impact of modulus based device variability on quality control of ...

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IMPACT OF MODULUS BASED DEVICE VARIABILITY ON QUALITY CONTROL OF COMPACTED GEOMATERIALS USING MEASUREMENT SYSTEM ANALYSIS

Mehran Mazari, MSCE (Corresponding Author) PhD Research Assistant Center for Transportation Infrastructure Systems (CTIS) The University of Texas at El Paso, El Paso, Texas [email protected]

Gerardo Garcia, BSCE Research Assistant Center for Transportation Infrastructure Systems (CTIS) The University of Texas at El Paso, El Paso, Texas [email protected]

Jose Garibay, MSCE Laboratory Manager Center for Transportation Infrastructure Systems (CTIS) The University of Texas at El Paso, El Paso, Texas [email protected]

Imad Abdallah, Ph.D. Associate Director Center for Transportation Infrastructure Systems (CTIS) The University of Texas at El Paso, El Paso, Texas [email protected]

Soheil Nazarian, Ph.D., P.E., D.GE Director Center for Transportation Infrastructure Systems (CTIS) The University of Texas at El Paso, El Paso, Texas [email protected]

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Transportation Research Board, 92th Annual Meeting, Washington D.C., 2013

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ABSTRACT The advances in technology have resulted in a new generation of in-situ nondestructive testing devices that can estimate stiffness parameters of compacted geomaterials. These include the light weight deflectometers1, portable impulse plate load test devices, electro-mechanical stiffness devices and seismic devices. Despite a number of formal research and pilot studies, only a few agencies are attempting to implement these devices in their acceptance specifications. One of the main concerns is with the large variability in the stiffness parameters obtained with these devices when compared to densities measured with traditional devices (e.g. nuclear density gauge). The sources of the variability can be material-related, operator-related or device-related. It would be beneficial to systematically delineate the contributions of these sources of variability so that the equipment developers can improve their devices, highway agencies can modify their testing protocols, and pavement geotechnical engineers can address the material-related issues. This paper contains the results of an effort to quantify the equipment- and operator-related variabilities in a systematic manner. Measurement system analysis principles were applied to a database of stiffness measurements made with four devices on eighteen separate specimens that were prepared from the same material at similar densities and moisture contents. It was found that most devices are reasonably repeatable and reproducible as long as the moisture content and density are rigidly controlled. Most of the site specific variability reported in the literature may be due to lack of rigid process control during construction.

1

Since several entities manufacture Portable FWDs we have used the two generic names recommended by ASTM for these devices.

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INTRODUCTION Adequate in-place density and moisture content during compaction are vital to the success of compacted geomaterials. However, satisfying these criteria may not necessarily yield adequate modulus. It is desirable to migrate from the traditional density specifications to a modulus-based approach to provide continuity among the design, construction and laboratory testing. Field moduli should be measured during construction with an appropriate device to ensure that the design modulus has been achieved. Appropriate equipment must satisfy the following three criteria: 1. sensitive enough so that poor and high quality materials can be readily delineated, 2. accurate enough to provide feedback to pavement designer and laboratory personnel, and 3. precise enough so that it can be confidently used in the acceptance process.

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For a fair and equitable quality management program, appropriate tolerances should be allowed based on the uncertainties associated with a measurement device. The focus of this paper is the third attribute in the list. To estimate the reproducibility and repeatability of available devices, eighteen small-scale [3 ft (0.9 m) diameter 19 in. (480 mm) deep] specimens from the same geomaterial were compacted with similar moisture contents and densities. Four devices consisting of a Light Weight Deflectometer, a Portable Impulse Plate Load device, an electromechanical stiffness device and a seismic device were used on top of these specimens 24 hours after compaction. Two operators conducted six replicate tests with each device at three locations within the 3 ft (0.9 m) diameter surface of each test box. These results were used to quantify the repeatability and reproducibility of each device using algorithms widely implemented in the field of industrial engineering measurement system analysis. The processes, algorithms and conclusions associated from this activity are reported here.

