ayp26 16 hma seasonal temperature
TRANSCRIPT
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Fecha de Recepción Artículo: ABRIL 17 DE 2013
Fecha de Aceptación Artículo: MAYO 09 DE 2013
XIAODI HU
Wuhan Institute of Technology
Wuhan, Hubei Province, China
ALLEX E. ALVAREZ
The Department of Civil Engineering
University of Magdalena, Santa Marta
Magdalena, Colombia
GEOFFREY S. SIMATE
School of Chemical and Metallurgical Engineering
University of the Witwatersrand, Johannesburg
P/Bag 3, Wits 2050, South Africa
OSCAR J. REYES
The Department of Civil Engineering
Nueva Granada Military University
Bogotá D.C., Colombia
LUBINDA F. WALUBITA
Texas Transportation Institute (TTI) – The Texas
A&M University System, College Station
Texas, USA
HMA seasonal-temperature and modulicharacterization for perroad analysis of long-life
(perpetual) pavements: a case study
A s f a l t o s y P a v i m e n t o s
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AbstractPerRoad is one of the mechanistic-empirical
software used for the structural design and analysis
of perpetual pavements. By definition, a long-life orperpetual pavement (PP) is a thick rut- and fatigue
-resistant pavement structure designed to have a
structural life in excess of 50 years; often designed
for heavily-trafficked highways. In this study, the
applicability and suitability of the PerRoad software
(Version 3.2 denoted herein as PerRoad3.2) for
modeling the Texas PP structures was evaluated
with a focus on characterizing the Texas environment
and dynamic modulus of hot-mix asphalt (HMA)
as a function of seasonal-temperature variations.
Both temperature and modulus are required as the
PerRoad3.2 input data. The in-service PP sectionson State Highway 114 in Texas (USA) were used as
the case study. Both the generated yearly-seasonal
temperature profiles and the seasonal HMA dynamic
moduli as a function of temperature are presented
in this paper including moduli predictions with the
PerRoad model. Overall, the study indicated that
the adopted approach successfully generated the
structural (layer moduli) and seasonal (temperature
profiles) information required for PerRoad3.2
analysis. However, more research is recommended to
further validate the methodology and the applicability
of the PerRoad3.2 to the Texas PPs.
Keywords: PerRoad, Perpetual pavement,
Hot-mix asphalt, Temperature, Dynamic modulus
Introduction
PerRoad is a mechanistic-empirical (M-E) based
software used for the structural design and response
(stress, strain, and deflection) modeling of perpetual
pavements (PP). It is also used for predicting therutting and cracking (bottom-up fatigue) life of PPs.
However, PerRoad software (Version 3.2, denoted
as PerRoad3.2) (Timm 2004), does not directly
generate layer thickness designs; instead it evaluates
a proposed design against user defined failure criteria
through manual and iteratively changing of the layer
thicknesses and/or the material properties. Details
of the PerRoad software can be found elsewhere
(Timm 2004). Note that while some latest versions
of the PerRoad software maybe available to date, the
version available to these researchers at the time of
this work was Version 3.2, denoted as PerRoad3.2.
During execution, the PerRoad3.2 computes
the worst case pavement response using a five
layered linear-elastic program, WESLEA (Timm
2004). If the computed response (i.e., stresses,
strains, and/or deflections) exceeds the specified
mechanistic threshold values, then the pavement
design thicknesses and/or material properties need
to be adjusted accordingly. The current M-E design
procedure for PP is based on two main response-
limiting criteria, namely (Timm 2004, Walubita &
Scullion 2007):
• The horizontal tensile microstrain at the bottom
of the lowest asphalt layer (εt): ≤ 70µε.
• The vertical compressive microstrain at the top of
the subgrade layer (εv):≤ 200µε.
The principle assumption behind the PerRoad3.2
is that PP structures should have no fatigue cracking
or deep-seated rutting problems during their design
life (Timm 2004). For given traffic loading and
environmental conditions, a pavement structure
is theoretically considered a PP if the above M-E
response threshold values are met; otherwise the
material properties and/or layer thicknesses need to
be modified.
Like any other pavement design and analysis
software, the required input data for PerRoad3.2
include the pavement structure, environment,
material properties, and traffic loading. The focus
of this paper was on the pavement structure,
environment, and material property characterization,
which are relatively more complex to model than
traffic loading; in particular for PP structures.
Details of the traffic loading spectra can be found
elsewhere (Timm 2004, Walubita & Scullion 2007).
As input data, the current version of the
PerRoad3.2 requires the environment to be
characterized in terms of the yearly seasonal
subdivisions (basically summer, fall, winter, and
spring) as a function of temperature variations
(Timm 2004). Each season is further categorized in
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HMA seasonal-temperature and moduli characterization for perroad analysis of long-life (perpetual) pavements: a case study
7/25/2019 AyP26 16 HMA Seasonal Temperature
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terms of the number of weeks per year. The material
properties required for PerRoad3.2 analysis are the
layer elastic moduli (E) (or layer moduli) and the
Poisson’s ratio (n). Since the year is subdivided
into seasons, the layer moduli for the HMA must
also preferably be specified for each season as afunction of seasonal temperature variations and
pavement depth. Alternatively, the layer moduli
can be assumed and then a temperature correction
applied during the PerRoad3.2 analysis. The former
approach was applied in this study.
By definition, a PP is a thick rut-resistant and
fatigue (bottom-up)-resistant pavement structure
designed to have a structural life in excess of 50
years (particularly for the intermediate and bottom
layers); often designed for heavily-trafficked
highways. During their service lives, PP structuresgenerally require no major structural maintenance
and/or rehabilitation activities, but are subject to
periodic surface maintenance and/or renewals in
response to surface distresses in the upper layers
of the pavement structure (Sidess & Uzan 2008,
Timm & Newcomb 2006, Timm 2004, Walubita
& Scullion 2007). Deep seated structural defects
such as bottom-up fatigue cracking and/or full-depth
rutting are considered unlikely or if present, are
very minimal; hence these structures are ideal for
heavily-trafficked highways (APA 2002).
