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Temperature sensitivity of foamed asphalt mixstiffness: field and lab studyPengcheng Fu a & John T. Harvey aa University of California at Davis , Davis, CA, 95616, USAPublished online: 08 Mar 2007.

To cite this article: Pengcheng Fu & John T. Harvey (2007) Temperature sensitivity of foamed asphalt mix stiffness: field andlab study, International Journal of Pavement Engineering, 8:2, 137-145, DOI: 10.1080/10298430601149486

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Temperature sensitivity of foamed asphalt mix stiffness: fieldand lab study

PENGCHENG FU* and JOHN T. HARVEY

University of California at Davis, Davis, CA 95616, USA

(Received 1 November 2005; revised 7 July 2006; in final form 15 September 2006)

Knowledge of the temperature sensitivity of foamed asphalt stiffness is very important in mix andstructural design, field non-destructive testing and advanced research. However, this subject has notbeen studied extensively, especially the effects of the stress state on the temperature sensitivity, which isessential to understand the behavior of weakly bonded granular materials. This paper first presentstriaxial resilient modulus testing results of foamed asphalt treated materials with various asphaltcontents at various temperatures. General observations are made in terms of the effects of the bulkstress, deviator stress, temperature and their interactions. Based on these observations, the temperaturesensitivity coefficient of foamed asphalt stiffness is defined and a simplified model to predict foamedasphalt mix stiffness at any triaxial stress state and temperature is proposed and validated. A procedureto normalize back-calculated resilient modulus to a standard temperature is also presented. Theessential step of this procedure is to estimate the temperature sensitivity coefficient based on the fieldtest results at various temperatures. Finally, an example is presented comparing the stiffness of afoamed asphalt material over two years. It was found that the stiffness did not change significantly overthe two years period, despite the accumulation of traffic loading.

Keywords: Foamed asphalt; Stiffness; Temperature susceptibility; Deep in situ recycling; Fallingweight deflectometer; Triaxial

1. Introduction

As a flexible pavement rehabilitation technique, Deep

in situ recycling with foamed asphalt (DISR-FA) has

been used in California for five years (Raffaelli 2004).

California has a number of climate regions and most

DISR-FA project locations have wide seasonal and daily

temperature variation (Ongel and Harvey 2004). Know-

ledge of the temperature sensitivity of foamed asphalt mix

properties, especially of stiffness, is an important issue in

both project level pavement mix and structural design and

advanced research for the following three reasons.

First, Young’s modulus (or more generally, stiffness) is

an important input parameter in mechanistic-empirical

pavement design and values at different temperatures are

needed. However, laboratory testing is usually carried

out at 20–258C while a significant range of subsurface

pavement temperatures (0–408C at a depth of 10–15 cm)

are expected in California.

Second, it is impossible to control the pavement

temperature during field testing, such as deflection testing

with the falling weight deflectometer (FWD). This makes

interpreting the test results very difficult since comparison

of moduli at the same temperature is essential.

Finally, studying the temperature sensitivity of foamed

asphalt treated mixes can provide useful insight into the

stabilization mechanism of foamed asphalt mixes. The

temperature sensitivity of the mix properties is primarily

due to the rheological characteristics of the asphalt binder

which is the stabilizing agent. The rheology of asphalt

binder has been studied very extensively (Heukelom 1966,

Heukelom 1973) as two of hundreds of examples. The

roles of the asphalt binder can be inferred by analyzing the

temperature sensitivity of the mix properties.

The temperature sensitivities of hot mix asphalt (HMA)

and foamed asphalt mix stiffness are somewhat similar in

that they are dependent on the asphalt rheology. However

their micro-structures and the roles of the asphalt binder

are different: foamed asphalt mixes have “partial coating

of large aggregate with ‘spot welding’ of mix with fines

mortar” while HMA has “coating of large aggregate with

controlled film thickness” (Jenkins 2000). The stiffness

of foamed asphalt mixes is fairly sensitive to the stress

state of the specimen, especially the bulk stress, which

International Journal of Pavement Engineering

ISSN 1029-8436 print/ISSN 1477-268X online q 2007 Taylor & Francis

http://www.tandf.co.uk/journals

DOI: 10.1080/10298430601149486

*Corresponding author. Email: pfu@ucdavis.edu

International Journal of Pavement Engineering, Vol. 8, No. 2, June 2007, 137–145

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is a typical behavior of weakly bonded granular materials.

