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NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report (1997)

Chapter: A: Diametral Test Equipment and Equations for Data Reduction

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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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Suggested Citation:"A: Diametral Test Equipment and Equations for Data Reduction." Transportation Research Board. 1997. NCHRP Web Doc 14 Laboratory Determination of Resilient Modulus for Flexible Pavement Design: Final Report. Washington, DC: The National Academies Press. doi: 10.17226/6353.
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1X A i I~I HEM ~ NATIONS ~R LEA ~LCI1ON A-1

APPENDIX A DIAMETRAL TEST EQUIPMENT AND EQUATIONS FOR DATA REDUCTION DIAMETRAL TEST DEVICES This section gives a detailed description of the different diametral test devices used in Me study to evaluate the resilient modulus of asphalt concrete. Bow the construction of the equipment and its operation are described. Retsina Device. The Retsina device is We most simple device studied. This device uses a fixed bottom loading strip with an independent loading strip that is placed on the top of the specimen. The load is transferred through a small (0.5 in. diameter) metal ball which rests on an inverted conical groove on the top of Me upper loading strip (Figure Add. For this device to work properly, the loading plane should be perfectly aligned with the vertical diametral plane of the specimen, and the loading system should be very accurately aligned. Due to the absence of a rigid connection between the loading strip and the load cell, or Me loading system which applies load through He ball, a tendency exists for separation of Me loading system (ram) from the loading strip. Also, there is a tendency for the upper loading strip to move during testing. Since there is no room on the upper loading strip to measure the deformation using a spring- loaded EVDT, the vertical deformation of the MTS ram was used to calculate resilient modulus. Deflections in the horizontal diametral plane were measured using both mountable and stand-alone measurement devices (extensometers and EVDTs). EVDTs were attached to the side walls of the bottom portion of the MTS device which acted as the fixed bottom loading strip. A high degree of freedom exists in the Retsina device, and hence it is more liable to equipment and operator errors. This fixture can be easily used in many standard environmental chambers without modifications. M7S Device. An MTS Mode! 643.01A Resilient Modulus Fixture was also used in this study (Figure A-21. The fixture can be installed in a load unit having either a crosshead or a baseplate mounted actuator. It is small and simple enough to be used in many small environmental chambers. The MTS device has upper and lower platens goading plates). A pulfrod (ram) connects the upper platen to the load cell. To insure Mat the longitudinal center line of the loading strips remain in the vertical diametral plane of the test specimen throughout the testing, an alignment bar is connected to one side of the upper loading platen. This alignment bar is guided between tow cam rollers mounted on the side plate of Me lower loading platen hence preventing the rotation of Me upper plate in a horizontal plane. The specimen seats between He loading strips attached to the upper and lower loading platen. Different loading strips are used for 4 in. and 6 in. diameter specimens. The deformations are measured by extensometer assemblies supplied by MTS. A vertical extensometer can be mounted between the upper and lower platen on one side wall of He lower platen (wall opposite to the one with the alignment bar and cam rollers). A horizontal extensometer assembly can be mounted on He specimen to measure horizontal deformation. The assembly consists of two extensometers held by springs against He sides of the specimen. Two slots are provided in each side wall of He lower platen to help mount the extensometers on to the specimen. Four thumbscrews are provided with He device (Figure Add. These hold the extensometer assembly in place while a new specimen is A-2

Figure A-lb. LOAD sea BAR L UPPER LOADING ~ STRIP PLACED ON INS Mu CONIC ~ SPECIMEN GROOVE ~I - ~- 1 1 \ \~ SPECIE I . ~ -7 , , =~/BOTTOM LOADING ~ jet S1 RIP AND PLATE T. ~ Figure A-la. Sehcmatic view of the Retsina device Retsina device test setup at NCSU with Extensometers A-3

