TRANSPORTATION RESEARCH RECORD 1272

Extension of AASHTO Remaining-Life Methodology of Overlay Design

SAID M. EASA

An extension of the AASHTO remaining-life methodology of overlay design that achieves consistent results is presented. The extended methodology permits an existing pavement after an overlay to deteriorate between two extremes: deterioration like a new pavement (traditional approach) and like an existing pave­ment without overlay (AASHTO approach). The methodology involves refining the AASHTO pavement condition curves and developing weighted condition curves for an existing pavement after an overlay. A deterioration parameter is incorporated that provides both design flexibility and consistency. Two types of design consistency are achieved: overlay-related and existing pavement-related. Sensitivity of the structural capacity of the overl!!Y to failure serviceability , the minimum pavement condi­tion factor, and variations of the valid range of deterioration parameter with effective structural capacity are examined.

Overlay design procedures can be organized into three types: deflection procedures, analytical procedures, and effective­thickness procedures (1). The deflection procedures make use of nondestructive testing to estimate the in situ structural capacity of pavement (2-6). Deflection measurements are then used to determine the required overlay thickness based on empirical correlations with field performance. The ana­lytical procedures are quasi-mechanistic and rely on empirical correlations for establishing overlay design requirements (7-10). The effective-thickness procedures involve comparison of the existing pavement structure with a new pavement design for site-specific conditions and traffic (2, 11-13). If the requirements for new construction exceed the existing pave­ment structural capacity, the difference between the two tra­ditionally represents the required structural capacity of the overlay . This traditional approach implicitly assumes that existing pavement after overlay deteriorates like a new pavement, which is less conservative.

The effective-thickness procedure of the Asphalt Institute improves upon the traditional approach by considering a con­dition factor that accounts for the increased deterioration rate of an existing pavement after an overlay compared with a new pavement (2). This condition factor depends on the remaining life (or present serviceability index) of the existing pavement at the time of the overlay. The AASHTO effective-thickness procedure also improves upon the traditional approach by considering a remaining-life factor (12, 13). This factor more realistically depends on the remaining life of the existing pave­ment as well as the desired remaining life of the overlaid pavement.

Despite the strong rationale behind the AASHTO remaining­life factor, inconsistent results may be obtained when the

Department of Civil Engineering, Lakehead University, Thunder Bay, Ontario , Canada P7B 5El.

factor is applied to overlay design (14) . In addition, the factor implicitly assumes that the existing pavement after an overlay deteriorates like one without an overlay, which is too conser­vative. The purpose of this paper is to investigate the AASHTO remaining-life methodology and to present an extended meth­odology that (a) achieves consistent overlay designs and (b) permits existing pavements after overlay to deteriorate between the two extremes of the traditional and AASHTO approaches .

The following sections present a brief description of the AASHTO overlay design procedure, the extended remaining­life methodology , sensitivity analysis of key variables, and conclusions.

AASHTO OVERLAY DESIGN PROCEDURE

This section first presents fundamental principles related to the AASHTO overlay design procedure, followed by the overlay thickness design equation, which includes the remaining-life factor. Difficulties with the remaining-life factor, which forms the basis for the extended methodology, are then presented .

Fundamental Principles

The AASHTO revised procedure of overlay thickness de­sign (12) is based on the interrelationship between the serviceability-traffic and structural capacity-traffic concepts, which are shown in Figure 1. As traffic repetitions increase to x, the initial serviceability of the existing new pavement, P0 , is gradually reduced to its terminal serviceability, P,x. During that period, the initial structural capacity of the exist­ing pavement, SC0 , is reduced to its effective structural capac­ity, sex. If x repetitions correspond to the time an overlay is required, the new structural capacity to support overlay de­sign traffic y is SCY, as shown in Figure lb. After y repeti­tions, the terminal serviceability of the overlay is P,Y and the corresponding effective structural capacity of the overlaid pavement is SCr Note that N1x and NIY represent the total repe­titions required for the existing and the overlaid pavements, respectively, to reach failure serviceability P1.

The remaining lives of the existing pavement, RLn and the overlaid pavement, RLY, are given by

RLx = (N1x - x)IN1 ,

RLY = (Nfy - y)/Nfy

(1)

(2)

The damage to the existing and the overlaid pavements is defined as (1 - RLJ and (1 - RLy), respectively.

2

OVERLAY THICKNESS DESIGN

The AASHTO equation for overlay thickness design takes the following general form (12):

SC(;, = SC~ - FRL (SC,)" (3)

where

SC01 = required structural capacity of the overlay; scy = total structural capacity required for a new pave­

ment to support the estimated overlay traffic y over the existing subgrade conditions for a terminal ser­viceability, P,Y;

a.. Po

> I-...J

al Ptx <( w

Pty (.)

> a: w Pt en

L x 1 ..

