the SuperPave IDT Analysis Procedure - DiVA portal468390/FULLTEXT01.pdf · 2011-12-20 · Implementation of the SuperPave IDT Analysis Procedure Masters Degree Project Guangli Du

Master of Science Thesis

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 DuGraduate StudentInfrastructure EngineeringDivision of Highway and Railway EngineeringSchool of Architecture and the Built EnvironmentRoyal Institute of Technology (KTH) SE- 100 44 Stockholm

[email protected]

Abstract: Cracking is one of the most severe distress modes of asphaltpavements. Thus characterising the fracture resistance properties of as-phalt mixtures is the key issue for improving the performance relatedmixture design. The present master thesis project addresses the imple-mentation of the theoretical framework, which is used to characterise thefracture resistance of mixtures based on the SuperPave indirect tensiletest (IDT). An open source Matlab-based software for analysing resilientmodulus, Poisson’s ratio, creep parameters and fracture resistance para-meters has been developed. The software analyses the the IDT results, toestimate mixture’s fracture resistance based on hot mix asphalt FractureMechanics. Predictions form the field specimens concerning the fractureresistance 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

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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 andprofessional instructions during my thesis work.

Second, I would like to express my sincere acknowledgement to my thesisproject 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, pricelesscomments and help through the thesis writing.

I also owe my sincere gratitude to all my classmates and friends thataccompanied with me during the master degree studying.

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List of Symbols

A DCSEminrelated parameterCBX strain correction factorCBXT correction factorCBY T correction factorCBXI correction factorCBY I correction factorCSXI correction factorCSY I correction factorCSXT correction factorCSY T correction factorCSX stress correction factorCcompliance creep compliance correction factorCCMP L,I correction factor for instantaneous

resilient modulusCCMP L,T correction factor for total resilient

modulusCnorm normalisation factord specimen diameterDCSE Dissipated Creep Strain EnergyDCSEmin Minimum Dissipated Creep Strain

EnergyDCSEf Dissipated Creep Strain Energy to

failureD0 reciprocal of resilient modulusD(t) creep compliance at time t

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Hi,tn,k the horizontal deformation ofspecimen i for face k at time tn

i specimen numberk face numberm-value creep compliance parameterMr resilient modulusPi,tn the force of specimen i at time tnSt tensile strengthT specimen thicknesst timeVi,tn,k the vertical deformation of

specimen i for face k at time tnXAvg the average value of parameter Xσx horizontal stressσy vertical stressσ stressσfail failure stress∆H horizontal deformation∆V vertical deformationεfail failure strainεx horizontal strainεy vertical strainν poisson’s ratio

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List of Abbreviations

AASHO American Association of StateHighway and TransportationOfficials

EE Elastic EnergyER Energy RatioFEM Finite Element MethodFE Fracture EnergyFHWA Federal Highway AdministrationGL Gage LengthHMA Hot Mix AsphaltIDT Indirect Tensile TestLVDT Linear Voltage Differential

TransducersNCHRP The National Cooperative

Highway Research ProgramSHRP Strategic Highway Research

Program

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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

3.1.5 Determine the Poisson’s ratio . . . . . . . . . . . 15

3.1.6 Correction factors for buckling effect . . . . . . . 17

3.1.7 Determine the resilient modulus . . . . . . . . . . 19

3.2 Data analysis of creep test . . . . . . . . . . . . . . . . . 19

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

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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

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1 Introduction

Cracking is one of the most important distress modes of asphalt pa-vements, cracks in asphalt initiate and propagate due to the combinedimpact from environmental and traffic loading. To a great extent, crackinitiation governs the service life of asphalt structure, once the crack hasinitiated it will act as a stress concentration and facilitate the entranceof moisture into the pavement. Consequently pavement deteriorationwill be dramatically accelerated leading to premature failure and highmaintenance costs (Beer, 1992). Characterising the fracture resistanceproperties of asphalt mixtures is the key issue for improving the perfor-mance related mixture design. The cracking related properties of asphaltmixtures 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 astraightforward task as the mechanical properties of asphalt are knownto be severely dependent on temperature, time and mode of loading. Ho-wever Zhang et al. (2001) found there exists a fundamental energy basedthreshold which governs the fracture initiation in asphalt - the dissipatedcreep strain energy threshold. This threshold is a measurement of theamount of ’micro damage’ which mixture can tolerate before the fractureoccurrence. By measuring this threshold experimentally and combiningit with hot mix asphalt (HMA) fracture mechanics, it is possible to ob-tain realistic prediction concerning mixtures fracture resistance in thefield (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),

2 1 OBJECTIVES

—the test method developed by Roque, et al., (1993-1994a) as a part ofthe Strategic Highway Research Program (SHRP) (NCHRP, 2004). TheSuperPave IDT consist of three tests performed consequently: ResilentModulus test, Creep test, and Strength test. However, the parameterswhich are essential for characterising HMA fracture resistance can notbe obtained directly from the SuperPave IDT test. The test transducerof the SuperPave IDT only records the applied load and deformationdata of the specimen. The present project is focused on developmentof an open-source and platform independent matlab-based software ca-pable of analyzing the raw experimental measurements, and obtainingthe fracture resistance related parameters which are listed as: Resilientmodulus (Mr) and Poisson’s ratio (ν) determined from indirect tensileResilient Modulus test; Creep compliance D(t) and m-value obtainedfrom 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 bythe software developed in this thesis project, thus the cracking resistanceproperties can be obtained based on the SuperPave IDT theory and HMAFracture 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 preciseand practical data analysing softeware, that can be used for obtaining

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cracking related properties of asphalt mixture from SuperPave IDT data.The study is carried out based on the surveying from published literaturetheory and experimental work in laboratory with test data processing andanalysis. 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 platformindependent 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 ofthe asphalt mixtures and predict the cracking performance basedon HMA fracture mechanics.

4 1 OBJECTIVES

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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 whichare 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 usingan MTS Model 418.91 Micro-Profiler, this type of load frame is amicroprocessor-based, single output precision waveform generationdevice. By selecting different test control modes and load wave-forms, a unique load waveform can be applied to the specimen.

6 2 SUPERPAVE IDT LABORATORY TEST

2. Specimen deformation measuring devices: The specimendeformation 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 specimento measure both horizontal and vertical deformations.

3. Environmental chamber: The environmental chamber includesa digitally controlled refrigeration and heating system which iscapable 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 specimenscould be stored in the environmental chamber before the test.

4. Data acquisition and control system: During the test, theloads and deformations data are recorded and stored by the dataacquisition and control system. The system provides a closed-loopfeedback control to the loading frame, which allows the SuperpaveIDT 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 fieldpavements or prepared in the laboratory. In order to produce smooth andparallel 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. Thespecimens should be cooled at test temperature for at least 3 hours beforethe test, then four stainless steel "buttons" are glued to each specimenface, 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 attachedto these buttons, and the LVDTs are mounted to the gage points formeasuring the vertical and horizontal deformations on each side of thespecimen. Afterwards, the specimen is placed onto the load frame andfixed by the top and bottom loading plates (Roque et al., 1997; Birgissonet al., 2007), as present in Figure 2. Normally the test is performed onthree 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 specifictest 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 to30°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, eachfocuses 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 specimenfor 0.1 second followed by a rest period of 0.9 seconds, this 1 second isregarded as 1 cycle and the specimen is loaded for 5 cycles. Each testincludes 3 specimens and the magnitude of the load is adjusted so thatthe 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 appliedstress σ to the recoverable strain ε as repeated loads are applied (UW,2006). The Poisson’s ratio is the ratio of the transverse strain εx to theaxial strain εy. The basic principle for calculating resilient modulus andPoisson’s ratio are illustrated in Figure 3.

The IDT creep test: In order to observe the viscoelastic behavior andaccumulated 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 Figure4. Three mixture parameters can be obtained from creep test: the creepcompliance curve, the m-value and D1. D1 and the m-value are a pairof relational parameters which can be calculated by applying power-lawcurve fit to the creep compliance curve. D1 describes the initial portion ofthe creep compliance curve. The m-value illustrates the long term slopeof the creep compliance curve. Daniel (2004) showed that the m-value isrelated 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 accumulationof asphalt mixtures. According to NCHRP (2003), the basic formula forcalculating D(t) for the biaxial stress state on the specimen is obtainedthrough Hooke’s law, expressed by the horizontal stress σx, vertical stressσy and the horizontal strain εx:

D(t) = εx

σx − νσy

(1)

For reducing the three dimensional effect and the error caused bythe buckling phenomenon, the stress and strains are further adjusted bycorrection factors presented in next chapter.

The IDT strength test: The strength test is performed by applyingan increasing load at a constant displacement rate until the failure occursin the specimen. The purpose of strength test is to find the failure limitparameters of the asphalt mixtures (Birgisson et al., 2007). The tensilestrength of the asphalt mixture can be expressed as:

St = 2 × Failure force

π × thickness×Diameter(2)

The parameters obtained from strength test are failure strain, theDissipated Creep Strain Energy (DCSE), the total fracture energy andthe energy ratio.


Figure 3: Definition of resilient modulus (UW, 2006)

Figure 4: Creep test plot (UW, 2006)

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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, Creeptest and Strength test, based on Roque and Buttlar (1992) and ProtocolP07 (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....), tn is theinstant moment for recording the data, and k is the specimen face (k=1or 2). X can represent loading P , horizontal deformation H or verticaldeformation 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 arerecorded by transducers. The deformations are measured independentlyon two faces of the specimen. The acquisition of test data are present asin 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,t1,22nd point t2 Pi,t2 Hi,t2,1 Vi,t1,1 Hi,t2,2 Vi,t1,23rd point t3 Pi,t3 Hi,t3,1 Vi,t3,1 Hi,t3,2 Vi,t3,2.............. ...... ...... ...... ......... ...... .........

the last point tend Pi,tendHi,tend,1 Vi,tend,1 Hi,tend,2 Vi,tend,2

12 3 DATA ANALYSIS OF SUPERPAVE IDT

3.1.2 Total and instantaneous deformations

For determining the total and instantaneous recoverable deformationof each specimen, two regression lines are fitted on the deformation dataplot. Figure 5 presents the determination of instantaneous and totalrecoverable deformation of a specimen.

The first regression line 1, starts from the third point after thepeak in each cycle and is fitted through the next five points; the secondregression line, starts from the end of each cycle and is fitted through theprevious 100 points. The intersection of two regression lines are used todetermine the instantaneous recoverable deformation. The instantaneousrecoverable deformation is defined as the vertical difference between thepeak and the intersection point in each cycle. The total recoverabledeformation is defined as the vertical difference between the peak andthe last point in each cycle (Roque, 1997). For specimen i, there are2 faces and 3 cycles correspond to 2×3 sets data for each parameter,Table 2 presents the parameter of total and instantaneous deformationdetermined by regression fitting for specimen i.

