Stockholm, Sweden 2010
Implementation of the SuperPave IDT Analysis Procedure
Guangli Du
Master of Science Thesis Stockholm, Sweden 2010
Implementation of the SuperPave IDT Analysis Procedure
Masters Degree Project
Guangli Du
Division of Highway and Railway Engineering Department of Civil and Architectural Engineering
Royal Institute of Technology SE-100 44 Stockholm
TRITA-VBT 10:08 ISSN 1650-867X ISRN KTH/VBT-10/08-SE
Stockholm 2010
Implementation of the SuperPave IDT Analysis Procedure
Guangli Du Graduate Student
Infrastructure Engineering
Division of Highway and Railway Engineering School of Architecture and the Built Environment
Royal Institute of Technology (KTH) SE- 100 44 Stockholm guangli@kth.se
Abstract: Cracking is one of the most severe distress modes of asphalt pavements. Thus characterising the fracture resistance properties of as- phalt mixtures is the key issue for improving the performance related mixture design. The present master thesis project addresses the imple- mentation of the theoretical framework, which is used to characterise the fracture resistance of mixtures based on the SuperPave indirect tensile test (IDT). An open source Matlab-based software for analysing resilient modulus, Poisson’s ratio, creep parameters and fracture resistance para- meters has been developed. The software analyses the the IDT results, to estimate mixture’s fracture resistance based on hot mix asphalt Fracture Mechanics. Predictions form the field specimens concerning the fracture resistance obtained from IDT are compared with observed field perfor- mance.
Key Words: SuperPave indirect tensile test, resilient modulus, creep com- pliance, fracture energy, dissipated creep strain energy
i
Acknowledgement
This master thesis project was initiated and carried out at the Depart- ment of Civil and Architectural Engineering, Kungliga Tekniska högsko- lan (KTH) in Stockholm, Sweden.
I would like to express my gratitude to my examiner Prof. Björn Bir- gisson, who kindly provided me with a summer internship and the op- portunity to work on this project. I appreciate his encouragement and professional instructions during my thesis work.
Second, I would like to express my sincere acknowledgement to my thesis project supervisor Dr. Denis Jelagin, for his patient, expert guidance, and invaluable help with this thesis. I would like to provide my deep ap- preciation to Dr. Michael T Behn, for his meticulous guidance, priceless comments and help through the thesis writing.
I also owe my sincere gratitude to all my classmates and friends that accompanied with me during the master degree studying.
iii
List of Symbols
A DCSEminrelated parameter
CBX strain correction factor
CBXT correction factor
CBY T correction factor
CBXI correction factor
CBY I correction factor
CSXI correction factor
CSY I correction factor
CSXT correction factor
CSY T correction factor
CSX stress correction factor
Ccompliance creep compliance correction factor
CCM P L,I correction factor for instantaneous
resilient modulus
CCM P L,T correction factor for total resilient
modulus
Cnorm normalisation factor
d specimen diameter
DCSE Dissipated Creep Strain Energy
DCSEmin Minimum Dissipated Creep Strain Energy
DCSEf Dissipated Creep Strain Energy to failure
D0 reciprocal of resilient modulus
D(t) creep compliance at time t
v
Mr resilient modulus
Pi,tn the force of specimen i at time tn
St tensile strength
T specimen thickness
t time
Vi,tn,k the vertical deformation of specimen i for face k at time tn
XAvg the average value of parameter X
σx horizontal stress
σy vertical stress
σ stress
σf ail failure stress
∆H horizontal deformation
∆V vertical deformation
f ail failure strain
x horizontal strain
y vertical strain
ν poisson’s ratio
vi
List of Abbreviations
AASHO American Association of State Highway and Transportation Officials
EE Elastic Energy
ER Energy Ratio
FEM Finite Element Method
FE Fracture Energy
FHWA Federal Highway Administration
GL Gage Length
HMA Hot Mix Asphalt
IDT Indirect Tensile Test
LVDT Linear Voltage Differential Transducers
NCHRP The National Cooperative
Highway Research Program
SHRP Strategic Highway Research
Program
vii
Contents
Acknowledgement Abstract
List of Symbols v
List of Abbreviations vi
