverse cracking and/or faulting, while RadiCAL can then be used to
check the design’s longitudinal cracking performance. A sensitivity analysis for
thicknesses and load transfer efficiencies surrounding the expected design values could
be performed to see if longitudinal cracking is limited to a maximum value, for example,
of ten percent at 30 years. Further calibration of RadiCAL will enhance its ability to
serve as an independent JPCP design program in the future.
Acknowledgment and Disclaimer
The research team would like to acknowledge the co-developer of RadiCAL, Professor
Jeffery Roesler of University of Illinois at Urbana-Champaign. This paper describes
research activities requested and sponsored by the California Department of
Transportation (Caltrans), Division of Research and Innovation. Caltrans sponsorship is
gratefully acknowledged. The contents of this paper reflect the views of the authors and
do not reflect the official views or policies of the State of California or the Federal
Highway Administration.
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Public transit, particularly buses in Baltimore City, plays a vital role in sustainable transportation in the United States as well as providing mobility to those without cars. Bus pads are usually constructed in the street, adjacent to a bus zone, to accommodate the weight of a bus. Bus pads are highly durable areas of the roadway surface at bus stops, usually made of concrete, addressing the common issue of asphalt distortion at bus stops. These concrete slabs bear the burden of the daily stream of buses better than asphalt. The major problem with the asphalt bus pads is shifting asphalt creating waves or ripples under buses’ weight, and when asphalt shifts, it cracks and can create potholes. Roadway pavements need to be strong enough to accommodate repetitive bus axle loads. Exact pavement designs will depend on site specific soil conditions. Areas where buses start, stop, and turn will be of particular concern for pavement design. Concrete pavement is desirable in these areas to avoid the failure problems that are experienced with asphalt. Concrete bus pads should be constructed based on the bus service frequency and type of transit vehicle used. However, if the concrete bus pad is not properly designed, it will encounter different problems with serviceability and strength of the slab. During a case study in Baltimore City that was used to collect preliminary data for the proposed research, it was observed that most of the concrete bus pads require more than regular routine maintenance due to surface cracks and local failure, resulting in major replacement costs for Baltimore City. Lack of appropriate load identification and definition of critical load scenarios for the appropriate design of the concrete bus pad were noted as shortcomings in addition to the design assumption of uniform distribution of soil pressure under the concrete slab, which was not the case noted in the field. This research carried out a field study and extracted two concrete strips in longitudinal and transvers axis from a bus pad in Baltimore. The concrete strips were tested at the Structures Laboratory of Morgan State University, under a four-point bending produced by two concentrated monotonic loads. The load and deflection were measured using precise instruments including LVDTs and load cells to investigate the concrete strips’ performances under the applied load until failure. All load cases and combinations were identified and determined based on possible loading scenarios. A numerical model was developed and soil-structure interaction was studied using the Winkler method. The maximum design forces and moments were extracted from the FE model, which considers the effect of moving loads on a two-way slab as well as the temperature. This research evaluated the load-bearing capacity of the current design of Baltimore bus pads and compared it to the tested strips as well as the required bending capacity of FE models. Results show that both design and construction of bus pads in Baltimore need to be modified. In conclusion, design and construction recommendations were proposed to enhance bus pads’ life span in Baltimore City to address the current issues and reduce maintenance costs.
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SUMMARY Traditional methods for road concrete pavements design do not take into account the structural contribuition of cemented bases and its fatigue consumption under the traffic loads. Sections designed without major care about the structural reponses of those bases can develop early cracks, decreasing the structural capacity of the pavement. This paper presents a closed numerical solution for computing the maximum flexural stress on cemented bases when the concrete slab is loaded by a dual tire single axle of 100 kN; wheel loads had been considered near the transversal joint for plain concrete pavements. No bond and full contact between slab and base are supposed. On the basis of experimental relation for fatigue of a typpical cement treated crushed stone it was allowed to define consistent thicknesses for bases as function of the forecasted number of load repetitions.
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This paper demonstrates a simplified method to capture the effect of temperature non-linearity on rigid pavement stress responses utilizing a single parameter (NOLA) and a graphical understanding of temperature non-linearity. This method allows users to easily post-process rigid pavement solutions with linear temperature assumptions to account for these self-equilibrating stresses at any depth in the slab. In addition, this paper also reveals the impact of accounting for self-equilibrating stresses in terms of projected structural fatigue damage at locations along both the top and bottom of the transverse joint and longitudinal edge of a concrete pavement section using a rigid pavement analysis program named RadiCAL.
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The prediction of fatigue cracking in jointed concrete pavements has traditionally focused on transverse cracking initiating from the bottom of the slab and propagating both up and across the slab width. However, field surveys of several locations, particularly in the Western United States indicate that alternative fatigue cracking mechanisms, such as top-down and bottom-up longitudinal cracking, top-down transverse cracking, and corner cracking, exist in substantial quantity. To better understand these alternative cracking mechanisms and to account for such mechanisms in both the analysis and design of jointed concrete pavements, a mechanistic analysis software program named RadiCAL was developed. Mechanistic parameters such as built-in and cyclical curling, axle spacing effects, load transfer, etc. was utilized to predict the critical fatigue crack location using the method of linear fatigue damage accumulation. Several sites in California that have exhibited both traditional and alternative fatigue cracking mechanisms were examined using RadiCAL to validate the proposed mechanistic analysis principles for stress and fatigue damage development.
