Research Report -562-

INTERPRETATION OF DYNAMIC PAVEMENT DEFLECTIONS

by

Gary W. Sharpe

Research Engineer Principal

Herbert F. Southgate Research Engineer Chief

Robert C. Deen Assistant Director

Division of Research

Bureau of Highways

DEPARTMENT OF TRANSPORTATION

Commonwealth of Kentucky

October 1980

ABSTRACT

In 1977, a methodology was .developed to evaluate pavement

performance using dynamic (Road Rater) deflections. Since then,

additional research has resulted in modifications ill the

procedu1:es. This paper presents the procedures presently used to

evaluate flexible pavement structures. Background information is

included on various procedures used by others. A sample set of

data is presented and evaluated. A discussion is included on how

the analyses of dynamic pavement deflections can be used to design

overlays and in pavement management.

INTRODUCTION

In 1977, a methodology was developed to evaluate the behavio~

oz: performance of flexible pavements using dynamic

deflections (14). This method utilized deflections

(Road Rate~)

computed by

elastic theo~y using the Chev~on compute~ p~og~am (7, 15) to

simulate Road Rate~ deflections. This methodology involved a

series of g~aphical inte~polations and ~equi~ed conside~able

engineering judgment. Modifications p~~sented in this pape~

~efine and simplfy the p~ocedu~e conside~ably.

Nondest~uctive tests of pavements have been empi~ically

co~~elated with field st~ength tests. There has been conside~able

use of elastic theo~y and dynamic testing to estimate laye~

the moduli. Equipment used has included the

Califo:r:nia t~aveling deflectomete~.

deflectomete~. the Dynaflect, the Road Rate~.

teste~s (8).

Benkelman beam,

a fall ing-tJe i_g h t

and other vib~ato~y

Of the va~ious devices available fo~ the nondest~uctive

measu~ement of pavement deflections, the simplest and most

commonly used is the Benkelman beam. The Benkelman beam uses a

lever to measu~e the rebound deflection as the tires of a test

vehicle of known weight roll past the tip or 'p~obe' of the beam

( 2 9 ) . The beam has been successfully mechanized, making it

possible to measure deflections continuously under: a moving

axleload. The California traveling deflectometer is one device.

utili::ing the principle (3, 291.

Ben~alman beam deflections can be used to evaluate pavement

performanc2; such analyses have been incorporated into ove1:lay

3

design pJ:oceduJ:es ( 12, 29). Benkelman beam deflections have also

been COJ:J:elated with Road RateJ: deflections (16).

The second geneJ:ation of measuJ:ement devices the

vibxatoxy and Cox) impact testexs. Included in this gJ:oup axe the

Dynaflect, the Road RateJ:, the WES 72.6- and 40. 1-kN ( 16- and

9-kip) vibJ:atoJ:s, and the Shell 18.1-kN (4-kipl vibxatoJ: (8). In

gener:al, vibxatoJ:y testeJ:s induce a steady-state sinusoidal

vibxation in the pavement with a dynamic foxce geneJ:atox. The

magnitude of the dynamic foJ:ce and the means by which the foJ:ce is

genexated axe the pJ:imaxy diffexences among vibxatoJ:y testexs. An

impact device Cthe falling-weight deflectometeJ:) measures the

sur: face deflection resulting when a known weight is dropped a

specified distance (8).

Deflection bowls have been used to study pavement response

characteristics C3, 5.

theoxetical

consideJ:ed.

anal~rses

Factoxs

6. 1 0 • 11. 2 5) . Both empirical and

utilizing elastic theory have been

considexed in the evaluation of the

deflection bowls, such as defined by dynaflect data, are maximum

deflection, spreadability, suJ:face cuJ:vatuxe index, base cuJ:vatuJ:e

index. and the fifth sensoJ: deflection. Spreadability, defined as

the average deflection for all five Dynaflect sensors expressed as

a percentage of the maximum deflection. is a measure of

ability of the pavement str:uctur:e to distribute the load.

the

The

surface curvature index is the diffexence in deflections at the

first and second sensor:s. It is a measure of the condition of the

upper layers of tlte pavement str:uctur:e. Tl1e base curvature index

is the di£fe~ence between the deflections at the fourth a11d fiftlt

4

sensors and is meant to be an indication of the condition of the

lower layers. Normally, the maximum deflection is an indicator of

the condition of the bound layers while the deflection at the

fifth sensor is an indicator of subgrade adequacy C3, 5' 6 ' 1 0 '

11, 25l.

The falling-weight deflectometer also has been used to study

pavement behavior. P:roceduzes have been developed which

incorporate falling-weight data into overlay designs for flexible

paveMents (4).

Kentucky research has used Road Rater deflections since 1972.

Other organizations have used Road Rater deflections

the structural condition of flexible pavements (1, 9l.

to evaluate

Procedures

presented in this paper have evolved from several earlier studies

( 1 4 ' 1 5 ' 1 8 ' 1 9 ' 2 2 ' 2 3) and represent those currently use~ in

Kentucky. Research is continuing to further refine the evaluation

process.