Contents xi
1 Introduction 1
Objectives 2
2 SuperPave IDT laboratory test 5
2.1 SuperPave IDT equipment . . . . 5
2.2 Specimen preparation . . . . 6
2.3 Test procedure . . . . 8
3 Data analysis of SuperPave IDT 11 3.1 Data analysis of resilient modulus test . . . . 11
3.1.1 Data acquisition . . . . 11
3.1.2 Total and instantaneous deformations . . . . 12
3.1.3 Data normalisation . . . . 14
3.1.4 Data trimming . . . . 15
ix
3.2.1 Data acquisition from creep compliance test . . . 20
3.2.2 Determine the absolute deformation . . . . 20
3.2.3 Data normalisation . . . . 21
3.2.4 Determine the trimed average deformation . . . . 22
3.2.5 Determination of creep compliance curve . . . . . 22
3.3 Data analysis for IDT strength test . . . . 24
3.3.1 Data acquisition in the strength test . . . . 25
3.3.2 Determine the absolute deformation . . . . 25
3.3.3 Determine the failure load . . . . 26
3.3.4 Determine the stresses and strains . . . . 26
3.3.5 Fracture resistance characterization . . . . 28
4 Implementation of the SuperPave IDT 31 4.1 Implementation of IDT resilient modulus test . . . . 31
4.2 Implementation of IDT Creep test . . . . 34
4.3 Implementation of IDT strength test . . . . 39
5 Case study results and discussion 45
6 Summary 49
x
References 51
Appendix A Road information 55
Appendix B Matlab code of Mr test 58
Appendix C Matlab code of Creep test 67
Appendix D Matlab code of Strength test 73
xi
1
1 Introduction
Cracking is one of the most important distress modes of asphalt pa- vements, cracks in asphalt initiate and propagate due to the combined impact from environmental and traffic loading. To a great extent, crack initiation governs the service life of asphalt structure, once the crack has initiated it will act as a stress concentration and facilitate the entrance of moisture into the pavement. Consequently pavement deterioration will be dramatically accelerated leading to premature failure and high maintenance costs (Beer, 1992). Characterising the fracture resistance properties of asphalt mixtures is the key issue for improving the perfor- mance related mixture design. The cracking related properties of asphalt mixtures should be measured, specified in the laboratory and incorpora- ted into existing pavement design procedures (Roque et al., 1997).
Characterisation of fracture resistance of asphalt mixtures is not a straightforward task as the mechanical properties of asphalt are known to be severely dependent on temperature, time and mode of loading. Ho- wever Zhang et al. (2001) found there exists a fundamental energy based threshold which governs the fracture initiation in asphalt - the dissipated creep strain energy threshold. This threshold is a measurement of the amount of ’micro damage’ which mixture can tolerate before the fracture occurrence. By measuring this threshold experimentally and combining it with hot mix asphalt (HMA) fracture mechanics, it is possible to ob- tain realistic prediction concerning mixtures fracture resistance in the field (Birgisson et al., 2004).
A practical way to measure material parameters used in HMA Frac- ture Mechanics is provided by SuperPave indirect tensile test (IDT),
—the test method developed by Roque, et al., (1993-1994a) as a part of the Strategic Highway Research Program (SHRP) (NCHRP, 2004). The SuperPave IDT consist of three tests performed consequently: Resilent Modulus test, Creep test, and Strength test. However, the parameters which are essential for characterising HMA fracture resistance can not be obtained directly from the SuperPave IDT test. The test transducer of the SuperPave IDT only records the applied load and deformation data of the specimen. The present project is focused on development of an open-source and platform independent matlab-based software ca- pable of analyzing the raw experimental measurements, and obtaining the fracture resistance related parameters which are listed as: Resilient modulus (Mr) and Poisson’s ratio (ν) determined from indirect tensile Resilient Modulus test; Creep compliance D(t) and m-value obtained from Creep test; Failure strain, dissipated creep strain energy to failure (DCSE), fracture energy (FE), Energy ratio (ER) and tensile strength (St) determined from Strength test.