In Texas, PP structures have been used on heavy
truck trafficked-highways where the 20-year traffic
estimate of 80 kN equivalent single axle loads is in
excess of 30 million. Ten Texas PP sections were in-
service as of 2009. As part of a study to validate the
Texas PP structural design concept and recommend
a suitable design software, the objectives of the work
presented in this paper were twofold:
• 1) To characterize the Texas environment
and material properties (layer modulus) as a
function of seasonal-temperature variations; that
are required as the PerRoad input data for the
structural and seasonal information.
• 2) To evaluate the applicability and suitability
of the PerRoad3.2 software for the structural
design, modeling, and performance prediction of
the Texas PP structures.
To achieve these objectives, the research
approach incorporated computational analyses using
the enhanced integrated climatic model (EICM) to
generate the yearly-seasonal temperature profiles as
well as extensive laboratory testing to characterize
the HMA dynamic moduli. The in-service PP sectionson State Highway (SH) 114 in the Fort Worth
District of Texas were used as the case study.
In the paper, after presenting the methods and
materials (including climatic data, laboratory
testing, and description of the SH 114 PP
structural sections), the results are presented
in terms of: (i ) environmental characterization,
HMA dynamic modulus characterization, and (iii )
PerRoad3.2 demonstration examples. Discussion
and synthesis of results are then presented, followed
by a summary of findings and recommendations toconclude the paper.
Materials and
Methods
This section presents the experimental design
defined for this study, which includes climatic data
and dynamic modulus (DM) laboratory testing as
well as the description of the PP sections on SH 114.
Climatic data characterization
Based on the AASHTO Mechanistic-Empirical
Pavement Design Guide (AASHTO), the EICM in
combination with the hourly climatic data from a
given weather station has the potential to generate
temperature profiles at various depths within agiven pavement structure. Table 1 presents the mean
pavement surface- and subsurface-temperatures
obtained using the EICM, based on the climatic data
for the closest weather station (Alliance Airport) to
the SH 114 location in Fort Worth.
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Table 1.
Fort Worth seasonal subdivisions and mean temperatures
Season Summer Fall Winter Spring 1 Spring 2
Duration (weeks) 10 (19.2%) 16 (30.8%) 2 (3.8%) 18 (34.6%) 6 (11.5%)
0-mm depth (°C) 46 31 4 25 13
90-mm depth (°C) 42 30 6 21 12
287-mm depth (°C) 39 29 9 20 14
500-mm depth (°C) 38 29 12 20 16
550-mm depth (°C) 37 29 11 19 15
As shown in Table 1, the Fort Worth environment
was subdivided into five representative seasons,
together with the associated durations. The spring
season was sub-divided into two sub-seasons, Spring1 and Spring 2, merely to improve on the accuracy
for the temperatures following the winter season and
for the temperatures proceeding the summer season,
respectively.
Laboratory DM testing
DM testing of HMA was conducted in accordance
with the AASHTO TP 62-03 test procedure
(AASHTO 2001). Consistent with the TxDOT mix-
design procedures (TxDOT 2007), replicate HMAspecimens were molded at 7±0.5% air voids and
tested at various temperatures ranging from -10°C
to 54°C. While the DM test was conducted over the
entire loading frequency spectrum (i.e., 0.1, 0.5,
1, 5, 10, and 25 Hz), only the DM data obtained
at 10 Hz were used for the PerRoad3.2 analysis
(AASHTO 2001, Walubita & Scullion 2007). A
loading frequency of 10 Hz is considered a close
approximation of a truck speed on a Texas highway
(Walubita & Scullion 2007)
The SH 114 PP structuralsections
The SH 114 PP structures in Fort Worth District
consists of two five-layered sections; namely the
Superpave (denoted as FW 01) and the Conventional
(denoted as FW 02). Both sections consist of two 3.7
m wide lanes and are subjected to the same traffic
loading of about 18,000 ADT (average daily traffic),
27.3% trucks, and a designated maximum speedof about 113 km/h. Figure 1 shows the layer and
material characteristics for these PP sections.
Lay er M at eria l Bin de r + A gg reg at eThickness
(mm)La yer M at eria l Bin de r + A gg re gat e
Thickness
(mm)
112.5-mm
HDSMA
6.8% PG70-28 +
Igneous/Granite50 1
12.5-mm
HDSMA
6.8% PG70-28 +
Igneous/Granite50
2 19-mm SFHMAC4.2% PG76-22 +
Limestone75 2
TxDOT
Type C
4.4% PG70-22 +
Limestone75
3 25-mm SFHMAC4.0% PG70-22 +
Limestone325 3
TxDOT
Type B
4.5% PG64-22 +
Limestone325
419-mm SFHMAC
(RBL)
4.2% PG 64-22 +
Limestone100 4
TxDOT Type C
(RBL)
5.3% PG 64-22 +
Limestone100
5Stabilized
Subgrade6% Lime Treated 200 5
Stabilized
Subgrade6% Lime Treated 200
8 8
FW 01: Superpave
Subgrade
FW 02: Conventional
Subgrade
Figure 1.
SH 114 PP structural sections (Walubita & Scullion 2007)
In Figure 1, HDSMA stands for heavy-duty stone
mastic (matrix) asphalt and SFHMAC stands for
stone-filled hot-mix asphalt concrete. RBL refers to
the rich-bottom layer, which is primarily designed
to retard bottom-up fatigue cracking as well as
providing impermeability functions. TxDOT Type B
and C are conventional Texas coarse- to dense-graded
22-mm and 16-mm nominal maximum aggregate
size (NMAS) mixes, respectively (TxDOT 2004).
The preceding number in the materials column, e.g.,
12.5 mm in front of HDSMA, refers to the NMAS,
such as 12.5-mm NMAS. PG refers to performance-
graded binder (Asphalt Institute 1996). Note that
NMAS is defined as one sieve size larger than the
first sieve to retain more than 10% of the aggregate.
Table 2 presents the aggregate gradations of the
mixes included in the SH 114 PP structure.
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HMA seasonal-temperature and moduli characterization for perroad analysis of long-life (perpetual) pavements: a case study
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Table 2.