Ntx •I

TRANSPORTATION RESEARCH RECORD 1272

FRL = remaining-life factor, which depends on the remain­ing life of the existing pavement and desired remaining life of the overlaid pavement at the end of the overlay traffic;

sex = effective structural capacity of the existing pave­ment at the time the overlay is placed; a.nd

n = a constant that depends upon the type of the exist­ing pavement and the overlay (for example, for a flexible overlay over a flexible pavement, n = 1).

The structural capacity for flexible-overlay design is repre­sented by the structural number (SN). For rigid-overlay design, the structural capacity is a function of the respective thickness of portland cement concrete (D). The following sections briefly

Overlaid Pavement

(a)

y . I

Nty

REPETITIONS, N

(.) en > l-o <( a.. <( (.) ...J <( a: ::::> l­o ::::> a: I-­en

x y

REPETITIONS, N

FIGURE 1 Serviceability-traffic and structural capacity-traffic relationships.

(b)

Easa

describe how the variables sey, sex, and FRL in Equation 3 are established.

Structural Capacity of Overlaid Pavement

The required structural capacity of the overlaid pavement, scy, is the total struccural capacity of a new pavement required to carry y repetition to a terminal serviceability P,,. using the same existing subgrade support. This is simply a new pave­ment design for either a flexible or rigid system. Once seY is established, the corresponding N1Y can be computed given the failure serviceability, P1 . (Note that SC0 and N1x of existing pavement can be computed similarly.)

Effective Structural Capacity of Existing Pavement

The AASHTO guide presents two nondestructive test (NDT) methods for determining effecti~(in situ) structural capacity of the pavement to be overlaid, sex. NDT Method 1 involves determination of the pavement layer moduli and NDT Method 2 involves determination of total structural capacity . Both methods utilize deflection data generated from an NDT device.

Approximate non-NDT methods are also presented in the guide for determining the effective structural capacity. One of these methods is based on the pavement condition factor, ex, which is defined as

(4)

If Cx and S00 are known, Equation 4 can be used to compute sex. The determination of Cx is described next as part of the remaining-life factor.

Remaining-Life Factor

The remaining-life factor, FRL> is defined as follows (12):

where

ex = condition factor of the existing pavement at the time the overlay is placed,

CY = condition factor of the overlaid pavement at its ter­minal serviceability, and

c;,. = condition factor of the existing pavement after over­lay at the time of overlay terminal serviceability.

A relationship between the pavement condition factor and remaining life is developed in the AASHTO guide using the AASHTO flexible pavement design equation for a variety of design conditions (P1 = 1.5 to 2.5). The relationship, based on a best-fit regression, is given by

c = RD.165 (6)

where C is the condition factor Cx or Cy, and R is the remain­ing life RLx or RLy.

3

The relationship of Equation 6 is shown by the dashed curve in Figure 2. This theoretical relationship indicates that at R = 0, C = 0. This implies that at failure the pavement has no effective structural capacity, which is not practical. For this reason, AASHTO implements a modified relationship that agrees reasonably well with the original relationship (Equation 6) for remaining-life values greater than about 5 to 10 percent and provides a finite structural capacity at and beyond failure. The modified relationship, shown by the solid line in Figure 2, is a sigmoidal function given by

C = 1 - 0. 7 exp [ - (R + O.S5)2] (7)

A few comments on the modified relationship of Equation 7 are worthy of note. First, the relationship provides a finite condition factor at failure, C = 0.66. This implies that the structural capacity of pavement at failure is two-thirds of its original capacity. This is a reasonable value because the pave­ment does provide some support capacity at failure, perhaps equivalent to a granular base. Second, beyond failure (R < 0) the condition factor of existing pavement decreases until it reaches an absolute minimum value, Cmin = 0.3. This value is considered realistic because if an overlay is placed at failure (R = 0) and existing pavement were to deteriorate like a new pavement, the condition factor would be 0.44 (square of 0.66). Third, the pavement life beyond failure (R < 0) is designated by a negative value. This indicates that the life of existing pavement, from original construction to failure serviceability, has been reached. Therefore, the life beyond failure ser­viceability that is used to determine the condition factor of existing pavement while under an overlay is considered negative .

The variables Cx and Cy for calculating the remaining life factor in Equation 5 are computed using Equation 7 by sub­stituting RLX and RLy for R. c~x is also computed using Equa­tion 7 by substituting RLyx for R. RLyx is defined as the remaining life of existing pavement after overlay, which is the life between overlay terminal serviceability and failure serviceability of the existing pavement. RLyx is given by

(Sa)

(Sb)

where dy is the damage to the overlaid pavement, which equals (1 - RLY). As noted, when the damage to the overlaid pavement is greater than the remaining life of the existing pavement (dy > RLx), RLyx of Equation Sa will be negative. This indicates that terminal serviceability of the overlaid pave­ment occurs beyond failure serviceability of the existing pave­ment. Figure 3, adapted from AASHTO (12), shows the remaining-life factor for various values of RLx and RLy, with the condition factors computed using Equation 7 (except for R < -0.S5, where C is set equal to 0.3).