Once the deformation data of specimens are obtained from the Su- perPave IDT, the above parameters can be determined automatically by the software developed in this thesis project, thus the cracking resistance properties can be obtained based on the SuperPave IDT theory and HMA Fracture Mechanics Model. In order to evaluate the developed software, it has been used to characterize fracture resistance characteristics of as- phalt mixtures with known field performance.
Objectives
The main purpose of this master thesis project is to develop a precise and practical data analysing softeware, that can be used for obtaining
3
cracking related properties of asphalt mixture from SuperPave IDT data.
The study is carried out based on the surveying from published literature theory and experimental work in laboratory with test data processing and analysis. The specific aim of the study can be divided into four parts:
1. Reviewing the technical literature on the determination of the as- phalt mixture mechanical properties from SuperPave IDT.
2. Implement the theory and develop an open-source, and platform independent software for SuperPave IDT data analysis.
3. Perform SuperPave IDT tests on mixtures with known field perfor- mance.
4. Use the developed software to estimate mechanical properties of the asphalt mixtures and predict the cracking performance based on HMA fracture mechanics.
5
2 SuperPave IDT laboratory test
2.1 SuperPave IDT equipment
Figure 1: Superpave IDT equipment (FHWA, 2006)
The Superpave IDT equipment consists of four principle parts which are present in Figure 1. Based on the SuperPave IDT framework deve- loped by Roque (1997) and laboratory procedures published by FHWA (2006), the SuperPave IDT equipment can be described in detail as:
1. MTS model loading device: The loads are controlled using an MTS Model 418.91 Micro-Profiler, this type of load frame is a microprocessor-based, single output precision waveform generation device. By selecting different test control modes and load wave- forms, a unique load waveform can be applied to the specimen.
2. Specimen deformation measuring devices: The specimen deformation measuring device consists of four linear voltage diffe- rential transducers (LVDT), which are capable to measure defor- mations up to 0.25 mm. The resolution of LVDT is 0.000125 mm.
Two LVDTs are placed perpendicularly on each side of a specimen to measure both horizontal and vertical deformations.
3. Environmental chamber: The environmental chamber includes a digitally controlled refrigeration and heating system which is capable to control the temperature in the range of -30 to 30°C, and maintaining the required temperature within the accuracy of
±0.2°C. It includes a viewing window, de-humidification device, interior lights, and an interface for remote control. The specimens could be stored in the environmental chamber before the test.
4. Data acquisition and control system: During the test, the loads and deformations data are recorded and stored by the data acquisition and control system. The system provides a closed-loop feedback control to the loading frame, which allows the Superpave IDT to make adjustments of performing precise programmed test.
Parameters such as position, load, and strain can be used as feed- back. The system operates under a Microsoft Windows environ- ment with displays of data and real time plots.
2.2 Specimen preparation
The specimens tested by the Superpave IDT can be cored from field pavements or prepared in the laboratory. In order to produce smooth and parallel faces with standard dimension of 150 mm diameter and 50 mm
2.2 Specimen preparation 7
thick, the test specimens are cut using water cooled masonry saw. The specimens should be cooled at test temperature for at least 3 hours before the test, then four stainless steel "buttons" are glued to each specimen face, these buttons have a diameter of 8 mm and a thickness of 3 mm.
Two strain gages with a length of 38.1 mm (or 25mm) are attached to these buttons, and the LVDTs are mounted to the gage points for measuring the vertical and horizontal deformations on each side of the specimen. Afterwards, the specimen is placed onto the load frame and fixed by the top and bottom loading plates (Roque et al., 1997; Birgisson et al., 2007), as present in Figure 2. Normally the test is performed on three specimens, the final test results are based on the average values (Gregory, 2004).
