Determining thermal properties of asphalt concrete using field data and laboratory testing

Construction and Building Materials xxx (2014) xxx–xxx

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Determining thermal properties of asphalt concrete using field data and laboratory testing Md Rashadul Islam ⇑, Rafiqul A. Tarefder Department of Civil Engineering, University of New Mexico, MSC01 1070, 1 University of New Mexico, Albuquerque, NM 87131, USA

h i g h l i g h t s  Determines Coefficients of Thermal Contraction and Expansion using field data.  Specific heat capacity (C) is measured in the laboratory.  Thermal conductivity (k) is determined by developing Finite Element Model.  Measured C and the FEM determined k values are validated using real field data.

a r t i c l e

i n f o

Article history: Received 7 September 2013 Received in revised form 11 February 2014 Accepted 25 March 2014 Available online xxxx Keywords: Asphalt concrete Thermal strains Coefficient of thermal expansion and contraction Thermal conductivity Specific heat capacity Field validation

a b s t r a c t Recently developed pavement design guide, Mechanistic-Empirical Pavement Design Guide (MEPDG), uses thermal properties such as Coefficient of Thermal Contraction or Expansion (CTC or CTE), thermal conductivity (k) and specific heat capacity (C) as inputs to predict pavement distresses such as thermal cracking and aging. To this day, thermal properties of asphalt concrete have been determined based on laboratory testing. This study determines CTC and CTE using field collected strain and temperature data from an instrumented pavement section on Interstate 40 at mile post 141 near Albuquerque, New Mexico, USA. Average CTC and CTE values of asphalt concrete are determined to be 2.69  105 per °C and 2.42  105 per °C in fall (October–November) and 2.47  105 per °C and 2.77  105 per °C in winter (December–February) respectively. For validation, CTC and CTE values of asphalt concrete are measured in the laboratory and found to be 2.64  105 per °C and 2.28  105 per °C respectively. In addition, C value is measured in laboratory and k value is determined by developing Finite Element Model (FEM). The measured C and the FEM determined k values are validated using real field data. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction When Asphalt Concrete (AC) is subjected to extreme temperatures (hot summer, cold winter), it expands or contracts to relax temperature-induced stresses. If this stress is restrained, (for example, base course under an asphalt layer does not move rather it restrains movements on the top), thermally induced stresses build up in AC. These thermal stresses cause cracking in the pavement including low temperature cracking. Thermal properties such as Coefficient of Thermal Contraction (CTC), Coefficient of Thermal Expansion (CTE), thermal conductivity (k) and specific heat capacity (C) are used to define such thermal distress or cracks. Indeed, Mechanistic-Empirical Pavement Design Guide (MEPDG), uses

⇑ Corresponding author. Tel.: +1 (505) 363 6902; fax: +1 (505) 277 1988. E-mail address: [email protected] (M.R. Islam).

CTC value as input to predict low temperature cracking of asphalt pavements. These k and C values are also key inputs in MEPDG and are also used to predict temperature and moisture profiles in pavement structure and subgrade over the design life of a pavement [1,2]. CTC and CTE can be defined as the fractional change in dimensions (x, y, z direction) due to unit change in temperature. Thermal conductivity, k measures the heat flux flowing through a material at unit temperature gradient and is expressed in W/(m K). The specific heat capacity, C (measured in J/(kg K)) of a material is the amount of the heat energy required to increase unit temperature of unit mass of a body. The Thermal inertia, so called thermal diffusivity (a) can be determined using Eq. (1) if these two thermal properties are known.

a¼

k

qC

ð1Þ

http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Islam MR, Tarefder RA. Determining thermal properties of asphalt concrete using field data and laboratory testing. Constr Build Mater (2014), http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040