Consequently, the effects of stress and the potential

interaction between temperature and stress must also be

considered when the effects of temperature on FA mix

stiffness are investigated.

Nataatmadja (2002) reported that the stiffness of foamed

asphalt mixes with binder content of 1.5–4.2% has a 30–

44% reduction when the temperature increases from 10 to

408C. Saleh (2006) investigated the temperature sensitivity

of the resilient modulus of foamed asphalt mixes and the

effects of asphalt binder’s temperature susceptibility and

curing conditions. However, both studies used the repetitive

indirect tensile test to measure the resilient modulus, which

cannot control the stress state of the specimen. In the study

presented in this paper, cyclic triaxial tests under different

combinations of confining stresses and deviator stresses

were used to investigate the effects of stress states and

temperature, as well as their potential interaction.

Another objective of this study is to investigate the

temperature sensitivity of foamed asphalt stiffness

observed in non-destructive tests in the field, such as

FWD test, and to present a method to normalize stiffnesses

measured at various temperatures to a standard tempera-

ture, especially when laboratory temperature sensitivity

test data are not available.

2. Lab test results: lab mixes

2.1 Material and test method

The granular material treated with foamed asphalt in this lab

study is the mix (70: 30: 5, in mass) of a recycled asphalt

pavement (RAP), coarse aggregates and inertial dust

passing the 75mm sieve. The gradation curves of the RAP

and the mix are shown in figure 1. Ninety-eight percentage

of the RAP passes the 9.5 mm sieve and the residual asphalt

binder has been mostly oxidized. Nine percent of the mix

passes the 75mm sieve. No active filler was used, so the

effects of the foamed asphalt as the only stabilizer can be

observed more clearly. The asphalt binder used is AR-4000

from the Shell Refinery in Richmond. The foam was

produced by a Wirtgen WLB-10 unit. The binder was

heated to 1508C and 2% foaming water was added. The

Expansion Ratio of the foam was 12 and the half-life

t1/2 ¼ 10 s. The granular materials weremixed by a pugmill

and the foam was ejected into the pugmill directly during

mixing. Triaxial specimens (nominal diameter ¼ 152mm

and nominal height ¼ 305mm) were compacted by the

Nottingham dynamic method, which uses a pneumatic

hammer. Before being tested, all specimens have been

cured in a forced draft oven at 508C for more than one week.

Since no active filler was involved, the curing is achieved

primarily by losing and redistributing moisture. Three

specimens with different foamed asphalt contents as shown

in table 1 were fabricated and tested.

The resilient modulus (Mr) test procedure followed the

“Long-Term Pavement Performance Protocol P46”,

resilient modulus of unbound granular base/subbase

materials and subgrade soils (LTPP P46) except that the

load sequence was adjusted. A part of the modified load

sequence used in this study and the original load sequence

in LTPP P46 are shown in figure 2. Five confining

pressures (20.7, 34.5, 68.9, 103.4 and 137.9 kPa) and three

deviator stresses for each confining stress were used. The

deviator stress levels are relatively low and no significant

structural damage was observed during testing. No

temperature control chamber was available, so the

temperature of the specimen was decreasing during

testing. Surface temperature and the temperature at the

specimen center were measured and the average value was

used as the equivalent temperature of the specimen.

2.2 The effects of confining, deviator stress,temperature and their interactions

Some observations were made with regard to the effects of

confining stress, deviator stress, temperature and their

interactions on measured resilient modulus of the foamed

asphalt specimens. Since the three specimens have various

foamed asphalt contents and density, the significance of each

effect varies. However, the following behaviors are common

to all of them, so they are only demonstrated by selected data.

More quantitative analysis will be shown in Section 2.3.