DIFFICULTIES WITH REMAINING-LIFE FACTOR

The main difficulty of the remaining-life factor is that it may produce inconsistent results for the required structural capac­ity of overlay in Equation 3. This has been pointed out by

0

a: 0 .__ 0 <( u.. z 0 E Cl z 0 0

1.0

0.8

0.6

0.4

0.2

0.0

~ \

C=Ro.1ss/\ (original) ' ' \

I I I

C = 1 - .7e -(R+.85)•

-------------------------------· ---------------------- --

' I I I

I I

1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0

REMAINING LIFE, R

FIGURE 2 Original and modified AASHTO relationships of condition factor and remaining life.

1.0

.....J a:

u. 0.9

a: 0 .__ 0.8 0 <( u.. w 0.7 u.. .....J C) z 0.6 z < :; 0.5 w a:

0.4

1.0 0.8 0.6 0.4 0.2 0

REMAINING LIFE OF OVERLAID PAVEMENT, Rly

FIGURE 3 AASHTO remaining-life factor.

Easa

Elliott, who examined the variations of the required structural number of the (flexible) overlay as the overlay terminal ser­viceability Pry varied (14). Pry ranged from 1.5 to 3 .5, and FRL

was determined from Figure 3 for different values of RLx. Elliott found that for a certain range of overlay terminal ser­viceabilities, the required overlay structural number decreased as the terminal serviceability increased. This trend, which of course is not logical, was critical to the author's thinking in conducting the research for this paper.

A great deal of time was expended in investigating the remaining-life methodology. The remaining-life factor in Equation 5 was fundamentally correct. The difficulty lay in the way the condition factor for the existing pavement after overlay, C'yx, was assumed to change with remaining life. The relationship of Equation 7 (for R ?: 0) definitely represents the condition factor of the existing pavement (without over­lay) or the overlaid pavement. For negative remaining lives (R < 0), it can be argued that Equation 7 represents the condition factor of the existing pavement without overlay. This is true because the condition factor curve for R < 0 is a smooth continuation of that for R ?: 0, as noted in Figure 2.

In computing the AASHTO remaining-life factor, the rela­tionship of Equation 7 is also used to estimate the condition factor of the existing pavement after overlay, c;x. This implies that the existing pavement after an overlay deteriorates like an existing pavement without an overlay, which is too conser­vative. For example, for RLx = 0.6 and RLY = 0.6, RLyx = 0.2 and, as noted in Figure 2, the curve representing the condition factor of the existing or the overlaid pavement is used to estimate the condition factor of the existing pavement after an overlay.

Excluding remaining-life considerations in overlay design (traditional approach) is not realistic because this implies that the existing pavement after overlay deteriorates like a new pavement, which is less conservative. Thus, the traditional and AASHTO approaches represent two design extremes. The following section presents an extension of the AASHTO remaining-life methodology that allows the existing pavement after an overlay to deteriorate between the above two extremes so that consistent overlay designs are achieved.

EXTENDED REMAINING-LIFE METHODOLOGY

The extension of the AASHTO remaining-life methodology mainly involves developing weighted condition curves for the existing pavement after an overlay and establishing consisten­cy requirements for overlay design. Before a description of these elements, a refinement of the AASHTO pavement condition curve (Equation 7) is presented.

Refined AASHTO Pavement Condition Curve

The modified AASHTO relationship of Equation 7 exhibits two undesirable features (see Figure 2). First, the resulting curve does not give a condition factor equal to 1 when the remaining life equals 1 (C = 0.977 when R = 1). As a result, the remaining-life factor of Equation 5 is sometimes greater than 1. This is the reason the various curves for RLx in Figure 3 do not meet at the point FRL = 1, RLy = 1, as they should.

5

Second, for negative remaining lives ( - 0.85 to -1.0) the condition factor increases rather than decreases. However, this can be approximately overcome by setting C = 0.3 in that range, as was done in establishing the AASHTO remaining-life factor of Figure 3.

Several mathematical functions were examined, but no sin­gle function that eliminated the above undesirable features and at the same time provided a good fit to AASHTO data was found. For example, the following S-shaped function was tried and proven unsatisfactory:

C = 1 - a exp { -(b/(1 - R)]c} ls Rs -1 (9)

This function fitted AASHTO data well with parameters a = 0.9, b = 0.98, and c = 1.17, but provided an unrealist­ically large value for the minimum condition factor ( Cm;n = 0.42 at R = -1) . This value is unrealistic because it is too close to the condition factor of the existing pavement if it were to deteriorate like a new pavement after an overlay is placed at failure serviceability ( C = 0.44).

Therefore, it was decided to model the deterioration of the existing pavement by two functions: one for the regime before failure serviceability (R ?: 0) and the other for the regime after failure serviceability (R s 0). The two functions are established so that they have the same intercept and first derivative at their connecting point R = 0, as shown by the solid curve of Figure 4.