RAM SPECIMEN . . . - . ~ VERTICAL DISH ~J\ [ATERAL DEFOR~ON ~ ~ ~ EXTENSOM=F~.RY.~ ~ ~-~ i ~ ~ ~ ~7 Jl SPECIMEN LOADING STRIPS / / LOWER PENSION ROD :111 ·1< / LOW FRICTION ANTI-ROTATE FUTURE . ~ it. EXTFNSOME I OR AND SPECIMEN ALIGNMENT FIXTURE Figure A-2. Schematic view of the MTS Resilient Modulus Fixture with an installed specimen A-4

a a - ~ screw in En.} 1 i r 1 storage 0 0 0 (, ~ front view assembly pulled away ED ton view Figure A-3. Using the Thumbscrews on the MTS device (installation arid removal of the specimen) r ~ AT ~ ,~,n install, center on loading strip 41_ roll gently against bracket 1. 1 -- ' ' -~l _ It,tillll~ylU~tl j At, jar, \ Q~ ~n - 1 _ ~ I ~' 1t - = Figure A-4. Aligning the specimen in the MTS device A-5

put in or replaced. The specimen can be rocked in the lower platen to make sure that it has full contact with the extensometer assembly and hence ascertaining the longitudinal alignment of the specimen with the loading strips (Figure And. Once Mat is accomplished, the thumbscrews are unscrewed which pulls the extensometer assembly on to the specimen in the horizontal diametral plane. To facilitate the simultaneous use of the stand-alone and mountable measurement devices for horizontal deformation, holes were drilled in Be side plates to mount spring-Ioaded EVDTs. Also, long arm attachments were designed and fabricated to hold vertical EVDTs (that could be spring-Ioaded on the top of the upper platen on opposite sides of the ram). These were fixed to the base of the side walls of the lower platens with a rotating arm on the top which held the EVDTs. The same attachment was used for the SHRP EG device setup for the measurement of vertical deformation. A marking device (described later) was developed to accurately mark mutually perpendicular axes on both faces of the specimen with precision. The specimens were then aligned between We loading strips and the extensometer assembly using He marked axes as datum. This was generally observed to provide a good control on rocking. Very thin lines were precisely drawn at the ends of the loading strips to facilitate alignment of the specimen. However, it should be ensured that the loading system is perfectly aligned to minimize rocking. The alignment of the MTS loading system was periodically checked. A very short Hence smaller weight) ram attached to the upper loading platen was used in one experiment to determine if a significant difference existed in the control of rocking compared to a long, heavy ram. The MTS device is simple in design. The upper loading platen is thinner than those used in the Baladi and SHRP devices. However, only the MTS device is rigidly connected to the loading system. A little control over the rotation of the upper platen is provided by the presence of an alignment bar and cam rollers, but careful alignment of the loading system is still required. Due to the absence of heavy guide columns, friction is not a major concern to the movement of the device in either the transverse or the vertical direction. The absence of resistance to the movement in the transverse direction might be considered as a drawback of the device. However, absence of resistance friction in the vertical direction ensures that the load cell measures the full load applied to the specimen. The MTS device is open enough to be adaptable to different measurement systems, a flexibithe SHRP EG and Baladi~s device. Baladi's Device. The Baladi device used in this study was supplied by the Gilson Company, Inc. (Ohio) as mode} MS 40 (Figure A-51. This device can only be loaded from the top. The Baladi device consists mainly of a fixed top and bottom cylindrical assembly supported by four columns, two on the side and one each in the front and back of the specimen (when installed). Holes are drilled in these columns so that the deformations can be obtained by use of EVDTs mounted through them. A short attachment is made on the fixed upper part of the device to obtain measurements in the vertical direction with a EVDT mounted through it. The Baladi device is the only one to permit deformation measurements in three dimensions. The upper part has five holes, one for the loading piston and four for the low friction guide posts, and through which the upper plate moves. The load is applied through a standard ~ in. diameter steel ball that rests on the upper loading plate in an inverted conical groove on the center. The Baladi device, in contrast to the others, has a hinged upper loading strip so as to accommodate a nonuniform diameter specimen. The device is compact, and hence it is very cumbersome to put the extensometer assembly on the specimen. Also, the installation of the specimen is not easy, although a rubber stopper is provided at the top to assist in the installation of specimen. centerlines were marked on the end of the loading A-6

LOAD STANDARD 1. STEEL BALL UNBAR MORON BUSHING 1 LOADING PISTON ' or 11 1 \ 11 I Let for r LOADING PISTON I GUIDE PLANE -___' r- ~ I l l r GUIDE POST . .~ . UPPER STATIONARY _ PILATE ,7 ll f' BEARING RETAINER CUP - UPPER LOADING- S1RIP, HINGED ~ !1_ ~ a---~ ~ T___d I r-~ \ L . ~ \ _1_ . ~1 cot--~ ! ·! I . . 11 : r ~ \ . , L TEST SPECIMEN 1 1 1 \ BOrrOM LOADING STRIP, FIXED Figure A-S. Schematic view of Baladi's device A-7 POST, LVDT ! HOMER - LO\VER STATIONARY PLATE