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where a, k, q and C are the thermal diffusivity (m2/s), thermal conductivity, mass density and specific heat capacity of the material respectively. Thermal diffusivity along with other properties is used to predict pavement temperature, thaw settlement, frost penetration, and estimating time for compaction of overlay [3–5]. 2. Typical CTC and CTE values of HMA In the past, several researchers studied CTC and CTE of AC and these are summarized in Table 1. It can be observed that all of these studies are based on laboratory testing. The basic procedure for determining CTEs in laboratory involves cooling down or heating up an AC sample uniformly in a temperature controlled chamber and measuring the change in sample length. From Table 1, CTE value of Hot-Mix-Asphalt (HMA) varies from 1.3  105 to 3.8  105 per °C. Though laboratory CTEs are useful, these may differ from field CTEs values due to difference in sample size, testing mode, heat boundary conditions, sample constraints and geometry. These CTC and CTE values are also dependent on type and volume of stone aggregates and binder used in preparing HMA mixture. Typically, CTC or CTE of asphalt binder is 1.1  104 per °C and of rock ranges 0.9  105 to 1.3  105 per °C [14,15]. Therefore, CTC or CTE of a particular HMA mixture increases with binder content. Al-Qadi et al. [16] and Bayat and Knight [17] measured the field thermal strain using installed sensors. However, those studies did not focus on the CTC and CTE values and behavior such as seasonal effects, orientation effects, etc. In addition, no information regarding sensor calibration was mentioned. To this end, the present study describes a procedure for determining CTC and CTE of HMA based on field data in an instrumented pavement section on Interstate 40 (I-40) in the state of New Mexico, USA. The Horizontal Asphalt Strain Gages (HASGs) are calibrated for temperature following manufacturer’s recommendation. However, this study neglects the friction between base course and HMA layer and temperature gradient in HMA. In addition, the CTC and the CTE values are determined in the laboratory to validate the field results. 3. Typical k and C values of HMA Typically, k and C values are determined through laboratory testing and numerical analysis. Some of laboratory tests outcomes are listed in Table 2. It can be observed that k and C values ranges 0.74–2.89 W/(m K) and 800–1853 J/(kg K) respectively. There are several tests standards to measure the k value such as Hot Wire Method (ASTM C1113), Guarded Heat Flow Meter Method (ASTM E1530), and Guarded Hot Plate Method (ASTM C177) [26–28]. Hot Wire Method is suitable for liquids and plastics of low k value. In ASTM E1530, a very small amount of sample is tested under compressive load and an axial temperature gradient is applied. This extremely small sample and static flow conditions do not represent the conditions for flexible pavement. Traditionally, ASTM C177 test standard is used to characterize the k which is based on steady-state assumption in one-dimensional configuration. Thickness of specimen must not exceed 33% of the maximum linear dimension. These assumptions make the outcome inappropriate for real flexible pavement. Tan et al. [18] proposed a practical approach using Fourier equation for transient heat flow. However, this method is suitable only for thin pavement. Luca and Mrawira [5] developed a chamber to evaluate thermal properties of 100 mm  100 mm  20 mm beam samples. Samples were prepared from 150 mm diameter gyratory compacted samples and temperature readings were obtained at the edges. The experimental outcomes of this test procedure were matched with the Fourier equation for transient heat

flow in solid materials. This test program attained k and C by matching the measured and the Fourier equation predicted temperature curve. As edges of a beam sample are saw cut, the coated aggregate become exposed. k value is affected by exposed stone because the k value of stone (ranges 1.1–6.45 W/(m K)) is much more than the k value of binder (usually 0.65–0.75 W/(m K)) [19]. Mamlouk et al. [13] also used an environmental chamber to determine k and C values for the field cores and laboratory prepared beam samples. Heat Flow Computer Program was used to determine k and C values. Again, their results were not validated by field measurements. The present study determines k and C values using a cylindrical sample instead of a beam sample. The above determined k and C values are validated using real field data. 4. Objectives The main objective of this study is to determine the basic thermal properties of AC. Specific objectives are:  Determining CTC and CTE of AC based on measured field strains and temperature variations neglecting bonding between base and HMA, geometry and boundary conditions.  Determining CTC and CTE of AC in the laboratory using field cored sample and comparing the results with field observations.  Determining the specific heat capacity, C based on a simplified laboratory set up.  Determining the thermal conductivity, k based on a simple laboratory testing and numerical analysis with developed Finite Element Model (FEM).  Validating the k and the C for real field conditions based on an instrumentation section. 5. Instrumented section 5.1. Geometry and materials Thermal strain data were collected from an instrumented pavement section on I-40 east bound lane at milepost 141, near Albuquerque in New Mexico in the United States of America. The longitudinal profile of the instrumented section is shown in Fig. 1. The section has four layers. The top layer is a 263 mm HMA followed by a 150 mm thick crushed stone base course. There is a subbase layer, called Process Place and Compact (PPC) of 200 mm thickness. The section has fourteen HASGs, eight Vertical Asphalt Strain Gages (VASGs), four Earth Pressure Cells (EPCs), three moisture probes, six temperature probes, three Axle Sensing Strips (ASSs), a weather station and a Weigh-in-Motion (WIM) station. Readings of HASGs and temperature probes are used in this study. The AC used in this pavement was a dense graded SuperPave (SP) mix, type SPIII, which was widely used by New Mexico Department of Transportation (NMDOT). This mix contained plant screened Reclaimed Asphalt Pavement (RAP) materials around 35%. Performance Grade (PG) binder PG 70-22 was 4.4% (by weight of mixture). The maximum aggregate size was 25 mm. About 5% of the materials passed through a No. 200 sieve (0.075 mm).

5.2. Temperature probes Six temperature probes were inserted at different depths (i.e. 0, 50, 90, 263, 375, 488 mm depths) of the pavement to monitor the continuous temperature variations at these depths. The readings of the temperature probes installed at 90 mm and 263 mm depths are used in this study to calculate the CTC and the CTE values. The HASGs are also installed at these depths. The data of the temperature probe installed at the surface are used to validate the determined k and C values using laboratory and FEM analysis.

5.3. HASGs installation The ‘H’ and ‘I’ shaped sensors in Fig. 2(a) represent the HASGs. ‘H’ gages were installed parallel to the traffic direction and ‘I’ gages were embedded in transverse direction. Twelve gages were installed below the HMA, at 263 mm depth and two were embedded on the top of 2nd lift of the HMA, at 90 mm depth. Both types of gages are identical. The strain data of all the fourteen HASGs were used to calculate the CTC and the CTE.