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BACKGROUND Four different devices that were used in this study are briefly discussed below. A number of excellent references contain comprehensive information about the theoretical background and the strengths and limitations of these devices. Among these references, Puppala (1) contains a synthesis of these devices and Von Quintus et al. (2) includes a systematic field evaluation of them. Light Weight Deflectometer (LWD, ASTM E2583) imparts a pulse load to the surface of a layer through a circular plate to measure the soil surface deflection and to estimate an effective modulus of the pavement system. An LWD directly measures the applied load and the displacement of the soil. Portable Impulse Plate Load Device (PIPLD, ASTM E 2835) measures the deflection of the loading plate (not the soil) and estimates the applied load based on the weight and height of the drop mass. Even though the LWD and PIPLD conceptually perform the same tests, they may yield different deflections under the same applied load. Nevertheless, the same analysis technique is used to estimate an “effective modulus” with both devices. The effective modulus is theoretically the same as the modulus of elasticity for a uniform compacted soil layer (2). The main advantages of these deflection devices are that they generate a state of stress that is close to those applied by a vehicular traffic, and that the pavement community is familiar with the concept of deflection testing. The main concerns include a lack of ability to consistently identify areas with anomalies (2), and the reported moduli can be influenced by the underlying layers (1). As per ASTM D6758, an Electro-Mechanical Stiffness Device (a.k.a. Geogauge) reports a modulus by inducing small displacements using a harmonic oscillator operating over a

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frequency of 100 to 200 Hz. Geogauge measures both force and displacement to estimate an effective modulus similar to LWD. The main advantages of Geogauge are the acceptable success rate in identifying areas with different physical conditions or anomalies, ease of training, and the ability to provide a reasonable estimate of laboratory measured moduli with proper calibration (2). The main concerns expressed are that intimate contact between Geogauge and soil may be difficult to achieve without due diligence by the operator (1), that moduli do not represent the stress levels which occur under truck loadings (2), and that underlying materials can influence the results, especially for relatively thin unbound layers (1). Seismic Device (a.k.a. Portable Seismic Property Analyzer, PSPA) consists of two accelerometers and a source packaged into a hand-portable system. PSPA measures the linear elastic average modulus of a layer based on generating and detecting stress waves. The advantages of the PSPA are that it measures a layer-specific modulus without a need for backcalculation and independent of thickness of the layer (3), high success rate in identifying areas with different physical conditions or anomalies (2), and the results can be calibrated prior to construction during moisture-density lab tests (2). The concerns with the PSPA have been the need to calibrate the test results to the material and site conditions under evaluation (2), more sophisticated training of technicians (2), and high standard deviation of measurements (2,3). ASTM standards are available for all devices used in this study except for the PSPA. A careful study of the three available specifications reveals that the repeatability and reproducibility of these devices are not set based on a formal and rigorous study. The single operator-single equipment coefficients of variation (COV) between 4% and 60% are reported with a caveat that those values are preliminary. The standards are generally either silent about the device reproducibility or suggest preliminary values. Nazzal et al. (4) reported COVs ranging from 2 to 28% for LWD effective modulus. Alshibli et al. (5) reported COVs from 1 to 46% for LWD with poor repeatability when testing weak subgrades. White et al. (6) comprehensively studied the repeatability and reproducibility of five PIPLDs and three LWDs using a stiff and a soft rubber pads as supporting layers. They used two-way analyses of variance (ANOVA) with device and testing condition as random effects to quantify the repeatability and reproducibility of the devices. They reported a COV of 2 to 3% for PIPLD and 18 to 72% for the LWD. Abu-Farsakh et al. (7) reported the repeatability of the Geogauge between 6 and 9.5%. Von Quintus et al. (2) reported a COV of 1 and 7% for the Geogauge measurements as long as the test location was prepared carefully. Celaya et al. (3) reported that the variability of the PSPA on concrete slabs was less than 3% when the device is not moved and about 7% when the device is moved in a small area. The variability of the test method on aggregate bases was reported in the range of 7 to 80% (2). Based on this small sample of results reported, a systematic study may be useful. A few industry standard methods considered in this study are described below. METHODOLOGY FOR ESTIMATING REPEATABILITY AND REPRODUCIBILITY Device-related uncertainties can be classified into three categories: accuracy, repeatability (precision) and reproducibility. The so-called Gauge R&R method as a part of a measurement system analysis can be used to quantify the repeatability and reproducibility (8). Gauge is defined as any device used for any kind of measurement. R&R is defined as the combination of the device variability (repeatability) and operator variability (reproducibility) (9). The parameters estimated from a Gauge R&R study are: EV (repeatability or equipment variability), AV