Aggregate gradations of mixtures used in the SH 114 PP structure
Sieve Size
Design Aggregate Percent (%) Passing
Layer 1 Layer 2 Layer 3 (RRL) Layer 4 (RBL)
(mm)12.5-mmHDSMA
19-mmSFHMAC
Type C25-mm
SFHMACType B
19-mmSFHMAC
Type C
1½” 37.5 100 100 100 100 100 100 100
1” 25 100 100 100 100 100 100 100
⅞” 22 100 100 100 100 96.9 100 100
¾” 19 100 91.8 - 89.3 - 92.0 -
⅝” 16 100 - 99.8 - 90.3 - 99.3
½” 12.5 93.3 77.1 - - - 77.6 -
⅜" 9.375 65.5 - 77.3 - 67.7 - 76.6
No. 4 4.75 27.0 - 49.9 33.6 44.5 - 53.5
No. 8 2.36 - 23.1 - 23.2 - 24.8 -
No. 10 2 28.7 - 34.2 - 30.2 - 34.8
No. 16 1.18 - 15.3 - 15.6 - 15.3 -
No. 30 0.6 - 9.4 - 9.7 - 8.9 -
No. 40 0.425 - - 15.4 - 12.9 - 15.6
No. 50 0.3 - 6.0 - 6.2 - 5.6 -
No. 80 0.18 12.0 - 7.0 - 5.6 - 7.2
No. 200 0.075 8.4 2.0 4.0 2.3 3.2 2.3 4.0
*RRL = rut-resistant layer (main structural layer for the Texas PP concept).
Layer Thickness (mm) Material Comment
1 125
All top HMA layers(12.5-mm HDSMA +19-mm SFHMAC)
(or 12.5- mm HDSMA+Type C)
Compound all the top HMA layers into one composite layer;with a summed average modulus value, i.e., average modulus
value of all the layers
2 325 Rut-resistant HMA layer(25-mm SFHMAC or Type B)
Main structural layer - vary the design layer thickness
3 100RBL (lowest HMA layer)
(19-mm SFHMAC or Type C)Calculate tensile strains at the bottom
(≤ 70 µε)
4 200 Stabilized subgrade 6% lime-treated subgrade soil material
5 ∞ Subgrade, e.g. soil Calculate vertical compressive strains on top (≤ 200 µε)
Figure 2.
SH 114 PP structural configuration for PerRoad analysis
Since PerRoad3.2 is limited to evaluating
pavement systems with no more than 5 layers,
including the subgrade, the SH 114 structural
sections (Figure 1) were configured as shown in
Figure 2. With the PerRoad3.2 and considering the
Texas PP structural design concept, the main layersof structural interest for M-E strain response analysis
and thickness design are the RBL (horizontal tensile
strains at the bottom ≤ 200 me), the subgrade
(vertical compressive strains on top ≤ 200 me), and
the rut-resistant layer (vary the thickness) (Figure
2). While the other layer thicknesses are held fixed,
the design intent is to vary the thickness of the rut-
resistant layer (the main structural layer) until a
suitable thickness is attained that simultaneously
meets the prescribed M-E strain responses. On thisbasis, a simplistic approach as shown in Figure 2 was
adapted to combine the top layers into one composite
layer with a summed average modulus value.
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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Results andAnalysis
The results are presented, analyzed, and discussed
in the subsequent text and includes the environment,
moduli values, and sensitivity analysis of the PerRoad
software. PerRoad demonstration examples are also
presented in this section.
Environmental characterizationFigure 3(a) shows the generated yearly pavement
surface temperature variations based on the Fort
Worth Alliance Airport weather station, and
Figure 3(b) is a plot of the temperature-frequencydistribution as a function of pavement depth and
seasonal subdivisions.
(a)
Winter,3.8% @ 4 °C
Spring2, 11.5%@ 13°C
Spring1, 34.6%@ 25°C
Fall, 30.8%@ 31°C
Summer,19.2% @46°C
0%
20%
40%
60%
80%
100%
-20 0 20 40 60 80
F r e q u e n c y
Temperature (°C)
0 mm Depth
25 mm Depth
87.5 mm Depth
287.5 m m Depth
500 mm Depth
550 mm Depth
(b)
Figure 3.
(a) Yearly pavement surface temperature variations, and (b)
temperature cumulative frequency distributions and seasonal
subdivisions.
From Figure 3(a), the minimum temperature
calculated was -3.8 °C, occurring at the pavement
surface and in winter. The maximum summer
temperature calculated was 64.6 °C, also occurring
at the pavement surface. In general and as
theoretically expected, the highest temperaturevariation was recorded at the pavement surface
with a coefficient of variation (COV) of 30%, and
decreased with pavement depth. These temperature
statistics are shown in Figure 4.
-3.8C0.1C
4.1C
6.4C
26C
25.4C
25C
64.6C
50.3C
43.1C
40.9C
0
100
200
300
400
500
-20 0 20 40 60 80
P a v e m e
n t D e p t h ( m m )
Temperature (°C)
Minimun (Winter) Average
Maximum (Summer)
24%
21%
20%
0
100
200
300
400
500
600
10% 15% 20% 25% 30% 35%
P a v e m e n t D
e p t h ( m m )
Coefficien t of Variation (COV)
Figure 4.
Temperature statistics (yearly minimum-maximum and
coefficient of variation)
The temperature statistics shown in Figure 4 are
a typical representation of the Texas environment.
Low winter temperatures of around -3.8 °C or
even lower and high summer temperatures of
around 65.6 °C are not uncommon in Texas. As
expected, it is also evident from Figure 4 that the
winter temperature profile tended to increase with
pavement depth and vice versa for the summer
Edición No. 26 Enero - Junio de 2013 Bucaramanga · Colombia ISSN 0123-8574 AsfaltosyPavimentos
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HMA seasonal-temperature and moduli characterization for perroad analysis of long-life (perpetual) pavements: a case study
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temperature profile. Summarized, these figures
suggest that the effects of seasonal and daily
temperature fluctuations are more pronounced at
the pavement surface and that the temperature
is less variable (smaller COV) with increasing
pavement depth. Evidently, these results confirm
that the materials used as the pavement surfacing
are exposed to the harshest environmental
conditions, particularly with respect to the
temperature fluctuations. Consequently, care
should always be exercised when selecting and
designing materials for the surfacing layers
especially the asphalt-binder. Stiffer polymer
modified asphalt-binders such as PG 76-22, which
are relatively less temperature sensitive, are
usually preferred.