2.2.1 The effects of bulk stress. For Specimen B_30, the

resilient moduli measured at various temperatures and

stress states are plotted in figure 3 with respect to the bulk

stress u ¼ 3p0 þ sd, where p0 ¼ the confining stress and

sd ¼ the deviator stress. Corresponding equivalent

specimen temperature is labeled for selected points. The

results show that as the bulk stress increases, the resilient

modulus also increases. It can also be observed that

generally the specimen has lower stiffness when its

temperature is higher. The relatively large varianceFigure 1. Gradation of the RAP and the mix of RAP, aggregate and dust(70:30:5, in mass).

Table 1. Three specimens tested.

SpecimenBulk density

(g/cm3)Nominal foamed asphalt content

(%)

A_15 2.256 1.5B_30 2.157 3.0C_45 2.061 4.5

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of stiffness at each bulk stress level is due to the variation of

temperature and deviator stress, since they both have effects

on stiffness, as well as random errors involved in the testing

and measuring. The significant stress dependency of

resilient modulus indicates foamed asphalt mixes’ nature

as a weakly bonded granular material.

2.2.2 The effect of temperature. Figure 4 (the Mr axis is

in log scale) shows the relation between equivalent

specimen temperature and resilient modulus for different

bulk stresses. Test results for one (sd ¼ 2p0) out of three

deviator stresses for each confining stress are plotted for

simplicity. The one third of the total testing data for

Specimen A_30 shown, are representative. The effects of

deviator stress will be discussed in Section 2.2.3. The

temperature-Mr curves for different confining stresses are

generally parallel. This suggests that the effects of

temperature and bulk stress are largely independent.

2.2.3 Deviator stress and its interaction with

temperature. In the triaxial stress state, the deviator

stress has two opposite effects (Witczak and Uzan 1988).

First, increasing the deviator stress will increase the bulk

stress, which tends to increase the stiffness. On the other

hand, increasing the deviator stress also increases the

octahedral shear stress toct, which tends to reduce the

stiffness. Figure 5 shows the overall effects of deviator

stress at various temperatures. Only the testing results for

specimen A_15 at p0 ¼ 137.9 kPa and p0 ¼ 68.9 kPa are

plotted for demonstration. It can be observed that as the

temperature increases the materials tends to show more

“stress-softening” behavior. In other words, the effect of

deviator stress depends on temperature.

2.3 Model fitting

As shown in Section 2.2, the resilient modulus of foamed

asphalt is dependent on its stress state at a given

temperature. This stress dependency is a common

behavior for granular material and equation (1) is a

general model proposed by Witczak and Uzan (1988).

Mr ¼ k1pau

pa

� �k2 toct

pa

� �k3

ð1Þ

where pa ¼ atmospheric pressure used to nondimension-

alize stress; toct ¼ octahedral shear stress, and in triaxial

stress state toct ¼ffiffiffi2

psd=3; k1; k2; k3 ¼ material related

constants.

This model is modified as equation (2) to take the

effects of temperature into account.

MrðT ; u; toctÞ ¼ Mr0ðTÞu

u0

� �k4ðTÞ toct

toct 0

� �k5ðTÞ

ð2Þ

Figure 2. Load sequence (combinations of bulk stress and deviator stress) of triaxial resilient modulus test: (a) part of the modified load sequence;(b) original load sequence in LTPP P46.

Figure 3. Dependency of resilient modulus on bulk stress, specimenB_30.

Figure 4. Effects of specimen temperature on Mr for various bulkstresses, when sd ¼ 2p0, specimen A_15.

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where MrðT; u; toctÞ ¼ resilient modulus of foamed

asphalt at temperature T and stress state ðu; toctÞ; i.e. intriaxial stress state where p0 ¼ ðu2 3toct=

ffiffiffi2

pÞ=3 and

sd ¼ 3toct=ffiffiffi2

p; Mr0ðTÞ ¼ Mr at temperature T for a

reference stress state ðu0; toct 0Þ, i.e. Mr0ðTÞ ¼

MrðT ; u0; toct 0Þ; u0; toct 0 ¼ bulk stress and octahedral

shear stress, respectively, for a reference stress state where

p0 ¼ 103.4 and sd ¼ 2p0; k4ðTÞ; k5ðTÞ ¼ material and

temperature dependent constants.