For R s 0, the AASHTO sigmoidal function is used with a restriction. That is,

C=l-0.7exp(-(R+0.85)2] -0.85sRsO (lOa)

C = 0.3 Rs - 0.85 (lOb)

For R ?: 0, a second-degree polynomial was approximately fitted to the data used in establishing the original AASHTO best-fit relationship of Equation 6. The polynomial is given by

C = 0.66 + 0.58R - 0.24R2 R?: 0 (11)

A comparison between the condition factors of the AASHTO best-fit relationship in Equation 6 and the polynomial of Equation 11 is given in Table 1. As noted, the results are quite close except for very small values of R, where the curve has a finite structural capacity at failure. It can also be verified that Equations lOa and 11 have the same intercept and first derivative at R = 0 (0.66 and 0.58, respectively). The inter­cept 0.66 is the same as that of the modified AASHTO relationship.

It is worthy of note that the refined (two-function) pave­ment condition curve can be easily modified for other values of the minimum condition factor than the assumed value of 0.3. This is especially useful for conducting a sensitivity analysis for this variable.

Weighted Pavement Condition Curves

As previously indicated, the solid curve in Figure 4 represents the condition factor of an existing pavement without an over­lay. If an existing pavement after an overlay were to deteri-

6

TABLE 1 COMPARISON OF ORIGINAL AASHTO RELATION WITH QUADRATIC POLYNOMIAL

Remaining Condition Fac tor. C Life, R Original AASHTO Quadratic Polynomial

1.0 1.000 1.000 0.9 0.983 0.988 0.8 0.964 0.970 0.7 0.943 0.948 0.6 0.919 0.922 o.s 0.892 0.890 0 . 4 0.860 0.854 0 . 3 0.820 0.812 0.2 0.767 0. 766 0 .1 0.684 0.716 o.o o.ooo 0.660

orate like one without an overlay, then the solid curve would represent this extreme. On the other hand , if the existing pavement were to deteriorate like a new pavement, the dete­rioration curve would depend on the pavement condition at the time of the overlay. Deterioration curves representing this extreme are shown in Figure 4 for different values of RLx.

1.0

0.8

TRANSPORTA TJON RESEARCH RECORD 1272

Clearly , the actual deterioration of an existing pavement after an overlay should lie between these two extremes.

The extreme deterioration curves for RLx = 0.4 are mag­nified in Figure 5. For a given RLy, the product CxCy repre­sents the condition factor of existing pavement after overlay if it were to deteriorate like a new pavement. c;x represents its deterioration if it were to deteriorate like an existing pave­ment \vithcut cvcduy. Let the actuat condit~11 factu1 ~ txisi­

ing pavement after overlay be denoted by Cyx· Then Cyx can be expressed as a weighted function of c;x and cxcy by

(12)

where A is the parameter that controls the deterioration of existing pavement after overlay (varies from 0 to 1). A = 1 indicates deterioration like an existing pavement without overlay and A = 0 indicates deteriorations like a new pavement. An average deterioration between these extremes is obtained when A = 0.5 . Pavement condition curves for various values of A. are shown in Figure 5. The remaining-life factor of Equation 5 can now be written as

(13)

(.)

ci 0 I­(.) <( LL

C = 0.66 + 0.58R - 0.24R2

z 0 ~ c z 0 (.)

0.6

0.4

0.2

o.o

1.0 0.8 0.6 0.4

C = 1 - .7e-(R+.85)2

0.2 0.0 -0.2 -0.4 -0.6 -0.8

REMAINING LIFE, R

FIGURE 4 Refined AASHTO condition curve (with remaining life) and condition curves (without remaining life).

-1.0

Easa

where Cyx is given by Equation 12. For A. = 0, FRL = 1 (traditional approach) and for A. = 1, Equation 13 reduces to Equation 5 (AASHTO approach). For intermediate values of A., the remaining-life factor would be greater than that of AASHTO. Figure 6 shows the remaining-life factor for X. = 0.5. The trend for FRL is similar to that of AASHTO (Figure 3) except that the curves for different RLx correctly meet at one point.

Overlay-Related Consistency

Overlay-related consistency implies that as the overlay ter­minal serviceability increases, the required structural capacity

1.0

0.9

0.8

0.7

(.) 0.6

ci 0 I-(.) c( u. 0.5 z 0 j:: Ci z 0.4 0 (.)

0.3

0.2

0.1

0.0

0.4

(1.0)

0.3

(0.9)

0.2

(0.8)

0.1 0.0

(0.7) (0.6)

7

of the overlay increases (for a given remaining life of existing pavement). It is necessary to determine the valid range of X. that achieves this consistency.