Winter and summer seasonaltemperature-depth relationships
Using the data shown in Figure 3, seasonal
temperature-depth relationships representing winter
and summer seasons were developed as shown in
Figure 5. Based on Figure 5, the following second-
order polynomial relationships were formulated to
illustrate the temperature-depth relationships for the
SH 114 location in Fort Worth (Texas), for summer
and winter seasons:
T summer =0.00003t 2 - 0.0219t + 44.75 (1)
T winter
= ‒ 0.00002t 2 - 0.0178t + 5.3698 (2)
In Equations 1 and 2, T is the pavement
temperature in ºC and t is the pavement depth in mm.
For the SH 114 location in Fort Worth (Texas), the
above relationships can be used to approximate the
pavement design temperatures for the HMA layers
for the summer and winter seasons, respectively.
Winter and summer represent the lowest and highest
temperatures that are considered critical for the
HMA modulus characterization and response due to
HMA’s visco-elastic nature.
y = -2E-05x2 + 0.0178x + 5.3698
R² = 0.8526
y = 3E-05x2 - 0.0219x + 44.75
R² = 0.8029
0
10
20
30
40
50
60
0 100 200 300 400 500 600
T e m p e r
a t u r e ( °
C )
Pavement Depth (mm)
Winter Summer
Poly. (Winter) Poly. (Summer)
Figure 5.
Seasonal temperature-depth relationships for Fort Worth
HMA modulus characterization
As discussed previously, PerRoad3.2 requires
the HMA layer moduli to be varied seasonally as
a function of temperature and pavement depth;
otherwise a temperature correction needs to be
applied. In this study, the HMA layer moduli were
obtained from extensive laboratory testing with the
DM test (AASHTO 2001). Additionally, HMA layer
moduli predictions with the PerRoad3.2 model were
also conducted and are discussed in this section.
Modulus test results and analysis
Figure 6 shows the HMA DM values plotted as a
function of temperature for the materials included in
the SH 114 PP sections (Figure 1). Notice in Figure
6 the typical visco-elastic nature of HMA (i.e., the
modulus is exhibiting, as expected, a decreasing
trend with an increase in temperature and vice versa
with a decrease in temperature).
0
6000
12000
18000
-20 -10 0 10 20 30 40 50 60
M o d
u l u s ( M P a )
Temperature (°C)
12.5-mm HDSMA
19-mm SFHMAC
19-mm SFHMAC (RBL)
25-mm SFHMAC
TxDOT Type C
TxDOT Type C (RBL)
TxDOT Type B
PerRoad Pred ictions
Figure 6.
Laboratory dynamic modulus (DM) test results at 10 Hz
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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Using the generated seasonal-depth temperatures in Table 1 and Figure 3(b), the HMA moduli at
various temperatures and pavement depths were approximated from Figure 6 and are listed in Table 3.
Table 3.
Mean HMA dynamic modulus as a function of temperature and pavement depth
Depth (mm) HMA MixModulus (MPa)
-10°C 4 °C 21°C 38 °C 54 °C
0 ~ 50 12.5-mm HDSMA 14004 13700 4082 1227 1165
75 ~ 150 Type C 15872 14142 4461 1882 1048
150 ~ 325 Type B (RRL) 14142 12445 6150 2048 1124
> 325 Type C (RBL) 12859 5923 3737 938 841
75 ~ 150 19-mm SFHMAC 17458 15341 7322 2648 1255
150 ~ 325 25-mm SFHMAC (RRL) 15341 14114 9405 3061 1896
> 325 19-mm SFHMAC (RBL) 13790 9260 4171 1282 669
*RRL = rut-resistant layer (main structural layer for the Texas PP concept; RBL = rich-bottom layer
In a nutshell, the generated Figure 6 or Table 3 can be used to approximate the HMA layer modulus at
any desired temperature of interest; thus generating the required input moduli values for the PerRoad3.2
software. As an example, the seasonal HMA layer moduli for the SH 114 PP sections (see Figure 2) were
estimated as shown in Table 4. These would be the design moduli values to input for PerRoad3.2 analysis; with
no temperature correction.
Table 4.
Seasonal HMA layer moduli characterization for PerRoad3.2 input
Seasons
FW 01 – Superpave Section (MPa) FW 02 – Conventional Section (MPa)
Layer 1(12.5-mm HDSMA
+ 19-mm SFHMAC)
Layer 2(RRL)
Layer 3(RBL)
Layer 1(12.5- mmHDSMA+ Type C)
Layer 2(RRL)
Layer 3(RBL)
Summer (46 ºC) 1723 2620 1034 1137 1378 896
Fall (31 ºC) 4481 6550 2171 4136 5171 2137
Winter (4 ºC) 14520 14113 9259 13920 12445 5923
Spring 1 (25 ºC) 5412 7584 3516 4516 6136 3447
Spring 2 (13 ºC) 11721 12410 6894 8273 11031 5515
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In general, Table 4 shows that the Superpave
section is stiffer than the Conventional section
based on the higher HMA layer moduli values. This
trend is partly due to the fact that the Superpave
volumetric mix-design is composed of a coarser
aggregate gradation (Table 2) and used higher PGasphalt-binder grades with relatively lower asphalt-
binder contents (Figure 1) than the Conventional
mix-design (Walubita & Scullion 2007).
In general, the smaller the percentage passing,
the coarser the aggregate gradation is. Conversely,
Table 2 indicates that the aggregate gradations
for the Superpave mixes (Layers 2, 3, and 4) were
relatively coarser than the Conventional mixes. This
partly explains the stiffness and higher moduli values
of the Superpave section. Field moduli measurements
with the falling weight deflectometer (FWD) hadalso yielded similar findings (Walubita & Scullion
2007). The Superpave section was in fact found to
be about 1.2 times stiffer than the Conventional
section when the FWD moduli were analyzed at a
similar reference temperature of 25 °C (Walubita
& Scullion 2007).