Since the constants in this model are temperature

dependent, model fitting shall be based on resilient moduli

measured at a constant temperature, which are not

available in this study. As a compromise, model fitting was

done for each adjacent fifteen combinations of confining

pressure and deviator stress, which have the full

combination of stress states tested and relatively small

temperature variation. Model fitting results are shown in

tables 2 – 4 for the three specimens; the average

temperature and the standard deviation of the temperature

in each pool are also shown. It should be noted that values

for Mr0ðTÞ shown in the table are the model fitting results,

not the measured resilient modulus at corresponding

temperature and stress state.

The following observations can be made based on

model fitting results.

R 2 values are all greater than 0.96, which indicates that

the proposed model captures the effects of the temperature

and stress state reasonably well. R 2 values at higher

temperatures are generally greater.

The resilient modulus for the reference stress state

Mr0ðTÞ increases significantly with decreasing

temperature.

k4ðTÞ, the indicator of resilient modulus’ sensitivity to

bulk stress shows rather random fluctuation with changing

temperature. This is consistent with the observation that

little or no interaction is observed between the effects of

temperature and bulk stress.

k5ðTÞ, the indicator of octahedral shear stress’ softening

effect, shows a generally decreasing trend in its absolute

value as the temperature decreases. This is consistent with

the observation in Section 2.2.3 that the stress-softening

effect is more significant at higher temperature. Weaker

bonding for softer asphalt binder is implied.

2.4 Temperature sensitivity coefficient

A temperature sensitive coefficient a of resilient modulus

(or stiffness) is proposed as shown in equation (3) where

T0 is a reference temperature. To take the interaction

between the stress state and material temperature, this

coefficient has to be a function of the stress state ðu; toctÞ.According to the observations and analysis made before,

Figure 5. Effects of deviator stress and its interaction with temperature, specimen A_15: (a) p0 ¼ 68.9 kPa; (b) p0 ¼ 137.9 kPa.

Table 2. Model fitting results for specimen A_15.

Loadsequence

Ave.T (8C)

SDT (8C)

Mr0ðTÞ(MPa) k4ðTÞ k5ðTÞ R 2

1 , 15 42.7 0.74 1156 0.466 2 0.169 0.99216 , 30 39.4 0.77 1279 0.458 2 0.139 0.99231 , 45 36.4 0.69 1337 0.457 2 0.129 0.98946 , 60 33.9 0.58 1407 0.460 2 0.126 0.98661 , 75 31.9 0.46 1452 0.467 2 0.118 0.98576 , 90 30.2 0.39 1480 0.471 2 0.128 0.98291 , 105 28.9 0.33 1514 0.480 2 0.129 0.982106 , 120 27.8 0.29 1532 0.476 2 0.125 0.982121 , 135 22.0 0.18 1604 0.467 2 0.118 0.978136 , 150 21.6 0.18 1631 0.482 2 0.115 0.982

Table 4. Model fitting results for specimen C_45.

Loadsequence

Ave.T (8C)

SDT (8C)

Mr0ðTÞ(MPa) k4ðTÞ k5ðTÞ R 2

1 , 15 38.7 0.58 1373 0.422 2 0.134 0.99116 , 30 36.3 0.77 1520 0.419 2 0.111 0.97831 , 45 33.8 0.65 1613 0.433 2 0.107 0.97346 , 60 31.7 0.54 1688 0.443 2 0.103 0.97261 , 75 29.6 0.46 1798 0.466 2 0.108 0.97376 , 90 28.3 0.33 1848 0.473 2 0.116 0.96891 , 105 27.2 0.27 1898 0.486 2 0.120 0.963106 , 120 26.2 0.23 1937 0.495 2 0.119 0.964

Table 3. Model fitting results for specimen B_30.