Consider the flexible overlay design example of Elliott (14) in which overlay design traffic y = 5 million equivalent single­axle loads (ESAL~and the effective structural number of existing pavement SNx = 4.5. The remaining life of the exist­ing pavement RLx = 0. The total structural number, SNr, and the remaining life of the overlay, RLr, were computed using the AASHTO design equation (12) for overlay terminal serviceability ranging from 1.5 to 3.5. Other data (which are also used in later examples) include an initial serviceability of 4.2, a failure serviceability of 1.5, reliability of 50 percent, and subgrade resilient modules of 3,000 psi. The remaining-

-0.1

(0.5)

-0.2

(0.4)

-0.3

(0.3)

Aly

-0.4

(0.2)

-0.5

(0.1)

-0.6

(0.0)

REMAINING LIFE, A (Aly)

FIGURE 5 Weighted pavement condition curves (RLx = 0.4).

8

life factor was computed using Equation 13 for A ranging from 0 to 1. The required structural number of overlay SN0, was computed using Equation 3 (n = 1). The results are shown in Table 2 and graphically in Figure 7.

It is clear that the results are inconsistent for A ~ 0.6, as indicated in the table by the values enclosed by dashed lines. This is also indicated in Figure 7 by the negative slopes of the

overlay structural number decreases as overlay terminal ser­viceability increases, which is not logical. The curve for A = 1 is similar to the curve obtained by Elliott (14) and corre­sponds to AASHTO remaining life methodology. As noted , the negative slope decreases as A decreases. For A ::s 0.5, there is no negative slope and the results are consistent. The curve for A = 0 (FRL = 1) is always strictly increasing. This is because the required structural number in this case is the difference between SNY, whi~is strictly increasing, and the effective structural number, SNx, which is constant.

Determination of the specific value of A (within the valid range) to be used in design is largely a matter of judgment. As more field data and experience are accumulated, the user agency should be able to select the value of deterioration

1.0 1.0

....I 0.9 a:

u. 0: 0 I-(..) c( u. w u. ::::i (!) z z < 0.8 ::? w 0:

0.7

0.0 0.1 0.2 0.3 0.4

TRANSPORTATION RESEA RCH RECORD 1272

parameter most appropriate to its specific conditions and requirements .

Existing Pavement-Related Consistency

Existing pavement-related consistency implies that as the remainin_g life of the existing pavement decreases, the required overlay structural capacity increases (for a given overlay terminal serviceability or remaining life). This can be exam­ined mathematically by differentiating both sides of Equation 3 with respect to RLx. Letting n = 1 for simplicity and substituting for sex and FRL from Equations 4 and 5'

(dSCo/dRLx) = -(SCc/Cy)[A(dC;)dRLJ

+ (1 - A) (dCx/dRLJ] (14)

Note that SC0 and Cr are constants. Cx is given by Equation 11 and c;x is given by Equation 10 or 11 depending on whether RLyx is negative or positive, respectively. The first derivatives in brackets are always positive (except as indicated below). Therefore, the right-hand side of Equation 13 is always neg-

0.5 0.6 0.7 0.8 0.9 1.0

REMAINING LIFE OF OVERLAY, RLy

FIGURE 6 Remaining-life factor of extended methodology (>. = 0.5).

TABLE 2 VALID RANGE OF A FOR OVERLAY-RELATED CONSISTENCY

Re uired Structural Number of Over la for ). equal to p SN RL 1.0 o. o.8 0.7 o.6 0. 5 0 .4 0.3 0.2

ty y y

1.50 4.46 o.oo 1.38 1. 24 1.09 0.95 0.81 o.67 o.53 0.39 0.25 1. 7.5 4.56 0.16 1.82 1.65 1.47 1.30 1.12 0.94 o. 77 0.59 0.42 2.00 4.69 0.3 2 2.04 1.85 1.67 1.48 1.30 1.12 o.93 0.75 o. 56 2.25 4 . 84 0 .47 i-c.-9-9---1-.ay---1~66--; 1. so 1.33 1.17 1.00 0.84 0.67

I L.---------- - ----2.50 5.03 0.61 I 1.85 l, 72 1.58 1.45 1.32 1.19 1.06 0.93 0.80

5.26 o. 73 I r- - ----

1. 25 1.15 1.06 1.96 2.75 I 1. 72 1. 72 1.53 1.43 I 1.34 0.83

I ~--------·--------'

1. 39 1. 33 1. 27 1. 21 3.00 5.59 L_1...:JJ ____ !_._6] __ _J 1.57 1.51 1.45 3.25 6.02 0.91 1.86 1.83 1. 79 1. 75 1. 72 1. 69 1. 66 1. 62 1.60 3.50 6.64 0.96 2.29 2.28 2.26 2.25 2.23 2.22 2.20 2 .19 2 .17

(y = 5 million ESAL, SNX = 4.5, RL = 0) x

0 z en > <( __J

a: w > 0 LL 0 a: w al ~ :::::> z __J

<( a: :::::> ..... 0 :::::> a: ..... en 0 w a: :::::> 0 w a:

2.8

2.4

2.0

1.6

1.2

0.8

0.4

1.5 (0.0)

2.0 (0.32)

2.5 (0.61)

Asphalt~ Institute

B ,

,/

,.,,'' ,,

/ ,/

,/

Without Remaining Life (traditional)

,,,,,,''

A,,'' /

3.0 (0.83)

TERMINAL SERVICEABILITY OF OVERLAY, Pty (Aly)

FIGURE 7 Valid range of A for RLx = 0 (y = 5 million ESALs, SNx = 4.5).