Please cite this article in press as: Islam MR, Tarefder RA. Determining thermal properties of asphalt concrete using field data and laboratory testing. Constr Build Mater (2014), http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040

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2.62 3.786

–

Cores of 150 mm diameter 50 mm high were tested between 25 °C and 0 °C. The expansion and contraction were measured by Linear Variable Differential Transformers (LVDTs). HMA beams of 51 mm  51 mm  340 mm were tested from 40 °C to +40 °C. LVDTs were attached outside the chamber Beams of 50 mm  50 mm  390 mm were placed inside the chamber and LVDTs were placed outside the chamber with rubber plug. The temperature range was 0–60 °C

(105)/°C

– 1.6 3.69 – 1.33– 2.97 1.58– 2.33 1.35 3.745 Beams of 63 mm  100 mm  250 mm were tested from 31 °C to 9.4 °C and the expansion was measured with strain gage With an extensometer the length change of a beam sample was measured for temperature change of 0–54 °C For the wider temperature range of 23 °C to 60 °C, length change of beam specimen was measured with dial deflection gage and glass dilatometer Beam specimens were tested between 10 °C and 55 °C. LVDT was used on a precision push rod type dilatometer Cores of 150 mm diameter and 50 mm high were tested between 25 °C and 0 °C. The expansion and contraction were measured with strain gages

Test descriptions

Table 2 Thermal conductivity and specific heat capacity reported in previous studies. References

k (W/(m K))

C (J/(kg K))

Luca and Mrawira [5] Tan et al. [18] Highter and Wall [19] Kavianipour and Beck [20] Solaimmanian and Bolzan [21] Wolfe et al. [22] Johnston [23] Jordan and Thomas [24] Barber [25]

1.62–2.06 1.30–1.42 0.80–1.60 2.28–2.88 0.74–2.89 1.37–1.75 1.05–1.52 0.80–1.42 1.21

1475–1853 – 800–1600 – – 879–963 1674 – 920

One of the HASGs installed inside the I-40 pavement is shown is Fig. 2(b). It has two steel arms (H shape) and a middle spring embedded inside a membrane. When there is contraction in the pavement due to temperature reduction, the AC material between the steel arms is squeezed or shortened, and the resulting strain is measured. The HASGs are calibrated for temperature following manufacturer’s recommendation which is not described here.

6. Determination and analysis of CTC and CTE 6.1. Field data Strain and temperature data were collected for fifteen days for the period of October 16th to November 05th, 2012 in fall and five days in winter. Five days in winter are December 3rd, December 25th in 2012 and January 25th, January 29th and February 12th in 2013. These days are chosen as extreme low temperatures have been noticed during these days at the test site. All the twenty-day data were used in analysis. Surface temperature varies 6.53– 34.66 °C and 4.76 to 6.4 °C in fall and winter respectively. Data from the HASGs were gathered through a high-speed data acquisition system, DI785 and processed by a data analysis software, DaDisp. Air and pavement temperature data are collected by a slow-speed data acquisition system, CR1000. Fig. 3 shows the thermal strain and temperature variations with time from October 15, 2012 to February 28, 2013. The strain values are plotted assuming the reference as the mean temperature of the test site (13.4 °C). The decrease in thermal strain with respect to the temperature is considered the CTC and the increase in thermal strain with respect to the temperature is considered CTE. For further clarification, the temperature induced horizontal strain from twelve sensors at 263 mm depth and temperature on October 16, 2012 are plotted in Fig. 4. The strain at 12 am (midnight) is considered zero to plot the responses. It shows that the thermal strain decreases with decrease in temperature and vice versa due to the contraction and expansion respectively. Fig. 4 shows that the twelve sensors measure the strain very consistently. It also shows that the peaks of the horizontal strain follow the peak of the temperature. 6.2. Calculation of CTC and CTE CTC and CTE can be defined mathematically as in Eq. (2):

Zeng and Shiels [12] Mamlouk et al. [13]

Domaschuk et al. [6] Littlefield [7] Jones et al. [8] Osterkamp [9] Stoffels and Kawanda [10] Metha et al. [11]

CTC ðor; CTEÞ ¼

References

Table 1 CTC and CTE of HMA reported in different studies.

CTC

CTE

3.15 2.4 3.71 1.98 –

M.R. Islam, R.A. Tarefder / Construction and Building Materials xxx (2014) xxx–xxx

DL L1

DT

ð2Þ

where DL is the change in length due to temperature = L2  L1; where L1 is initial length of sample, L2 is final length; DT is change in temperature = T2  T1; T1 is initial temperature, and T2 is the final temperature. In the present study, strain, e = DL/L1 is obtained from the embedded strain gages neglecting base friction and boundary conditions and temperature changes were measured with installed temperature probes.

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M.R. Islam, R.A. Tarefder / Construction and Building Materials xxx (2014) xxx–xxx

Traffic Direction

HMA 90 mm 87 mm 87 mm

263 mm

Base 150 mm 75 mm

PPC 200 mm

231 mm

Subgrade All dimensions are in mm

50 VASG

50

50

50

50

Moisture Probes

50

50

50 EPC

HASG

75

125 mm Temperature Probes

ASS

Fig. 1. Longitudinal profile of the instrumented section.