Loadsequence

Ave.T (8C)

SDT (8C)

Mr0ðTÞ(MPa) k4ðTÞ k5ðTÞ R 2

1 , 15 40.7 0.52 1469 0.568 2 0.147 0.99416 , 30 38.2 0.75 1718 0.513 2 0.100 0.99731 , 45 35.3 0.73 1855 0.501 2 0.100 0.99446 , 60 32.9 0.61 1951 0.483 2 0.102 0.98861 , 75 29.0 0.50 2136 0.538 2 0.147 0.982

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the absolute value of k4ðTÞ is always more than four times

larger than the absolute value of k5ðTÞ, so the effects of

octahedral or deviator stress on resilient modulus are

relatively insignificant. Consequently, the interaction

between effects of temperature and stress state is of less

importance too. If the interaction between the stress state

and temperature is neglected, equation (3) can be

simplified to equation (4) without losing much of its

explanatory power.

aðu; toctÞ ¼log10MrðT ; u; toctÞ2 log10MrðT0; u; toctÞ

T0 2 T

ð3Þ

a ¼log10Mr0ðT ; Þ2 log10Mr0ðT0Þ

T0 2 Tð4Þ

The value of a can be obtained by plotting Mr0 versus

temperature on a logarithmic scale and measuring the

slope coefficient, using data such as that found in tables

2–4. Every decrease of temperature by log102=a ¼

0:301=a8C doubles the resilient modulus. The results for

the three specimens are plotted in figure 6. Their

temperature sensitivity coefficients are 0.0065, 0.0131

and 0.0115, respectively. The general trend is that

increasing the foamed asphalt content from 1.5% to 3%

increases the temperature sensitivity significantly, with no

significant further change when the foamed asphalt

content moves from 3 to 4.5%. It must be remembered

that only one sample was available for each foamed

asphalt content, and their densities are not the same, so the

exact values of this coefficient are of less importance than

the general observations. More extensive testing is

necessary to investigate the effects of asphalt content as

well as other factors such as density, gradation of the

granular material and active fillers.

A simplified model combining equations (2) and (4) to

estimate the resilient modulus of foamed asphalt mix at

any various temperature and various triaxial stress states

can be presented as equation (5).

MrðT; u; toctÞ ¼ 10aðT02TÞMr0ðT0Þu

u0

� ��k4 toct

toct 0

� ��k5

ð5Þ

which uses the same notations as equations (2) and (4),

except that �k4 and �k5 are the average values of k4ðTÞ and

k5ðTÞ over various temperatures, i.e. the mean values of the

corresponding columns in tables 2–4. For specimen B_30,

according to the previous regression results in table 4 and

figure 6, the parameters can be determined as T0 ¼ 258C,

a ¼ 0.0131, Mr0ðT0Þ ¼ 103:72–0:0131T0 , �k4 ¼ 0:512 and�k5 ¼ 20:119. The calculated resilient modulus values of

specimen B_30 at various temperature and stress states

using equation (5) is plotted in figure 7 versus the

measured values from the triaxial testing. Reasonably

good correspondence is achieved, implying that this model

can capture the effects of both the stress state and

temperature on resilient response of foamed asphalt well.

2.5 Lab test results: field mixes

Loose mix of foamed asphalt treated RAP was obtained

from a DISR-FA construction project in July 2005. The

mix design called for 3.0% foamed asphalt and 1.5%

cement slurry. The loose mix was sampled and compacted

in situ immediately after recycling. Compaction, curing

and triaxial testing on these specimens followed similar

procedures as stated in Section 2.1. Gradation of the

parent granular material is not available. Empirical and

subjective observation indicates that the material does not

have many particles passing the 4.25mm sieve and the

refusal bulk density is approximately 2.0 g/cm3, which is

rather low. Figure 8 shows the temperature sensitivity

testing results on two of the samples. For each confining

pressure, only results for the case where sd ¼ p0 are

plotted. Although the data were insufficient for model

fitting and statistical study, the graphs still show similar

trends as the laboratory prepared specimens. The

temperature sensitivity coefficients are estimated as

0.011, which is fairly close to the values obtained forFigure 6. Relation between Mr0 and temperature for the threespecimens.

Figure 7. Comparison of measured Mr from triaxial testing and thevalue predicted by the simplified model (equation 5).

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the lab specimens mentioned before. This supports the

conclusions drawn before.

3. FWD back-calculation and normalizing Mr with

temperature

3.1 Significance

Resilient modulus back-calculation of FWD or heavy

weight deflectometer (HWD) tests is a powerful tool to

evaluate and monitor the condition of pavement structures.

Since it has been observed in heavy vehicle simulator

(HVS) testing (Long and Theyse 2004) that the resilient

modulus of foamed asphalt mix decreases with the

accumulation of repetitive traffic loading, the back-

calculated stiffness is also an indicator of the remaining

structural capacity. FWD tests and back-calculation on

DISR-FA sections have been reported by Mohammad et al.