O. l o . o

0.11 0.00 0.24 0 .06 0.38 0 .19 0.51 0 .34 0.67 0.53 0.86 o . 77 1.15 1.09 1.56 1.52 2.16 2 -14

10

ative. This implies that as RLx increases, SC01 decreases, which is the correct trend.

For A. = 1, the right-hand side of Equation 13 is a function of only the first derivative of c;x. This first derivative equals zero for RLx ~ 0.15 and some value of RLY ~ 0.15. For example, for RLy = 0, the required structural capacity of the overlay would be the same for any value of RLx ~ 0.15, which is not reasonable. Under these cucumstances, a vaiue of II. < 1 should be used. Figure 8 shows the above points for P 'Y = 1.5. It is noted that the pavement condition curves for small values of A. (deteriorates like a new pavement) exhibit an increasing rate of deterioration and therefore the marginal overlay structural capacity increases, and vice versa for large values of A. . This is a reasonable trend that clearly would have implications on the life-cycle cost analysis.

Comparison with Asphalt Institute Procedure

The Asphalt Institute effective-thickness procedure of overlay design (2) accounts for deterioration of an existing pavement after an overlay, but in a way different from that of AASHTO. The overlay thickness is the difference between the thickness required for a new pavement to support the future overlay traffic and the effective thickness of the existing pavement. The effective thickness is computed by multiplying the actual thickness by a conversion factor, which takes into account the

TRANSPORTATION RESEARCH RECORD 1272

deterioration of the existing pavement after an overlay, and an equivalency factor. Two linear curves between the con­version factor and present serviceability index are presented. Curve A assumes that the existing pavement after an overlay deteriorates at a reduced rate relative to that before an over­lay. Curve B assumes the deterioration rate to be about the same as the rate before the overlay (somewhat similar to AASHTO). Uniike the AASHTO methodoiogy, the Asphah Institute conversion factor depends only on the present ser­viceability of the existing pavement; the remaining life of the overlaid pavement is not considered.

The conversion factor was used instead of the remaining­life factor to compute the required structural number of the overlay for the previous examples. The present serviceability of the existing pavement (required for determining the con­version factor) was computed for various values of RLx using the AASHTO design equation. The effective thickness of the existing pavement was computed assuming that it is a full­depth asphalt concrete. The results are shown by dashed curves in Figures 7 and 8. The upper line corresponds to Curve B of the conversion factor, and the lower line corresponds to Curve A.

The conversion factor, which does not depend on overlay terminal serviceability, is constant in Figure 7. Consequently, the dashed curves are parallel to the curve for A. = 0 (without remaining life). It is noted that the required structural number of the valid range of A. is less than that of the Asphalt Institute

2.6 ------------------------------0 z

en ' > r-~---­<( ..J 2.2 a: w > 0 LL 0 1.8 a: w ID ~ ~ z 1.4 ..J <( a: ~ .,__ () ~ a: .,__ en c w a: ~ 0 w a:

1.0

0.6

0.0 0.2

Without Remaining Life (traditional)

0.4 0.6 0.8

REMAINING LIFE OF EXISTING PAVEMENT, RLx

1.0

FIGURE 8 Variations of structural number of overlay with remaining life of existing pavement for P 1y = 1.5 (y = 4 million ESALs, SN0 = 4).

Easa

for large values of overlay terminal serviceability. This is expected because, in the extended remaining-life methodol­ogy, an existing pavement after an overlay shows less dete­rioration. For Pry = 1.5 in Figure 8, where the effect of overlay terminal serviceability is eliminated, the results show that the Asphalt Institute procedure is comparable with the average design between the extreme deterioration curves.

SENSITIVITY ANALYSIS

This section examines the sensitivity of the required structural capacity of the overlay to the minimum condition factor (which was assumed to be 0.3 in the remaining-life methodology) and to the failure serviceability. In addition, variations of the valid range of pavement deterioration rate to effective structural capacity are examined.

Minimum Condition Factor

The use of different values of Cmin requires determining the respective parameters of Equations 9 and 10. Let cx, !), and Cmin denote the values 0.7, 0.85, and 0.3 in Equation 9, and a0 , a1 , and a2 denote the constants of Equation 10, respec­tively. These parameters were determined for values of Cmin ranging from 0.10 to 0.35, so that the polynomial and sig­moidal functions have the same intercept and first derivative at R = 0. A summary of these parameters is given in Table 3 (the polynomial also provides a close fit to the AASHTO data). The condition factor of the existing pavement at failure (intercept) remains close to the original value corresponding to cmin = 0.3.