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(reproducibility or the appraiser variability), and SV (specimen variability). The Automotive Industry Action Group (AIAG) indicates that a combined Gauge R&R value under 10% indicates an acceptable device, and between 10% and 30% the device may be acceptable depending on the importance of the application and the initial and operational costs of the device. Different methods can be used to perform Gauge R&R analysis including: Average and Range (X-bar/R) and Analysis of Variance (ANOVA) (8, 10). The X-bar/R method considers specimen-to-specimen variability, repeatability and reproducibility without considering the device-operator interaction. The Gauge R&R study utilizing two-way crossed ANOVA method is more sophisticated than X-bar/R method since it also considers the interaction between the device and operator. This method not only provides similar parameters as X-bar/R method, it also indicates whether a device is capable of discriminating between different specimens. The equations used in X-bar/R and ANOVA methods are presented in Table 1. As indicated in this table, m replicate measurements are performed by p operators on n specimens. Parameter yijk, which refers to a measurement made with device i by operator j on specimen k, can be expressed in the following equation: yijk= xi + uj + wij + εijk (1)

17 18 19

where xi is the actual value of the desired parameter, uj represents the operator variation, wij represents the interaction between specimens and operators; and εijk represents the repeatability error. The Gauge R&R is obtained from.

20


&     √            

21 22





(2)

The Total Variation (TV) of measurement system is calculated by combining the gauge R&R with the specimen variation (SV, ! ):

23

"    √      #         

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LABORATORY TESTING PROGRAM Eighteen different independent small-scale laboratory specimens were prepared using a finegrained soil classified as SM under unified soil classification system (A-2-4 under the AASHTO classification system) with a specific gravity (Gs) of 2.65. The soil consisted of 73% sand (passing No. 4 retained on No. 200 sieves) with a 27% fines content (passing No. 200 sieve). Based on the Atterberg Limit tests, the soil was non-plastic. The optimum moisture content (OMC) and the maximum dry density (MDD) as per Standard Proctor tests were 15.2% and 112 pcf (1794 kg/m3). The laboratory resilient modulus (MR) test, as per AASHTO T307 protocol, was performed. The MEPDG constitutive model using recommended representative values for octahedral shear stress, τoct, of 3 psi (21 KPa) and bulk stress, θ, of 12.4 psi (85 KPa) was employed to calculate the representative value of resilient modulus. The representative laboratory resilient modulus of the material at the OMC was 4.2 ksi (29 MPa) at OMC-1% was 8.2 ksi (56 MPa, 1.95 times the modulus at OMC) and at OMC+1% was 2.6 ksi (18 MPa, 0.62 times the modulus at OMC). As such, a change in moisture content from OMC-1% to OMC+1% resulted in a change in modulus of more than 3 times, while the density change was less than 2%. These drastic changes in the moduli with relatively small changes in moisture content or density should be considered when the material-related variability is discussed below. Figure 1a shows a schematic of the general setup of the small-scale specimens. The specimens were prepared in a 36 in. (900 mm) diameter PVC pipe that was placed on a hard

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 ! 

(3)

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floor, 4 ft (1.2 m) of concrete, to minimize the movement of the bottom of the specimen. The appropriate size of the small-scale specimen, to ensure that the interaction between the horizontal and vertical boundaries is minimal, was determined through finite-element modeling as discussed by Amiri et al. (11). A geophone was used to monitor the movement of the floor to ensure that the specimen did not move excessively. The final soil profile in each specimen consisted of 6 in. (150 mm) of various base materials and 16 in. (400 mm) of the SM material described above as subgrade. The test results discussed here were obtained about 24 hours after the compaction of the SM subgrade layer and before the placement of the base layer. A 3 in. (75 mm) thick layer of pea gravel was placed at the bottom of the specimen to facilitate the saturation of the subgrade under capillary conditions for other aspects of the study. Resistivity probes and moisture sensors were incorporated to monitor the changes in moisture with time. Geophones were embedded in the specimen to measure the responses of the specimens during modulus testing in order to calibrate existing numerical response models. Those aspects of the study are not discussed here. To ensure uniformity, a concrete mixer was used to prepare the material to the desired moisture content. Adequate amount of dry geomaterial necessary to achieve a desired density for a 2 in. (50 mm) lift was placed in the mixer. Precise amount of water was added to the soil with a water sprayer to ensure precise moisture content. The moist material was transferred into the PVC container and was compacted to the desired density with a hand compactor. This process was repeated until the 16 in. (400 mm) thick subgrade layer was completed (i.e., eight completed layers). TABLE 1 Equations Used to Calculate Variability Parameters a) X-bar/R Method according to AIAG Guidelines (8) Equipment Variation (EV)   