For SuperPave IDT, different asphalt mixtures can be tested at dif- ferent temperatures in the range of -20 to 30°C, depending on the specific test objectives. Creep compliances and indirect tensile strengths are tes- ted at low temperatures (-20, -10 and 0°C) for thermal cracking analysis, while indirect tensile strength is tested at higher temperatures ( -10 to 30°C ) for fatigue cracking analysis (FHWA, 2006).
Figure 2: Specimen for SuperPave IDT (Birgisson et al., 2007)
2.3 Test procedure
Three different tests are involved as part of the SuperPave IDT, each focuses on different material properties:
The IDT resilient modulus test: The resilient modulus test is conduc- ted by applying a dynamic load of half sine wave mode to the specimen for 0.1 second followed by a rest period of 0.9 seconds, this 1 second is regarded as 1 cycle and the specimen is loaded for 5 cycles. Each test includes 3 specimens and the magnitude of the load is adjusted so that the measured horizontal strain is in the range of 150 to 350 micro-strains.
The parameter of Resilient Modulus (Mr) and Poisson’s Ratio (ν) are de- termined from the recorded horizontal and vertical deformations (Roque, et al., 1997). The resilient modulus is defined as the ratio of the applied stress σ to the recoverable strain as repeated loads are applied (UW, 2006). The Poisson’s ratio is the ratio of the transverse strain x to the axial strain y. The basic principle for calculating resilient modulus and Poisson’s ratio are illustrated in Figure 3.
The IDT creep test: In order to observe the viscoelastic behavior and accumulated damage of the asphalt mixtures, the creep test applies a sta- tic load to the specimen for 1000 seconds. During the load application, the horizontal and vertical deformations are recorded as present in Figure 4. Three mixture parameters can be obtained from creep test: the creep compliance curve, the m-value and D1. D1 and the m-value are a pair of relational parameters which can be calculated by applying power-law curve fit to the creep compliance curve. D1 describes the initial portion of the creep compliance curve. The m-value illustrates the long term slope of the creep compliance curve. Daniel (2004) showed that the m-value is related to the accumulated rate of damage in asphalt. Specifically, a low
2.3 Test procedure 9
m-value corresponds to low rate of accumulated damage and vise versa (Birgisson et al., 2007). The creep compliance D(t) represents the rela- tionship between time-dependent strain and stress in asphalt mixtures, and it is commonly used to evaluate the rate of damage accumulation of asphalt mixtures. According to NCHRP (2003), the basic formula for calculating D(t) for the biaxial stress state on the specimen is obtained through Hooke’s law, expressed by the horizontal stress σx, vertical stress σy and the horizontal strain x:
D(t) = x
σx− νσy (1)
For reducing the three dimensional effect and the error caused by the buckling phenomenon, the stress and strains are further adjusted by correction factors presented in next chapter.
The IDT strength test: The strength test is performed by applying an increasing load at a constant displacement rate until the failure occurs in the specimen. The purpose of strength test is to find the failure limit parameters of the asphalt mixtures (Birgisson et al., 2007). The tensile strength of the asphalt mixture can be expressed as:
St= 2 × F ailure force
π × thickness × Diameter (2)
The parameters obtained from strength test are failure strain, the Dissipated Creep Strain Energy (DCSE), the total fracture energy and the energy ratio.
Figure 3: Definition of resilient modulus (UW, 2006)
Figure 4: Creep test plot (UW, 2006)
11
3 Data analysis of SuperPave IDT
This chapter present the algorithm for determining the mechanical pro- perties of HMA from the SuperPave IDT Resilient Modulus test, Creep test and Strength test, based on Roque and Buttlar (1992) and Protocol P07 (2001). The data acquisition, normalisation and trimming proce- dure are identical in theses three tests. For the purpose of simplification, the symbols presented in tables in this master thesis has the form Xi,tn,k, where i is the specimen number in each test group (i=1, 2, 3....), tnis the instant moment for recording the data, and k is the specimen face (k=1 or 2). X can represent loading P , horizontal deformation H or vertical deformation V .
