ayp26 16 hma seasonal temperature

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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

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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

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



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.

Xiaodi HU • Allex E. ALVAREZ • Oscar J. REYES • Geoffrey S. SIMATE • Lubinda F. WALUBITA

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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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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.


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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


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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


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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


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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


25




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)


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26



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)


27




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


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28



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


29




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


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1 2 3 - 8 5 7 4


30



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


3




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.


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32



• 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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standards/MEPDG_hma_User_instructions.pdf

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ayp26 16 hma seasonal temperature

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