(2003), Marquis et al. (2003) and Collings et al. (2004).

By multiple tests on the same section, and tracking the

changes of stiffness or deflection, it is possible to identify

the effects of repetitive traffic loading and environmental

factors. Similar research has been reported by Loizos et al.

(2004) and Overby et al. (2004).

3.2 Methodology

To track the changing of material states represented by its

stiffness, it is essential to compare the stiffnesses from

different tests at the same temperature. However the FWD

is a field testing method for which material temperature is

impossible to control, and even very difficult to measure

since the temperature varies with the depth and it is often

practical to measure only the pavement surface tempera-

ture. Consequently, a special issue for analyzing and

comparing multiple testing results is to normalize the

stiffness to a standard temperature.

The essential task of normalizing resilient modulus to a

reference temperature is to measure or estimate the

temperature sensitivity coefficient. If the in situ material

is available, either by coring or lab compaction of recycled

and treated loose material, it is possible to measure the

temperature sensitivity coefficient by triaxial resilient

modulus testing. However, it is usually impractical due to

the following reasons:

. Coring is not always feasible or economical for

highway agencies.

. Samples are very likely to be disturbed or damaged

during coring because foamed asphalt mix is a weakly

bonded material.

. The thickness of DISR is usually less than the required

height of a triaxial sample.

Another more practical strategy is to estimate the

temperature sensitivity coefficient from FWD back-

calculation results. The back-calculated resilient modulus

of foamed asphalt mix can be plotted in a similar manner to

figures 6 and 8. The temperature sensitivity coefficient can

be calculated by simple regression. Several assumptions

have to be made: (1) the testing on a section covers a

reasonably wide range of material temperature; (2) though

the foamed asphalt mixes in the same section tested usually

have significant spatial variation in terms of stiffness even at

the same temperature, it must be assumed that their

temperature sensitivity is similar; (3) the interaction between

temperature sensitivity and stress states is negligible, which

has been validated in Section 2 of this paper.

3.3 Example

The route tested is a two-lane highway in a mountainous

region. Approximately, 16 centre-line kilometers of the

original pavement of this route were rehabilitated and

upgraded using a Wirtgen WR 2500 machine in July 2002.

The recycled pavement was designed for 800,000–

1,000,000 equivalent standard axle loads. The average

daily traffic on the project segment is 740 vehicles per day,

with 17% trucks, and 53% of the trucks having five or more

Figure 8. Triaxial test results for two field compacted specimens (sd ¼ p0).

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axles (Caltrans 2005). The original structure before

rehabilitation contained conventional HMA with a

nominal thickness of 150 mm that varied throughout the

project. The existing AC layer was recycled with some

existing weathered granite subgrade to produce a foamed

asphalt treated layer of 200 mm thick, which was overlaid

with 37 mm of asphalt concrete. The nominal portland

cement and asphalt contents were 1.0 and 2.5%,

respectively.

FWD testing was carried out in June 2003 and July

2005. The testing in 2003 covered both lanes and the entire

section with a test interval of 100 m. Two sets of testing

were carried out on the same section on the same days but

with different apparatus by independent operators (Teams

A and B). The two machines operated together with one

following the other. The back-calculated results match

very well between these two sets of data. The testing in

2005 covered one half mile (800 m) in every one mile

(1609 m) with a test interval of 40 m, and only by Team

A. CalBack, based on the Odemark–Boussinesq method

(UCPRC 2004) was used for back-calculation.

Both tests covered two full working days from early

morning to afternoon. Pavement surface temperature

measured with an infrared thermometer while testing is

shown in figure 9. The empirical BELLS2 equation

(Baltzer et al. 1994) was used to estimate the subsurface

temperature at the depth of interest. In this study, the

representative depth is selected at 150mm deep, which is

roughly the mid depth of all the bituminous layers

including the DGAC overlay and the foamed asphalt

layer. The estimated subsurface temperature is also shown

in figure 9. The surface temperature in the 2003 test

ranged from 16 to 638C, and the subsurface temperature

ranged from 14 to 408C. For the 2005 test, surface

temperature ranged from 23 to 678C, and the subsurface

temperature ranged from 21 to 478C.