strips to help in the alignment of the specimens. Friction in the vertical direction generated by the use of four guide posts, reducing the load applied to the specimen, is a concern. To overcome this problem, a load cell can be place between the lower curved loading strip and the lower stationary plate [171. SHRP Load Guide (ZG) Device. The SHRP EG device was developed as a part of the Strategic Highway Research Program's Long-Term Pavement Performance project (Figure Add. The device has to be used under a top loading system. The device is a die set with upper and lower loading platens constrained to remain parallel during testing by the presence of two heavy guide posts. The guide posts are in line with the loading strips hence assuring minimal lateral movement of the top loading strip with reference to the lower. the lading platens are very heavy and rigid. The loading system is connected to the device with a complex arrangement using a metal ball and springs between two flanges (Figure Ado. The loading system is a compromise between the very rigid connection used in the MTS device and a free connection used in Baladi's device. A counterweight system prevents the heavy weight of the loading system from being applied to the specimen (which is very critical at high temperatures). Two standoffhor~zontal transducer holders are attached to the lower platen of the load frame such that the EVDTs can be positioned at the mid height of the specimen on either side. The holders are movable by a fine screw adjustment that makes it very easy to zero the EVDTs prior to testing. Stee! loading strips. curved to a diameter of a 4 in. specimen are fixer! to the Platens. The outer edges of , ~ . · ~ · . . e _ ~ ~ these strips are rounuecl to remove Sharp edges mat might cut specimens during testing. l he LVL) 1 S and the extensometers cannot be used simultaneously for He measurement of horizontal deformation. Therefore, two sets of tests had to be performed to evaluate these measurement systems wig the SHRP device. The bulky guide columns and the counterbalance systems could be a source of appreciable friction to the vertical movement and causing a lower load to be applied to the specimen. Due to the size of the device and counterbalance system, the device cannot be conveniently used within a conventional environmental chamber. Also, the loading strips are not easily removable, and hence it would be difficult, but not impossible, to test 6 in. diameter specimens in in the device is cumbersome and requires a significant amount of time and patience to obtain proper alignment. Some modifications have been made by SHRP personnel to the SHRP EG device since its use on this project. The loading strips have been changed and the transducer standoff devices have been modified to account for the thicker loading strips now used. The thinner load strips formerly used were provided less contact area and were believer to be deforming due to a pre-existing deformation in the upper platen. The SHRP personnel also suggested mounting the EVDTs directly on to He top of He upper loading strip by drilling a hole through the upper loading platen or to use snap-in spring-Ioaded EVDTs between He loading strips (while using a stop collar on the guide posts to avoid damaging the EVDTs during testing). Marking Devices The device used to accurately mark diametral specimens is described in detail in this section. The device has two parallel metal plates wig windows to facilitate the marking of axes through them. These metal plates are connected by steel rods through He bottom. The metal plates can be slid over these rods so as to adjust to any Sickness of the specimen. A marking tool, which is essentially a long steel bar plate rod, etc., with a tapered edge, is used to etch a thin line on the sample surface. A hinged plexi- glass window is provided wig horizontal lines etched on it. The horizontal lines are precision-etched so A-8

Cl c: \ in o :, ME 1 ~ - c) ·5 · _ V A-9 :r UJ G G n o VO · 3 as en U] a' it_ o 3 ·5 Cat ._ U] set AS ._