The sensitivity of the required structural number of the overlay to Cmin (for A = 0.5) is shown in Figure 9. As noted, SN01 is quite insensitive to cmin for large values of RLX and somewhat sensitive for small values of this variable. For RLx = 0 the difference between SN01 for Cmin of 0.2 and 0.3 is 6 percent (for A = 1, the difference is 8 percent).

Failure Serviceability

For a given overlay design problem, variations of failure ser­viceability affect only the remaining life of the overlay, RLY,

11

and consequently the remaining-life factor. The required structural number of the overlay was computed for failure serviceability values of 1.5, 2.0, and 2.5; a remaining life of the existing pavement of 0.2; and different values of P,Y and A. The results are shown in Figure 10. The required structural number of the overlay appears to be sensitive to failure ser­viceability for intermediate values of Pry and large values of A. For example, for Pry = 3 and A = 1, an increase of 0.5 in the failure serviceability recommended in the AASHTO guide (P1 = 2) results in a 13 percent increase in SN01. When the remaining life of the existing pavement and the overlay ter­minal serviceability are large (or the deterioration parameter is small), the selection of failure serviceability would not be critical.

Valid Range of Deterioration Parameter

The variation of the valid range of deterioration rate with effective structural number is shown in Figure 11 for y = 5 million ESALs and RLx = 0. For SNx = 4.5, the valid range of X. is 0.5 or less. This value of SNx is used previously in the example illustrating overlay-related consistency .~s noted, the valid range increases as SNx decreases. For SNx = 2.5, the entire range of X. provides consistent design. It is inter­esting to note that the large effective structural capacity of existing pavement tends to make the pavement deteriorate more like a new pavement.

SUMMARY AND CONCLUSIONS

The AASHTO remaining-life methodology for overlay design assumes that the existing pavement after overlay deteriorates like one without an overlay. As a result of this assumption, the methodology may produce inconsistent results. This paper extends this methodology by developing weighted condition curves for an existing pavement after an overlay. With the appropriate selection of this curve, consistent overlay designs can be achieved. The extended methodology utilizes the AASHTO condition curve for the existing pavement that con­siders remaining life. This curve was refined to achieve greater accuracy and to permit the conduct of sensitivity analysis for

TABLE 3 VARIATION OF PARAMETER VALUES AND CHARACTERISTICS WITH MINIMUM CONDITION FACTOR

Minimum Polynomial Sigmoidal Condition Factor,

cm in ao al a2 C at Slope C at Q 8 C at Slope R=O at R=O R=0.5 R=O at R=O

0.35 0.67 o. 54 -0.21 0.67 o.54 0.89 0.65 0.825 0.67 0.54 0.30 0.66 o. 58 -0.24 0.66 o.58 0.89 o. 70 0.850 0.66 0.58 0.25 0.65 0.61 -0.26 0.65 0.61 0.89 0.75 0.875 0.65 0.61 0.20 o.64 0.64 -0.28 o. 64 0.64 0.89 0.80 0.900 0.64 0.64 0 .15 0.64 0.67 -0.31 0.64 0.67 0.90 0.85 0.920 0.64 0.67 0.10 0.63 o. 70 -0.33 0.63 o. 70 0.90 0.90 0.940 0.63 o. 70

12

the minimum condition factor. The following are the main conclusions of the study:

1. The extended AASHTO methodology provides flexibil­ity for designing overlays between the two extremes, which presume that existing pavement after overlay deteriorates like a new pavement (traditional approach) and like an existing pavement without overlay (AASHTO approach). In addition, the methodoiogy accoums for rhe remaining iives of both existing and overlaid pavements and makes it possible to achieve consistent overlay designs.

2. A deterioration parameter less than one is recommended for use, especially when the remaining lives of the existing and the overlaid pavements are less than about 20 percent. Generally, overlay-related consistency will control the valid range- of this parameter. The specific value within this range to be used in a given design situation would depend on the good judgment of the designer.

3. The required structural capacity of the overlay is quite insensitive to the minimum condition factor when the remain­ing life of the existing pavement is large (greater than about

0 z Cl)

>-­< .....J 3.0 a: w > 0 u.. 0 2.5 a: w m ::E ::> z .....J <( a: ::> .,_ () ::> a: .,_ Cl)

Cl w a: ::> Q w a:

2.0

1.5

1.0

TRANSPORTATION RESEARCH RECORD 1272

30 percent). The sensitivity increases moderately as the existing pavement approaches its failure serviceability.

4. The required structural capacity of the overlay appears to be sensitive to the failure serviceability when the remaining life of existing pavement and the overlay terminal ser­viceability are small. Under these conditions, failure ser­viceability needs to be selected carefully.