5

SIMULATION OF ROAD RATER DEFLECTIONS

Characteristics of the Road Rater

The testing head of the Kentucky Road Rater consists of a

vibrating mass weighing 72.6 kg (160 pounds) which impulses the

pavement. The test head is lowered to the pavement until the

hydraulic pressure of 4.82 MPa (700 psi) produces a static load of

7.428 kN (1,670 pounds). The mass is vibrated using preselected

frequencies of 10, 20, 25, and 40 H:::;. The forced motion of the

pavement is measured by velocity sensors normally located at 0 mm

CO feet), 305 mm (1 foot), 610 mm (2 feetl, and 914 mm (3 feet)

from the center of the test head.

Vibrating the mass at a frequency of 25 H:::; and an amplitude

of 1.524 mm (0.06 inchl results in a peak-to-peak dynamic force of

2.668 kN (600 pounds).

frequency and amplitude,

Once the dynamic force is set for a g~ven

the other preset frequencies will vary

the amplitude

remains fixed.

of the vibrating mass such that the dynamic force

The composite loading consists of a dynamic force

of 2.668 kN (600 pounds) amplitude oscillating about the static

load of 7.428 kN (1,670 pounds).

Superposition Principles

The Road Rater loading is transmitted to the pavement by two

'feet' symmetrically located on either side of a beam extending

ahead and carrying the sensors. Superpositioniilg is applicable

provided the defo:::mations are small and do not substantially

affect tl1e action of external forces. A linear relationship

between displacement and external force must exist or be assumed

( 2 4) . Applying superposition principles to the Road

7

Rater, the deflection resulting from the load applied to one

'foot' is added to the deflection due to the load applied by the

other 'foot'. For the symmetrical conditions of the Road Rater,

deflection calculations only need be made for one 'foot' and the

radii corresponding to each sensor location.

The dynamic loading (sine wave) of the Road Rater can be

approximated by a square wave such that its amplitude is 1/ 2

times the amplitude of the sine wave. The maximum and minimum

loadings of the square wave are 8.37 kK (1,882 pounds) and 6.49 kK

(1,458 pounds). From symmetry, the loads on each 'foot' of the·

test head are equal to 4.186 kK (941 pounds) and 3.24~ kK (729

pounds). The dynamic deflection is defined by DCtotall = CDC4.19l

- D ( 3 • 2 4 l l l{ 2. in which D ( 4. 1 9 l and DC3.24l represent the

deflections calculated by the Chevron computer program for the

maximum and minimum loading conditions on one 'foot'.

Input Parameters for the Chevron Computer Program

In addition to load, required inputs to the ChevEon program

include a co11tact pzessure corresponding to the load; the number

of layers; and tl1e tl1ickness, Young's modulus, and Poissot1's ratio

for each layer. The contact pressure of the maximum and minintim

loads are varied to maintain a constant area ( 102 by 178 mm (4 by

7 inches)) for each 'foot'. The following constants were used to

calcul~te simulated Road Rater deflections (22):

Poisson's Ratio:

8

Asphaltic Concrete-- f'- = 0.40

Granular Base --)A = 0. 40

Sub grade -- fl = 0. 45

'

Load= 4.186 kH (941 pounds): Contact P:r:essure = 0.231 MPa

(33.5 psil

Load= 3.243 kH (729 pounds): Contact Pressure = 0. 1 8 3 MPa

( 2 6 . 5 psil

A matrix of asphaltic concrete (A C l thicknesses and moduli,

dense-graded aggregate (DGAl thicknesses, and the constants

indicated above were used as input. Simulated deflections were

calculated using elastic theory; these deflections were used to

develop theoretical relationships presented in this paper ( 1 4 •

1 5 ) .

Moduli of granular bases (E2l are a function of the moduli of

the confining layers of asphaltic concrete CEll and subgrade CE3l.

The modulus of the crushed stone layer is estimated from the

relationship E2 = F X E3, in which there is an inverse linear

relationship between F and log E3. The ratio of the modulus of

the base to the modulus of the subgrade is equal to 2.8 at a

California bearing ratio (CBRl of 7 and is equal to 1.0 when E1

equals E3 (i.e., E1=E2=E3 the case of a Boussinesq semi-

infinite half-space) ( 2 2 ) . Subgrade moduli in psi may be

approximated by the product of the CBR and 1,500. This method of

normal design estimating base moduli appears adequate for

considerations up to a CBR of about 18 (2, 14, 27, 28).

Reference Conditions

The modulus of elasticity of asphaltic concrete va:r:ies as a

function of frequency of loading and temperature. Conditions for

the current Kentucky thickness design procedures and the method

for conducting Benkelman beam tests correspond to a modulus of

9

3.31 GPa (480 ksil at 0.5 Hz and a pavement temperature of 21.1 C

(70 f). The reference frequency for the Road Rater was selected

at 25Hz, and the corresponding asphaltic concrete modulus at 21.1

C (70 Fl is 3.27 GFa (1,200 ksil (19, 20, 211.