PerRoad HMA DM predictions
PerRoad3.2 uses the following exponential model
to predict the HMA modulus as a function of known
temperature (T ) values and material coefficients(Q i ) (Timm 2004):
+
×= 3
22 )(
1
Q
QT
AC eQ E (3)
AC
Where E AC
is the predicted HMA DM in MPa,
T is the temperature in ºC, and Q i are the material
coefficients. The default Q i values in-built into the
PerRoad3.2 software are: Q 1 = 16693.4;Q
2 = 26.2;
and Q 3 = -1459.7. For a temperature spectrum
ranging from -17.8 °C to 71.1 °C, DM values were
predicted using Equation 3 for comparison with the
laboratory determined values. The predicted DM
values based on Equation 3 and the default material
coefficients Q i are shown in Figures 7 and 8. Figure
8 is the frequency-modulus distribution as a function
of pavement depth and is synonymous to Figure 3b.
Based on the comparison analysis conducted, the
PerRoad3.2 predictions were only comparable with
the laboratory DM values for the 19-mm SFHMAC
(RBL) mix within the temperature range of -10 °C
to 54.4 °C; see Figure 7). This was attributed to the
material coefficients, Qi , of the exponential model.
y = 0.0035x4 - 0.1363x3 - 5.6528x2 - 103.76x + 14697
0
5000
10000
15000
20000
-20 -10 0 10 20 30 40 50 60
M o d u l u s ( M P a )
Temperature (°C)
19-mm SFHMAC
25-mm SFHMAC
19-mm SFHMAC (RBL)
PerRoad Predictions
Poly. ( 25-mm SFHMAC)
Figure 7.Comparison of PerRoad HMA dynamic moduli (DM) predictions
Winter,3.8% @ 4 °C
Spring2, 11.5%@ 13°C
Spring1, 34.6%@ 25°C
Fall, 30.8% @31°C
Summer, 19.2%@46°C
0%
20%
40%
60%
80%
100%
0 2000 4000 6000 8000 10000 12000
F r e q u e n c y
Modulus (MPa)
0 mm Depth
25 mm Depth
87.5 mm Depth
287.5 mm Depth
500 mm Depth
550 mm Depth
Figure 8.
HMA dynamic moduli (DM)-cumulative frequency distributions
and seasonal subdivisions
In consideration of the HMA mixes evaluated in
this study, a review of both Figures 6 and 7 suggests
that a third-order polynomial model, as illustrated
in Equation 4, would best describe the moduli-
temperature relationship better than the exponential
model in Equation 3.
43
2
2
3
1 aT aT aT a E AC
+++= (4)
AC
Where T is the temperature anda iare regression
coefficients representing material constants. For
all the HMA mixes shown in Figure 6 and the
PerRoad3.2 model predictions, the coefficient of
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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correlation values obtained for the fitted third-
order polynomial trend lines were greater than
95%. Figure 9 shows the linear relationship
between the laboratory determined DM values and
the third-order polynomial predictions for the 25-
mm SFHMAC and Type B mixes. Both the slopesand the coefficient of correlation of the fitted linear
trend lines are around a unit, indicating that the
laboratory-measured and predicted moduli were
almost equivalent. Thus, a third-order polynomial
model best describes the DM-temperature
relationships of the HMA mixes evaluated in this
study.
y = 1.1443x - 2183.6
R² = 0.9976
y = 1.3303x - 580.29
R² = 0.9954
0
5000
10000
15000
20000
0 5000 10000 15000 20000
M o d u l u s P r e d i c t
e d ( M P a )
Modulus Measured (MPa)
25-m m SFHMAC
TxDOT Type B
Figure 9.
Comparison between laboratory-measured and predicted DM
values
Sensitivity evaluation of thePerRoad3.2 HMA modulus model
As a means to calibrate the PerRoad3.2 model
for DM characterization of the Texas HMA mixes, a
sensitivity analysis was conducted to develop material
coefficients that best fit the laboratory determined
DM values. The sensitivity analysis was based on the
sum of square error (SSE) minimization technique
through iterative variation of the material coefficients
(Q 1, Q
2, and Q
3 ) to match the laboratory measured
DM values. The fundamental concept is to get a zero
error difference between the laboratory measured and
the predicted DM values as illustrated in Equation 5.
[ ] [ ]( ) 00.0loglog 2 ≅−= −∑ measured lab predicted E E SSE (5)
And:
+
×== 3
22 )(
1
Q
QT
AC predicted eQ E E (6)
AC
In this SSE minimization approach, convergence
is achieved by iteratively changing theQ i coefficients
until Equation 5 is satisfied or at least the SSE is
close to zero. For this analysis, the HMA mixes were
grouped into five independent categories; (1) SMA,
(2) Type C, (3) 19-mm SFHMAC, (4) Type B, and
(5) 25-mm SFHMAC. The generated Q i
values that
best satisfied Equation 5 are listed in Table 5 and the
respective demonstration results for the SMA mixare illustrated in Figure 10.
Table 5.
Developed Q i coefficients for the HMA mixes evaluated
HMA Mix Q1
Q2
Q3
SMA 1.80E+04 1.80E+01 -1.59E+03
Type C 1.55E+04 2.20E+01 -1.99E+03
19-mm SFHMAC 1.67E+04 1.83E+01 -1.95E+03
Type B 1.67E+04 2.92E+01 -2.47E+03
25-mm SFHMAC 1.67E+04 2.10E+01 -2.47E+03
Minimum Q i
1.55E+04 1.80E+01 -2.47E+03
Average Q i (COV) 1.67E+04; (3.26%) 2.17E+01; (18.99%) -2.09E+03; (15.53%)
Maximum Q i
1.80E+04 2.92E+01 -1.59E+03
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0
5000
10000
15000
20000
0 50 100 150
M
o d u l u s ( M P a )
Temperature (°C)
E(measured)_SMA
E(predicted)_SMA
Expon. (E(measured)_SMA)
y = 0.9932 x + 1019.9R² = 0.95 49
0
5000
10000
15000
20000
0 5000 10000 15000 20000
M o d
u l u s P r e d i c t e d ( M P a )
Modulus Measured (MPa)
Figure 10.