Table 2: Total and instantaneous deformation for each specimen

∆Hk, ∆Vk Cycle 1 Cycle 2 Cycle 3instantaneous ∆Hface1 ∆Hface1 ∆Hface1horizontal deformation ∆Hface2 ∆Hface2 ∆Hface2total ∆Hface1 ∆Hface1 ∆Hface1horizontal deformation ∆Hface2 ∆Hface2 ∆Hface2instantaneous ∆Vface1 ∆Vface1 ∆Vface1vertical deformation ∆Vface2 ∆Vface2 ∆Vface2total ∆Vface1 ∆Vface1 ∆Vface1vertical deformation ∆Vface2 ∆Vface2 ∆Vface2

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 totalvertical 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 3presents 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 theaverage thickness of 3 specimens in the test group, defined as:

TAvg =∑3

i=1 Ti

3 (4)

di is the diameter of each specimen in the test group. dAvg is the averagediameter of 3 specimens in the test group, defined as:

dAvg =∑3

i=1 di

3 (5)

Pmax,i is the maximum peak load for specimen i within 3 cycles. PAvg isthe average peak load of each test group for 3 specimens, defined as:

PAvg =∑3

i=1 Pmax,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)


3.1.4 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: ratingthe deformation data set in test group, remove the highest and lowestdeformation and average the remaining four. Take the parameter of ins-tantaneous horizontal deformation ∆Hi,instantaneous,k as an example. Thetrimmed instantaneous horizontal deformation ∆Htrim,instan,cycle1 can beobtained by subtracting the maximum and minimum value from the 6data and averaging the remaining four values, as shown in Equation 9.The data sets are presented in Table 3.

∆Htrim,instan,cycle1 =∑ ∆Hi,instan,k −max−min

4 (9)

The trimming procedure is applied for both the horizontal and verticaldeformation data, thus there will be a corresponding trimmed value ineach 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 byRoque and Buttlar (1992), if the thickness of the specimen is lager thanone inch, the horizontal stress of the specimen will vary significantlyalong 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 3cycle 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 aconstant 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 thePoisson’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)


The final total Poisson’s ratio νT,Avg and instantaneous Poisson’s ratioνI,Avg for a test group are defined as :

νT,Avg =∑3

j=1 νT,cycle j

3 (12)

νI,Avg =∑3

j=1 νI,cycle j

3 (13)

3.1.6 Correction factors for buckling effect

Roque and Buttlar (1992) studied buckling using the three dimensionalfinite element analysis. Results showed that non-uniform buckling existsboth in the loading direction and the transverse direction. Thus when

Figure 6: Tensile stress distributions along axis of symmetry (Buttlaret al., 1996)

applying the load to the specimen, the sensors will deform and rotateddue to the deformation of the specimen. For this reason, Roque and


Buttlar (1992) generated the correction factors for eliminating the effectsof buckling and deformation. These correction factors are further usedin determination of total resilient modulus, expressed as:

CCMP L,T = 1.071 × π × CBXT

2 × (CSXT + 3 × νT,Avg × CSY T ) (14)

where

CBXT = 1.03 − 0.189( TAvg

DAvg) − 0.081 × νT,Avg + 0.089( TAvg

DAvg)2

CBY T = 0.994 − 0.128 × νT,Avg

CSXT = 0.9480 − 0.01114( TAvg

DAvg) − 0.2693 × νT,Avg + 1.436

CSY T = 0.901 + 0.138νT,Avg + 0.287( TAvg

DAvg) − 0.251νT,Avg( TAvg

DAvg)2

−0.264( TAvg

DAvg)2

Similarly the correction factors used in determine the instantaneousresilient modulus are expressed as:

CCMP L,I = 1.071 × π × CBXI

2 × (CSXI + 3 × νI,Avg × CSY I) (15)

where

CBXI = 1.03 − 0.189 × ( TAvg

DAvg) − 0.081 × νI,Avg + 0.089 × ( TAvg

DAvg)2

CBY I = 0.994 − 0.128 × νI,Avg

CSXI = 0.9480 − 0.01114 × ( TAvg

DAvg) − 0.2693 × νI,Avg + 1.436

CSY I = 0.901 + 0.138νI,Avg + 0.287( TAvg

DAvg) − 0.251νI,Avg · ( TAvg

DAvg)2

−0.264( TAvg

DAvg)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 MLT

(16)

MRI,cycle j = GL ∗ PAvg

∆Htrim,instan,cycle j ×DAvg × TAvg × CCP MLI

(17)

whereMRT,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 gagelength.

The average total and instantaneous resilient modulus for the testgroup can be calculated:

MRI =∑3

j=1 MRI,cycle j

3 (18)

3.2 Data analysis of creep test

This section describes the algorithm of data analysis procedure forobtaining the creep compliance and m-value from the SuperPave IDTcreep test.


3.2.1 Data acquisition from creep compliance test

Similar to the resilient modulus test, the data files are recorded from3 specimens in SuperPave IDT creep test. Table 6 shows the content ofa creep test data file.

3.2.2 Determine the absolute deformation

Since the transducers recorded the accumulated displacement of eachspecimen, the absolute deformation ∆H and ∆V should be calculatedby using the recorded displacement minus the first recorded displacementHi,min,k (or Vi,min,k), this is expressed as:

Table 6: The content of one creep test data file

Datainput

time(s)

Force(N)

Hi,tn,k1(mm)

Hi,tn,k2(mm)

Vi,tn,k1(mm)

Vi,tn,k2(mm)

1st t1 Pi,t1 Hi,t1,1 Hi,t1,2 Vi,t1,1 Vi,t1,22nd t2 Pi,t2 Hi,t2,1 Hi,t2,2 Vi,t1,1 Vi,t1,23rd 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 ∆H i,t,k is the absolute horizontal deformation for specimen i of facek at each creep time t, mm. ∆V i,t,k is the absolute vertical deformation


for specimen i of face k at each creep time t, mm. H i,t,k is the horizontaldisplacement recorded for creep time t each specimen i of face k, mm.V i,t,k is the vertical displacement recorded for creep time t each specimeni 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 Cnormi

foreach 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 theaverage thickness of 3 specimens in the test group, defined as:

TAvg =∑3

i=1 Ti

3 (22)

di is the diameter of each specimen in the test group. dAvg is the averagediameter of 3 specimens in the test group, defined as:

dAvg =∑3

i=1 di

3 (23)

Pi is the average axial load of each specimen i, defined as:

Pi =∑3

0 Pi,t

3 (24)


PAvg is the average axial load of each test group for 3 specimens, definedas:

PAvg =∑3

i=1 Pi

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 lowestdeformation data are removed from the 6 data sets at instant tn, andthe remaining four data are averaged. This average value is the trimedaverage 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 dependentstrain and the corresponding stress, as described earlier. It is an im-portant parameter for evaluating the damage accumulation in asphalt


mixtures. Figure 7 present the creep compliance plot, the related para-meter D1 and m-value. The parameter D1 and m-value can be obtainedby applying power-law fitting curve on the logarithm creep compliancecurve (Birgisson et al., 2007). NCHRP report (2004) has specified theexpression 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 previousEquation 19, the elastic deformation is already excluded from the data.This means that the creep compliance is plotted from time (1) insteadof time (0). Thus the power law curve fitting should be applied to thefollowing equation without considering the parameter D0:

Dj = D(t) −D0 = D1 × tmnewn(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

MrI, 1

Gpa. 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 , 1Gpa

. m is the further slopeof 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 loadwith a constant displacement rate is applied to the specimen until thefirst fracture initiates. Roque and Buttlar (1992) found that the tensilestresses vary along the axis of specimen symmetry, thus the load whichcauses tensile fracture at the edge is less than the load required to failthe entire specimen. Based on this observation, it is important to deter-mine the instant fracture occurs in the specimen, and the magnitude ofcorresponding tensile strength.

3.3 Data analysis for IDT strength test 25

3.3.1 Data acquisition in the strength test

The test data are record by the transducer from 3 specimens duringthe strength test, Table 7 presents an example of test data acquired forspecimen i.

3.3.2 Determine the absolute deformation

Since the transducer records the accumulated displacements of eachspecimen, the absolute horizontal deformation ∆Hi,t,k expressed in Equa-tion 33 is calculated by using each original recorded horizontal displace-ment Hi,t,k minus the minimum horizontal displacement Hi,min,k. Theminimum displacement is defined as the first recorded horizontal dis-placement in the data file. Similarly the absolute vertical deformation∆Vi,t,k is calculated as in Equation 34.

∆Hi,t,k = Hi,t,k −Hi,min,k (33)

∆Vi,t,k = Vi,t,k − Vi,min,k (34)

Table 7: The content of strength test data file

Specimen i tn 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,t1,22nd point t2 Pi,t2 Hi,t2,1 Vi,t1,1 Hi,t2,2 Vi,t1,23rd point t3 Pi,t3 Hi,t3,1 Vi,t3,1 Hi,t3,2 Vi,t3,2.............. ..... ...... ...... ........ ...... ........last point tend Pi,tend

Hi,tend,1 Vi,tend,1 Hi,tend,2 Vi,tend,2


3.3.3 Determine the failure load

During the IDT strength test, the difference between the vertical andhorizontal deformation will increase at a constant rate as long as thespecimen is undamaged. However, the difference between the horizontaland vertical deformation will reach to the peak value at the instant ofspecimen failure occurrence (NCHRP, 2003). Since this peak value existin both faces of the specimen, Roque and Buttlar (1997) determined thetime of failure tf as the time of first fracture on either face. An exampleis presented in Figure 8. The failure load is determined at time tBD,when the displacement difference first reaches to its peak.

3.3.4 Determine the stresses and strains

The failure load Pi,fail can be determined for each specimen by com-putational tool, the detailed procedure is discussed in section 4.3. Thecorresponding stress σ of each specimen at each instant time t can becalculated as in Equation 35. In order to simulate a zero load at thestart of load cycle, an assumed seating load 30 N is subtracted from theinstant load Pi,t (Roque, 1997):

σi,t = (Pi,t − seating load) × 2π × T ×D

× CSXi (35)

where CSXi is the stress correction factor. CSXi a function of Poisson’sratio, determined from the resilient modulus test result, expressed as

CSXi = 0.948 − 0.01114 × ( Ti

Di

) − 0.2693 × ν + 1.436 × ( Ti

Di

) × ν (36)


Figure 8: Determination of failure load


The failure strain εi,t is calculated using Equation 37, where ∆Hi,t,k isthe horizontal deformation of the side in which the fracture instant tfdetected.