Steel Arms

(a) Layout of twelve HASGs

(b) Close view of a HASG

Fig. 2. Installation of HASGs below the HMA (263 mm depth).

30 200 100

10

0 0

-100

-10

-200 -300

-20

Horizontal Strain (µε)

20

Temperature (°C)

300

Temperature Horizontal Strain

-400

-30 10/15/2012 0:00

11/24/2012 0:00

1/3/2013 0:00

-500 2/12/2013 0:00

Time of Year Fig. 3. Temperature and horizontal strain variations at the bottom of HMA.

6.3. Seasonal effects Fig. 5 presents CTC and CTE values of fall and winter calculated at the bottom of asphalt concrete. The up most and the lowest horizontal lines of each box represent the maximum and the minimum values of the corresponding data as indicated by arrows in the figure. The box itself contains the middle fifty percent of the data. Therefore, the upper and the lower vertical dash lines indicate the length of upper twenty five percent and lower twenty five

percent of the data respectively. The bold line inside the box dictates the median value of the data. Average values of CTC and CTE of asphalt concrete at the bottom of HMA are determined to be 2.67  105 per °C with Standard Deviation (SD) of 0.24  105 per °C and 2.42  105 per °C with SD of 0.408  105 per °C in fall respectively. The CTC and the CTE in winter are 2.47  105 per °C with SD of 0.322  105 per °C and 2.73  105 per °C with SD of 0.15  105 per °C respectively. Combining both depths data, the average values of CTC and CTE

Please cite this article in press as: Islam MR, Tarefder RA. Determining thermal properties of asphalt concrete using field data and laboratory testing. Constr Build Mater (2014), http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040

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20

30

0

Thermal Strains from

-40

26

HASG 1 to HASG 12

-60

24

-80

Temperature

Temperature ( C)

Horizontal Strain (µε)

28 -20

22

-100 -120 12:00 AM

20 4:30 AM

9:00 AM

1:30 PM

6:00 PM

10:30 PM

Time of Day (24 Hour Format) Fig. 4. Expansion and contraction of the HMA at 263 mm depth on October 16th, 2012.

Maximum value

Minimum value Median value Box contains middle 50% dat

CTC (Winter) CTE (Fall)

Lower 25% data

CTC (Fall)

CTE (Winter)

Fig. 5. CTC and CTE at the bottom of HMA in fall and winter.

of asphalt concrete are determined to be 2.69  105 per °C with SD of 0.3  105 per °C and 2.42  105 per °C with SD of 0.411  105 per °C in fall respectively. These values are 2.47  105 per °C with SD of 0.321  105 per °C and 2.77  105 per °C with SD of 0.13  105 per °C in winter respectively. Table 3 lists averages and standard deviations of all sensors’ data of both fall and winter calculated at both depths. Formal statistical tests have been conducted to evaluate mean (average) values of CTC and CTE to confirm whether mean values are statistically equal or not, based on 95% Confidence Interval (CI). As a first step, One Way Analysis of Variance (ANOVA) test is conducted to compare means of CTC and CTE of both fall and winter. However, ANOVA test has prerequisite that the data are normally distributed. The normality assumption is evaluated by formal normality tests, like Shapiro–Wilk, Anderson–Darling and Cramer–von Mises Normality tests. The null hypothesis of the formal normality test is that the data is normally distributed and the alternative hypothesis is that the data is not normally distributed. It can be observed from Table 4 that p-values (probability of null hypothesis be true, the minimum value is 0.05 for 95% CI) of all the formal normality tests are much greater than 0.05. Therefore, the alternative hypothesis is rejected and the null hypothesis becomes true. Hence, both CTC and CTE values in fall and winter at the bottom of HMA are normally distributed. Therefore, ANOVA test can be conducted on the data. The null hypothesis of the ANOVA test is that all means of CTC and CTE in fall and winter are equal and the alternative hypothesis is that at least one pair of means is not equal. The ANOVA test shows insufficient evidence for the null hypothesis to be true. The produced p-value is <2  1016 which is very close to zero (listed in Table 4). Therefore, the null hypothesis is rejected and the conclusion is that means of CTC and CTE in fall and winter are not equal at 95% CI.