3.1 Data analysis of resilient modulus test
3.1.1 Data acquisition
For each specimen with 2 faces, the data of loading and deformation are recorded by transducers. The deformations are measured independently on two faces of the specimen. The acquisition of test data are present as in Table 1.
Table 1: The acquisition of test data
Specimen i t Pi,tn Hi,tn,k Vi,tn,k Hi,tn,k Vi,tn,k 1st point t1 Pi,t1 Hi,t1,1 Vi,t1,1 Hi,t1,2 Vi,t1,2 2nd point t2 Pi,t2 Hi,t2,1 Vi,t1,1 Hi,t2,2 Vi,t1,2 3rd point t3 Pi,t3 Hi,t3,1 Vi,t3,1 Hi,t3,2 Vi,t3,2 ... ... ... ... ... ... ...
the last point tend Pi,tend Hi,tend,1 Vi,tend,1 Hi,tend,2 Vi,tend,2
3.1.2 Total and instantaneous deformations
For determining the total and instantaneous recoverable deformation of each specimen, two regression lines are fitted on the deformation data plot. Figure 5 presents the determination of instantaneous and total recoverable deformation of a specimen.
The first regression line 1, starts from the third point after the peak in each cycle and is fitted through the next five points; the second regression line, starts from the end of each cycle and is fitted through the previous 100 points. The intersection of two regression lines are used to determine the instantaneous recoverable deformation. The instantaneous recoverable deformation is defined as the vertical difference between the peak and the intersection point in each cycle. The total recoverable deformation is defined as the vertical difference between the peak and the last point in each cycle (Roque, 1997). For specimen i, there are 2 faces and 3 cycles correspond to 2×3 sets data for each parameter, Table 2 presents the parameter of total and instantaneous deformation determined by regression fitting for specimen i.
Table 2: Total and instantaneous deformation for each specimen
∆Hk, ∆Vk Cycle 1 Cycle 2 Cycle 3
instantaneous ∆Hf ace1 ∆Hf ace1 ∆Hf ace1
horizontal deformation ∆Hf ace2 ∆Hf ace2 ∆Hf ace2
total ∆Hf ace1 ∆Hf ace1 ∆Hf ace1
horizontal deformation ∆Hf ace2 ∆Hf ace2 ∆Hf ace2
instantaneous ∆Vf ace1 ∆Vf ace1 ∆Vf ace1
vertical deformation ∆Vf ace2 ∆Vf ace2 ∆Vf ace2
total ∆Vf ace1 ∆Vf ace1 ∆Vf ace1
vertical deformation ∆Vf ace2 ∆Vf ace2 ∆Vf ace2
3.1 Data analysis of resilient modulus test 13
Figure 5: Total and instantaneous recoverable deformation
where ∆VI is the instantaneous vertical deformation, ∆VT is the total vertical deformation, ∆HI is the instantaneous horizontal deformation,
∆HT is the total horizontal deformation.
3.1.3 Data normalisation
For reducing the dimention and loading difference effect for each spe- cimen in a test group, a normalisation procedure is applied. Equation 3 presents the normalisation factor for specimen i:
Cnorm,i = ( Ti
TAvg) × ( di
dAvg) × (Pmax,i
PAvg ) (3)
where T is the thickness of each specimen in the test group. TAvg is the average thickness of 3 specimens in the test group, defined as:
TAvg =
P3
i=1Ti
3 (4)
di is the diameter of each specimen in the test group. dAvg is the average diameter of 3 specimens in the test group, defined as:
dAvg =
P3
i=1di
3 (5)
Pmax,i is the maximum peak load for specimen i within 3 cycles. PAvg is the average peak load of each test group for 3 specimens, defined as:
PAvg =
P3
i=1Pmax,i
3 (6)
Therefore, the total and instantaneous recoverable deformations pre- sented in Table 2 is normalised by the factor Cnorm,i as:
∆Hnormalized = ∆Hk× Cnormal,i (7)
∆Vnormalized = ∆Vk× Cnormal,i (8)
3.1 Data analysis of resilient modulus test 15
3.1.4 Data trimming
There are 6 sets data for each parameter in each cycle in a test group.