εi,t = ∆Hi,t,k

GL× CBX × 1.072 (37)

3.3.5 Fracture resistance characterization

Zhang et al. (2001) found the existence of a fundamental energythreshold related to cracking propagation. The theory states that be-fore exceeding the fundamental energy threshold, only recoverable micro-cracking is generated and no macro-cracking occurs, the damage genera-ted is fully healed. After exceeding the energy threshold, cracking relatedmacro-cracking occurs and causes further fracture. The tensile stress isthe maximum stress that mixture can withstand before macro-crack ini-tiation. The failure strain is the horizontal strain when the first fracturegenerated. Roque et al. (2002) found two distinct thresholds for crackinitiation in asphalt mixtures, as showed in Figure 9. The fist threshold isthe Dissipated Creep Strain Energy (DCSEf ), which means the mixturecan fail under repeated loads with low magnitude when reaching theDCSEf . Another threshold is the Fracture Energy (FE) which is thecritical limit capable to fail the mixture with a large single load whileexceeding FE. Fracture energy is the energy required to fail a mixtureand is determined by the area under the stress-strain curve, while thedissipated creep strain energy at failure is defined as the fracture energyminus the elastic energy, and the Elastic energy (EE) is the differencebetween the FE and DCSE (Birgisson et al., 2007).


Figure 9: DCSE and EE in fracture mechanics

DCSEf = FE − EE (38)

EE = S2t

2Mr

(39)

Based on the fracture mechanics model, Roque et al. (2004) generatedthe parameter of Energy Ratio (ER), which is a dimensionless parameter.ER is defined as the dissipated creep strain energy threshold (DCSEf )of the asphalt mixture divided by the minimum dissipated creep strainenergy (DCSEmin). In order to get a good cracking performance, ERshould exceed 1 (Birgisson et al., 2007). This is expressed as:


ER = DCSEf

DCSEmin

(40)

where DCSEminis the minimum dissipated creep strain energy, relatedto the creep parameters D1 and m value, expressed as:

DCSEmin = m2.98 ×D1/A (41)

Parameter ”A” is determined as in Equation 42:

A = 0.0299 × σ−3.1 × (6.36 − St) + 2.46 × 10−8 (42)

where St is the tensile strength, A default value 150 psi is used for tensilestresses, σ, unless a different value is given (Kim et, al. 2009).

31

4 Implementation of the SuperPave IDT

The SuperPave IDT has been implemented as part of this master the-sis project using matlab-based programme. The programme comprisesa package of three sub-programmes called as: Mr programme, Creepprogramme, and Strength programme. These programmes are used forprocessing data from the corresponding resilient modulus test, creep testand strength test. The following sections discuss the detailed implemen-tation process of the SuperPave IDT.

4.1 Implementation of IDT resilient modulus test

The Mr programme is one of the sub-programmes used for analysingdata from the SuperPave IDT resilient modulus test. It consists of 4matlab.m documents named as mrRunNorm.m, mrMutiSpecimenAnaly-sis.m, resample.m, and curvefit.m. mrRunNorm.m is the main file fordata processing and the remaining three files define the functions formrRunNorm.m, as shown in Figure 10.

User manual for the Mr module

By pressing the run button in mrRunNorm.m document, all the para-meter results for the resilient modulus test will be calculated and savedin resultreport.mat document automatically. The process for using theMr programme is discussed in detail in this section, and is illustrated inFigure 10.

32 4 IMPLEMENTATION OF THE SUPERPAVE IDT

Figure 10: Flow chart for using Mr programme

4.1 Implementation of IDT resilient modulus test 33

1. Formatting the data file: In the IDT resilient modulus test,the computer recorded the test data for each specimen, and savedthe data in an excel file. Before run the programme, the format ofeach data sheet should be changed manually to a standard matlabreadable format. By adding ”%” in front of the text cells, and byadding the dimension of specimen in the last two rows, as showedas in Figure 11. The name of the data file should be changed tospecimen_1, specimen_2, and specimen_3 repectively. Now thesedata files can be imported into the Mr programme package.

2. Run the programme: Start analysing the data by pressing therun button in mrRunNorm.m document as showed in Figure 10.

Figure 11: Data file of a specimen in resilient modulus test


3. Data analysis process: During the Mr program execution, fivedata plots are displayed for each specimen (load history, two hori-zontal and two vertical displacements). In order to determine themaximum and minimum displacements corresponding to each loa-ding pulse, the user should define the location where the programcan find out the maximum and minimum value for each cycle. Thisis accomplished by specifying the division line on every plot. Thepeak values for each cycle will be above this line, while the mini-mum values will be below. In order to define this line, the usershould do a left mouse click on two points on every plot. The pro-gram will define the line through the two selected points and use itas division line, as illustrated in Figure 12. Thus the instantaneousand total deformation can be determined by the program.

4. Save: After finish clicking all figures, the parameter result of re-silient modulust test will be saved in matlab workspace with thename resultreport.mat, as showed in Figure 10.

4.2 Implementation of IDT Creep test

The Creep program is used for analysing the data from the SuperPaveIDT creep test, it comprises of 4 matlab files named as creep.m, mr-MutiSpecimenAnalysis.m, fitlineonloglog.m and resultreport.mat. The fileresultreport.mat is copied from the previous Mr program results. creep.mis the main program used for data analysis and the remaining two m-fileare the defined functions, as shown in Figure 15.

4.2 Implementation of IDT Creep test 35

Figure 12: Click on plotting figure in Mr program


User manual for the Creep module

By pressing the run button in the creep.m document, the programstarts analysing the data, and the parameter results will be saved inthe fileonecreep.mat document automatically. The process of using thethe Creep programme for data analysis is illustrated in Figure 15, anddescribed in detail below.

1. Formatting the data file: The procedure is similar to the onedescribed for the Mr test. The computer records the test data ofcreep test in an excel file. Before run the program, the formatof each data sheet should be changed manually by the user to astandard matlab readable format. This can be done by adding ”%”in front of the text cells and by adding the dimension of specimen inthe last two rows, as shown in Figure 13. The name of the data fileshould be changed to specimen_1, specimen_2, and specimen_3respectively. Now copy these modified data files into Creep programpackage.

2. Run the program: The Creep program starts analysing the databy pressing the run button in creep.m document, as shown in Fi-gure 15.

3. Data analysing process: While the Creep program running, thecreep compliance curve is plotted as in Figure 14. The red line inthe plot is the creep compliance curve from the original data, whilethe black line is the power-fitting curve obtained by the power-lawfitting function fitlineonloglog.m. The slope of this fitted curve isthe m-value.

4.2 Implementation of IDT Creep test 37

4. Save: Finally, the result of the tensile strength test are savedautomatically in matlab workspace with the name fileonecreep.mat.It includes the analysis result resultreport.mat from Mr program,as shown in Figure 15.

Figure 13: Data file of a specimen in resilient modulus test

Figure 14: Creep compliance curve


Figure 15: Flow chart for using Creep program

4.3 Implementation of IDT strength test 39

4.3 Implementation of IDT strength test

The Strength program is used for analysing data from SuperPaveIDT strength test. It comprises of 4 matlab documents named as run.m,StrengthMutiSpecimenAnalysis.m, resample.m and fileonecreep.mat. Thefile fileonecreep.mat is copied from the creep program result.

User manual for the Strength module

By pressing the run button in run.m document, the program presentthe plot of the tensile strength curve and the stress-strain curve, and theparameter results are saved in fileonecreep.mat document automatically.The process for data analysis are illustrated in Figure 19 and describedin detail in following text.

1. Formatting the data file: The procedure is similar to the onedescribed for the Mr test and the Creep test. Each specimen has acorresponding data sheet recorded by computer, saved as an excelfile. Before running the program, the format of each data sheetshould be changed manually by the user to a standard matlab rea-dable format. This can be done by adding ”%” in front of theletters and by adding the dimension of specimen in the last tworows, as showed in Figure 16. The name of the data file shouldbe changed to specimen_1, specimen_2, and specimen_3 respec-tively. Now, these modified data files can be imported into theStrength program package.

2. Run the program: Start analysing the specimen data by pressingthe run button in run.m document of IDT strength program, asshown in Figure 19.


3. Data analysing process: While the strength program running,the plot of failure load and stress-strain curve are shown to theuser, as in Figure 17. The method for detecting the failure force inplotting is based on Roque, et al. (1997), which was mentioned inSection 3.3.3.

• Roque, et al. (1997) states the theoretical difference betweenthe vertical and horizontal deformation (∆Hi,t,k − ∆Vi,t,k) willincrease at a constant rate before specimen damaged. Thusthe failure load is detected at the same point that (∆Hi,t,k −∆Vi,t,k) reaches to the peak, as shown in Figure 17. Finally,the stress-strain curve of the specimen is plotted, and used fordetermining the specimen fracture resistance properties.

• In case of unusually soft mixtures, it has been observed thatasphalt may not respond to fracture until reach the specimenmaximum load, as presented in Figure 18. Thus to avoid over-estimating the fracture energy of the specimen, the fracturepoint will be shifted to the linear part. This is done manuallyin program, and the instant horizontal displacement ∆Hi,t,k inEquation 37 will be adjusted to the average value of horizontaldisplacement ∆Hi,t,k in both sides. The strains εi,t at eachtime instant tn can be rewritten as:

εi,t = (∆Hi,t,1 + ∆Hi,t,2)2 ×GL

× CBX × 1.072 (43)

• If (∆Hi,t,k − ∆Vi,t,k) of the specimen reaches to the peak afterthe maximum load, the maximum load is used as the failureload. The strains εi,t in this case at each time instant tn is thesame as in Equation 43.


4. Save: The result of the test are saved in the matlab workspace un-der the name St.mat. The file includes the comprehensive analysisresult from the Mr program, the Creep program and the Strengthprogram, as shown in Figure 19.

Figure 16: Data file of a specimen in strength test


Figure 17: Plotting of failure force and stress-strain curve

Figure 18: Plotting of failure load (when deformation difference arrivelater than peak load)


Figure 19: Flow chart for using Strength program


45

5 Case study results and discussion

The HMA Fracture Mechanics has been extensively evaluated for Flo-rida conditions (Zhang, et al., 2001; Birgisson, et al., 2004). It has beenshown that using the SuperPave IDT allows to successfully distinguishbetween mixtures with good and bad fracture resistance. In order tofind out if the same framework is fully applicable for the mixtures usedin Scandinavia, mixtures with known field performance were tested andprediction concerning the mixtures fracture resistance were made.

Nynas Bitumen supplied four sets of field samples denoted as 2a, 4d, 4e,4f, which were drilled from road test sections with known performance.A detailed information about the performance of each road section isgiven in Appendix A along with layer thicknesses and traffic counts. Insummary the test sections 2a and 4d were found to reach the end of theirlives, while groups e and f were found to be in a good shape. Sections4d, 4e and 4f had the same daily traffic of 1786 ESALs, while section 2ahad a daily traffic of 609 ESALs.

For each road section three specimens were tested with SuperPaveIDT and the program developed in this thesis was used to obtain me-chanical properties of the asphalt mixtures and characterize the fractureperformance of the mixtures in the field. The elastic parameters foreach specimen are given in Table 8, along with the tensile strengths andfracture energies measured. One of the specimens in group a failed pre-maturely during the strength test and strength data is reported for it.One may observe in Table 8 that the resilient modulus and Poisson’sratios measured on the specimens from the same road section are veryclose to each other. The tensile strength, fracture energy and dissipated

46 5 CASE STUDY RESULTS AND DISCUSSION

creep strain energy data were however found to have significantly biggerscatter. This is expected, as the failure process is governed by mechani-cal properties of material in the small area in the center of the specimen.These properties may vary significantly from specimen to specimen andresult in a different fracture responses.