The next step is to evaluate which pair(s) of mean values of data is not equal. A statistical formal pairwise test, Fisher’s Least Significant Difference (LSD or FSD) test is conducted on these data. It is obtained that no pair of means has p-value greater than 0.05 as shown in Table 4. Therefore, no pair of mean is equal at 95% CI. To conclude, fall CTC is greater than winter CTC and fall CTE value is smaller than winter CTE at the bottom of HMA as shown in Fig. 5. It also shows that CTC value (2.67  105 per °C) is larger than CTE value (2.42  105 per °C) in fall and CTE value (2.73  105 per °C) is greater than CTC value (2.47  105 per °C) in winter below the asphalt concrete. Combining both depths’ values, CTC (2.69  105 per °C) is greater than CTE (2.42  105 per °C) of asphalt concrete in fall. On the otherhand, winter CTC value (2.47  105 per °C) is smaller than winter CTE value (2.77  105 per °C). This non-linear behavior of CTC and CTE with temperature change was first reported by Zeng and Shields [12]. In addition to the seasonal change, the present study observered another issue. That is, material shrinks faster at high temperature range (usually above the average annual mean temperature, usually 13.4 °C in Albuquerque, NM) than lower temperature and therefore, CTC value (2.69  105 per °C) is larger than CTE value (2.42  105 per °C) in fall. Similarly, material expands faster at low temperature range (usually below the average annual mean temperature) than high temperature and therefore, CTE is greater than CTC in winter. 6.4. Depth effects CTC in two different depths are considered for both fall and winter to evaluate the depth effect. Distribution of these values are presented in Fig. 6. In the figure, ‘Bottom’ means the bottom of AC (263 mm depth) and ‘Top’ means the top of 2nd lift (90 mm depth). In winter, the average CTCs at 90 mm and 263 depths are 2.46  105 per °C and 2.47  105 per °C respectively. Therefore, CTC at the bottom of HMA is almost equal to that of at 90 mm depth in winter. Fall CTCs at 90 mm and 263 depths are 2.79  105 per °C and 2.67  105 per °C respectively which means fall CTC at the bottom of HMA is smaller than that of at 90 mm depth. Therefore, no regular effect of depth is observed. 6.5. Edge effects Edge effect has been analyzed for transverse fall CTC values at the bottom of HMA (263 mm depth) which are plotted in Fig. 7. In this figure, ‘CTC (Inner)’ means CTCs measured by the transverse sensors located at the inner side of driving lane. Similarly, ‘CTC (Outer)’ means CTCs measured by the transverse sensors located at the outer side of driving lane. ‘CTC (Middle)’ dictates in between of ‘CTC (Outer)’ and ‘CTC (Inner)’. It can be observed that the CTC

Please cite this article in press as: Islam MR, Tarefder RA. Determining thermal properties of asphalt concrete using field data and laboratory testing. Constr Build Mater (2014), http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040

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Winter (December–February)

2.74 ± 0.13 2.74 ± 0.17 2.69 ± 0.12 2.71 ± 0.17 2.80 ± 0.11 2.78 ± 0.11 2.69 ± 0.16 2.68 ± 0.12 2.75 ± 0.13 2.68 ± 0.21 2.70 ± 0.08 2.69 ± 0.13

2.94 ± 0.13 3.02 ± 0.11

2.77 ± 0.13

Fall (October–November)

2.36 ± 0.37 2.46 ± 0.44

2.42 ± 0.411

value is the smallest at the inner side and the largest at the outer side of the pavement. Average values of CTC (Inner), CTC (Middle) and CTC (Outer) are 2.66  105 per °C, 2.71  105 per °C and 2.77  105 per °C respectively. However, there are some overlapping data between the pairs. Similar trend is observed for fall CTE and winter CTC and CTE values.

2.53 ± 0.43 2.54 ± 0.34 2.24 ± 0.38 2.31 ± 0.32 2.37 ± 0.52 2.34 ± 0.43 2.37 ± 0.31 2.42 ± 0.36 2.51 ± 0.53 2.32 ± 0.31 2.51 ± 0.36 2.33 ± 0.31

CTE (105 per °C)

6

6.6. Transverse vs. longitudinal CTC Longitudinal (L) and Transverse (T) average fall CTC values are plotted in Fig. 8 for both depths. Averages of all transverse and longitudinal sensors output are considered. Average CTC values at the bottom of AC are 2.71  105 per °C and 2.62  105 per °C in transverse and longitudinal directions respectively. These values are 2.84  105 per °C and 2.75  105 per °C respectively at 90 mm depth. Therefore, the transverse CTC is observed to be greater than the longitudinal one for any depth in fall. The same trend is observed for winter CTC also (not presented in the figure). However, longitudinal CTC values are observed to have no edge effect at both depths and seasons. 7. Laboratory CTC and CTE values

2.47 ± 0.321

2.39 ± 0.22 2.54 ± 0.21

2.43 ± 0.38 2.53 ± 0.16 2.49 ± 0.38 2.43 ± 0.19 2.48 ± 0.40 2.48 ± 0.39 2.40 ± 0.22 2.43 ± 0.39 2.46 ± 0.08 2.54 ± 0.20 2.50 ± 0.12 2.43 ± 0.27

2.69 ± 0.301

2.745 ± 0.41 2.843 ± 0.44

Average (combined)

HASG 13 HASG 14 90 mm Depth

2.77 ± 0.26 2.62 ± 0.22 2.59 ± 0.22 2.69 ± 0.23 2.65 ± 0.27 2.75 ± 0.23 2.67 ± 0.22 2.70 ± 0.31 2.67 ± 0.28 2.64 ± 0.20 2.61 ± 0.23 2.71 ± 0.24 HASG HASG HASG HASG HASG HASG HASG HASG HASG HASG HASG HASG Bottom of HMA (263 mm Depth)

1 2 3 4 5 6 7 8 9 10 11 12

Sensor

Fall (October–November)

The laboratory CTC and CTE values are determined by a new laboratory procedure using dynamic modulus environmental chamber and LVDT. The LVDTs were calibrated in the temperature range of 10 °C to 50 °C using a zerodur whose CTC and CTE values are considered zero (shown in Fig. 9(a)). Then a field cored cylindrical sample of 100 mm diameter and 150 mm height from the instrumentation section (air void of 5.1%) was exposed to a temperature cycle between 10 °C and 50 °C as shown in Fig. 9(b). The resulting deformation of the sample was measured by LVDTs and the CTC and the CTE were calculated using Eq. (1). 7.2. Test results

Sensor location

Table 3 Calculated average CTC and CTE values with standard deviations.