The relation between subsurface temperature at 150 mm

depth and the back-calculated foamed asphalt mix

resilient modulus from all the data in 2003 (including

both northbound and southbound, from both Teams A

and B) is shown in figure 10(a); the results for 2005 are

plotted in figure 10(b). Data from both years show a trend

of decreasing foamed asphalt stiffness with increasing

temperature. In the 2003 data, this trend appears to flatten

at temperatures lower than 228C. In the 2005 data, there

are no data for which the subsurface temperature is below

228C, so this specific finding in the 2003 data was not

either supported or weakened.

The temperature sensitivity coefficient for the 2003 data

is 0.03 from regression when the material temperature is

higher than 228C, and it is assumed that the foamed

asphalt mix has approximately constant stiffness at

temperatures below 228C. The temperature sensitivity

coefficient for the 2005 data is 0.0164. The resilient

modulus at each test point can be normalized to a

reference temperature T0 ¼ 258C according to equation

(6) and the temperature sensitivity coefficient a obtained

by regression. The comparison between the normalized

foamed asphalt resilient modulus in the eastbound lane is

shown in figure 11. For both years, only testing results by

Team A are plotted. At most locations, resilient moduli

match well between these two years. This implies the

Figure 9. Measured pavement surface temperature and estimated subsurface temperature.

Figure 10. Relation between subsurface temperature (at 150 mm deep) and back-calculated foamed asphalt mix (with 2.5% foamed asphalt and 1%cement) resilient modulus: (a) for 2003 data; (b) for 2005 data.

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foamed asphalt layer did not experience major deterio-

ration in these two years.

MrðT0Þ ¼ 10aðT2T0ÞMrðTÞ ð6Þ

4. Conclusions

The following conclusions are drawn from the results

presented in this paper.

As an asphalt bonded granular material, the stiffness

or resilient modulus of foamed asphalt mix depends on

both the stress state and temperature. It is important to use

a test method where temperature and stress state can be

controlled independently, such as the triaxial test, to study

the effects of temperature sensitivity of foamed asphalt,

because it is a weakly bonded granular material.

From testing of three triaxial specimens with 1.5–4.5%

foamed asphalt and no active filler, it was found that the

hardening effect of the bulk stress dominates the effects of

the deviator stress (or octahedral stress), and is largely

independent of temperature. On the other hand, interaction

between the deviator stress and temperature was observed:

at higher temperature the material tends to show more

“stress-softening” behavior. Fitting the test data to a

simple model quantitatively supports these observations.

By neglecting the interactive effects of the stress state and

temperature, a temperature sensitivity coefficient can be

defined to characterize the temperature susceptibility of

foamed asphalt mix stiffness. A simplified model with

only four material related parameters was presented to

predict the resilient modulus of foamed asphalt mix at any

triaxial stress state and temperature. It should be

mentioned that the three samples contain neither cement

nor any other active fillers. The purpose was to observe the

effects of foamed asphalt better. Foamed asphalt mixes

containing active fillers might behave differently.

It is important to normalize foamed asphalt stiffnesses

back-calculated from field deflection data with respect to

temperature. A method to filter out the effects of

temperature in FWD test results by normalizing the

stiffness to a standard temperature was presented. The

essential component is the temperature sensitivity

coefficient, which is usually impractical to measure by

laboratory testing for most field test tasks. Based on the

conclusions drawn in the lab study, a method to estimate

the temperature sensitivity coefficient by regression on the

field test data was presented. An example comparing the

foamed asphalt stiffness of a DISR-FA project in two years

is demonstrated with stiffnesses normalized with regard to

pavement subsurface temperature. Change of stiffness due

to the accumulation of traffic loading over two years was

not evident after temperature normalization.

Acknowledgements

The work presented in this paper was sponsored by the

California Department of Transportation, Division of

Research and Innovation, for which the authors are grateful.

The authors also wish to thank their collaborators in the

California Department of Transportation. The results

presented in this paper do not represent any standard or

specification of the California Department ofTransportation,

and the opinions expressed are those of the authors alone.

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