In order to obtain values representative for the field performance of themixtures, the average properties for each material have been computedwith a procedure outlined in Section 3. The average results for each testgroup are presented in Table 9. The resilient modulus (Mr) for the group fis significantly lower as compared to other groups, however it also has thelowest m-value indicating the lowest damage accumulation rate. Groups2a and 4d have high m-values implying high damage accumulation rate.DCSE at failure is the measurement of how much damage mixture cantolerate before the macro-crack initiates. Material 4d and 4e have highDCSE at failure values, which indicating that these materials can toleratemore damage as compared to materials f and a.

The energy ratios (ER) given in Table 9 measure a relative proportionbetween the damage thresholds of the materials and the rate of damageaccumulation due to loading. Generally higher ER indicate better frac-ture resistance, with ER=1 being a threshold between good and bad fieldperformance. ER for the group a is significantly lower as compared toother groups indicating that section a has poor cracking resistance. Forthe group 4d ER is very close to unity, indicating the pavement to be atthe end of it’s service life. ER for materials 4f and 4e are significantlyhigher than those of 2a and 4d. Thus, mixtures 4f and e may be expectedto perform better in the field, which agrees well with field observationssummarized in Appendix A. Based on the results presented in Table 9and Appendix A it may be concluded that SuperPave IDT is capable of

47

predicting the fracture resistance potential of the asphalt mixtures usedin Scandinavia.

Table 8: Analysing result of each specimen

MRI

GpaMRT

Gpa νI νTSt

MpaFEKJm3

failurestrain DCSEfER

d1 13.36 10.32 0.34 0.37 2.51 2.48 1494 2.18 0.544d d2 14.13 10.48 0.22 0.27 1.88 7.02 5421 6.85 1.88

d3 13.67 10.37 0.34 0.34 2.47 2.85 1722 2.56 0.64e1 10.11 8.72 0.22 0.22 1.37 1.33 1476.00 1.223 1.79

4e e2 10.61 8.9 0.19 0.22 2.57 5.93 3105.00 5.57 6.77e3 10.45 8.64 0.22 0.25 2.30 2.21 1395.00 1.91 2.43f1 6.59 5.49 0.15 0.16 1.40 0.77 770.83 0.59 1.89

4f f2 6.46 5.43 0.15 0.16 1.61 0.75 713.83 0.51 1.58f3 6.59 5.47 0.15 0.17 1.04 0.49 818.31 0.39 1.3a1 10.92 8.12 0.25 0.25 0.98 0.18 314.00 0.12 0.06

2a a2 10.54 7.84 0.25 0.26 *** *** *** *** ***a3 10.65 7.95 0.25 0.22 1.61 1.08 107.00 0.91 0.46

Table 9: Analysing result of test group

No MRI

GpaMRT

Gpa νI νTD0

1Gpa

D1 m St

Mpafailurestrain

FEKJm3

DCSEfER

4d 13.7 10.4 0.30 0.33 0.07 0.20 0.58 2.28 2879 4.11 3.86 1.024e 10.4 8.7 0.21 0.23 0.10 0.08 0.45 2.09 1989.0 3.17 2.90 3.664f 6.5 5.5 0.15 0.17 0.15 0.15 0.28 1.34 767.7 0.67 0.50 1.582a 10.7 8.0 0.25 0.24 0.09 0.16 0.51 0.86 691.4 0.63 0.52 0.26

48 5 CASE STUDY RESULTS AND DISCUSSION

49

6 Summary

The HMA fracture mechanics method developed at the Universityof Florida provides a fundamental theoretical framework to describe thecrack initiation and propagation in asphalt pavements. According toHMA fracture mechanics, crack initiation in asphalt mixtures can becompletely described by two distinct thresholds: the dissipated creepstrain energy limit and fracture energy limit. In the present thesis pro-ject, the HMA fracture mechanics framework was reviewed and it wasshown how the two thresholds may be obtained from the viscoelasticproperties and tensile strength of the mixtures.

SuperPave IDT is a practical and reliable way to measure all the para-meters needed in the HMA Fracture Mechanics method, i.e. resilient mo-dulus and Poisson’s ratio, creep compliance and tensile strength. Thus,by combineding HMA fracture mechanics method with the results fromthe SuperPave IDT tests, we can predict mixture’s fracture performancein the field.

In this thesis an open source, Matlab-based software for the processingof the SuperPave IDT results has been developed. Procedures to findthe parameters of resilient modulus, Poisson’s ratio, creep complianceand tensile strength, as originally developed by Roque et al. (1997),were implemented and adjusted for Swedish conditions. In particular,the developed software is capable of evaluating results obtained at lowertemperatures and with softer mixtures, than those used during the origi-nally in Florida. The program uses the IDT results to estimate mixture’sfracture resistance based on HMA Fracture Mechanics.

SuperPave IDT tests were performed on the field specimens fromthe roads with known fracture performance. Prediction concerning the

50 6 SUMMARY

fracture resistance obtained from the IDT tests were found to be in goodagreement with field observations.

Further research may be done on mixtures with different properties,at different temperatures, to further verify the HMA fracture mechanicsframework. By applying the developed program to different mixtures,sampled in different countries, can be further improved the test and dataanalysis procedure.

51

References

AASHTO, ”Standard Test Method for Determining the Creep Com-pliance and Strength of Hot Mix Asphalt (HMA) Using the IndirectTensile Test Device”, T322, American Association of State Highway andTransportation Officials, Jan 1, 1996, pp. 15.

AASHTO, LTPP Protocol P07, ”Test Method for Determining the CreepCompliance, Resilient Modulus and Strength of Asphalt Materials Usingthe Indirect Tensile Test Device”, Version 1.1, American Association ofState Highway and Transportation Officials, August 2001, pp. 79.

Beer, F., and Johnston, E.R., Mechanics of Materials, Second Edition,McGraw-Hill, New York, 1992, pp. 616.

Birgisson, B., Roque, R., Kim, J., and Pham, L. V., ”The use of com-plex modulus to characterize the performance of asphalt mixtures andpavements in Florida”, Summary of Final Report BC354-22 to the Flo-rida Department of Transportation, http://www.dot.state.fl.us/research-center/Completed_StateMaterials.shtm, 2004, pp. 321.

Birgisson, B., Antonio, M., Elena, R., Roque, R., Gabriele, T., ”The ef-fect of SBS asphalt modifier on hot mix asphalt (HMA) mixtures crackingresistance”, 4th International SIIV Congress, Palermo, 12-14 September2007, pp. 12.

Birgisson, B., Montepara, A., Romeo, E., Roncella, R., Napier, J.A.L.,Tebaldi, G., ”Determination and prediction of crack patterns in hot mixasphalt (HMA) mixtures”, Engineering Fracture Mechanics, Vol. 75,2008, pp. 664–673.

52 6 REFERENCES

Buttlar, W. G., Roque, R., and Kim, N., ”Accurate Determination ofMixture Tensile Strength”, Proceedings of the Fourth Materials Enginee-ring Conference, American Society of Civil Engineers, Washington, D.C.,November, 1996, pp. 163-172.

Daniel, J.S., W. Bisirri, and Y.R. Kim, ”Fatigue Evaluation of AsphaltMixtures using dissipated energy and viscoelastic continuum damage ap-proaches”, Journal of Association of Asphalt Paving Technologists, Vol.73, 2004, pp. 557-583.

Federal Highway Administration, ”SuperPave Indirect Tensile Test Bitu-minous Mixtures Laboratory (BML) Equipment”; http://www.fhwa.dot.gov/pavement/asphalt/labs/mixtures/idt.cfm; Accessed: January 17th,2010.

Gregory A. S., ”Evaluating the use of lower VMA requirements for Su-perpave mixtures”, Master thesis, University of Florida, Gainesville, FL,2004, pp. 87.

Kim, S., Gregory, A., Byron, S. T., ”Laboratory Evaluation of PolymerModified Asphalt Mixture with Reclaimed Asphalt Pavement (RAP)”,National Research Council, Washington, DC, July, 2009, pp. 109-114.

Lu Xiaohu, ”Personal Communication”, Nynas AB, 28th August, 2009.

National Cooperative Highway Research Program (NCHRP), ”Guide forMechanistic-Empirical Design of new and rehabilitated pavement struc-tures, TRB’s Appendix H.H.— Field calibration of the thermal crackingmodel”, December, 2003, pp. 243.

53

National Cooperative Highway Research Program (NCHRP), ”Evalua-tion of Indirect Tensile Test (IDT) Procedures for Low-TemperaturePerformance of Hot Mix Asphalt”, Report 530, Transprotation ResearchBoard Of The National Academies, Washington, D.C., 2004, pp. 62.

Roque R., and Buttlar, W. G., ”The development of a measurementand analysis system to accurately determine asphalt concrete propertiesusing the indirect tensile mode”, Journal of the Association of AsphaltTechnologists, Vol.61, 1992, pp. 304–332.

Roque, R., Buttlar, W.G., Ruth, B.E., Tia, M., Dickison, S. W., andReid, B., ”Evaluation of SHRP indirect tension tester to mitigate cra-cking in asphalt concrete pavements and overlays”, FL-DOT-MO-0510755,University of Florida, Gainesville, 1997, pp. 335.

University of Washington, ”Mixture Characterization Tests, InteractiveTraining Guides”, Chapter 6.1, http://training.ce.washington.edu/PGI/,Accessed: January 28th, 2010.

Zhang, Z., Roque, R., and Birgisson, B., ”Evaluation of Laboratory mea-sured crack growth rate for asphalt mixtures”, Transportation ResearchBoard of the National Academies, Washington, D.C., 2001, pp. 67-75.