Because of the significant effects

of elasticity of asphaltic concretes,

of temperature on modulus

a system was developed to

adjust deflection measurements to a reference temperature and

modulus. The adjustment scheme used ratios of deflections at

refezence conditions to deflections resulting from arrayed

variables of layer thicknesses and moduli (14, 1 5' 1 6 ' 1 3' 2 0'

2 1 ) .

10

EVALUATION OF THE PAVEMENT STRUCTURE

Foundation (subg~adel stiffness is a facto~ affecting the

behavio~ of a pavement st~uctu~e. Va~iations in subgrade suppo~t

occur mainly as a result of variations in moisture contents and in

soil types. A significant dec~ease in subg~ade stiffness (o~

modulus of elasticity) will ~esult in a loss of ability to suppo~t

the pavement st~uctu~e adequately and will lead to increased

distress in the laye~s of the structu~e. Signs of distress

include rutting, inc~eased ~oughness, and c~acking C29l.

Estimates of subg~ade strength are necessary to evaluate

ove~all pavement conditions. A 'design' condition exists when

there is no loss of 'effective' thickness in any of the laye~s. A

knowledge of as-built (design) thicknesses of layers is necessary

before an evaluation of the pavement structu~e can be made. Those

thicknesses should be available from const~uction and (or l

maintenance records; cores also may be obtained to determine or

verify layer thicknesses. Generally, conditions involve

dete~ioration in the laye~s of the st~ucture. This means that tlte

individual laye~s are behaving similar to another combination of

layer thicknesses composed of new-quality mate~ials;

structu~e is behaving as an 'effective' structure.

that is. the

In such a

case1 it is necessary to estimate the 'effective' thicknesses of

the deteriorated structure.

11

DESCRIBING THE SHAPE OF THE DEFLECTION BOWL

The analysis of deflections involves the shape of the

deflection bowl (3, 5, 6, 10 - 12, 14, 15, 23- 26). The No.

projected deflection, an empirical evaluation of Road Rater

deflection data ( 1 4 - 1 6 ' 2 3) ' is obtained by extrapolating a

straight line through the deflection values of the No. 2 and No. 3

Sensot:s when log deflection is plotted as a function of the

arithmetic distance from the load head. The deflection at the

position corresponding to the No.

deflection (Figure 1J:

Sensor is the No.

No. 1 projected • exp[C2 log No. 2 deflection)

- Clog No. 3 deflection J] .

1 projected

The slope of the semi-log line (secant line), the difference in

magnitude between the No. projected and the No. Sensor

deflections, and the magnitude of all deflections are indicative

of the shape of the deflection bowl.

For a given pavement structure, asphaltic concrete modulus,

and subgrade modulus, there is a difference between the No.

projected and the No. Sensor deflections for theoretical

deflections (figure 1). Similarly, there is also a difference

between these values for field-measured deflections. No~mally,

the differences between the No. 1 projected deflection and the l!o.

1 Sensor deflection for both tl1eory and field measurements are tl1e

same. Slab dete~iot:ation is indicated w11en field measut:ements

indicate a No. Sensor deflection greater than the l!o.

projected deflection (Figure ZJ and the diffet:ence between these

values is greater than tl1e difference for theoretical deflections.

A foundation problem. or lack of supporting capability, may be

13

FEET 0

3 2

-r<l

'o SENSOR NUMBERS -I[) ><

15 'o (/)

4 0:::

><

LLJ (/) 1- LLJ LLJ J: ~ 5 20 (.)

:J z _J

~

~ NORMAL BEHAVIOR - 6 z 25 0

z 1-0 7

(.)

1- LLJ (.) 30

_J

LLJ 1.1.. _J 8 LLJ 1.1.. 0 LLJ 0 9

35

100 100 200 300 400 500 600

MILLIMETERS

Figu:re 1 . Deflection versus Distance from Load Head and

Determination of No. 1 P:rojected Deflection: Example

Difference between No. 1 Sensor: Deflection C Hll and No.

1 P:rojected Deflection ( 1 p ) fo:r Normal Pavement

Behavior: ( 1 4 ' 1 5) .

indicated by increased magnitudes of all field deflections and a

No. p:rojected deflection gr:eater than the No. Senso:r:

deflection (Figure 3). Also. the diffe:rence between the No.

pr:ojected deflection and the No. 1 Senso:r deflection for field

measurements should be greater than the difference for tl1eo~etical

deflections.

14

FEET

3or------------------.-------------------.2--~

-r<'l SENSOR NUMBERS -'o 10

)(

(f) 4

a::: LLJ t-LLJ :::?: 5 ::J _J

:::?: - 6

z IM 0 7 t-(.) w .....J 8 l.L.. LLJ 0 9

100

Figure 2.

15

20

WEAK AC 25

30

35

100 200 300 400 500 600

MILLIMETERS

Deflection versus Determination of No.

Distance from Load Head and

Difference between No. 1 Projected Deflection: Example

1 Sensor Deflection C1Ml and Mo. 1 Projected Deflection C IP) for a Pavement with a 1Jeak Asphaltic Conciete Layei C14, 15) .