Example of measured and predicted HMA DM values for the
SMA mix
The results shown in Table 5 and Figure 10 indicate
that the appropriate material coefficients applicable
to the Texas HMA mixes evaluated in this study are
the average summation of the Q i values reported for
all the HMA mixes listed in Table 5 (Q 1 = 1.67E+04;
Q 2 = 2.17E+01; Q 3 = -2.09E+03). In particular,Q 3
is substantially different from the default value of
-1.46E+03. The average Q 1
value did not change,
while a different Q 2 value was obtained. With these
new Q i values, the DM predictions were reasonably
comparable to the laboratory measured DM values with
an R 2 value of over 95% (e.g., Figure 10). However,
more studies of this nature are recommended with a
wide spectrum of Texas HMA mixes to further validate
the PerRoad3.2 model for application in Texas.
PerRoad demonstrationexamples
As a demonstration example, the SH 114 PP
structures in Figure 1 were structurally analyzed using
PerRoad3.2. For the traffic load spectra, the SH 114
was functionally classified as a Rural Interstate with
a traffic loading configuration shown in Figure 11.
Figure 11.
PerRoad3.2 input load spectra for SH 114 (1 kip ≅ 4.45 kN)
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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i c i ó n N o .
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Both the Superpave and Conventional sections
(Figure 2) were evaluated. Based on FWD
measurements, the average base and subgrade moduli
were determined as 345 and 82 MPa, respectively,
and were maintained constant throughout the seasons
(Walubita & Scullion 2007). Note that althoughthe base and subgrade modulus vary seasonally
(predominantly as a function of moisture), the
primary focus of this study was the HMA modulus.
So, for simplicity of PerRoad analysis and to put more
weighting on the HMA, the base and subgrade moduli
values were conservatively held constant at 345 and
82 MPa, respectively, throughout the seasons.
An example of a PerRoad3.2 input screen for
the structural and seasonal information for the
SH 114 Conventional section is shown in Figure
12 (layer moduli values shown correspond to thesummer season). Variability in terms of the layer
moduli and thickness were taken as 20% and 5%,
respectively (Medani et al 2004, Timm 2004).
Typical M-E strain responses for PP were used as the
performance criteria, at a selected 95% reliability
level (i.e., ≥ 95%). These performance criteria and
the PerRoad3.2 results for both PP sections are
listed in Table 6.
According to Table 6, both structural sections
sufficiently met the prescribed M-E performancecriteria with a structural life of up to 58 years based
on the tensile strain criteria (for the conventional
section). The computed strain responses were at least
99% below the threshold value. In consideration
of the thickness and conservative design nature
of these PP structural sections, these numerical
results were not unexpected. From Table 6, bottom-
up fatigue cracking based on the tensile strain
criterion is the theoretically expected governing
distress mechanism. With a predicted zero damage
and an infinite structural life, rutting problems are
theoretically least expected on these sections. Todate, pavement surface rutting in the field has also
remained negligibly very low; only about 2.3 mm
was measured in summer 2009, after over four years
of conventional trafficking (Walubita et al 2010).
No cracking was observed either.
Figure 12.
Example of PerRoad3.2 input structure for SH 114 - Conventional section
(1 psi ≅ 6.89E-3 MPa, 1 in ≅ 25 mm, 1 F = 1.8 C + 32)
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Table 6.
Summary of performance criteria and PerRoad3.2 results for SH 114
M-E Criteria Layer and Location Section %Below CriticalDamage per Million
AxlesStructural Life
(Years)
Horizontal tensile
strain ≤ 70 µeLayer 3 at the bottom Superpave 99.92% 3.00E-05 103
Conventional 99.46% 2.38E-04 58
Vertical compressive
strain ≤ 200 µeLayer 5 on top Superpave 100% 0.00E+00 ∞
Conventional 100% 0.00E+00 ∞
As a second demonstration example, the in-service 6.4 km and 4 laned (2 northbound and 2 southbound)
PP structural section on Interstate Highway (IH) 35 in Laredo District (La Salle County, Zumwalt 2) wasevaluated using the PerRoad3.2 software. The IH 35 on this PP section (road mile maker 49+0.431 –
53+0.427) was functionally classified as a Rural Interstate with the following traffic load spectra: AADT
(average annual daily traffic) = 11,900; %Trucks = 46.2; %Growth rate = 3; %Trucks in design lane =
60; %Directional distribution= 50. The seasonal subdivisions, environmental temperatures (based on EICM
analysis), and the HMA moduli values (based on DM testing) were characterized similar to the approach
discussed previously for Fort Worth and SH 114 highway. The hourly climatic data from Cotulla Airport
weather station were used for generating the yearly-seasonal temperature profiles. The input data and results
for this section are shown in Tables 7 and 8, respectively.
Table 7.
PerRoad3.2 structural and seasonal input data for IH 35 (Zumwalt 2, Laredo)
Season Summer Fall Winter Spring1 Spring2
Duration, weeks 10 16 2 18 6
Representative mean temperature, ºC 49 31 3 24 10
Layer 1: Modulus of all upper HMA layers, MPa
(thickness =150 mm, v =0.35)1724 4827 13790 7240 6206
Layer 2: Modulus of the 25-mm SFHMA layer, MPa
(thickness = 200 mm, v=0.35)2758 6206 23443 10343 14480
Layer 3: Modulus of RBL, MPa
(thickness = 75 mm, v =0.35)
1345 2930 7412 6206 5516
Layer 4: Base modulus in MPa
(thickness = 200 mm, v =0.40)345 345 345 345 345
Layer 5: Subgrade modulus, MPa(thickness = ∞, v =0.45)
138 138 138 138 138
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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Table 8.
Summary of performance criteria and PerRoad3.2 results for IH 35 (Zumwalt 2, Laredo)
M-E Criteria Layer and Location%BelowCritical
Damage perMillion Axles
Structural Life(Years)
Vertical deflection ≤ 5 mm Layer 1 on top 100% N/A N/A
Horizontal tensile strain ≤ 70 µe Layer 3 at the bottom 99.68% 1.26E-04 90
Vertical compressive strain ≤ 200 µe Layer 5 on top 100% 0.00E+00 ∞
Table 8 shows that the IH 35 PP section
structurally met the M-E response criteria with a
prediction of 99% below the threshold value and a
structural life of up to 90 years. The predicted and
expected governing distress mechanism is fatigue
cracking based on the tensile strains. Both the
vertical deflections and rutting (based on the vertical
strains) are 100% below the threshold value (i.e.,
no predicted damage or infinite structural rutting
life). In concurrence with these results, the 2009
measured field surface rutting was only 1.8 mm
after five years of service. No cracking was observed
either (Walubita et al. 2010)
Discussion and
synthesis of the
resultsThe methodological approach adapted in this study
for the environmental and HMA DM characterization
yielded reasonable input data for the PerRoad3.2
analyses. The PerRoad3.2 computational results
were consistent with theoretical expectations. In
particular, the generated moduli-temperature
profiles constitute a resourceful database for future
design preferences.