54 6 REFERENCES

55

Appendix A Road information

56 6 APPENDIX A

57

58 6 APPENDIX B

59

Appendix B Matlab code of Mr test

Code of mrRunNorm.m%mr a f t e r normal i za t ionclcclear

n =3; %numOfSpecimenc y c l e = 3 ;gage length =0.025;[ tAvg dAvg pAvg]= dea l (0 ) ;c (n) =0; % normal f a c t o r[ horABvi horABvt verCDvi verCDvt ] = dea l ( zeros ( cyc l e , 2∗ n) ) ;r e s S t r u c t = mrMutiSpecimenAnalysis (n) ;

for i i = 1 : ntAvg = tAvg+r e s S t r u c t ( i i ) . t h i c k ;dAvg = dAvg+r e s S t r u c t ( i i ) . diam ;pAvg = pAvg+r e s S t r u c t ( i i ) . peakForce ;

endtAvg = tAvg/n ;dAvg = dAvg/n ;pAvg = pAvg/n ;

for i i = 1 : nc ( i i ) = r e s S t r u c t ( i i ) . t h i c k /tAvg∗ r e s S t r u c t ( i i ) . diam/dAvg∗pAvg/

r e s S t r u c t ( i i ) . peakForce ;r e s S t r u c t ( i i ) . DisplA . v i = r e s S t r u c t ( i i ) . DisplA . v i .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplA . vt = r e s S t r u c t ( i i ) . DisplA . vt .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplB . v i = r e s S t r u c t ( i i ) . DisplB . v i .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplB . vt = r e s S t r u c t ( i i ) . DisplB . vt .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplC . v i = r e s S t r u c t ( i i ) . DisplC . v i .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplC . vt = r e s S t r u c t ( i i ) . DisplC . vt .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplD . v i = r e s S t r u c t ( i i ) . DisplD . v i .∗(10^( −3) ) ∗c ( i i ) ;r e s S t r u c t ( i i ) . DisplD . vt = r e s S t r u c t ( i i ) . DisplD . vt .∗(10^( −3) ) ∗c ( i i ) ;horABvi ( : , 2 ∗ i i −1:2∗ i i ) = [ r e s S t r u c t ( i i ) . DisplA . v i ( : ) r e s S t r u c t ( i i ) .

DisplB . v i ( : ) ] ;horABvt ( : , 2 ∗ i i −1:2∗ i i ) = [ r e s S t r u c t ( i i ) . DisplA . vt ( : ) r e s S t r u c t ( i i ) .

DisplB . vt ( : ) ] ;verCDvi ( : , 2 ∗ i i −1:2∗ i i ) = [ r e s S t r u c t ( i i ) . DisplC . v i ( : ) r e s S t r u c t ( i i ) .

DisplD . v i ( : ) ] ;

60 6 APPENDIX B

verCDvt ( : , 2 ∗ i i −1:2∗ i i ) = [ r e s S t r u c t ( i i ) . DisplC . vt ( : ) r e s S t r u c t ( i i ) .DisplD . vt ( : ) ] ;

endf inalHorABvi = sum( horABvi , 2 ) ;f inalHorABvt = sum( horABvt , 2 ) ;f inalVerCDvi = sum( verCDvi , 2 ) ;f inalVerCDvt = sum( verCDvt , 2 ) ;i f n>1

maxABvi = max( horABvi , [ ] , 2 ) ;minABvi = min( horABvi , [ ] , 2 ) ;maxABvt = max( horABvt , [ ] , 2 ) ;minABvt = min( horABvt , [ ] , 2 ) ;maxCDvi = max( verCDvi , [ ] , 2 ) ;minCDvi = min( verCDvi , [ ] , 2 ) ;maxCDvt = max( verCDvt , [ ] , 2 ) ;minCDvt = min( verCDvt , [ ] , 2 ) ;f inalHorABvi = ( finalHorABvi−maxABvi−minABvi ) . / ( 2 ∗ n−2) ;f inalHorABvt = ( finalHorABvt−maxABvt−minABvt) . / ( 2 ∗ n−2) ;f inalVerCDvi = ( finalVerCDvi−maxCDvi−minCDvi ) . / ( 2 ∗ n−2) ;f inalVerCDvt = ( finalVerCDvt−maxCDvt−minCDvt) . / ( 2 ∗ n−2) ;

elsef inalHorABvi = finalHorABvi /2 ;f inalHorABvt = finalHorABvt /2 ;f inalVerCDvi = finalVerCDvi /2 ;f inalVerCDvt = finalVerCDvt /2 ;

end

po i s sonTi =−0.1+1.48∗( f inalHorABvt . / f inalVerCDvt ) .^2 −0.778∗( tAvg/dAvg)^2∗( f inalHorABvt . / f inalVerCDvt ) . ^ 2 ;

p o i s s o n I i =−0.1+1.48∗( f inalHorABvi . / f inalVerCDvi ) .^2 −0.778∗( tAvg/dAvg)^2∗( f inalHorABvi . / f inalVerCDvi ) . ^ 2 ;

poissonAvgpoiT=mean( po i s sonTi ) ;po i ssonAvgpoi I=mean( p o i s s o n I i ) ;CBXT=1.03 −0.189∗( tAvg/dAvg) −0.081∗ poissonAvgpoiT +0.089∗( tAvg/dAvg) ^2 ;CBXI=1.03 −0.189∗( tAvg/dAvg) −0.081∗ poissonAvgpoi I +0.089∗( tAvg/dAvg) ^2 ;CBYT=0.994 −0.128∗ poissonAvgpoiT ;CBYI=0.994 −0.128∗ poissonAvgpoi I ;CSXT=0.948 −0.01114∗( tAvg/dAvg) −0.2693∗ poissonAvgpoiT +1.436∗( tAvg/dAvg) ∗

poissonAvgpoiT ;CSXI=0.948 −0.01114∗( tAvg/dAvg) −0.2693∗ poissonAvgpoi I +1.436∗( tAvg/dAvg) ∗

poissonAvgpoi I ;

61

CSYT=0.901+0.138∗ poissonAvgpoiT +0.287∗( tAvg/dAvg) −0.251∗ poissonAvgpoiT ∗(tAvg/dAvg) ^2 −0.264∗( tAvg/dAvg) ^2 ;

CSYI=0.901+0.138∗ poissonAvgpoi I +0.287∗( tAvg/dAvg) −0.251∗ poissonAvgpoi I ∗(tAvg/dAvg) ^2 −0.264∗( tAvg/dAvg) ^2 ;

CCMPLT=1.071∗ pi∗CBXT. / 2 / (CSXT+3∗poissonAvgpoiT . ∗CSYT) ;CCMPLI=1.071∗ pi∗CBXI. / 2 / ( CSXI+3∗poissonAvgpoi I . ∗ CSYI) ;MRTi=gage length ∗pAvg . / ( f inalHorABvt . ∗ dAvg∗tAvg∗CCMPLT) ;MRIi=gage length ∗pAvg . / ( f inalHorABvi . ∗ dAvg∗tAvg∗CCMPLI) ;MRT=mean(MRTi) ;MRI=mean(MRIi ) ;

Code of mrMutiSpecimenAnalysis.m

function r e s S t r u c t = mrMutiSpecimenAnalysis (n)for j j =1:n

rawData = [ ] ;eval ( [ ’ rawData = load ( ’ ’ specimen_ ’ num2str( j j ) ’ . dat ’ ’ ) ; ’ ] ) %load

the datatime_sec = rawData ( 3 : end−2 ,1) ; % load d i f f e r e n t

column data%displacement_mm = rawData ( 2 : end −2 ,2) ;force_n = rawData ( 3 : end−2 ,3) ;DisplA_mm = rawData ( 3 : end−2 ,4) ;DisplB_mm = rawData ( 3 : end−2 ,5) ;DisplC_mm = rawData ( 3 : end−2 ,6) ;DisplD_mm = rawData ( 3 : end−2 ,7) ;dj = rawData (end , 1 ) ; % diametert j = rawData (end , 2 ) ; % t h i c k n e s sforce_n = −1∗ force_n ;DisplC_mm=−1∗DisplC_mm ;DisplD_mm=−1∗DisplD_mm ;r e s S t r u c t ( j j ) . t h i c k = t j ; % endow data to d i f f e r e n t

specimen j j = 1 , 2 , 3 . . . . nr e s S t r u c t ( j j ) . diam = dj ;r e s S t r u c t ( j j ) . peakForce = max( force_n ) ;[ r e s S t r u c t ( j j ) . f o r c e . v i r e s S t r u c t ( j j ) . f o r c e . vt ]= mrAnalysis ( time_sec ,

force_n , ’ f o r c e ’ , j j , 4 0 0 ) ; % according to mrAnalysis fu nc t i on[ r e s S t r u c t ( j j ) . DisplA . v i r e s S t r u c t ( j j ) . DisplA . vt ]= mrAnalysis (

time_sec , DisplA_mm , ’ DisplA [mm] ’ , j j , 4 0 0 ) ;[ r e s S t r u c t ( j j ) . DisplB . v i r e s S t r u c t ( j j ) . DisplB . vt ]= mrAnalysis (

time_sec , DisplB_mm , ’ DisplB [mm] ’ , j j , 4 0 0 ) ;

62 6 APPENDIX B

[ r e s S t r u c t ( j j ) . DisplC . v i r e s S t r u c t ( j j ) . DisplC . vt ]= mrAnalysis (time_sec , DisplC_mm , ’ DisplC [mm] ’ , j j , 4 0 0 ) ;

[ r e s S t r u c t ( j j ) . DisplD . v i r e s S t r u c t ( j j ) . DisplD . vt ]= mrAnalysis (time_sec , DisplD_mm , ’ DisplD [mm] ’ , j j , 4 0 0 ) ;

endend

function [ v i vt ]= mrAnalysis ( time_sec , measuredData , measuredDataType ,specimentNum , sam2 , r e sFacto r )

% t h i s resample s t e p might he lp me to determine the i n t e r v a l t h a t i sused

% in d e f S t a r t I n d e x = ge tDe fS tar t Index ( force_n , peakValuesIndex , i n t e r v a l )% p l o t the f i g u r e a f t e r sample ONLY.i f nargin == 4

sam2 = 400 ;r e sFacto r = 1 ;

endi f nargin == 5

resFacto r = 1 ;endmeasuredData2 = resample ( measuredData , r e sFacto r ) ;time_sec2 = resample ( time_sec , r e sFacto r ) ;figure ( ) ;plot ( time_sec2 , measuredData2 ) ;xlabel ( ’ time [ s ] ’ )ylabel ( measuredDataType )t i t l e ( [ ’ specimen ’ num2str( specimentNum ) ’ . P lease s e l e c t the t r i g e r : ’ ] )

% here s t a r t s the t r i c kfor i i =1:2[ xx ( i i ) yy ( i i ) ] = ginput (1 ) ;hold onplot ( xx ( i i ) , yy ( i i ) , ’ ro ’ )end%conver xx from time to indexxind1 = find ( time_sec2>xx (1) ) ;xind2 = find ( time_sec2>xx (2) ) ;xind = [ xind1 (1 ) , xind2 (1 ) ] ;i n t e r v a l = 27 ; % I could modify t h i s va lue i f i t shows a r i d i c u l o u s

r e s u l t o f the deformation s t a r t po in t !

63

peakValuesIndex = getPeakValueIndex ( measuredData , xind , yy ) ;de fS ta r t Index = getDefStart Index ( measuredData , peakValuesIndex , i n t e r v a l ) ;% the ’ index ’ here i s NOT the time v e c t o r !