CTC (105 per °C)

Winter (December–February)

7.1. Testing

Fig. 10 shows the variations of axial strain with the sample temperature. It shows the loading (contraction from 50 °C to 10 °C) and unloading curve (expanison from 10 °C to 50 °C) form a close loop (no irrecoverable strain). The CTC and CTE are defined as the slope of the strain versus temperature. Therefore, the overall CTC and CTE for the temperature range of 10 °C to 50 °C are found to be 2.635  105 per °C and 2.283  105 per °C, respectively, as presented by the best fit curve. These values are close to the field observation (varies 2.43  105 per °C to 3  105 per °C). The strain variations (in Fig. 10) can be divided into two regions to examine the season effect. The first region (roughly 10 °C to 5 °C), marked by rectangle, can be considered the low temperature region and the rest of the part to be the high temperature region. In the low temperature region, the contraction slope is smaller than the expansion slope as observed by visual observation. These values are opposite in the high temperature region. That means, the CTC is smaller in the low temperature and greater in the high temperature. Similar observation has been obtained in the field. Therefore, it can be said that field observation neglecting base friction and boundary conditions, agrees with the laboratory findings. 8. Determination of c in the laboratory 8.1. Laboratory testing A foam ice box was used as a calorimeter as shown in Fig. 11. This box is believed to be thermally insulator material. To confirm,

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M.R. Islam, R.A. Tarefder / Construction and Building Materials xxx (2014) xxx–xxx Table 4 Statistical test results (p-value) of CTC and CTE at the bottom of HMA. Data type

p-Value

CTC (Fall) CTE (Fall) CTC (Winter) CTE (Winter)

Shapiro–Wilk normality test

Anderson–Darling normality test

Cramer–von Mises normality test

0.1024 0.0613 0.0900 0.4311

0.2157 0.0838 0.0649 0.2680

0.3270 0.1230 0.0539 0.2617

One Way Analysis of Variance (ANOVA) Test CTC (Fall) CTE (Fall) CTC (Winter) CTE (Winter) Difference (LSD or FSD) Test CTC (Fall) <2e-16 0.0170 <2e-16

CTC (Winter) CTE (Fall) CTE (Winter)

CTC (Winter) – <2e-16 0.0022

CTE (Fall) – – <2e-16

CTC (e-5) /°C

Fisher’s Least Significant CTC (Fall) CTE (Fall) CTC (Winter) CTE (Winter)

<2e-16

CTC (L) at Bottom

Fig. 6. CTC at different depths and seasons.

CTC (T) at Bottom

CTC (L) at 90 mm

CTC (T) at 90 mm

Fig. 8. Longitudinal (L) and transverse (T) CTCs in fall.

thermometer was inserted into the box to measure the samplewater temperature. Then, the decrease in temperature was monitored to determine the stable temperature. 8.2. Calculation for determining the C

CTC (Outer)

CTC (Middle)

CTC (Inner)

Fig. 7. Transverse CTCs at different distances from edge in fall.

The test was stopped when the temperature reached to a stable condition. It took 42 min to reach to the stable position. Even though, the test was continued up to 1 h to ensure the accuracy of reading. The heat loss of 1.9 °C was compensated for calculating the final stable temperature. Then, using Eq. (3) the C value of the AC was determined.

C¼ hot water of 50.5 °C was kept inside the box and the temperature was monitored for 3 h with a thermometer inserted into the box. The decrease in temperature was measured to be 1.9 °C per hour (0.1 °C per 3 min) in first hour and 1.7 and 1.6 °C for the second and the third hour respectively. Then, hot water of 50.5 °C was taken and the mass of water was measured carefully. A cylindrical sample was prepared and cut into small pieces in the laboratory. The same mixture of the instrumented section was used to prepare the sample. Details of sample preparation is described in next section. The weight of these cut samples were measured and the body temperature was recorded. Prior to measuring the temperature, the samples were conditioned in room temperature for at least 24 h. The sample was then immersed into water very quickly and the bowl was covered to maintain the temperature. One

mw cw ðhw  hf Þ mAC ðhf  hAC Þ

ð3Þ

where mw, Cw and hw are the mass, specific heat capacity and initial temperature of water, mAC, hAC are the mass and initial temperature of the AC respectively and hf is the final temperature of the mix. In this test, 2.525 kg of AC of 20.6 °C was mixed with the 4.019 kg of water of 50.1 °C. The final temperature was 44.8 °C after applying the temperature correction. The laboratory C of the AC is measured to be 1464 J/(kg K). 9. Determination of the k The k value is determined through FEM analysis using laboratory data. Thermal gradient was applied in a cylindrical sample in the laboratory. Increase in temperature with time at the colder

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M.R. Islam, R.A. Tarefder / Construction and Building Materials xxx (2014) xxx–xxx

(a) Calibrating the LVDT

(b) Testing of HMA Sample

Fig. 9. Determining CTC and CTE in the laboratory.