. ~ plot of No. projected deflections versus No. 1 Sensoz:

deflections in log-log form may be used to identify variatioilS in

pavenent structure. The solid lines in Figure 4 show the

tl1eoretical relationship between No. 1 projected and No. 1 Sensor

deflections for a constant stJ:ucture and asphaltic concrete

modulus. Subgrade modulus varies along the line. Points about

the line represent field-measured deflections. The two dashed

'o )(

C/) w J: (.)

z -z 0 1-(.) w .....J l.L.. w 0

15

FEET 0

3 2

-ro -'o _. ll'l - 3 15

)( SENSOR NUMBERS --4 -en --0:: --w -1- NORMAL BEHAV~R- __...-; w :::2: -5 - 20 -::J --_J

:::2: - 6 25

z 0 FOUNDATION 1- SUPPORT PROBLEM (.) 30 w _J 8 l.J.. w 0 9 35

I p 100 100 200 300 400 500 600

MILLIMETERS

Figure 3. Deflection versus Distance from Load Head and Determination of No. 1 Projected Deflection: Example Difference between No. 1 Sensor Deflection ( 1M l and No. 1 Projected Deflection ( 1 p ) for a Pavement with a Foundation Support P:t:oblem ( 1 4 • 1 5) .

lines indicate the va:.:iation in position of the theoretical line

due to changes in the magnitudes of the deflections by ± one unit

(2.54 x 10- 4 mm or I:< 10-S inchl on the Road Rater meters and the

associated cllange in calculated No. 1 projected deflection. The

3one inside these lines represents a normal variation due to

reading the meters of the Road Rater.

16

'o )(

en w ::::c (.)

z .......

z 0 1-(.) w _J l.J.. w 0

ROAD RATER NO. I MEASURED DEFLECTION (INCHES)

101 ~4--~~6~-;8-.ilo~-_4 ______ ~2~---r---4r--.-;6~-T8-rl~o-_~ ______ _,2~---.--,

(/) 8 ~ w f- 6 w :::E ....J ....J 4 :::E

E 1 = 8.27 GPo ( 1,200,000 PSI l

172.7 mm AC ( 6.8" l

482.6 mm DGA ( 19.0")

~

(/) w ::r: u

2 z ~

z 0 f-

z 0

LANE NO.

OUTSIDE

INSIDE

10-3 ~

t; 2 w ....J u. w Cl

oi0-2

w f- 8 u w ..., 0 6 ~ 0...

ci z 4

WHEEL TRACK ..

WHEEL TRACK • TEST DATE 9/29/77

/ . /_ / . . /_ /

THEORY

FOUNDATION

SUPPORT

PROBLEM

// -!'/

/•/ • / / ZONE OF NORMAL VARIATION

/ . / /

/ / / ./

/ SLAB PROBLEM

8

6

4

2

....J u. w Cl

Cl w f-u w ..., 0 ~ 0...

ci z

~ w f-

~ w

10-4 < ~

!;;;: 2 ~

Cl < 0

8

6

~ 163~~----~----~--~~--~~~~.-------~--~--~--~~~~~4 10-3 2 4 6 8 10-2 2 4 6 8 10-1

ROAD RATER NO. MEASURED DEFLECTION (MILLIMETERS)

Figure 4. Relationship between Road Rater Deflection and Road Rater No. 1

Field Measurements Indicate a

Problem (14, 15).

No. 1 Projected Sensor Deflection; Foundatio!l S~ppo~t

Cl < 0 ~

17

ESTIMATING SUBGRADE STRENGTH

Knowing layeE thicknesses, Eelationships weEe developed (fEom

elastic theoEyl between theoEetical deflections and subgEade

moduli foE a constant (EefeEencel asphaltic concEete modulus of

elasticity CFiguEe 5). FoE a given pavement stEuctuEe, Road Rater

deflections adjusted to a constant (EefeEencel modulus of

asphaltic concEete and associated tempeEatuEe may be used as

input. FoE each field deflection, theEe is a coEresponding

predicted value of the subgEade modulus ( 14, 15, 23).

The methodology foE estimating subgrade stEength has evolved

thEough seveEal stages. Initially, the first three sensor

deflections weEe used to obtain thEBe estimates of the subgEade

modulus. The methodology was simplified so only the Mo. '

2 SensoE

deflection was used ( 1 4 ' 1 5 ' 2 3) • ~efinements in ~he

pEocedure utilize the Mo. 2 and Mo. 3 deflections to compute a Mo.

projected deflection (14 1 6 • 2 3) . The No. Sensor

deflections and Mo. 1 pEojectad deflections aEe then plotted and

compared to values predicted by elastic theoEy.

Interpretation of Deflection Data

Foundation DE Subgrade Problems When a foundation DE

subgrade problem exists, the deflection bowl is much 'broader' and

'flatte~' than would be theoretically expected, and the magnitudes

of all the measured deflections are greater than those predicted

by elastic theory CFiguEes 1 - 3) • Limited test data have

indicated that excessive moisture in the subgEade could result in

a measttred deflection bowl of this shape (9, 1 5. 2 3) . In

areas t..'he:!'e there were suspected problems with the subgrade and

19

10-l

8

6 en 0: w 4 1-w :2 ...J ...J 2 :2 ~

z 0 1- 10-2 (..)

w ...J 8

"'-w 6 Cl

0: w 1-

4 <{ 0:

Cl <{ 0 2 0:

-3 10

Figure 5.