.3. The; 1uaguituJc of effective structural capacity influences the valid range of deterioration parameters. For a large struc­tural capacity, the valid range is expected to be small, which implies that the existing pavement after an overlay deterio­rates more like a new pavement.

6. Field data concerning the conditions of existing pave­ments after overlays are needed. These data are essential for reliable estimation of the pavement condition curve, which significantly influences overlay design. Great opportunities exist for collecting such data as part of the Strategic Highway Research Program (SHRP) in the United States and its counterparts in Canada and the United Kingdom (C-SHRP, UK-SHRP).

0.2

0.4

0.6

0.8

RLx = 1.0

I I

O' I- : J: : C/) I

~ 1

0 .5 ~-----:-~----~~----~------..._ ______ .._ ______ .._ ____ ...... 0.0 0.10 0.15 0.20 0.25 0.30 0.35 0.40

MINIMUM CONDITION FACTOR, Cmin

FIGURE 9 Sensitivity results (y = 4 million ESALs, SN0 = 4): minimum condition factor (P 1y = 2.5, A = 0.5).

4.0 0 z

(/}

>-" A= <( 3.6 1 _J

A= er 0.5 w > Pty = 3.5 A= 0 0 LL A= 0 3.2

er A= w al ~ :::> 2.B A= 0.5 z _J .,,,.,. <( er .,,,.,,,

:::> >..= 0.5 ..... 2.4 __...-----(.) Pty = 3.0 A= 0 :::> --er ----..... -- 0 en t-

I Cl

2.0 en

w < a: < :::> Pty = 2.5 ----------- ---------- A= 0 0 w er 1.6

1.5 2.0 2.5

FAILURE SERVICEABILITY, Pt FIGURE 10 Sensitivity results (y = 4 million ESALs, SN0 = 4): failure serviceability (RLx = 0.2).

1.0

...< 0.8

u. 0 w :::> _J 0.6 <( > er w a.. a.. :::> 0.4 Cl _J <( >

0.2

0.0

2.5 3.0 3.5 4.0 4.5 5.0

EFFECTIVE STRUCTURAL NUMBER OF

EXISTING PAVEMENT, SNx

FIGURE 11 Variations of valid range of A with effective structural number of existing pavement (y = 5 million ESALs, RLx = 0).

5.5

14

REFERENCES

1. F. Finn and C. Monismith . NCHRP Synthesis of Highway Prac­tice 116: Asphalt Overlay Design Procedures. TRB, National Research Council, Washington, D.C., 1984.

2. Asphalt Overlays for Highways and Street Rehabilitation. Manual Series, No. 17 (MS-17). The Asphalt Institute, College Park, Md., 1983.

3. Pavement Mana'1ement Cuide. Ro~ds ~nrl Tr~nsnnrt:>tinn

Association of Cinada, Ottawa, Canada, 1977. • 4. C. Kennedy and N. Lister. Prediction of Pavement Performance

and the Design of Overlays. TRRL Laboratory Report 833. U.K. Transport and Road Research Laboratory, Crowthorne, Berkshire, England, 1978.

5. Asphalt Concrete Design Manual. California Department of Transportation, Sacramento, 1979.

6. Airport Pavement Bulletin: Evaluation Using Nondestructive Testing and Overlay Design. FHWA, U.S. Department of Transportation, 1983.

7. Asphalt Concrete Overlays of Flexible Pavements. Reports FHWA­RD-75-75, FHWA-RD-75-76. FHWA, U.S. Department of Transportation, 1975.

8. A. Claessen and R. Ditmarsch. Pavement Evaluation and Over­lay Design: The Shell Method. Proc., Fourth International Con-

TRANSPORTATION RESEARCH RECORD 1272

ference. 011 Structural Design of Asphalt Pavement, University of Michigan Ann Arbor, '1977.

9. K. Majidzadeh and G. fives. Flexible Pavement Overlay Design Procedures. Repon FHWA-RD-79-99. FHWA, U.S. Department of Transporiation , '1979.

10. R. Deen, H. outhgate. and G. Sharpe. Evaluation of Asphaltic Pav.cmcnrs for Overlay Design. Presented at the A TM Sym­posium on Pavement Maintenance and Rehabilitation Bal Harbor, Florida, 1983. '

11. R. G. Packard. Thickness Design for Concre1e Highway and Sm:et Paveme111s . Portland Cement A ociation, kokic, Ill ., 1984.

12. AASHTO Guide for Design of Pavement Structures, Vol. 1. AASHTO, Washington, D.C., 1986.

13. AASHTO Guide for Design of Pavement Structures Vol. 2, Appendix CC. AASHTO, Washington, D.C., 1986. ,

14. R. P. Elliott. An Examination of the AASHTO Remaining Life Factor. In Transportation Research Record 1215, TRB. National Research Council, Washington, D.C., 1989.

Publication of this paper sponsored by Committee on Pavement Rehabilitation.