~ 1 Figure A-7. SHRP LO Device setup at NCSU with a synthetic specimen A-10

as to be perfectly perpendicular to the marking edge in the window of Me front plate. The plexi-glass window can be rotated in the horizontal plane and locked in one the front plate. In an unlocked position it can be moved up and down. If it is required to mark axes at different angles (other Wan 90°), lines should be etched on Me window at the required angle. The marking of the axes on a specimen using this device is accomplished by Me following steps: The specimen is cradled between the connecting rods near the front plate so that it sits comfortably. Rocking tendency is checked by applying light pressure near the approximate vertical diametral plane on the top of the specimen near the front and back faces. 2. The back plate is Men brought close to the specimen and screwed in place. 3. The specimen is rotated again to ensure that it sits correctly between the two plates. Small light lines are marked at the front and the back near the center of Me specimen. 4. Rotate (approx. 120° or less) Me specimen and repeat the above step. Once at least three lines are marked, check Me specimen faces to see that they pass through a corrunon point. If the specimen is not of uniform diameter or was not seated properly, the liens will form a polygon. In Me first case, determine Me approximate center of Me polygon. For Me later case, repeat Me procedure again. J Once Me center is determined for both faces, cradle Me specimen correctly between Me rods wig Me plates as close to Me specimen as possible. Then mark the diametral axis on Me front and back of Me specimen (without moving the specimen) making sure Mat it passes Trough the center points. 6. Rotate Me specimen and rotate the plexi-glass window about its hinge so that it locks into place on Me front plate, one of Me lines coinciding with Me center of Me specimen. Rotate the specimen so Mat Me first diametral axis coincides completely wig Me etched line on Me plexi- glass window. 7. Unlock Me window carefully so as net to disturb Me specimen and mark diametral axes on Me front and Me back. This marking device, along wig lines etched on the center of Me loading strips, helps in reducing rocking and making the alignment of Me specimen much easier. Indirect Tension Test Analysis Methods AS7M Analyst Lois analysis is from Me ASTM D 4123-82 procedure for Me resilient modulus testing of asphalt cohere. Absolute vadues of all deformations are to be Ken for He purpose of His analysis. Poisson's ratio (m) and resilient modulus (MR) are determined by Me following two equations: p=359g,~ -02~7 my t8, A-11 (1) (2,

where, P = applied repetitive load t = Sickness of the specimen ME = resilient modulus, and m = resilient Poisson's ratio dx,dy = measured deformations in Me x and y axis, respectively. According to ASTM D4123-82, a Poisson's ratio of 0.35 can be assumed, if n~;sary, at a temperature of 77 F. The above equations can be used ~ calculate Me instantaneous or Me gal Poisson ratio and resilient modulus depending upon whether instantaneous or total deformation is used. Elastic Analysis. The elastic analysis method was developed during this study and is based on an assumption of linear elastic behavior of a statically loaded specimen. The following equations were developed for Me strains along the tic and y axes from the stress equations given by Hondros [A-21: 4P £X = {MR7C -4P ~ {MR7C I where, (1 X ) · 2a _- + 2-cos2a + R2 R4 X4 (F 1)~ (R: + z teals) (I + lo) ~ ~ (l - Stan ( R 7 - Ye ) ex, e', = strains along the ~ and y axes, respectively (3) (4) 2a = angle subtended at the specimen center by Me loading strip R = radium of the specimen x, y = distances along the x and y axes, respectively P = applied repetitive load A-12

thickness of the specimen MR = m resilient modulus, and resilient Poisson's ratio By integrating these equations from -~/2 to L/2, where ~ is the gage length for Me mounted EVDT, We deformation over a gage length of ~ (symmetric over the center) can be found. The equations given below are only valid for 4 in. diameter specimens loaded with a 0.5 in. wide rigid loading strip. The equations derived for a 4 in. diameter specimen are also valid for a 6 in. diameter specimen loaded by a 0.75 in. wide loading strip, provided the ratio of gage length to specimen diameter is the same. For example, the equations derived for a 1 in. gage length on a 4 in. diameter specimen are valid for a I.5 in. gage length on a 6 in. diameter specimen. For Me purpose of this analysis, horizontal (tensile) deformation is considered positive, while vertical (compressive) deformation is considered negative. Equal gage lengths along the two ax" - - Integrating Equations (3) and (4) over a gage length of C, the deformation in the tic and y directions and, respectively, is obtained: AL = M ~ (a + tell) at = M , (C + by) (5) (6) where aJb,c, and d are constants given in Table A-1, dependent on Me gage length L (refer to Table A 1). . Table A-1. Values of constants a,b,c, and ~ in the elastic analysis for different gage lengths on a 4 in. diameter specimen Gage Length | Constants L (ins) a . . 1 0.1444 0.4508 0.4886 2 0.2339 0.7801 1.0695 3 1 0.2699 1 1 1 3.5879 . - d 0.1558 0.3074 .0627 A-13