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The assumption of a linear temperature change through the slab depth has been overwhelmingly used in pavement analysis since Westergaard proposed a curling solution for rigid pavements. However, the actual temperature profiles through the slab thickness are primarily nonlinear. These nonlinear temperature profiles produce stresses that can be divided into three components: a uniform temperature stress, an equivalent linear curling stress, and a nonlinear self-equilibrating stress. It is the self-equilibrating stress component that often goes unaccounted for in concrete pavement stress prediction and can significantly affect the tensile stress magnitude and critical location. This paper presents a solution for a piecewise method and proposes a simplified method termed NOLA, or nonlinear area, that easily captures the effect of temperature nonlinearity on rigid pavement responses. The proposed NOLA method enables the use of a three-dimensional temperature frequency distribution that allows simple postprocessing of rigid pavement curling stress solutions derived from a linear temperature assumption. The impact of accounting for self-equilibrating stresses in terms of projected fatigue damage levels and critical cracking locations is also explored using a mechanistic-based rigid pavement analysis program called RadiCAL.
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In an attempt to better understand and predict concrete pavement behavior, the incorporation of material and climatic factors in mechanistic-empirical design methods is fast becoming a necessity. With the wide range of climatic regions in the United States, the inclusion of localized factors can have a profound effect on the observed critical distresses and fatigue life of rigid pavements. A mechanistic analysis and design software (RadiCAL) was developed employing an influence line approach in conjunction with Miner’s Hypothesis to calculate the fatigue damage at numerous locations in the slab for typical jointed plain concrete pavement sections. Permanent built-in curling of concrete slabs, stress range-based concrete fatigue transfer functions, and the inclusion of self-equilibrating stresses from non-linear temperature profiles were found to have considerable effects on the predicted location and magnitude of concrete fatigue damage. A parameter named NOLA (Non-Linear Area) was developed and implemented in RadiCAL to provide a simple, visual method to account for these self-equilibrating stresses that are readily ignored in pavement analyses. Top-down and bottom-up transverse, longitudinal, and corner cracking were found to be critical fatigue mechanisms depending on the pavement geometry, climatic zone, and material parameters selected. These results are in contrast to the assumed bottom-up, mid-slab transverse cracking mechanisms, which are exclusively predicted using traditional mechanistic-empirical techniques. These predicted fatigue failure modes and locations correspond well to the wide variety of observed fatigue cracking patterns on existing rigid pavements sections in California and show promise for calibration and design adaptation in other regions as well. Results show that the use of doweled transverse joints will reduce the likelihood of these alternative cracking mechanisms significantly. The exception to this is with the use of widened slabs where the predominant predicted fatigue cracking mechanism in RadiCAL remains longitudinal cracking regardless of load transfer levels at the transverse joint. University of California Pavement Research Center, California Department of Transportation, Illinois Department of Transportation unpublished is peer reviewed
Differential expansion and contraction between the top and bottom of a concrete slab results in curling. Curling affects slab stresses and deflections and is an important component of any mechanistic-empirical design procedure for concrete pavements. Although some curling is caused by temperature and moisture gradients that fluctuate daily, a significant portion of the curling can be attributed to the combined effects of nonlinear "built-in" temperature gradients, irreversible shrinkage, and creep, which can be represented by an effective built-in temperature difference (EBITD). A procedure for estimating EBITD of in situ slabs using a falling-weight deflectometer and a finite-element program is presented. This procedure was used to estimate EBITD for instrumented slabs at Palmdale and Ukiah, California. Differences in restraints (from adjacent slabs, shoulder, base friction) and variability in concrete material properties resulted in EBITDs ranging from -5°C to greater than -30°C. Copyright © 2005 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.
Differential expansion and contraction between the top and bottom of a concrete slab results in curling. Curling affects stresses and deflections and is an important component of any mechanistic-empirical design procedure. A significant portion of curling can be attributed to the combined effects of nonlinear "built-in" temperature gradients, irreversible shrinkage, moisture gradients, and creep, which can be represented by an effective built-in temperature difference (EBITD). Several instrumented test sections utilizing several design features were constructed and evaluated using the Heavy Vehicle Simulator (HVS) in Palmdale, California. These instrumented slabs were loaded with a half-axle edge load without wander in order to study the effects of curling and fail the slab sections under accelerated pavement testing. A procedure for estimating EBITD using loaded slab deflections was developed using the HVS results. The advantages of using loaded slab deflections are that they can be used for measuring EBITD of slabs with high negative built-in curl and can also be adapted for a Falling Weight Deflectometer, making the procedure efficient and cost-effective for the back-calculation of EBITD of in-service pavements. Differences in restraints and variability in concrete material properties resulted in EBITDs ranging from –5�C to greater than –30�C. The HVS field tests were also used to examine Miner's hypothesis along with various fatigue damage models. Results indicate test slabs cracked at cumulative damage levels significantly different from unity. New models that incorporate stress range and loading rate along with peak stresses were developed. The coefficients for these models were developed to incorporate transverse cracking, longitudinal cracking, and corner breaks. The models can also be used for slabs that exhibit high negative EBITD. For slabs susceptible to high shrinkage gradients, microcracking resulting from restraint st
TP 60-00 -Standard Method of Test for Coefficient of Thermal Expansion of Hydraulic Cement Concrete American Association of State and Highway Transportation Officials
AASHTO (2005) TP 60-00 -Standard Method of Test for Coefficient of Thermal Expansion of Hydraulic Cement Concrete American Association of State and Highway Transportation Officials, Washington, D.C.
User's Guide for Rigid Pavement Analysis for Design in California (RadiCAL) Software. Version 1.2. UC-Berkeley/Caltrans. Partnered Pavement Research Center
  • Je Hiller
  • Jr Roesler
Hiller JE, Roesler JR (2005) User's Guide for Rigid Pavement Analysis for Design in California (RadiCAL) Software. Version 1.2. UC-Berkeley/Caltrans. Partnered Pavement Research Center, Richmond, CA.,