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Operator Variation (AV)  

$% &

'(

    $)  2 ∗+ , ./ 01/ .0 / 01/ &

Combined Device Variability (Gauge R&R) 3    

Total Variation (TV) 

Specimen Variation (SV) ! $! & ∗

3      # 

$% = average range of measurements, d2 = bias correction factor obtained from statistical tables, $) = range of operator averages, d2* = correction factor for estimating variances obtained from statistical tables, nspecimens= number of specimens, nmeasurements = number of measurement repetitions

b) ANOVA Method according to ASTM E 2782 Source of Variation

28 29 30 31

5

Degree of Freedom

Sum of Squares, SS 1

Specimens

n-1

45 6-7%.. , 7%... 2

Operators

p-1

.4 6-7%.@. , 7%... 2

Interaction

(n-1)(p-1)

Error

np(m-1)

9: 

@9:

##>  ##" , ##; , ## , ## 1



0

6 6 6-7@C , 7%@. 2 9: @9: C9:

Mean Sum of Squares, MSS

Estimate of Variance Component

##; .,1

=##; , =##> 45

##> -. , 12-5 , 12

=##> , =## 4

## 5,1

## .5-4 , 12

=## , =##> 4. =##

Expected Value of Variance Estimate** ? A

B



var(yijk)=υ2 + θ2 + α2 + σ2, SSO = Sum of Squares of Objects, SSA = Sum of Squares of Operators, SSI = Sum of Squares of Interactions, SSE = Sum of Squares of Errors, MSSO = Mean Sum of Squares of Objects, MSSI = Mean Sum of Squares of Interactions, MSSA = Mean Sum of Squares of Operators, MSSE = Mean Sum of Squares of Errors. 7%.. represents the average of the measurements from the ith object (the “dot” symbol shows averaging over the second and third indices, j and k).

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1 2

c) PSPA

d) LWD

e) Geogauge

f) PIPLD

3

4 5 6 7 8 9

FIGURE 1 Schematic of Small-Scale Specimens and Test Devices on Top of Compacted Layer

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Figure 1b through 1e show each device setup on top of the small-scale specimen surface in the laboratory. The testing program for each device and each specimen was similar with some differences. To investigate the repeatability, tests were carried out at three different locations three times per location. To study the reproducibility of these devices, the same measurements were repeated with another operator. In between measurements, the PSPA and Geogauge were picked up and repositioned in a slightly different location. Based on testing of a practice specimen, following the same testing pattern for the LWD or PIPLD was deemed too damaging since the ASTM standards require two seating drops followed by three additional drops to obtain data. As such, the LWD/PIPLD test at each location consisted of two seating drops, followed by three measurement drops. Each of these measurement drops was considered as an independent measurement. Since the PSPA and Geogauge tests are truly nondestructive, they were carried out before LWD/PIPLD tests. Despite conscientious effort to maintain the moisture contents at optimum for all specimens, the mean and standard deviation of moisture contents for all lifts of all specimens were 15.1% and 0.5% with a range of 0.9%. To account for these small differences, the moduli obtained from each device were adjusted to the optimum moisture content, using the equation proposed by Mechanistic Empirical Design Guide (MEPDG) as follows (12):