% draw the l i n e s :figure ( )plot ( time_sec , measuredData ) ; hold on ;xlabel ( ’ time [ s ] ’ )ylabel ( measuredDataType )t i t l e ( [ ’ specimen ’ num2str( specimentNum ) ] ) procedurenumOfPeakVal = 3 ;peakValInd = peakValuesIndex ( 1 : numOfPeakVal ) ;de fSt Ind = de fSta r t Index ( de fStart Index >peakValInd (1 ) & defStart Index <

peakValuesIndex ( numOfPeakVal+1) ) ;

nodes ( length ( peakValInd ) ) = 0 ; % point o f i n t e r s e c t i o n . This i s a l s o theindex , NOT the time .

i n te r sY = nodes ; % t h i s i s the r e a l d i sp lacement va lue atthe i n t e r s e c t i o n po in t

sam1 = 15 ;for ind = 1 : length ( peakValInd )

% the 1 s t l i n e : y = a + bx% the 2nd l i n e : y = c + dxx1 = ( peakValInd ( ind ) +3) : ( peakValInd ( ind )+3+sam1−1) ; % x1 and x2 are

not time v e c t o r ! ! !x2 = ( de fSt Ind ( ind )−sam2+1) : de fSt Ind ( ind ) ;coef_1 = c u r v f i t ( x1 , measuredData ( x1 ) ,1 ) ;coef_2 = c u r v f i t ( x2 , measuredData ( x2 ) ,1 ) ;a = coef_1 (1 ) ;b = coef_1 (2) ;c = coef_2 (1) ;d = coef_2 (2) ;nodes ( ind ) = round ( ( a−c ) /(d−b) ) ;in te r sY ( ind ) = ( a∗d−c∗b) /(d−b) ;plot ( time_sec ( [ peakValInd ( ind )+3 nodes ( ind ) de fSt Ind ( ind ) ] ) , [

measuredData ( peakValInd ( ind ) +3) inte r sY ( ind ) measuredData (de fSt Ind ( ind ) ) ] , ’ r .− ’ , ’ l i n e w i d ’ , 1 . 2 ) ;

endxlabel ( ’ time [ s ] ’ )ylabel ( measuredDataType )% RESULT! :vt = measuredData ( peakValInd )−measuredData ( de fSt Ind ) ;v i = measuredData ( peakValInd )−measuredData ( nodes ) ;

64 6 APPENDIX B

end

function peakValuesIndex = getPeakValueIndex (y , xind , yy )% PEAKVALUESINDEX = GETPEAKVALUEINDEX(Y,XIND,YY)% y i s the ve c t o r from which you want to f i n d out the peaks% xind i s the 2 index o f y o f the t r i g e r l i n e% yy i s 2 v a l u e s o f the t r i g e r l i n e%% f i n d the peak po in t

yIndArr = ( 1 : length ( y ) ) ’ ; % 1 , 2 , . . . l e n g t h ( y )s l o p = ( yy (2)−yy (1 ) ) /( xind (2 )−xind (1 ) ) ; % s l o p o f the t r i g e r l i n eyTr iger = s l o p ∗( yIndArr−xind (1 ) )+yy (1) ;indexArray = find ( ( y−yTr iger ) >0) ;Star t Ind = 1 ;peakValuesIndex = [ ] ;indOfIndexArray = 1 ;while indOfIndexArray < length ( indexArray )

i f ( indexArray ( indOfIndexArray+1)−indexArray ( indOfIndexArray ) )>7 | |( indOfIndexArray+1)== length ( indexArray ) % number 7 cou ld bemodi f ied[ peakValue indTemp]= max( y ( indexArray ( Star t Ind : indOfIndexArray ) )

) ;peakValuesIndex = [ peakValuesIndex indTemp+indexArray ( Start Ind )

−1];Star t Ind = indOfIndexArray +1;

endindOfIndexArray = indOfIndexArray +1;

end

end

function de fS ta r t Index = getDefStart Index (y , peakValuesIndex , i n t e r v a l )% DEFSTARTINDEX = GETDEFSTARTINDEX(Y, peakValuesIndex ,INTERVAL)

de fS ta r t Index ( length ( peakValuesIndex ) ) = 0 ;for ind = 1 : length ( peakValuesIndex )

defStartIndexTemp = peakValuesIndex ( ind ) ;i f ind == 1

o r i I n t e r v a l = i n t e r v a l ;i n t e r v a l = 2 ;

elsei n t e r v a l = o r i I n t e r v a l ;

65

endwhile y ( defStartIndexTemp−i n t e r v a l )<=y ( defStartIndexTemp )

defStartIndexTemp = defStartIndexTemp−i n t e r v a l ;endde fS ta r t Index ( ind ) = defStartIndexTemp ;

endend

Code of curvefit.mfunction c o e f = c u r v f i t (x , y , order )% COEF = CURVFIT(X,Y,ORDER)% return the c o e f f i c i e n t a , b , c . . . o f the expres s ion :% y = a + b∗x + c∗x^2 + d∗x^3 + . . . n∗x^ order% where a = coe f (1) , b = coe f (2) , c = coe f (3) . . .

i f length ( x )<order+1error ( ’The number o f sampled x must not be s m a l l e r than order+1 ’ ) ;

endx = x ( : ) ;y = y ( : ) ;x length = length ( x ) ;xMat = ones ( xlength , order +1) ;for ind = 1 : order

xMat ( : , ind +1) = x . ^ ind ;endc o e f = (xMat ’ ∗ xMat) \(xMat ’ ∗ y ) ;

Code of resample.mfunction resampledY = resample (y , resampleFactor )% RESAMPLEDY = RESAMPLE(Y,RESAMPLEFACTOR)% resample the v ec t o r ’ y ’ according to the f a c t o r ’ resampleFactor ’% f o r exsample :% resample ( [ 1 2 3 4 5 6 ] , 2 ) w i l l re turn :% [1 3 5 ]

resampledY = y ( 1 : resampleFactor : length ( y ) ) ;

end

66 6 APPENDIX B

67

Appendix C Matlab code of Creep test

Code of creep.mclear a l lclcload r e s u l t r e p o r tn=3;[ tAvg dAvg pAvg]= dea l (0 ) ;gage length =25;r e s S t r u c t = mrMutiSpecimenAnalysis (n) ;[CSX sigma ]= dea l ( zeros ( length ( r e s S t r u c t (1 ) . DisplA_mm) ,1) ) ;t i e m c a l c u l a t e {n } = [ ] ;[ TrimDeformAB TrimDeformCD ] = dea l ( zeros ( length ( r e s S t r u c t (1 ) . DisplA_mm)

,2∗n) ) ;p=[ r e s S t r u c t (1 ) . forceMean r e s S t r u c t (2 ) . forceMean r e s S t r u c t (3 ) . forceMean

] ;pAvg=mean(p) ;for j j =1:n

tAvg = tAvg+r e s S t r u c t ( j j ) . t h i c k ;dAvg = dAvg+r e s S t r u c t ( j j ) . diam ;

endtAvg = tAvg/n ;dAvg = dAvg/n ;

for j j =1:ntime=r e s S t r u c t ( j j ) . time_sec ;timenew=time−time (1 ) ;t i e m c a l c u l a t e { j j }=timenew ( 1 : end) ;endtimeone=t i e m c a l c u l a t e {1} ;timetwo=t i e m c a l c u l a t e {2} ;t imethree=t i e m c a l c u l a t e {3} ;D=c e l l (n , 4 ) ;for j j =1:nDisplAnew=r e s S t r u c t ( j j ) . DisplA_mm−r e s S t r u c t ( j j ) . DisplA_mm(1) ;DisplBnew=r e s S t r u c t ( j j ) . DisplB_mm−r e s S t r u c t ( j j ) . DisplB_mm(1) ;DisplCnew=r e s S t r u c t ( j j ) . DisplC_mm−r e s S t r u c t ( j j ) . DisplC_mm(1) ;DisplDnew=r e s S t r u c t ( j j ) . DisplD_mm−r e s S t r u c t ( j j ) . DisplD_mm(1) ;r e s S t r u c t ( j j ) . D i s p l A c a l c u l a t e=DisplAnew ( 1 : end) ;r e s S t r u c t ( j j ) . D i s p l B c a l c u l a t e=DisplBnew ( 1 : end) ;

68 6 APPENDIX C

r e s S t r u c t ( j j ) . D i s p l C c a l c u l a t e=DisplCnew ( 1 : end) ;r e s S t r u c t ( j j ) . D i s p l D c a l c u l a t e=DisplDnew ( 1 : end) ;Cnorm( j j ) = r e s S t r u c t ( j j ) . t h i c k /tAvg∗ r e s S t r u c t ( j j ) . diam/dAvg∗pAvg/

r e s S t r u c t ( j j ) . forceMean ;r e s S t r u c t ( j j ) . DisplAnormal=r e s S t r u c t ( j j ) . D i s p l A c a l c u l a t e ∗Cnorm( j j ) ;r e s S t r u c t ( j j ) . DisplBnormal=r e s S t r u c t ( j j ) . D i s p l B c a l c u l a t e ∗Cnorm( j j ) ;r e s S t r u c t ( j j ) . DisplCnormal=r e s S t r u c t ( j j ) . D i s p l C c a l c u l a t e ∗Cnorm( j j ) ;r e s S t r u c t ( j j ) . DisplDnormal=r e s S t r u c t ( j j ) . D i s p l D c a l c u l a t e ∗Cnorm( j j ) ;TrimDeformAB ( : , 2 ∗ j j −1:2∗ j j ) = [ r e s S t r u c t ( j j ) . DisplAnormal ( : ) r e s S t r u c t (

j j ) . DisplBnormal ( : ) ] ;TrimDeformCD ( : , 2 ∗ j j −1:2∗ j j ) = [ r e s S t r u c t ( j j ) . DisplCnormal ( : ) r e s S t r u c t (

j j ) . DisplDnormal ( : ) ] ;SumtrimDeformAB=sum(TrimDeformAB , 2 ) ;MaxtrimDeformAB=max(TrimDeformAB , [ ] , 2 ) ;MintrimDeformAB=min(TrimDeformAB , [ ] , 2 ) ;FinaldeformationAB=(SumtrimDeformAB−MaxtrimDeformAB−MintrimDeformAB )

. / ( 2 ∗ n−2) ;SumtrimDeformCD=sum(TrimDeformCD , 2 ) ;MaxtrimDeformCD=max(TrimDeformCD , [ ] , 2 ) ;MintrimDeformCD=min(TrimDeformCD , [ ] , 2 ) ;FinaldeformationCD=(SumtrimDeformCD−MaxtrimDeformCD−MintrimDeformCD )

. / ( 2 ∗ n−2) ;endPoissonRatioCreep =−0.1+1.45∗( FinaldeformationAB (513) / FinaldeformationCD

(513) ) ^2 −0.778∗( FinaldeformationAB (513) / FinaldeformationCD (513) ) ^2∗(tAvg/dAvg) ^2 ;