E3, SU BGRA DE MODULUS OF ELASTICITY (PSI)

2 4 6 8 104 2 4 6 8 10 5

THEORETICAL RELATIONSHIP E1 : 8,27 GPa(l,200,000 PSI)

172,7 mm AC (6.8 INCHES) 2 482.6 mm DCA ( 19.0 INCHES)

NO.I PROJECTION 10 3

NO.I SENSOR

N0.2 SENSOR 8

N0.3 SENSOR 6

4

2

164

8

6

4

10 7 2 4 6 8 10 6 2 4 6 8 109

E3, SUBGRADE MODULUS OF ELASTICITY (PASCALS)

Theoretical Relationships: Road Rater versus Subgrade Modulus of Elasticity fo~ a COJlstant Stzucture and Asphaltic Conc~ete Modulus. (Note: This figure zepresents a minoz zevision in Figuze 1 of Reference 14 and Figure 6 of Reference 15.)

supporting (unbound) layers. tests indicated there was more

variability among the No. 2 and No. 3 deflections than among the

measured No. 1 deflections. In such a situation, either the No. 2

20

-en w :t: (..)

z ~

z 0 1-(..) w ...J "'-w Cl

0: w lei 0:

Cl <{ 0 0:

or No. 3 Sensor deflections, or both, and the associated No.

Projected deflections are not matching elastic theory

and 6 ) .

(Figures 3

Bound Layer Problems -- Conversely, if there is a deficiency

in the bound layer (asphaltic concrete), the deflection bowl bends

sharply about the point of application of the load (Figures 1 -

3) . The measured No. Sensor deflection is considerably greater

than its theoretical counterpart while the No. 2 and No. 3

deflections

<Figure 2).

very closely match predictions from elastic theory

This condition can also be illustrated by the plot of

No. projected deflection versus No. Sensor deflections (Figure

6) . Deflection bowls of this shape are usually obse:r:ved whez::e

there are visible signs of pavement distress such as cracking and

rutting (9, 14, 15, 23).

Quantifying Effective Behavior Measured Road Rater

deflection bowls can be evaluated using theoretical relationships.

Pavement behavior (or condition) can be given in terms o£ a

predicted subgrade modulus, effective layer thicknesses, and

effective moduli of the layers. The effective behavior may be

expressed as any combination of these variables which matches the

measured deflections. In this paper, pavement behavior is

exp:ressed in tez::ms of a predicted subgrade modulus and an

effective thickness of 'refez::ence' new-quality materials.

Obviously, some combinations of subgrade modulus, effective

thicknesses, and layer moduli az::e not acceptable. An e.xample of

an unacceptable representation of pavenent behavior would be an

extrenely low (weak)

effective thickness

predicted value of subgrade modulus and an

of the reference material greater <thicker)

21

NO.I PROJECTED DEFLECTION (MILLIMETERS)

4 6 8 10-2 2

E 3 ,SUBGRAOE MODULUS I PASCALS)

107 2 4 6 7 8 9 108 2 4 6

(f)

UJ 6 J: '-' z to- 1

4

z NO.I DEFLECT I ON VS E3 8

2 r- 6 '-' [EFFECTIVE AC THICKNESS UJ 2 NO.I DEFLECTION VS NO.I _, OR AC MODULI u. PROJECTED DEFLECTION~ "' 4 UJ "' 0 3 :r:

u

0:: 2qo iii ;;;

0 10-3 ZONE OF NORMAL , 5 = (f) VARIATION _..-: <n

z ~/9"9" 1000

7'' "' "' 8 :> "' 2 UJ -t" :~

..J z (J) :> "' 6 ,_.,. / 7' 0 2000 <n ' 0 u

" / y ~" "' . ' 0 'I' d """-t" / y

.,_o <n :r: ::;; ....

z ~ u (.) u to-2 4 "'"' <(, y 0- -" _,. =-Z- <t <t

0:: 0\::J 'C"" / ,,. <J) -w ~ .,_o / / <(,.,. :> <J) 8 r- / ..J "' q / ,. ... :> "' <t / / .., 0 z 0:: / / o"'

0 "' 6

/ " !,; 0 2

/ / <..' u :r:

<t / "'""

.. .... 1000 0 / ""' (.)

4

0:: / ~0 .. 2000

10-4

IQ-4

NO.I

Figu:t:e 6.

to3 2

2 4 6 8 to-3

PROJECTED DEFLECTION ( INCHES)

Combined Plot of No. P:t:ojected Deflection Illust:t:ating a Method fo:t: and Effective Behavio:t:.