0 Contraction y = 2.6351x - 117.31 R² = 0.9931

Axial Strain (e-5)

-30

Thermometer

-60 Expansion y = 2.283x - 119.1 R² = 0.9786

-90

Sample

-120 -150 -10

0

10

20

30

40

50

Water Bath

Temperature (°C) Fig. 10. Variations of axial strains value upon cooling and heating.

Fig. 12. Testing the sample for measuring temperature increase at the colder end.

9.1. Sample preparation Foam box

Thermometer

Sample

Fig. 11. Test setup for determining the C of the HMA.

end of the sample was recorded. Based on the laboratory determined C value a FEM model is developed for the cylindrical sample and k value is assigned on trial and error basis. The increase in temperature at the colder end of the model sample is compared with the increase in temperature of the laboratory sample to determine the optimum k value. Using k and C values in FEM, field HMA temperatures at 90 mm depth were predicted from morning to afternoon and compared with measured values.

Some plant mix was collected from the instrumentation construction site in corporation with the NMDOT. The mix was compacted to prepare a 150 mm diameter and 170 mm height cylindrical sample using a gyratory compactor at 150 °C. Prior to the compaction a steel pin was inserted up to 70 mm depth at the top of it. The pin was carefully pulled out just after the compaction. No pin was inserted in the sample which was prepared to determine the C value. The sample was then cored into a 100 mm diameter sample using laboratory coring tool and the two edges remained uncut to avoid the cut edge effect. The air void and density of both samples were measured to be 4.3%, using AASHTO T166-07 [29] and AASHTO T209-05 [30] test standards. Prior to testing, the sample was oven dried for 24 h at 40 °C. 9.2. Laboratory testing The sample was covered with felt, an insulating material, as shown in Fig. 12. This insures no loss and gain of heat through the curved surfaces. Such a boundary condition represents the field condition, one-dimensional vertical downward flow. One end of the sample was immersed in hot water in a constant water temperature bath. The other end of the beam was kept open for heat

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convection to air to simulate heat flow or transmission of AC layer to the base layer in a pavement. Specifically, the top surface of the beam was kept open for heat convection to the laboratory air. The temperature of the hot water was stabilized before placing the specimen. A thermometer was inserted replacing the steel pin. The temperature of the hot water was maintained 43.1 °C and the laboratory air temperature was 22.5 °C, a total temperature differential of 20.6 °C. The increase in temperature at the colder end of the beam was recorded every 15 min. This test data was used to compare with FEM output for determining the k value of the asphalt concrete. 9.3. Determination of k using FEM The C value is determined in the laboratory and used as a input in FEM. The k value is assigned as trial and error basis and the laboratory measured temperature is matched with FEM results to obtain the optimum k. A three-dimensional FEM is developed in commercial finite element software, ANSYS. In the FEM analysis, the one dimensional transient heat transfer analysis is conducted. This method uses the basic transient heat transfer Fourier equation (Eq. (4)) [31].

k

@2T @T ¼ qC @x2 @t

ð4Þ

where k, C and q are the thermal conductivity, specific heat capacity and density of the AC respectively. T, t and x denote temperature, time and the length of the sample respectively. Carslaw and Jaeger [32] derived the analytical solution of this partial equation and is given as in Eq. (5):

Tðx; tÞ ¼

1 4X

1

p n¼1 ð2n þ 1Þ

2 2 sinð2n þ 1Þpxeað2nþ1Þ p t Þ

ð5Þ

where n is the number steps required for the convergence, i.e., 1, 2, 3 and so on, a is the thermal diffusivity (m2/s) as mentioned in Eq. (1). All the other parameters are discussed earlier. A solid cylinder of 100 mm diameter and 90 mm height is modeled. The laboratory sample height was 170 mm but the thermometer was inserted at 90 mm depth. Therefore, the effective length of the sample is 90 mm. A linear thermal property is assumed for asphalt concrete. A solid 87 element, readily available in ANSYS, is used to idealize an AC element. The solid 70 and solid 90 elements are also evaluated and observed to be consistent, though SOLID 87 is finally used in this study. No heat convection is assumed at the curved surface. A temperature of 20.6 °C is applied on one edge and the other edge was kept at 0 °C to simulate the laboratory condition. Several trial values of k are assigned in the FEM model. The optimum solution is obtained for the k value of 2.11 W/(m K). At the