19

log

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where MR = modulus at a degree of saturation S corresponding to the measured moisture content; MRopt = modulus at the maximum dry density and optimum moisture content; Sopt = degree of saturation at the maximum dry density and optimum moisture content; a = minimum value of log (MR/MRopt); b = maximum value of log (MR/MRopt). The MEPDG-recommended regression parameters β = -0.3997 and KS = 6.1324 for fine-grained geomaterials were used in this study. The average and standard deviation of moduli from all devices are presented in Figure 2. The results from the Gauge R&R analyses shown in Table 2 can be used to understand the sources of variability for each device. The average moduli among the four devices are quite different and vary from 22.3 ksi for PSPA to 2.7 ksi for LWD (see Table 2a). These occur because different devices measure different types of modulus. The PSPA measures the smallstrain linear-elastic modulus of the specimen, whereas the Geogauge measures the system response at small strains to calculate modulus. The two deflection devices measure the response (combined recoverable and permanent) deformation of the material due to heavier loads applied to obtain the high-strain modulus of the materials. The differences between the moduli between the LWD and PIPLD are due to the differences in the locations where displacements are measured (displacement of soil for LWD vs. load plate for PIPLD).

MR b−a =a+ ( β + K s .( S − Sopt )) M R opt 1+ e

(4)

Average and Standard Deviation of Measured Moduli, ksi

40 30 20 10 0 PSPA

36 37

Geogauge

PIPLD

LWD

FIGURE 2 Mean and Standard Deviation of Modulus Measurements with Devices

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TABLE 2 Results from Gage R&R Analyses of Modulus-Based Devices

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a) ANOVA Method

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Equipment Operator Combined * COV of Variation, Variation, Device Specimen Total Total σ due to Variation, Variation, Variation, σ due to Variation, Repeatability, Gauge SV, ksi TV, ksi Reproducibility, % ** R&R , ksi ksi ksi PIPLD 3.48 0.27 (8%) 0.24 (7%) 0.36 (10%) 1.18 (34%) 1.23 35 LWD 2.67 0.08 (3%) 0.33 (12%) 0.34 (13%) 0.65 (24%) 0.73 28 PSPA 22.33 3.22 (14%) 1.09 (5%) 3.40 (15%) 5.36 (24%) 6.35 29 Geogauge 6.21 0.71 (11%) 0.44 (7%) 0.84 (14%) 1.28 (21%) 1.52 24 Confidence level = 95%, Study variation = ±6σ, σ = standard deviation, No. of specimens = 18, No. of operators =2, No. of * measurement repetitions = 9, COV = Coefficient of Variation

5

b) X-bar/R Method

Mean of Measurement Modulus Device Measurements, ksi

Measurement Device

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Range of Modulus Measurements, ksi

Equipment Variation, σ due to Repeatability, ** ksi

Operator Variation, σ due to Reproducibility, ksi

PIPLD 5.43 0.15 (4%) 0.03 (1%) LWD 2.54 0.07 (3%) 0.05 (2%) PSPA 29.87 2.90 (13%) 1.10 (5%) Geogauge 9.01 0.63 (10%) 0.29 (5%) ** Numbers in parenthesis are the variation divided by mean

Combined Device Variation, Gauge R&R, ksi

Specimen Variation, SV, ksi

Total Variation, TV, ksi

0.15 (4%) 0.09 (3%) 3.10 (14%) 0.69 (11%)

1.32 (38%) 0.59 (22%) 5.66 (25%) 1.60 (26%)

1.33 (38%) 0.60 (22%) 6.45 (29%) 1.75 (28%)

Total Variation divided by Range, % 24 24 22 19

The total variabilities for all devices are proportional to their average moduli, yielding similar coefficients of variation of about 29±5% in the ANOVA analyses and 22±3% in the Xbar/R analyses (see last column of Table 2a). Given the rigid control in the preparation of the specimens, these COVs seem high. However, in the light of the variation in laboratory modulus with moisture content discussed above (i.e., a change in modulus of more than 3 times with a change in moisture content from OMC-1% to OMC+1%), these COVs are reasonable. These results confirm the findings of Pacheco and Nazarian (13) that the moisture contents at the time of compaction and at the time of testing contribute significantly to the measured moduli. From Table 2, the LWD and PIPLD are more repeatable than the PSPA and Geogauge partly because the LWD and PIPLD were not resituated between the tests. According to X-bar/R method, where the interaction between the operator and device is ignored, all four devices are reproducible with less than 5% variation. The more accurate ANOVA analyses indicate that when that interaction is considered, the reproducibility of the LWD and PIPLD diminishes somewhat. The contributions of the specimen changes to variability are similar among the devices with an average of about 24% from the ANOVA analyses, except for the PIPLD that is about 34%. These variabilities can be due to the non-uniformity in the construction of the specimens, non-uniform changes in properties between construction and testing, and the alteration of properties due to higher loads applied to the specimens with the two deflection devices. The sums of percent contributions of the variations in Table 2 do not add up to 100%. To eliminate this inconsistency, Wheeler (14) proved that the contribution of repeatability, reproducibility and specimen variations can be more accurately estimated from the following relationships:

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Repeatability Proportion =

20 21 22 23 24 25 26 27 28 29 30 31 32

E FGHGIJIKLMLJN O D

Reproducibility Proportion=

EJ D

O



E FGHSTUVWLKLMLJN D

Combined R&R Proportion=

EJ O D

EYIVZG D

O

EJ O D E\ O D

Specimen Variation Proportion=

EJ O D



O

9

PQ O RQ O



(5)

XQ O RQ O

(6)

   & O

!Q O

 RQ O

RQ O

(7) (8)

These values are reported in Table 3. Since the coefficients of variation estimated from the total variations and average moduli of all devices are similar, the values in Table 3 can be used to better understand the characteristics of the devices. The PIPLD and LWD are more repeatable than the PSPA and Geogauge, since less than 5% of the total variability is associated with repeatability. This is anticipated because as discussed earlier, the repeatability of these two devices was estimated by considering different drops from the same test point. The greater repeatability proportions from the ANOVA analyses for the PIPLD, PSPA and Geogauge as compared to the X-bar/R analyses demonstrate that the operator-device-specimen interaction are somewhat important for these devices, with the greatest importance for the PIPLD and Geogauge. TABLE 3 Contribution of each Variability Parameter to total variability of ModulusBased Devices a) ANOVA Method

PIPLD

Equipment Variation (Repeatability) Proportion, % 5

Operator Variation (Reproducibility) Proportion, % 4

9

Specimen Variation Proportion, % 91

LWD

1

20

21

79

PSPA Geogauge

26

3

29

71

22

8

30

70

1

0.1

1

99

LWD

1

1

2

98

PSPA

20

3

23

77

Geogauge

13

3

16

84

Measurement Device

19

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b) X-bar/R Method PIPLD

Combined R&R Proportion, %

The contributions of the reproducibility to the total variability are rather small for all devices in X-bar/R analyses. These values are significantly greater for the LWD and somewhat greater for the Geogauge measurements under the ANOVA analyses indicating that the operatordevice-specimen interaction is more critical for the reproducibility of those devices. This translates to a practical recommendation that the operator should pay more attention to placing these two devices than the other two. Based on the combined R&R values, PIPLD device yields the least uncertain values than the other three devices when the operator-device-specimen interaction is considered. The high uncertainty associated with the LWD was not anticipated since the operation of that device is very similar to the PIPLD. The only plausible explanation at this time is that the first set of tests by the first LWD operator might have altered the properties of the specimens for the second set of tests by the second LWD operator.

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APPLICATION OF RESULTS IN QUALITY CONTROL PROCESS For a fair and equitable quality management system, statistics-based methods should be used to optimize the sampling plan and testing frequencies for a transparent level of reliability (15, 16). The variability of measurements and the tolerable errors are the most important parameters in acceptance sampling and defining the required sample size. The tolerable error is defined as the limits that both the contractor and owner will accept during the construction process. Based on this brief discussion, the following equation can be used to estimate the sample size, n (17):

8

. 

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

O

]^_ `^a b DO O

(9)