4 6 8 104 2 4 E3,SUBGRAOE MODULUSIPSI)

Deflection ve:t:sus ve:t:sus Subg:t:ade Estimating Subg:t:ade

6 8 105

No. Modulus

St:t:ength

than the design o:t: as-constzucted laye:t: thicknesses. While this

combination of pa:t:amete:t:s might result in a deflection bowl which

resembles the measured bowl, it would not be logical for use in

designing ovezlays because a negative calculated overlay might

result. An alternative expression of pavement pezfozmance would

be an increased predicted subgrade modulus and a reduced effective

thickness of the reference material. Expressions of pavement

behavior using asp!1altic concrete moduli of elasticity othe:t: than

the :t:efe:t:ence upon which the flexible pavement design curves used

22

(J)

0:: UJ r-UJ ::; _, _, ::l!

(f)

z 0 i= '-' UJ _, u. UJ 0

0:: UJ r-<t 0::

0 <t 0 0:

in Kentucky are based also would not be usable. These same curves

are used in designing overlays (2, 14- 16, 19, 22, 23).

Determining the 'true' effective structure of an existing

pavement is an iterative process. If the quality of the asphaltic

concrete is held fixed at some reference value, there are a number

of combinations of predicted subgrade moduli and effective layer

thicknesses which will match the measured deflection bowl. Tl1e

magnitudes of the measured deflections and the constructed layer

thicknesses determine the reasonableness of the combinations. The

process involves selecting a subgrade modulus and iterative

effective thicknesses and comparing the resulting theoretical

deflection bowl to the measured bowl. If the theoretical bowl

does not match the measured deflection bowl, the subgrade modulus

and effective thicknesses are varied.

until a satisfactory match is obtained.

This process is continued

Figure 6 illustrates a procedure which usually eliminates the

need for a series of iterations. The methodology utilizes the

theoretical relationship of No. 1 projected deflections versus No.

Sensor deflections and the theoretical relationship between

subgrade modulus of elasticity and No. 1 Sensor deflections.

In Figure 6, the lines on the left represent a theoretical

relationship between No. 1 Sensor deflections and No. projected

deflections. The dashed lines represent normal operator vaEiation

in reading meter scales. The solid line on the right is the

theoretical relationship between Road Rater No. Sensor

deflections and subgrade moduli. Two different points are shown

in Figure 6. The "x's" are data points which would be suspected

of having problems in the bound layeEs (from the No. 1 deflection

23

Ve!:SUS No. projected deflection relationship). The "o's"

represent

problems.

points suspected of having foundation OJ:: subgrade

The "x" points (Figure 6l have a No. Sensor deflection

higher than would be predicted from the given values of the Nd. 2

and No. 3 deflections and the corresponding No. projected

deflections. Thus, it is necessary to adjust the deflection to

match the deflections at the No. 2 and No. 3 Senso!:s. The

adjusted No. deflection is then used to predict the subgrade

of Road Rater modulus to compare to the theoretical relationship

No. 1 deflection versus subgrade modulus. The point will plot

above the theoretical line, indicating behavior wealler than the

!:efe!:ence conditions. The behavior may be expressed either in

terms of reduced asphaltic concrete modulus o!: as a reduced

thickness of asphaltic concrete. For overlay designs, effective

behavior is more meaningful when expressed as a reduced thickness.

The "o" points (figure 6) have a No. 1 deflection lower than

expected from the measured deflections at the No. 2 and No. 3

the associated No. projected deflections. The Sensors and

deflection bowl is very 'broad' and 'flat' (F~gure 3) and

representative of a problem in the subgrade or supporting layers.

To rep!:esent the observed pavement performance in terms of a

predicted subgrade modulus and effective thickness of asphaltic

concrete of reference, new-quality material, it is necessary to

use the No.1 sensor deflection to predict the subgrade modulus.

The theoretical relationship of No. projected deflection versus

No.

No.

24

Sensor deflection is used ln combination witl1 tl1e measured

deflection to determi11e an adjusted No. deflection. The

adjusted value will have a greater magnitude than the measured Mo.

1 deflection and will be compatible with the measured Mo. 2 and

Mo. 3 deflections and the associated Mo. projected deflection.

When the predicted subgrade strength (based on the Mo. 1 Sensor

deflection) is plotted versus the adjusted Mo. deflection, the

expression of pavement behavior is in te:rms of a p:redicted

subg:rade st:rength and a :reduced thickness of new-quality material.

Analyses of field deflections indicated this p:rocedu:re will

p:roduce results which can be used as input into an overlay design

p:rocess.

ove:rlaying

Road

shows

Rate:r testing of pavements befo:re and after

that the ultimate behavior of the ove:rlaid

pavement is equal to that of a pavement having a total thickness

of new-quality material equal to the sum of the effective

thickness before ove:rlaying and the ove:rlay thickness ( 1 4 ' 1 5'

2 3) .

Subgrade moduli may be estimated using deflections measured

by any of the sensors singly or in combination, and these moduli

may vary slightly. These variations usually are not significant

because, for a constant asphaltic concrete modulus and any given

rneasu:red deflection bowl, there is a range of subgrade moduli and

asphaltic concrete thicknesses wltich are representative of the

measured deflections. If the measured deflection bowl and the

theoretical bowl were identical, the same subgrade moduli would be

predicted regardless of the way the deflections are manipulated.