Ccmplj =0.6354∗( FinaldeformationCD . / FinaldeformationAB ) −0.332;Dj=FinaldeformationAB .∗10^9∗dAvg∗tAvg . ∗ Ccmplj . / pAvg/ gage length +10^9/MRI;d a t a F o r f i t t i n g=Dj−10^9/MRI;[ a1 , c1 , x f i t 1 , f i t l i n e 1 ] = f i t l i n e o n l o g l o g ( timeone , d a t a F o r f i t t i n g ) ;D1=c1 ;X=[0 , d a t a F o r f i t t i n g (20) , timeone (50) , timeone (100) , timeone (150) , timeone

(180) , timeone (200) , timeone (220) , timeone (240) , x f i t 1 (1 ) , x f i t 1 (2 ) , x f i t 1(3 ) , ] ;

Y=[0 , d a t a F o r f i t t i n g (20) , d a t a F o r f i t t i n g (50) , d a t a F o r f i t t i n g (100) ,d a t a F o r f i t t i n g (150) , d a t a F o r f i t t i n g (180) , d a t a F o r f i t t i n g (200) ,d a t a F o r f i t t i n g (220) , d a t a F o r f i t t i n g (240) , f i t l i n e 1 (1 ) , f i t l i n e 1 (2 ) ,f i t l i n e 1 (3 ) ] ;

k=polyf it (X,Y, 2 ) ;s t r a i t=k (1) ∗X.^2+k (2) ∗X+k (3) ;figure ( )plot ( timeone , d a t a F o r f i t t i n g , ’ ro ’ )hold on

69

plot ( x f i t 1 , f i t l i n e 1 , ’ k ’ , ’ l i n e w i d t h ’ , 2 )plot (X, s t r a i t , ’ k ’ , ’ l i n e w i d t h ’ , 2 )t i t l e ( ’ c u r v e f i t t i n g a l l the data ’ )legend ( ’ c reep compliance curve ’ )xlabel ( ’ time ( s ) ’ )ylabel ( ’ c reep compliance ’ )mvalue=a1 ;D0=1./MRIi/10^( −9) ; %GpameanD0=mean(D0)clear CCMPLI CBXI CBXT CBYI CBYT CCMPLT CCMPLT CSX CSXI CSXT CSYI CSYT

a1 a2 a3 . . .b1 b2 b3 c1 c2 c3 c4 c5 c6 c y c l e dAvg dataAone dataAthree dataAtwo

dataBone . . .dataBtwo f inalHorABvi f inalHorABvt f i n a l >VerCDvi f inalVerCDvt

f i t l i n e 1 f i t l i n e 2 f i t l i n e 3 . . .f i t l i n e 4 f i t l i n e 5 f i t l i n e 6 gage length horABvi horABvt i i j j m1 m2

m3 maxABvi maxABvt maxCDvi . . .maxCDvt minABvi minABvt minCDvi minCDvt minCDvt pAvg sigma tAvg

t i e m c a l c u l a t e time timenew timeone . . .t imethree timetwo verCDvi verCDvt x f i t 1 x f i t 2 x f i t 3 x f i t 4 x f i t 5

x f i t 6 r e s S t r u c t nsave f i l e o n e c r e e p

Code of fitlineonloglog.m

% i f 2 parameters are s p e c i f i e d , xmin = 0 , and xmax i s the maximum va lue% t h a t occurs in the data% i f 3 arguments are s p e c i f i e d , the 3rd i s assumed to be xminfunction [ a lpha c x f i t f i t l i n e ] = f i t l i n e o n l o g l o g (x , y , xmin , xmax)

% i f no xmin i s s p e c i f i e d , s e t i t to 0i f ( nargin < 3)

xmin = x (500) ;xmax = max( x ) ;

end

i f ( nargin < 4)xmin = x (500) ;xmax = max( x ) ;

end

70 6 APPENDIX C

%e l i m i n a t e zeros because t a k i n g the logar i thmy = y (x>0) ;x = x (x>0) ;

x = x (y>0) ;y = y (y>0) ;

%a l s o ignore v a l u e s o u t s i d e min and max s p e c i f i e d by c a l lx f i t = x (x>=xmin ) ;y f i t = y (x>=xmin ) ;x f i t = x f i t ( x f i t <=xmax) ;y f i t = y f i t ( x f i t <=xmax) ;

% y=c∗x^ alpha[ a , b ] = polyf it ( log ( x f i t ) , log ( y f i t ) , 1 ) ;f i t l i n e = exp( log ( x f i t ) ∗a (1 )+a (2) ) ;b . normr ;alpha = a (1) ;c=exp( a (2 ) ) ;

% p l o t ( x , y , ’ ko ’ , x f i t , f i t l i n e , ’ r − ’ , ’ LineWidth ’ , 2 ) ;% a l p h a s t r = s p r i n t f ( ’ a lpha = %.4 f f i t , R = ’) ;end

Code of mrMutiSpecimenAnalysis.m

function r e s S t r u c t = mrMutiSpecimenAnalysis (n)for j j =1:n

close a l lrawData = [ ] ;eval ( [ ’ rawData = load ( ’ ’ specimen_ ’ num2str( j j ) ’ . dat ’ ’ ) ; ’ ] ) %load

the datar e s S t r u c t ( j j ) . time_sec = rawData ( 3 : end−2 ,1) ; % load

d i f f e r e n t column datr e s S t r u c t ( j j ) . DisplA_mm = rawData ( 3 : end−2 ,3) ;r e s S t r u c t ( j j ) . DisplB_mm = rawData ( 3 : end−2 ,4) ;% r e s S t r u c t ( j j ) . f o r c e=rawData (100: end −2 ,2) ;force_n=−rawData ( 1 0 0 : end−2 ,2) ;r e s S t r u c t ( j j ) . time50=rawData (503 ,1 )DisplC_mm = rawData ( 3 : end−2 ,5) ;

71

DisplD_mm = rawData ( 3 : end−2 ,6) ;dj = rawData (end , 1 ) ; % diametert j = rawData (end , 2 ) ; % t h i c k n e s sr e s S t r u c t ( j j ) . DisplC_mm=−1∗DisplC_mm ;r e s S t r u c t ( j j ) . DisplD_mm=−1∗DisplD_mm ;r e s S t r u c t ( j j ) . t h i c k = t j ; % endow data to d i f f e r e n t

specimen j j = 1 , 2 , 3 . . . . nr e s S t r u c t ( j j ) . diam = dj ;r e s S t r u c t ( j j ) . forceMean = mean( force_n ) ;

endend

72 6 APPENDIX C

73

Appendix D Matlab code of Strength test

Code of run.mclcclearclose a l lload f i l e o n e c r e e pn=3;r e s S t r u c t = StrengthMutiSpecimenAnalysis (n) ;tAvg=0;dAvg=0;gage length =25;

for i i = 1 : ntAvg = tAvg+r e s S t r u c t ( i i ) . t h i c k ;dAvg = dAvg+r e s S t r u c t ( i i ) . diam ;CSX( i i ) =0.948 −0.0114∗( r e s S t r u c t ( i i ) . t h i c k / r e s S t r u c t ( i i ) . diam )

−0.2693∗ poissonAvgpoiT +1.439∗( r e s S t r u c t ( i i ) . t h i c k / r e s S t r u c t ( i i ) .diam ) ∗ poissonAvgpoiT ;

CBX( i i ) =1.03 −0.189∗( r e s S t r u c t ( i i ) . t h i c k / r e s S t r u c t ( i i ) . diam ) −0.081∗poissonAvgpoiT +0.089∗( r e s S t r u c t ( i i ) . t h i c k / r e s S t r u c t ( i i ) . diam ) ^2 ;

Strength ( i i )=r e s S t r u c t ( i i ) . peak fo rce ∗2∗CSX( i i ) /pi/ r e s S t r u c t ( i i ) .t h i c k / r e s S t r u c t ( i i ) . diam∗10^( −6) ; %Mpa

a ( i i ) =(120^( −2.96) ) ∗( −0.0154) ∗( Strength ( i i ) −6.36) +0.0000000246;EE( i i )=Strength ( i i ) ^2/2/(MRT/10^9) ; % MRT in Gpa Streng th in MpaS t r a i n r e l a t i v e { i i }=r e s S t r u c t ( i i ) . DisplacementPlot / gage length ∗CBX( i i )

∗ 1 . 0 7 2 ;S t r e n g t h S e r i e s { i i }=( r e s S t r u c t ( i i ) . p e a k f o r c e S e r i e s −30)∗2∗CSX( i i ) /pi/

r e s S t r u c t ( i i ) . t h i c k / r e s S t r u c t ( i i ) . diam∗10^( −6) ; % s t in Mpa% spanA ( i i )=l e n g t h ( r e s S t r u c t ( i i ) . Displone_mm) ;% spanB ( i i )=l e n g t h ( r e s S t r u c t ( i i ) . Displtwo_mm) ;% strainA ( : , i i )=S t r a i n A r e l a t i v e ( 1 : spanA ( i i ) , i i ) ;% strainB ( : , i i )=S t r a i n B r e l a t i v e ( 1 : spanB ( i i ) , i i ) ;

endS t r a i n r e l a t i v e o n e=S t r a i n r e l a t i v e {1} ;S t r a i n r e l a t i v e t w o=S t r a i n r e l a t i v e {2} ;S t r a i n r e l a t i v e t h r e e=S t r a i n r e l a t i v e {3} ;S t r e n g t h S e r i e s o n e=S t r e n g t h S e r i e s {1} ;St rengthSer i e s two=S t r e n g t h S e r i e s {2} ;S t r e n g t h S e r i e s t h r e e=S t r e n g t h S e r i e s {3} ;co1=polyf it ( S t r a i n r e l a t i v e o n e , St rengthSer i e sone , 3 ) ;

74 6 APPENDIX D

y1=co1 (1 ) ∗ S t r a i n r e l a t i v e o n e .^3+ co1 (2 ) ∗ S t r a i n r e l a t i v e o n e .^2+ co1 (3 ) ∗S t r a i n r e l a t i v e o n e+co1 (4 ) ;

FE1=trapz ( S t r a i n r e l a t i v e o n e , S t r e n g t h S e r i e s o n e ) ∗1000 ;FE2=trapz ( S t r a i n r e l a t i v e t w o , St rengthSer i e s two ) ∗1000 ;FE3=trapz ( S t r a i n r e l a t i v e t h r e e , S t r e n g t h S e r i e s t h r e e ) ∗1000 ;%c a l c u l a t e DCSEhmaDCSEhmaone=FE1−EE(1) ;DCSEhmatwo=FE2−EE(2) ;DCSEhmathree=FE3−EE(3) ;DCSEhmaMatrix=[DCSEhmaone , DCSEhmatwo, DCSEhmathree ] ;DCSEhma=mean(DCSEhmaMatrix) ;

%c a l c u l a t DCSEminDCSEminOne=(mvalue ^2.98∗D1/145037 .7) /a (1 ) ;DCSEminTwo=(mvalue ^2.98∗D1/145037 .7) /a (2 ) ;DCSEminThree=(mvalue ^2.98∗D1/145037 .7) /a (3 ) ;%c a l c u l a t e energyRatioEnergyRatio1=DCSEhmaone/DCSEminOne ;EnergyRatio2=DCSEhmatwo/DCSEminTwo ;EnergyRatio3=DCSEhmathree/DCSEminThree ;Q=[ EnergyRatio1 , EnergyRatio2 , EnergyRatio3 ] ;AverageEnergyRatio=mean(Q) ;