colder end, the increase in temperature is 1.39 °C after 30 min for maintaining 20.6 °C temperature at the hot end. Variations of the temperature for FEM and laboratory testing are shown in Fig. 13. The initial part of the plot has the exact match and with time it deviates a little. However, these k and C values are validated with the field measured data. 10. Validation of laboratory C and FEM k values Using the determined k and C values in FEM model the temperature at 90 mm depth of the HMA is predicted. The predicted value is compared with measured temperature from morning to afternoon on the 16th October, 2012. The surface temperature is the minimum around 8:15 am and maximum around 3:15 pm; whereas these values are at 9:15 am and 4:45 pm respectively at 90 mm depth. The half an hourly surface temperature on the pavement was assumed constant. The increase in surface temperature from 8:15 am to 8:45 am is 0.56 °C as shown in Table 5. This increase in temperature heats up the pavement material up to 8:45 am (30 min). Similarly, the increase in temperature from 8:45 am to 9:15 am (i.e. 1.31 °C) heats up the pavement up to 9:15 am. Similarly, all the half an hourly increase in temperature with reference to the 8:15 am temperature (minimum temperature) are calculated and durations of heating are considered 30 min. When the temperature starts to decrease after reaching the peak at 3:15 pm the increase (negative values) in temperature is calculated with reference to the temperature at 3:15 pm. This increase in temperature is assigned at one end of the modeled sample and the other end was maintained at 0 °C. The corresponding

Table 5 Measured temperature variations at 90 mm depth on 16th October, 2012. Time

Surface temperature (°C)

Temperature increase (°C)

08:15 am 08:45 am 09:15 am 09:45 am 10:15 am 10:45 am 11:15 am 11:45 pm 12:15 pm 12:45 pm 01:15 pm 01:45 pm 02:15 pm 02:45 pm 03:15 pm 03:45 pm 04:15 pm 04:45 pm

12.92 13.48 14.23 16.66 19.51 21.44 23.26 25.99 28.50 28.82 30.44 32.00 33.28 34.11 34.50 34.28 33.83 33.06

0.00 0.56 1.31 3.73 6.58 8.52 10.33 13.07 15.58 15.90 17.52 19.08 20.36 21.19 21.58 0.22 0.67 1.44

30

6 5 4 3

FEM Laboratory

2 1 0 0

2000

4000

6000

Time (sec) Fig. 13. Variations of temperature with time.

Temperature (°C)

Increase in Temperature (°C)

7

25 20

Predicted Measured

15 10 8:00 AM

11:36 AM

3:12 PM

6:48 PM

Time of Day Fig. 14. Predicted and measured temperature variations at 90 mm depth.

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M.R. Islam, R.A. Tarefder / Construction and Building Materials xxx (2014) xxx–xxx

temperature increase at the colder end after 30 min is calculated and summed up with the minimum temperature at 90 mm depth (16.83 °C). The cumulative sum of the produced temperature is considered the predicted temperature at 90 mm depth. The predicted and the measured temperature at 90 mm depth are shown in Fig. 14. A promising agreement between these two values is observed. Therefore, conclusion can be drawn that the simplified numerical analysis and the practice ready, low cost laboratory procedure measure the thermal properties accurately. 11. Conclusions Based on the current study following conclusions can be made:  Using the field measured pavement temperature and strain variations, calculated CTC and CTE values of asphalt concrete are to be 2.69  105 per °C and 2.42  105 per °C in fall and 2.47  105 per °C and 2.77  105 per °C in winter respectively. These values are within the range of the laboratory values available in literature although base friction and boundary conditions are neglected.  Using the laboratory measured temperature and strain variations, calculated CTC and CTE values of asphalt concrete are to be 2.64  105 per °C and 2.28  105 per °C respectively. These values are very close to the field observations.  Transverse CTCs are larger than longitudinal CTCs and increase near the edge of pavement. Longitudinal CTCs values are independent of edge effect.  This study determines C value from laboratory cylindrical sample instead of beam sample. The determined C value is 1464 J/(kg K) which is similar to previous studies.  This study also determines k value from FEM analysis using cylindrical sample using the laboratory determined C value. The resulted k value is 2.11 W/(m K) which is similar to previous studies. In addition, this study validates the FEM determined k and the laboratory determined C using field measured temperature which has never been conducted in the past. The test procedure and the outcome of this study are expected to be extremely useful for characterizing thermal properties of AC and in study of temperature related stress–strain behavior of flexible pavement.

Acknowledgements This project is funded by the New Mexico Department of Transportation (NMDOT). Special thanks go to Dr. David Timm of NCAT, Auburn University, USA for his cooperation in the installation of the sensors on the I-40 pavement in New Mexico, USA. References [1] Chintakunta SR. Sensitivity of thermal properties of pavement materials using mechanistic-empirical pavement design guide. M.S. Thesis, Ames (Iowa): Iowa State University; 2007. [2] Baus R, Stires N. Mechanistic-empirical pavement design guide implementation, Report No. FWHA-SC-10-01, 2010, Submitted to the South Carolina Department of Transportation and the Federal Highway Administration. [3] Hildebrand E. Prediction of thaw settlement and surface roughness for highways in permafrost areas, Ph.D. Thesis, Canada: University of Waterloo; 1985.

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Please cite this article in press as: Islam MR, Tarefder RA. Determining thermal properties of asphalt concrete using field data and laboratory testing. Constr Build Mater (2014), http://dx.doi.org/10.1016/j.conbuildmat.2014.03.040