The trimming process was described in Protocol P07 (2001) as: rating the deformation data set in test group, remove the highest and lowest deformation and average the remaining four. Take the parameter of ins- tantaneous horizontal deformation ∆Hi,instantaneous,k as an example. The trimmed instantaneous horizontal deformation ∆Htrim,instan,cycle1 can be obtained by subtracting the maximum and minimum value from the 6 data and averaging the remaining four values, as shown in Equation 9.
The data sets are presented in Table 3.
∆Htrim,instan,cycle1 =
P∆Hi,instan,k− max − min
4 (9)
The trimming procedure is applied for both the horizontal and vertical deformation data, thus there will be a corresponding trimmed value in each cycle for 3 specimens in a test group, present as in Table 4.
3.1.5 Determine the Poisson’s ratio
Based on the three dimensional finite element analysis conducted by Roque and Buttlar (1992), if the thickness of the specimen is lager than one inch, the horizontal stress of the specimen will vary significantly along the Z axis, as shown in Figure 6.
Table 3: the data set of instantaneous horizontal deformation
∆Hi,instan,k specimen 1 specimen 2 specimen 3 cycle 1 ∆H1,instan,1 ∆H2,instan,1 ∆H3,instan,1
∆H1,instan,2 ∆H2,instan,2 ∆H3,instan,2
Table 4: Trimmed data for a test group
Cycle 1 Cycle 2 Cycle 3
∆Htrim,instan,cycle1 ∆Htrim,instan,cycle2 ∆Htrim,instan,cycle3
∆Htrim,total,cycle1 ∆Htrim,total,cycle2 ∆Htrim,total,cycle3
∆Vtrim,instan,cycle1 ∆Vtrim,instan,cycle2 ∆Vtrim,instan,cycle3
∆Vtrim,total,cycle1 ∆Vtrim,total,cycle2 ∆Vtrim,total,cycle3
It is apparent that the plane stress solution, which was considered as a constant stress, is not accurate for the real stress conditions. Therefore, Roque and Buttlar (1992) created the correction factors for compensa- ting the stresses effect variation. The formula used for calculating the Poisson’s ratio in Figure 3 is then modified as:
νI,cycle j = −0.1+1.48(∆Htrim,instan,j
∆Vtrim,instan,j
)2−0.778(TAvg
DAvg)2·(∆Htrim,instan,j
∆Vtrim,instan,j
)2 (10)
νT ,cycle j = −0.1+1.48(∆Htrim,total,j
∆Vtrim,total,j
)2−0.778(TAvg
DAvg)2·(∆Htrim,total,j
∆Vtrim,total,j
)2 (11)
where νI,cycle j is the instantaneous Poisson’s ratio for cycle j, (j=1,2,3);
νT ,cycle j is the total Poisson’s ratio for cycle j, (j=1,2,3)
3.1 Data analysis of resilient modulus test 17
The final total Poisson’s ratio νT ,Avg and instantaneous Poisson’s ratio νI,Avg for a test group are defined as :
νT,Avg =
P3
j=1νT ,cycle j
3 (12)
νI,Avg =
P3
j=1νI,cycle j
3 (13)
3.1.6 Correction factors for buckling effect
Roque and Buttlar (1992) studied buckling using the three dimensional finite element analysis. Results showed that non-uniform buckling exists both in the loading direction and the transverse direction. Thus when
Figure 6: Tensile stress distributions along axis of symmetry (Buttlar et al., 1996)
applying the load to the specimen, the sensors will deform and rotated due to the deformation of the specimen. For this reason, Roque and