%co2=polyf it ( S t r a i n r e l a t i v e t w o , StrengthSer i e s two , 3 ) ;y2=co2 (1 ) ∗ S t r a i n r e l a t i v e t w o .^3+ co2 (2 ) ∗ S t r a i n r e l a t i v e t w o .^2+ co2 (3 ) ∗

S t r a i n r e l a t i v e t w o+co2 (4 ) ;%co3=polyf it ( S t r a i n r e l a t i v e t h r e e , S t r e n g t h S e r i e s t h r e e , 3 ) ;y3=co3 (1 ) ∗ S t r a i n r e l a t i v e t h r e e .^3+ co3 (2 ) ∗ S t r a i n r e l a t i v e t h r e e .^2+ co3 (3 ) ∗

S t r a i n r e l a t i v e t h r e e+co3 (4 ) ;figure ( )hold onplot ( S t r a i n r e l a t i v e o n e , y1 , ’ r ’ , ’ l i n e w i d t h ’ , 2 )plot ( S t r a i n r e l a t i v e o n e , S t r e n g t h S e r i e s o n e )legend ( ’ f i t t e d curve ’ , ’ s t r e s s −s t r a i n curve ’ )

t i t l e ( [ ’ specimen 1 ’ ] )xlabel ( ’ S t r a i n ( t ) ’ )ylabel ( ’ S t r e s s ( t ) Mpa ’ )

figure ( )hold on

75

plot ( S t r a i n r e l a t i v e t w o , y2 , ’ r ’ , ’ l i n e w i d t h ’ , 2 )plot ( S t r a i n r e l a t i v e t w o , St rengthSer i e s two )legend ( ’ f i t t e d curve ’ , ’ s t r e s s −s t r a i n curve ’ )


figure ( )hold onplot ( S t r a i n r e l a t i v e t h r e e , y3 , ’ r ’ , ’ l i n e w i d t h ’ , 2 )plot ( S t r a i n r e l a t i v e t h r e e , S t r e n g t h S e r i e s t h r e e )legend ( ’ f i t t e d curve ’ , ’ s t r e s s −s t r a i n curve ’ )


%show the average f a i l s t r a i nS t r a i n r e l a t i v e o n e (end) ;S t r a i n r e l a t i v e t w o (end) ;S t r a i n r e l a t i v e t h r e e (end) ;F a i l s t r a i n =[ S t r a i n r e l a t i v e o n e (end) , S t r a i n r e l a t i v e t w o (end) ,

S t r a i n r e l a t i v e t h r e e (end) ] ∗ 1 0 ^ 6 ;A v e r a g e F a i l s t r a i n=mean( F a i l s t r a i n ) ;L=[FE1 , FE2 , FE3 ] ;AverageFE=mean(L) ;R=[DCSEminOne , DCSEminTwo, DCSEminThree ] ;AverageDCSEmin=mean(R) ;

tAvg = tAvg/n ;dAvg = dAvg/n ;[ peakforce1 , peakforce2 , peak force3 ]= dea l ( r e s S t r u c t (1 ) . peakforce ,

r e s S t r u c t (2 ) . peakforce , r e s S t r u c t (3 ) . peak fo rce )s t r ength =[ Strength (1 ) , Strength (2 ) , Strength (3 ) ]AverageStrength=mean( s t r ength )AverageFractureEnergy =[FE1 , FE2 , FE3 ]

clear FinaldeformationAB FinaldeformationCD X Y c k L s t r a i t CcmpljDCSEhmaone DCSEhmatwo DCSEhmathree Cnorm D a ans co1 co2 co3gage length y1 y2 y3 MaxtrimDeformCD MintrimDeformAB DisplAnewDisplCnew SumtrimDeformAB SumtrimDeformCD

save St

Code of StrengthMutiSpecimenAnalysis.m

76 6 APPENDIX D

function r e s S t r u c t = StrengthMutiSpecimenAnalysis (n)for j j =1:n

%input a l l the datarawData = [ ] ;eval ( [ ’ rawData = load ( ’ ’ specimen_ ’ num2str( j j ) ’ . dat ’ ’ ) ; ’ ] ) ;time_sec = rawData ( 3 : end−2 ,1) ;force_n = rawData ( 3 : end−2 ,3) ;DisplA_mm = rawData ( 3 : end−2 ,4) ;DisplB_mm = rawData ( 3 : end−2 ,5) ;DisplC_mm = rawData ( 3 : end−2 ,6) ;DisplD_mm = rawData ( 3 : end−2 ,7) ;Disp lARelat ive=DisplA_mm−DisplA_mm(1) ;Disp lBRelat ive=DisplB_mm−DisplB_mm(1) ;Disp lCRelat ive=DisplC_mm−DisplC_mm(1) ;Disp lDRelat ive=DisplD_mm−DisplD_mm(1) ;dj = rawData (end , 1 ) ;t j = rawData (end , 2 ) ;force_n = −1∗ force_n ;DisplC_mm=−1∗DisplC_mm ;DisplD_mm=−1∗DisplD_mm ;

r e s S t r u c t ( j j ) . DisplA_mm=DisplA_mm ;r e s S t r u c t ( j j ) . DisplB_mm=DisplB_mm ;r e s S t r u c t ( j j ) . DisplC_mm=DisplC_mm ;r e s S t r u c t ( j j ) . DisplD_mm=DisplD_mm ;r e s S t r u c t ( j j ) . Disp lARelat ive=Disp lARelat ive ;r e s S t r u c t ( j j ) . Di sp lBRelat ive=Disp lBRelat ive ;

% r e s S t r u c t ( j j ) . Disp lCRe la t i ve=Disp lCRe la t i ve ;% r e s S t r u c t ( j j ) . Disp lDRe la t ive=Disp lDRela t ive ;

r e s S t r u c t ( j j ) . force_n=force_n ;D i s p l o n e O r i g i n a l=r e s S t r u c t ( j j ) . DisplC_mm−r e s S t r u c t ( j j ) . DisplA_mm ;Disp l twoOr ig ina l=r e s S t r u c t ( j j ) . DisplD_mm−r e s S t r u c t ( j j ) . DisplB_mm ;

%cut the l a s t d i s t u r b par tDisplone_mm=D i s p l o n e O r i g i n a l ( 1 : end−200 , : ) ;Displtwo_mm=Disp l twoOr ig ina l ( 1 : end−200 , : ) ;r e s S t r u c t ( j j ) . Displone_mm=Displone_mm ;r e s S t r u c t ( j j ) . Displtwo_mm=Displtwo_mm ;

time_secnew=time_sec ( 1 : end−200 , : ) ;r e s S t r u c t ( j j ) . t h i c k = t j ;r e s S t r u c t ( j j ) . diam = dj ;

77

Displonesmoothed=smooth ( smooth ( smooth ( smooth ( smooth ( smooth ( smooth (smooth ( smooth ( smooth ( smooth ( smooth ( smooth ( Displone_mm ) ) ) ) ) ) ) ) ) ) )) ) ;

%peakindex=find ( Displonesmoothed==max( Displonesmoothed ) ) ;

%r e s S t r u c t ( j j ) . peak fo rce=force_n ( peakindex )%figure ( )subplot ( 3 , 1 , 2 )plot ( time_sec ( peakindex ) , D i s p l o n e O r i g i n a l ( peakindex ) , ’ ro ’ )hold onplot ( time_sec , Di sp loneOr ig ina l , ’ l i n e w i d t h ’ , 2 )plot ( time_secnew , Displonesmoothed , ’m’ )xlabel ( ’ time ( sec ) ’ )ylabel ( ’ DisplC−DisplA ’ )legend ( ’ peakpoint ’ , ’ DisplC−DisplA ’ , ’ smoothed curve ’ )

Displtwosmoothed=smooth ( smooth ( smooth ( smooth ( smooth ( smooth ( smooth (smooth ( smooth ( smooth ( smooth ( smooth ( smooth (Displtwo_mm) ) ) ) ) ) ) ) ) ) )) ) ;

peakindex2=find ( Displtwosmoothed==max( Displtwosmoothed ) ) ;

subplot ( 3 , 1 , 3 )plot ( time_sec ( peakindex2 ) , D i sp l twoOr ig ina l ( peakindex2 ) , ’ ro ’ )hold onplot ( time_sec , Disp l twoOr ig ina l , ’ l i n e w i d t h ’ , 2 )plot ( time_secnew , Displtwosmoothed , ’m’ )xlabel ( ’ time ( sec ) ’ )ylabel ( ’ DisplD−DisplB ’ )legend ( ’ peakpoint ’ , ’ DisplD−DisplB ’ , ’ smoothed curve ’ )maximumforceIndex=min( find ( r e s S t r u c t ( j j ) . force_n==max( r e s S t r u c t ( j j ) .

force_n ) ) )% f i n d the peak po in tl=min( peakindex , peakindex2 )

peak index_f ina l=min( l , maximumforceIndex ) −600r e s S t r u c t ( j j ) . peakindex=peak index_f ina l

subplot ( 3 , 1 , 1 )

78 6 APPENDIX D

plot ( time_sec ( peak index_f ina l ) , force_n ( peak index_f ina l ) , ’ r ∗ ’ )hold onplot ( time_sec , force_n )legend ( ’ f a i l u r e load ’ )t i t l e ( [ ’ specimen ’ num2str( j j ) ] )xlabel ( ’ time ( sec ) ’ )ylabel ( ’ force_n ’ )r e s S t r u c t ( j j ) . peak fo rce=force_n ( peak index_f ina l ) ;f o r c e S e r i e s=force_n ( 1 : peak index_f ina l ) ;r e s S t r u c t ( j j ) . p e a k f o r c e S e r i e s=f o r c e S e r i e s ;

switch peak index_f ina lcase peakindex −600DisplacementPlot=DisplA_mm−DisplA_mm(1)case peakindex2 −600DisplacementPlot=DisplB_mm−DisplB_mm(1)case maximumforceIndex −600DisplacementPlot=(DisplB_mm−DisplB_mm(1)+DisplA_mm−DisplA_mm(1) )

. /2endr e s S t r u c t ( j j ) . DisplacementPlot=DisplacementPlot ( 1 : peak index_f ina l ) ;

end

Code of resample.m

function resampledY = resample (y , resampleFactor )% RESAMPLEDY = RESAMPLE(Y,RESAMPLEFACTOR)% resample the v ec t o r ’ y ’ according to the f a c t o r ’ resampleFactor ’% f o r exsample :% resample ( [ 1 2 3 4 5 6 ] , 2 ) w i l l re turn :% [1 3 5 ]

resampledY = y ( ( 1 : resampleFactor : length ( y ) ) ) ;

end

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