Taking the ratio of vertical and horizontal deformation, is determined as follows: ~yL -c-a .. =- ~ L d+b A (7) The resilient modulus can then be determined by using Equation (3) for horizontal deformation. Equation (5) can then be solved ~ obtain the resilient modulus. Equation (5) when solved for resilient modulus and Equation (7) closely resemble We analogous equations for resilient modulus given in ASTM D 4123-82. Different gage lengths along the two axes - - The following equations were derived for the analysis of tests on 4 in. and 6 in. diameter specimens with a gage length to diameter ratio of 3/4 and ~ for vertical and horizontal deformation, respectively. Equation (2) was integrated over a gage length of 3 in. for the 4 in. diameter specimen (or 4.5 in. for a 6 in. diameter specimen) to obtain 6) ,3 ~ ~ M ~ (19345 + 0.430911) To determine Poisson ratio, a ratio of Me vertical deformation given by Equation (6) to Me horizontal deformation for a 4 in. gage length, given in Equation (5) was taken to obtain - I.9345 - 0~699 Y 6)r4 -0.4309+ Y a)~4 (9) The resilient modulus can Men be determined from Equation (5) using a gage length of 4 in. to measure horizontal deformation. SHRP PO? ALSO The SHRUB P07 (November I, 1992) procedure uses Me following equations: 0.859- O.O8R ~ = ~0.2851t - 0.04 (IO) In general, for different configurations of Me measurement system, Me venicalIhor~zon~ deformation ratio R' can be defined as, (1 l) A-14

In He above equation VO us He vertical compliance favor. The use of a compliance factor VO would improve He value of Be vertical deformation for He purpose of He calculation of Poisson's ratio. However, a compliance factor will have to be de=Tnined for each different test setup. The SHRP procedure limits Poisson's ratio to a range of 0. ~ to 0.5, even when He circular values go outside these bounds. For He purpose of comparison with over methods ~ this project, He value of Poisson's ratio was not array changed, even when it was out of He specified range. The resilient modulus Is Hen calculated accords to the following equation PD(O.08+0.297P ~0.0425[12) MR=- tH where (12) H = ~ e recoverable ~nstar~taneous or total horizontal deformation, in. (Absolute values of all deformations are to be taken for He purpose of Ads analyses.), applied repetitive load ,lbs. ~= sample thickness, in. D = ROqUe and Busier) A,~S`S Roque and Buttiar (A-3) proposM an analysis system for He Gage~o~nt-mount~ system of measuremerK. It only applies for a gage length to diameter ratio of I:4 and when He height of He surface mounted EVDT Is 0.25 in. from He specimen surf. Horizontal ( - site) deformation is considerM to be positive, while vertical (compressive) deformation is considered to be negative for this analysis. A stq~by~tep procedure for Ads analysis Is described below: sample diameter, in. t. Assume Poisson's ratio, m (for example, assume 0.35 at 77 E9. 2. Correct horizontal deformation (to ~ far bulging) H = (~.0 ~-0.12 p-0.O: ~-): HM where, = = measured specimen Lichens ~= H - M ~ standard specimen Richness (2.5 in. for 4 in. diameter specimen) measured horizontal deformation A-15 (13)

5. Correct vertical deformation (to account for bulged Y = (O .994 - O . 128~) $ Y.,' where YM is He measured vertical deformation. 4. Horizontal point swain at the center of speck s given by, Achy = ~ 07 Gil, and He vertical point strain at die center of specimen is given by, y £ CT3? = 0 98 GL, where, ~= H - - gage length, in. horizontal deformation, in. Y = vertical deformation, in. 5. Corrupts horizontal point stress at He center of specimen ~ = 0.! 859- SCOUR t,~ Corrected vertical point stress at He center of specimen Or =~.4636 COM (14) (15) (16) (1~ (18) (Note: Lee factors used in Equations (17) and (18) were obtained Tom Table I in Roque and Buttiar's paper and are only valid for a Richness to diameter ratio of 0.625 for He specimen and a Poisson ratio of 0.35) A-16

6. Capable Po~n's ratio use (£CTRX ~ XCOM ~ ~ ) YCOM C7Rr £CTR,` (S YCOM ~ ~ ECrR, , IS XCOM (19) If Poisson's ratio calculated In Step 6 differs by more Man 0.01 win Poisson ratio In Step ~ Men replace m in Step ~ by Me value calculated In Step 6 arm repeat Steps 2 - 6, else go on to the next stop. 7. The asphalt concrete modulus can Men be determined by, M * = (~ x ~ C TRY CON* rCO'R Notation Used In Experiments (20) A standard set of notations is described below which is used in presenting Me diametral test experimental findings. Additional notation employed is described where it appears. Value of Resilient Modulus and Poisson's Ratio Notation Used pr: mr: 1: EXSUM and GPM Alignment System Variable Presented Poisson's ratio Resilient modulus This letter is used as a suffix to the resilient modulus (mr) and Poisson's ratio (pr) notations given above if the value is calculated from the instantaneous values of recoverable deformation. Otherwise, the values of pr and mr were calculatM from the total recoverable deformation. A precision L~VDT alignment system was used in both Me gag~point-mounted (GPM) and the general EXSUM deflection measurement method. This alignment system and its installation is described here. Device Description' The device has two brass arms fitted perpendicular to each other. The arms are made using channel selections and have grooves in them in which small mounting blocks can be positionM. Along A-17