Estimation of Effective Structure

The determination of the effective pavement structure is

illustrated b>' the :right side of Figure 6. If the pavement is

25

behaving as one having a thickness equal to or greater than the

theoretical or 'design' thickness of asphaltic concrete, the field

data will plot on the theoretical line. This also may be

eKpressed in terms of the modulus of the asphaltic concrete -- if

the pavement is behaving as one having a modulus of elasticity of

the asphaltic concrete equal to or stronger than that of the

reference material, the field data will plot on the theoretical

line. If the field data plot above the line, the pavement is

performing as one made of the reference materials which is thinner

than the design or theoretical thickness. Alternatively, the

pavement's performance could be given in terms of a pavement of

the design thickness but having a modulus of elasticity of the

asphaltic concrete weaker than the reference material.

When pavement behavior is eKpressed in terms of reduced layer

thid:nesses, all layers may be varied in any combination of

thicknesses of reference materials and a predicted subgrade

modulus that result in a deflection bowl which best matches the

Jne as ure.d deflection bowl. The present procedure, hot.<Jever,

maintains a constant crushed stone (DGAJ thickness and expresses

pavement behavior as a reduced thickness of asphaltic concrete at

the reference modulus. If this method is used, lines of reduced

thicknesses of asphaltic concrete can be superimposed onto the

' plot of subgrade modulus versus No. Sensor deflection. The

effective thickness may be interpolated from these lines (Figu:re

6) .

Statistical analyses can be applied to either the measured

No. Sensor deflections, the predicted subgrade moduli, or the

interpolated effective tl1icknesses. It is recommended tl1at any

26

zep~esentation of pave~ent behavior encompass 90 percent of the

data. Other investigators have selected similar levels (1, 5, 6l.

For example, If an effective structure is desired which

encompasses 90 percent of the deflection data, the :recommended

effective thicknesses a:re equal to the mean effective thickness

less the p:roduct of 1.2816 and the standa:rd deviation. Figu:re 7

illustrates

deviation.

the selection of the multiplie:r fo:r the standa:rd

Note that the multiplie:r 1.2816 cor:responds to an

90 % OF DATA L MEAN + 1.2816 CT

10 % OF DATA.::,. MEAN + 1.2816 CT

(SHADED AREA)

10 % OF OATA

-4 -3

figure 7.

10 "to 0 F DATA

1.2816 CT -+--

-2 -1 0 2 3

STANDARD DEVIATION

Illustration of 90th-Percentile Deflection:

Theoretically, 90 Percent of the ~easured Deflections

Will Be Less than the Mean Deflection plus 1.2816 Times

the Standard Deviation.

4

27

80-pe~cent cumulative dist~ibution but ~esults in a 90th-

pe~centile effective thickness because one tail of the no~mal

dist~ibution is not included (13, 17).

Example Analysis of Road Rater Data

Tables 1 and 2 and Figu~e 8 p~esent a set of Road Rate~

measu~ements and illust~ate the p~ocedu~e to evaluate the data.

This p~ocedu~e utilizes concepts discussed in this pape~ and

represent modifications in ea~lier procedures ( 14, 15, 23).

28

TABLE 1. ADJUSTED ROAD RATER DEFLECTION DATA AND PREDICTIONS OF SUBGRADE MODULUS

US 60, BOYD COUNTY, KENTUCKY EASTBOUND SHOULDER LANE STATION 399+50 to 425+68 TEST DATE: 9/27/77 CORE THICKNESS:

172.7 mm. (6.8 in.J Asphaltic Concrete 482.6 mm. ( 19.0 in.) Dense Graded Aggregate

ADJUSTMENT FACTOR = 0.905 (TO ADJUST TO 70 F MEAN PAVEMENT TEMPERATURE)

ADJUSTED MEASURED DEFLECTIONS MILLIMETERS

No. 0.00782 0.00759 0.00'183 0.00305 0.00391 0.00691 0.00574 0.00919 0.00919 0.00759

NOTE:

No. 2 0.00505 0. 00528 0.00345 0.00691 0.00254 0. 00460 0.00391 0.00691 0.00874 0.00620

No. 3 0. 00277 0.00300 0.00160 0.00345 0.00160 0. 00277 0.00231 0.00345 0.00460 0.00434

in. = 25.1~ mm psi= 6,894.757 Pa

No. 1 P 0.00927 0.00935 0.00739 0.01330 0.00396 0.00767 0.00665 0.01330 0.01660 0.00881

PREDICTED SU BGR.~DE ~IODULUS

rrP a

1 6 0 167 303 155 455 186 245 123 128 1 6 7

T.~BLE 2: CALCULATION OF EFFECTIVE (BEHAVIORAL) THICKNESS

US 60, BOYD COUHTY, KENTUCKY EASTBOUND SHOULDER LANE STATIOH 399+50 to 425+68 CORE THIC!;NESS: 172.7 mm. (6.8 in. J Asphaltic Conc:.:ete

(19.0 in.J Dense G:.:aded Agg:.:egate

TEST DATE: 482.6 mm.

9/29/77

1. Read the effective st:.:uctu:.:e fo:.: each data point f:.:om

the plot of deflection ve:.:sus subg:.:ade modulus. Dense G:.:aded Agg:.:egate thickness remains constant (482.6 mml.