Buttlar (1992) generated the correction factors for eliminating the effects of buckling and deformation. These correction factors are further used in determination of total resilient modulus, expressed as:
CCM P L,T = 1.071 × π × CBXT
2 × (CSXT + 3 × νT ,Avg × CSY T) (14) where
CBXT = 1.03 − 0.189(DTAvgAvg) − 0.081 × νT,Avg + 0.089(DTAvgAvg)2 CBY T = 0.994 − 0.128 × νT,Avg
CSXT = 0.9480 − 0.01114(DTAvgAvg) − 0.2693 × νT ,Avg + 1.436 CSY T = 0.901 + 0.138νT ,Avg+ 0.287(DTAvgAvg) − 0.251νT ,Avg(DTAvgAvg)2
−0.264(DTAvgAvg)2
Similarly the correction factors used in determine the instantaneous resilient modulus are expressed as:
CCM P L,I = 1.071 × π × CBXI
2 × (CSXI + 3 × νI,Avg× CSY I) (15) where
CBXI = 1.03 − 0.189 × (DTAvgAvg) − 0.081 × νI,Avg + 0.089 × (DTAvgAvg)2 CBY I = 0.994 − 0.128 × νI,Avg
CSXI = 0.9480 − 0.01114 × (DTAvgAvg) − 0.2693 × νI,Avg + 1.436 CSY I = 0.901 + 0.138νI,Avg+ 0.287(DTAvgAvg) − 0.251νI,Avg·(DTAvgAvg)2
−0.264(DTAvgAvg)2
3.2 Data analysis of creep test 19
3.1.7 Determine the resilient modulus
The total and instantaneous resilient modulus of each cycle j (j=1,2,3) are calculated as (Roque, 1992):
MRT ,cycle j = GL ∗ PAvg
∆Htrim,total,cycle j× DAvg× TAvg× CCP M LT (16)
MRI,cycle j = GL ∗ PAvg
∆Htrim,instan,cycle j × DAvg × TAvg× CCP M LI (17)
where MRT ,cycle j is the total resilient modulus of cycle j (j=1,2,3). MRI,cycle j
is the instantaneous resilient modulus of cycle j (j=1,2,3). GL is the gage length.
The average total and instantaneous resilient modulus for the test group can be calculated:
MRI =
P3
j=1MRI,cycle j
3 (18)
3.2 Data analysis of creep test
This section describes the algorithm of data analysis procedure for obtaining the creep compliance and m-value from the SuperPave IDT creep test.
3.2.1 Data acquisition from creep compliance test
Similar to the resilient modulus test, the data files are recorded from 3 specimens in SuperPave IDT creep test. Table 6 shows the content of a creep test data file.
3.2.2 Determine the absolute deformation
Since the transducers recorded the accumulated displacement of each specimen, the absolute deformation ∆H and ∆V should be calculated by using the recorded displacement minus the first recorded displacement Hi,min,k (or Vi,min,k), this is expressed as:
Table 6: The content of one creep test data file inputData time
(s) Force (N)
Hi,tn,k1 (mm)
Hi,tn,k2 (mm)
Vi,tn,k1 (mm)
Vi,tn,k2 1st t1 Pi,t1 Hi,t1,1 Hi,t1,2 Vi,t1,1 (mm)Vi,t1,2 2nd t2 Pi,t2 Hi,t2,1 Hi,t2,2 Vi,t1,1 Vi,t1,2 3rd t3 Pi,t3 Hi,t3,1 Hi,t3,2 Vi,t3,1 Vi,t3,2 ... ... ... ... ... ... ...
last tend Pi,tend Hi,tend,1 Hi,tend,2 Vi,tend,1 Vi,tend,2
∆Hi,t,k = Hi,t,k− Hi,min,k (19)
∆Vi,t,k= Vi,t,k− Vi,min,k (20)
where ∆Hi,t,kis the absolute horizontal deformation for specimen i of face k at each creep time t, mm. ∆Vi,t,k is the absolute vertical deformation
3.2 Data analysis of creep test 21
for specimen i of face k at each creep time t, mm. Hi,t,k is the horizontal displacement recorded for creep time t each specimen i of face k, mm.
Vi,t,kis the vertical displacement recorded for creep time t each specimen i of face k, mm.