Both the generated temperatures and HMA
moduli values are consistent and representative
of the typical Texas environmental conditions
and local materials. The formulated seasonal
temperature models for winter and summer are
useful in estimating the design temperatures. The
seasonal HMA DM profiles, on the other hand, will
be useful in approximating the design HMA moduli
values at any desired temperatures and pavement
depth.
Typical and design HMA
moduli values at 25 ºCTypical HMA DM values were generated from
extensive laboratory testing and are listed in
Table 9. In this table, the HMA moduli values
“Recommended for Design” are the proposed
values to be considered for future designs of Texas
PP, which were computed based on all of the
available DM laboratory test data. These moduli
values were recommended on the conservative
basis that their usage analytically yielded the most
optimal PP structural designs in terms of the layer
thickness and projected performance as indicatedby the strain computations for both rutting and
fatigue crack prediction (Walubita et al. 2010).
Notice in Table 9 the high stiffness nature of the
25-mm SFHMAC mix with a minimum modulus of
5516 MPa. This is consistent with the mix-design
volumetrics given previously in Figure 1 and Table
2. The 25-mm SFHMAC is in fact a performance
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mix that is typically used as the main structural rut-resistant layer in the Texas PP structural designs. As
expected, the fine-graded Type F mix constitutes one of the least stiff mixes. The PFC mixes are optional,
usually adopted as non-structural, frictional surface mixes.
Table 9.
Summary of HMA moduli results at 25 ºC (and 10 Hz) based on laboratory DM testing
Type of HMA Lab Range (MPa) Lab Average (MPa) Recommended for Design (MPa)
PFC (permeable friction course) 2069-2758 2413 2413
SMA (performance mix) 3448-4827 4137 4482
19-mm SFHMAC (19-mm NMAS; performance mix) 4137-6895 5516 5516
25-mm SFHMAC (25-mm NMAS; performance mix) 5516-10343 8274 6895
RBL (e.g., 19-mm Superpave; dense-graded) 2758-4137 3448 3448
Texas Type A (coarse-graded) 5171-8274 6206 5516
Texas Type B (22-mm NMAS; dense-graded)) 4827-6895 5516 5516
Texas Type C and D (dense-graded) 3448-4482 3448 3448
Texas Type F (fine-graded) 2069-2758 2482 2413
PerRoad HMA modulus
model calibration of the
material coefficients
With the exception of one mix type, namely 19-
mm SFHMAC, the results presented in this study
generally showed that the currently existing default
material coefficients (Q i ) included in PerRoad 3.2
are not readily applicable to the Texas HMA mixes
evaluated in this study. Furthermore, while the
PerRoad3.2 prediction model is an exponential
fit function, Figure 7 indicated that a third-order
polynomial model provided a better functional fit
to model the Texas laboratory measured HMA DM
values as a function of temperature.
These findings were not unexpected as the
PerRoad3.2 model material coefficients were
developed based on different materials and not
calibrated to the Texas materials and environment.
A sensitivity analysis using the SSE minimization
technique was consequently conducted to calibrate
the PerRoad HMA moduli predictive model. From the
SSE sensitivity analysis, new material coefficients
for the Texas HMA mixes evaluated in this study
were developed and these are as follows:
Q 1= 1.67E+04; Q
2 = 2.17E+01; Q
3 = -2.09E+03
Note that these material coefficients are an
average representation of all the Texas HMA mixes
assessed. For specific mixes, the Q i values listed in
Table 5 can be used. Application of these coefficients
in the PerRoad3.2 model yielded a satisfactory
fit with the laboratory measured DM values (R 2
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
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i c i ó n N o .
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value greater than 95%). Evidently, these results
suggest that the PerRoad3.2 model still needs to
be calibrated and validated over the entire Texas
environment and typical HMA mixes, prior to
State-wise application. Otherwise, unrepresentative
designs maybe undesirably obtained.
Validation of the Texas PPstructural design concept
Based on the PerRoad3.2 analyses and the
examples evaluated in this study, the Texas PP
structural design concept was found to be sufficiently
valid, with a potential for even further optimization.
The Texas PP structures evaluated in this paper (SH
114 and IH 35) satisfactorily met the PP responsecriteria, with a predicted reliability of 99% below
the threshold values and a rutting/cracking life
greater than 20 years; thus validating the Texas PP
structural design concept.
Cracking due to tensile strains was computationally
predicted as the possible governing distress
mechanism, with an expected performance life of
up to 58 years. No rutting damage was numerically
predicted in either PP structures. With the thicker and
stiffer nature of the HMA mixes/layers used in these
PP structures, infinite rutting life prediction was not
theoretically un-expected. Even under high summer
temperatures of over 37.8 °C, the pavement surface
rutting on the IH 35 PP sections have remained
significantly low (an average of 2.3 mm after over 4
years of service); thus substantiating the PerRoad3.2
predictions (Walubita et al 2010).
In theory, however, and based on the Texas
historical experience of flexible HMA pavements, a
surface treatment, minor rehabilitation, or an overlay
would typically be required within the first 20 years
of service to restore the pavement (surface) functional
characteristics among other purposes (Walubita &Scullion 2007). Additionally, PerRoad3.2 analyses
indicated that some of the Texas PP structures were
conservatively designed and that the total HMA
layer thickness could have been reduced by at least
100 mm in some instances. For example, reducing
the rut-resistant layer thickness by 100 mm in the
SH 114 PP structure yielded the following results;
37 years structural life with 98% prediction below
the threshold level; based on the tensile strain
responses. This result is an indication that the Texas
PP structural design concept has some potential to
be further cost-effectively optimized. Overall, these
PerRoad3.2 results provide an analytical validationof the Texas PP structural design concept.