Mean

EFFECTIVE ASPHALTIC CONCRETE THICKNESS MILLIMETERS

1 6 50 1 1 52 0 4 76.2

1 2 1 0 9 152.4 17 2 0 7 1 6 5 0 1 88.9 8 1 0 3

167.6

Standard Deviation 1 3 4 0 4 40.9

2. Mean Effective Structu:.:e 134.4 mm. Asphaltic Concrete 482.6 mm. Dense G:.:aded Aggregate

3. Effective St:.:uctu:.:e Encompassing 90 % of the Data

1.2816 K standard deviation= 1.2816 K 40.9 mm. = 52.4 mm. Asphaltic Conc:.:ete

Mean- (1.2816 x standard deviation) = 134.4 mm.- 52.4 mm. = 82.0 mm. Asphaltic Concrete

Effective St~uctuze

HOTE:

82.0 mm. Asphaltic Concrete 432.6 mm. Dense Graded Aggregate

1 in.= 25.4 mm.

29

<f)

w 6 ::t: u z

4 z 0 t-u w

2 _, "-w 0

a: 0 -3 <ll I 0 z w 8 <f)

6 0 z a: 4 w !:;: a:

0 2 .. 0 a:

104

NO.I PROJECTED DEFLECTION(MILLIMETERS) 4 6 8 10-2 2

E3 , SUSGRADE MODULUS I PASCALS)

2 4 6 7 8 9 10 8 2 4 6

US 60 BOYD CO. STATION 399 +50 TO 425 + 68 SHOULDER LANE TEST DATE 9/29/77 CORE THICKNESS: 172.7 mm (6.8 INCHESlAC

482.6mm 119.01NCHESlAC

NOTElCONVERSION FACTORS INCHES TO MILLIMETERS MULTIPLY BY 25-4

KSI TO PASCALS MULTIPLY BY 6.894757 x 10 6

NO.I DEFLECTION VS NO-I PROJECTED DEFLECTION -------..,Y

2

7

2000

in "' "' "' "' ::> "' _, z ::> ,_ 0 '-'"' 0 -w :; "'"' >-u u uz

"' ..:::

"' "' "' u z

"' "' ;;; ., "' "' ::> z _, "' ::>

0 u 0 'i: :; 1-

u u

"' "' 3

5 1000 --.}- 7~

2000 --..

4 6 8 104 2 4

E3,sUBGRADE MODULUS I PSI l

!0-1

8

6

4

2

IQ-2

8

6

4

10-4

NO.I 2

PROJECTED 4 6 8 I0-3

DEFLECTION (INCHES)

Figu~e 8.

30

Example Analysis of Road Rate~ Deflections: Subg~ade

Moduli P~edictions from Mo. 1 Deflections and Mo. 1

Projected Deflections; G~aph of Mo. 1 Deflections

ve~sus No. 1 Projected Deflections; and No. 1

Deflections ve~sus Subg~ade Moduli.

u; a: w t-w ::. :::; _, ::.

"' z 0 t-u w _, "-w 0

a: w !:;: a: 0 .. 0 a:

SUMMARY

The procedures for the evaluation of pavement performance and

condition p~esented in this paper utilize the concepts developed

and published in 1978 (14, 15, 2 3) . Since then, these concepts

and the associated procedure has been modified and simplified to

provide a more workable procedure.

A key to an adequate design of an overlay for any pavement

structure is to be able to determine reasonable values for design

parameters that represent the condition

The parameters considered in Kentucky's

of the eKisting pavement.

procedure include the in-

place subgrade modulus and the effective thickness of the existing

pavement structure at a specified reference modulus of elasticity

of the asphaltic concrete. The total thickness of an overlay is

equal

future

to the difference between

design level (based on

the thickness needed for some

tt:affic volumes and associated

equivalent axleloads and the in-place subgrade modulus (CBRll and

the effective thickness of the existing asphaltic concrete layers.

There is a need for continued research in this area as

highway maintenance becomes mo~e and more significant. As costs

continue to rise, the pressure to adequately assess the condition

of existing pavements increases.

31

ACKNOWLEDGEMENTS

Th~ conc~pts, data, and analys~s z~po~ted in this paper are a

result in pa~t of R~s~arch Study KYHPR-75-77, Development of a

Rational Ov~rlay Design Method for Pavements, and Research Study

KYHPR-70-49, Full-Depth Asphaltic Concrete Pavements, conducted as

a part of Wozk Program HPR-PL-1(15), Part II. funded in part by

the Fed~ral Highway Administration and by the Kentucky D~paztm~nt

of Transportation. The contents of the r~port r~fl~ct th~ vi~ws

of the authors who ar~ r~sponsible foz the facts and accuracy of

th~ data pz~sented. The contents do not nec~ssarily reflect th~

official v iet.Js oz polici~s of the Kentucky Department of

Tzansportation noz of the Federal Highway Administration. The

zeport do~s not constitute

z~gulation.

a standard, specification, oz

33

1 •

2.

3.

4.

5.

6.

7.

3.

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38

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to

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