3.2.3 Data normalisation
In order to delimit the specimen dimension difference in each test group, Roque and Buttlar (1997) generated the normalisation factor Cnormifor each specimen i, present as:
Cnorm,i = ( Ti
TAvg) × ( di
dAvg) × (PAvg
Pi ) (21)
where Ti is the thickness of each specimen in the test group. TAvg is the average thickness of 3 specimens in the test group, defined as:
TAvg =
P3
i=1Ti
3 (22)
di is the diameter of each specimen in the test group. dAvg is the average diameter of 3 specimens in the test group, defined as:
dAvg =
P3
i=1di
3 (23)
Pi is the average axial load of each specimen i, defined as:
Pi =
P3
0Pi,t
3 (24)
PAvg is the average axial load of each test group for 3 specimens, defined as:
PAvg =
P3
i=1Pi
3 (25)
Thus the normalised horizontal and vertical deformation of each spe- cimen at time t and face k can be calculated as the absolute deforma- tion multiplied with the normalisation factor, denoted as ∆Hnormi,t,k and
∆Vnormi,t,k, as present in Equations 26 and 27.
∆Hnormi,t,k = Cnormi×∆Hi,t,k (26)
∆Vnormi,t,k = Cnormi×∆Vi,t,k (27)
3.2.4 Determine the trimed average deformation
The procedure to determine the trimed average deformation is simi- lar to the one uses for the resilient modulus. The highest and lowest deformation data are removed from the 6 data sets at instant tn, and the remaining four data are averaged. This average value is the trimed average deformation for each instant time tn, expressed as ∆HtrimAvg,t or
∆VtrimAvg,t (Protocol P07, 2001).
3.2.5 Determination of creep compliance curve
The creep compliance express the relation between the time dependent strain and the corresponding stress, as described earlier. It is an im- portant parameter for evaluating the damage accumulation in asphalt
3.2 Data analysis of creep test 23
mixtures. Figure 7 present the creep compliance plot, the related para- meter D1 and m-value. The parameter D1 and m-value can be obtained by applying power-law fitting curve on the logarithm creep compliance curve (Birgisson et al., 2007). NCHRP report (2004) has specified the expression of the curve used for power-law curve fitting, as Dj:
Dj = ∆HtrimAvg,t× dAvg × TAvg×109× Ccompliance,t
PAvg × GL (28)
where Ccompliance,t is the creep compliance correction factor at time t, expressed as:
Ccompliance,t = 0.6354 × (∆HtrimAvg,t
∆VtrimAvg,t
)−1−0.332 (29)
As shown in Figure 7, the creep compliance is equal to D0 at time (0).
However, when calculating the absolute deformation with the previous Equation 19, the elastic deformation is already excluded from the data.
This means that the creep compliance is plotted from time (1) instead of time (0). Thus the power law curve fitting should be applied to the following equation without considering the parameter D0:
Dj = D(t) − D0 = D1× tmnew
n (30)
The creep compliance D(t) can then be expressed as in Equation 31, defined as power law function of time tnew :
D(t) = D0+ D1× tmnewn (31)
Figure 7: Power model of creep compliance (Birgisson et al., 2007) where D0 is multiplicative inverse of instantaneous resilient modulus,
1
M rI, Gpa1 . tnewn is the absolute time used for curve fitting defined as the instant time t recorded by transducers minus the start time t1:
tnewn = tn− t1 (32)
D(t) is the creep compliance at time tnewn, Gpa1 . m is the further slope of the creep compliance curve.
3.3 Data analysis for IDT strength test
The IDT strength test is applied for predicting the fatigue and ther- mal cracking properties of HMA. During the test, an increasing load with a constant displacement rate is applied to the specimen until the first fracture initiates. Roque and Buttlar (1992) found that the tensile stresses vary along the axis of specimen symmetry, thus the load which causes tensile fracture at the edge is less than the load required to fail the entire specimen. Based on this observation, it is important to deter- mine the instant fracture occurs in the specimen, and the magnitude of corresponding tensile strength.