the length of Be arm, small holes are precision~rilled on Me side such ~at, when screws are put through them to hold the mounting blocks tight in the groove, the correct gage length is maintained between the glue points on the mounting blocks. Holes are drilled at regular intervals to define gage lengths from in. to 6 in. at a 0.5 in. interval. Support legs can be slid over the four ends of the brass arms to support the alignment device in place over the specimen while the glue sets. Lines are etched on He inside of the support legs which should coincide with the marked diametral axes. This design insures that the mounting blocks and the EVDT (Note: two EVDTs are used in the GEM setup) are in perfect alignment with the diametral axis. Setup of the EXSUM System The procedure for the setup of the EXSUM deformation measurement system on a diametral test specimen is as follows: 7. Just before testing, He diametral axes are marked on a specimen. Unless there is a requirement to perform testing along a particular axes, select the axes so that the gage-points are on the best side of the specimen and over relatively homogenous portions of He asphalt concrete. mark the axes on the front and back of the specimen using the marking device. Place the specimen on its side wig the top side being the one on which the EVDT is to be mounted. Position the alignment device, with He four support legs loosely slid over the ends, on the specimen such Hat the lines marked on the four legs match the diametral axes. Now, tighten the support legs in position. Remove the alignment device by vertically lifting it over the sample. Lay it upside down so Hat the channels of He brass arms are visible. Take a pair of mounting blocks and loosely tighten the EVDT body in one and screw in the EVDT core in the over. Position the mounting blocks in He groove (one by one) and hold them tight along the bottom and the side opposite to the one having holes in the brass channel. Insert He screws from the side and tighten them in place. This ensures that the mounting blocks, when glued, are perpendicular to the surface of the specimen. Zero He EVDT by screwing in or out the EVDT core connecting rod. Invert the alignment device and Den tighten He plastic screws so Hat the EVDT remains in the zero voltage output position. Next, uniformly mix the epoxy on a glass plate or other suitable surface. Apply the epoxy at the gluing surfaces on the mounting blocks, and then carefully align the alignment device such that the lines marked on the support legs match the diametral axes. Alignment should be easy to accomplish since the legs have already been fixed on He brass arms in ache proper positions. By aligning one or maybe two legs, all the four legs should be in position. Use a flashlight, if required, to make sure that the axes match with the center lines on He legs. Cure the epoxy at or above room temperature. Applying heat from a blower accelerates curing. Tape the EVDT connecting wires to the specimen so that He weight of He A-18

connecting wire does not pull down on the glued mounting block when the alignment assembly is taken off. 10. ~- References A-t A-2. A-3. Once the epoxy is hard enough (normally ~ to 10 hours), carefully loosen the screws holding the legs and the mounting blocks. Remove the alignment device by lifting it vertically from the surface of the specimen. Allow He specimen to cure for an additional 6 to ~ hours. The total recommended time for curing is approximately 16 hours. Mount the extensometer assembly on the specimen taking care that it does not touch the mounted EVDT. The specimen is ready for testing after bringing it to the required temperature in the environmental chamber. Baladi, G.Y. and Harichandran, R.S. (1989), "Asphalt Mix Design and the Indirect Test: A New Horizons, Asphalt Concrete Mix Design: Development of More Rational Approaches, ASTM STP 1041, W. Gartner, Ir., Ed., American Society for Testing and Materials, Philadelphia, PA. Hondros, G. (1959), "The Evaluation of Poisson's Ratio and the Modulus of Materials of a Low Tensile Resistance by the Brazilian Indirect Tensile3 Test with a Particular Reference to Concrete", Australian Journal of Applied Science, Vol. 10, No. 3. Roque, R. and Buttiar, W.G. (1992), "The Development of a Measurement and Analysis System to Accurately Determine Asphalt Concrete Properties Using the Indirect Tensile Mode", Draft for Association of Asphalt Paving Technologists, 1992, Annual Meeting, Charleston, South Carolina. A-19

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