where α = Type I (contractor’s) risk, β = Type II (owner’s) risk, Zα = the (1- α)th percentile of the standard normal distribution, Zβ = the (1- β)th percentile of the standard normal distribution, σ = standard deviation, and e = tolerable error. Typically, σ is an approximation of the variability of material properties (i.e. modulus of compacted geomaterials) tested by different devices (17). The tolerable error is often defined as 1.5 times the confidence interval which may defined as the standard deviation associated with the total variability , σt (i.e. TV in Table 2) (18). The overall patterns of sample size based on different α, β, σ and e are presented in Figure 3. Parameter e is assumed to be equal to 1.5 times σt (i.e. total variation) and σ is assumed to be equal to σGauge (combined device variation or gauge R&R). Based on the values reported in Table 2 for σt and σGauge for each device, the number of samples necessary per lot for a given level of α and β can be estimated. AASHTO (19) categorizes projects into four groups (critical, major, minor and contractual) with corresponding α and β values shown in Figure 3. Based on Figure 3 using α=5.0% and β=0.5% (critical project), the sample sizes necessary are 3 for PIPLD, 5 for LWD, 6 for PSPA and 7 for Geogauge. Given the limitation in assessing the repeatability of LWD and PIPLD, a sample size of five to seven for all devices may be reasonable. 20

Critical (α=5%, β=0.5%) Major (α=1%, β=5%) Minor (α=0.5%, β=10%) Contractual (α=0.1%, β=20%)

Sample Size, n

15

Geogauge LWD PSPA

10 PIPLD 5

0 0

25 26 27 28 29 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Ratio of Device Standard Deviation to Tolerable Error (σGauge/1.5σt)

FIGURE 3 Suggested Sample Size for Different Type I and II Risk Levels and Variability of Devices CONCLUSIONS The measurement system analysis method was used in this study to estimate the different constituents of measurement variation for four modulus-based devices (PIPLD, LWD, Geogauge

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and PSPA). The crossed analyses of variance (ANOVA) and the X-bar/R analyses were performed on the measurements conducted on 18 independent laboratory small-scale specimens constructed with the same soil nominally at optimum moisture content and maximum dry density. The total variation of each measurement system was fragmented into the variability associated with device (repeatability), operator (reproducibility), combined effect of device and operator (gauge R&R) and the differences in specimens. The results of the ANOVA method are more realistic as compared to the X-bar/R method since the ANOVA method considers the interaction of device-specimen-operator to calculate the variability components. The following conclusions can be drawn from this study: •

•

•

•

•

From the ANOVA analyses, the coefficients of variation of the total variations show that the overall uncertainty in the measured moduli are similar for all devices with Geogauge exhibiting slightly less uncertainty and the PIPLD slightly more uncertainty. The LWD and PIPLD demonstrated lower device-related variability than the Geogauge and PSPA. These results may be biased by the fact that the LWD and PIPLD were not resituated between repeat tests. The contributions of operator variation to total measurement variation are rather small for all devices except the LWD when the operator-device-specimen interaction is considered. This might mean that situating the device may need more care or the specimen properties may change due to repeated tests. The contributions of specimen variation to total measurement variation are the most significant factor for all devices. The pavement geotechnical engineering community should develop models to minimize this factor in actual field measurements. The different components of measurement variability discussed in this paper could be applied in quality control process. Based on the AASHTO-suggested risk levels for a critical decision, the required sample sizes of five to seven may be appropriate.

ACKNOWLEDGMENT This study was carried out as part of the NCHRP Project 10-84. The contents of this paper reflect the authors’ opinions, not necessarily the policies and findings of NCHRP. The authors are grateful to Dr. Ed Harrigan and the study panel for their help and advice throughout this study. REFERENCES 1. Puppala, A. J. Estimating Stiffness of Subgrade and Unbound Materials for Pavement Design. A synthesis of highway practice, NCHRP Synthesis 382, Transportation Research Board, Washington, D.C., 2008. 2. Von Quintus, H. L., C. Rao, R. E. Minchin, S. Nazarian, K.R. Maser, and B. Prowell. NDT Technology for Quality Assurance of HMA Pavement Construction. NCHRP Report 626, 2009. 3. Celaya, M., S. Nazarian, and D. Yuan. Implementation of Quality Management of Base Materials with Seismic Methods: Case Study in Texas. In Transportation Research Record: Journal of the Transportation Research Board, No. 2186, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp. 11–20. 4. Nazzal, M. D., K. Alshibli, and L. Mohammad. Evaluating the Light Falling Weight Deflectometer Device for In Situ Measurement of Elastic Modulus of Pavement Layers. In Transportation Research Record: Journal of the Transportation Research Board, No. 2016,

TRB 2013 Annual Meeting

Paper revised from original submittal.

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TRB 2013 Annual Meeting

Paper revised from original submittal.