Applicability and suitability ofthe PerRoad3.2 for modelingthe Texas PP structures
Based on this study and the results presented
herein, the PerRoad3.2 software was found to be
suitable for validating the Texas PP designs andpredicting the rutting/cracking life. The software
is user-friendly and fast to run, at most 3 minutes.
However, the following limitations and challenges
were found to be associated with the PerRoad3.2
software when applied to the Texas PP:
• Total number of layers: PerRoad3.2 is limited
to 5 layers, including the subgrade, and thus,
the PP structures have to be compounded into
composite layers (particularly the HMA layers
above the rut-resistant layer); which could be a
potential source of errors. However, the lowestHMA layer (RBL) need not be compounded as
this is where the tensile strain response is to be
computed. Also, the rut-resistant layer (e.g.,
25-mm SFHMAC) need not be compounded
as this is the layer whose thickness needs to be
varied. In addition, the modulus value for this
layer is substantially higher (approximately 1.5
to 2 times higher) than the other HMA layers.
• Layer thickness design: The PerRoad3.2 software
does not directly generate layer thickness
designs; instead this has to be done iteratively bymanually changing the layer thicknesses (and/or
material properties) and matching the predicted
performance against the desired threshold values.
• Damage ratio: The “Years to D=0.1” output
represents an estimation of the amount of time,
given the current traffic volume and growth as
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well as damage accumulation rate, before the
damage number (as calculated by Miner’s Law)
will reach a value of 0.1. This value is considered
to be a very conservative damage value, and
needs to be reviewed, since most traditional M-E
designs typically uses 1.0 as the damage value to
total failure.
• Output data: Unlike the previous PerRoad Version
2.4, PerRoad3.2 software does not give the
actual computed strain responses in the output
dialogue box. Inclusion of this option would
greatly aid the users in subsequent analyses and
making appropriate interpretation of the results
thereof.
• Calibration: Development of local transfer
function and material coefficients for the Texasmaterials and environmental conditions is
recommended. A limited preliminary laboratory
calibration was conducted for the material
coefficients, Q i , in this study. However, field
calibration is still required along with extensive
sensitivity analyses.
• Material Coefficients: To further improve on the
accuracy of the analysis, material specific Q i
values similar to the ones listed in Table 5 can
be developed for different mix types/categories
such as SMAs, SFHMAs, Type B, Type C, etc andincorporated in the PerRoad software as default
values; instead of just using average values.
However, such an undertaking entails conducting
an extensive research study with a wide array of
Texas HMA mixes and modifying the PerRoad
software; which was beyond the scope of this
paper.
• Composite Layer Moduli Values: In this study,
a simplistic approach was adapted to combine
the top two layers into one composite layer
with a summed average modulus value during
PerRoad analysis. For future studies and for
the purpose of further validating these results,
it is recommended to use a weighted average
modulus value determined as a function of the
layer thickness.
Summary and
recommendationsBased on extensive laboratory testing,
computational modeling, and field performance
evaluation of two perpetual pavements as presented
in this paper, the major findings of the study are
summarized as follows:
• The methodological approach adapted in this
study for the environmental and HMA DM
characterization for PerRoad3.2 analysis was
sufficiently sound and yielded satisfactory
results. The generated moduli-temperatureprofiles constitute a resourceful database for
future design of Texas PP structures.
• The formulated seasonal temperature models are
useful for estimating the design temperatures
in the Fort Worth District, while the seasonal
HMA DM profiles are ideal for approximating
the design HMA moduli values at any desired
temperatures and pavement depth. Additionally,
laboratory HMA moduli values for typical HMA
mixes at 25 ºC and 10 Hz based on the DM
testing have been proposed for the future designof Texas PP. These reference moduli values
can be used in most M-E design models and
software.
• Sensitivity analyses of the PerRoad3,2 HMA
modulus prediction model yielded local material
coefficients (Q i ) that produced a reasonable
temperature fit-functions for the laboratory
determined DM values. The predicted HMA DM
values with the newly developed coefficients were
comparable to the laboratory DM measured
values with R 2 values greater than 95%. By
contrast, the default material coefficients for
the PerRoad3.2 exponential DM model did not
produce satisfactory results. Nonetheless, the
PerRoad3.2 model still needs to be calibrated
and validated over the entire Texas environment
and typical HMA mixes, prior to consideration
for State-wise application.
Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA
E d
i c i ó n N o .
2 6 E n e r o - J u n i o d e 2 0 1 3 B u c a r a
m a n g a ·
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1 2 3 - 8 5 7 4
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• Based on the PerRoad3.2 analyses for both the
SH 114 PP and IH 35 PP structures evaluated,
the Texas PP structural design concept was
found to be sufficiently valid, but with potential
for further optimization.
Overall, the generated seasonal-temperature and
moduli values were found to be reasonably sufficient
for use not only in the PerRoad3.2 software but could
also be utilized in other M-E analysis applications.
On the whole, PerRoad3.2 software was also found
to be suitable for modeling and validating the Texas
PP designs and predicting the rutting/cracking life.
However, more computational analyses including
model calibration and addressing the challenges
highlighted in this paper are strongly recommended.
Lastly, it should be stated that while this case studywas focused only on the Texas PPs and conditions,
the approach and methods utilized can be extended
and applied to other PP structures, environments,
and conditions.
AcknowledgementsThe authors thank TxDOT and the Federal
Highway Administration (FHWA) for their support
in funding this research study and all those who
helped during the course of this research work.
In particular, special thanks are due to Zachary
L. Rolan, Gautam Das, Nick Sweet, Mohammad
Rhaman, and Charles Mushota for their help with
this work. Special thanks also go to David H.
Timm, the pioneer and proponent of the PerRoad
software.
DisclaimerThe contents of this paper reflect the views of
the authors who are responsible for the facts and
accuracy of the data presented herein and do not
necessarily reflect the official views or policies of any
agency or institute. This paper does not constitute a
standard, specification, nor is it intended for design,
construction, bidding, or permit purposes. Trade
names were used solely for information and not for
product endorsement.
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