TRANSPORTATION RESEARCH RECORD 1207

Application of Equivalent-Layer-Thickness Concept in a Mechanistic Rehabilitation Design Procedure

EMILE HORAK

The South African mechanistic rehabilitation design procedure is well established and has been verified with the help of a fleet of heavy vehicle simulators. Surface deflection basins can be measured with the road surface deflectometer or the National Institute for Transport and Road Research deflectograph. Typical South African pavement structures were analyzed, and various deflection basin parameters were calculated. The equivalent-layer-thickness (ELT) concept was investigated for its applicability to this analysis procedure and was found to be useful in representing the structural capacity of a pavement. The basis for the calculation of the EL T is the effective elastic modulus of the subgrade. Deflection points measured on the extremes of the deflection basin are used to calculate the subgrade effective elastic modulus. Various deflection basin parameters can be used to calculate pavement EL T, which can be related to typical distress determinants or directly to remaining life in a design-curve approach.

Odemark's (J) equivalent-layer-thickness (ELT) concept is often used as a simple method of approximation in pavement structural analysis, since it permits the conversion of a mul­tilayered system into a single layer with equivalent thickness. It is based on the principle that the equivalent layer has the same stiffness as the original layer, so as to give the same pressure distribution beneath the layer. This concept of clas­sifying a pavement by means of one number that represents the approximate bearing capacity of that pavement has been clearly illustrated by Molenaar and Van Gurp (2) and Mole­naar (3). In these cases the investigated pavement structures were mainly three-layered structures with different loading conditions.

Typical South African pavement structures found in the TRH4 catalog ( 4) were analyzed and converted into the EL T. In that catalog, various pavement structures are suggested for various traffic classes and categories of pavement. Pavement types are generally grouped together as bitumen, granular, cemented, or concrete base (Figure 1). Most of the typical flexible pavement structures analyzed, such as the granular­and the cemented-base pavements, have thin asphalt surfac­ings (30 to 50 mm). The calculated ELT values were then related to various distress determinants and fatigue life in order to evaluate this concept as a possible aid in the mechan­istic rehabilitation design procedure (5).

This study is part of an investigation in which various deflec-

National Institute for Transport and Road Research, CSIR, P.O. Box 395, Pretoria 0001, Republic of South Africa.

I. PAVEMENT CLASS

A, B, c

,. 2. PAVEMENT TYPE

GRANULAR BASE

BITUMINOUS BASE

CEMENTED BASE

CONCRETE

' 3. PAVEMENT STATE

VERY STIFF

STIFF

FLEXIBLE

VERY FLEXIBLE

4. PAVEMENT LAYER STATE

WET, DRY, CRACKED

+ 5. DESIGN INPUTS

LAYER THICKNESS

ELASTIC MODULI

6. EVALUATION

LINEAR ELASTIC

MODELS USED IN

MECHANISTIC ANALYSIS

FIGURE 1 Flow diagram of mechanistic pavement rehabilitation design method (5).

69

70 TRANSPORTATION RESEARCH RECORD 1207

TABLE 1 SUMMARY OF DEFLECTION BASIN PARAMETERS

Porometer Formula

I. Maximum deflection 80

2. Radius of curvoture R . r2 127 mm

2 80 ( 80 I 8 r - 11 ' r •

3 . Spreodability s ~ ( ( 80•81• 0 2 + 83)/SJ 100

' 81 ··· 83 space

80 305mm 4. Are o A . 6[ I+ 2 ( 01 /80) + 2(82/ 80 + 83/ 80]

5 Shope factors F = (80-82)/81 ' F 2 = ( 8 1 - 83) I 8 2

6. Sur face c urvoture index SCI . Bo - Or ; r = 305 or 500 mm

7. Bose curvature index SCI = 8s10- 0 s1s

8 Bose domoge index SDI = 8305 -8s10

9 Deflection rotio Or . 8r/ 8 o i where Sr~ 8o/2

10. Bending index BI = 80 /o i where o =deflection bosin length

11. Slope of deflection SD = ton- 1(80-Srl/r ; where r • 610mm

12. Tangen I slope ST = (8o-8rl/r; where r = distance to inflection point

13 Radius of influence RI = R'/80 '

where R' is the distance from

80 to where basin is tangent Io horizontal

TYPICAL DEFLECTION BASIN

a or R'

Deflection basin length

Deflected / shope of road surface

Applied load

Positive curvature

tion basin parameters were calculated for these pavement structures (6) and related to typical distress determinants. In Table 1 the most significant of these deflection basin param­eters are iisted with their formuias reiaied io the road surface deflectometer (RSD). The RSD is a modernized, automated Benkelman beam (7) which is used with the accelerated testing facilities, i.e., the heavy-vehicle simulators (HVSs). The National Institute for Transport and Road Research (NITRR) deflectograph has also been modernized and can measure the deflections on the deflection basin, thus enabling the calcu­lation of the deflection basin parameters as listed in Table 1.

An attempt is made in this paper to show how the mechan­istic design procedure (5, 8) can be enhanced with the aid of these nondestructive deflection measuring devices. These measurements can then also be used to calculate the EL T with a minimum of information. The purpose is to establish typical design curves whereby flexible pavements can be ana­lyzed without the need for detailed calculations typical of

fundamental linear elastic analysis. Such an approach can greatly enhance the South African mechanistic rehabilitation design procedure, which is well established and has been ver­ified with the HVS testing program (8, 9).

MECHANISTIC DESIGN PROCEDURE

The mechanistic pavement rehabilitation design procedure (5) is summarized in the flow diagram of Figure 1. The pavement classes identified as A, B, or C in step 1 can be broadly defined as freeways, major highways, or lightly trafficked roads, respectively ( 4). Pavement types (step 2) in the present study are restricted to granular, bituminous, and cemented bases, since the focus is on flexible pavements.

Pavement behavior states (step 3) are defined as very stiff, stiff, flexible, and very flexible (5). From data on deflection basins measured under accelerated tests ( 6), the ranges of

Horak

TABLE 2 BEHAVIOR STATES DEFINED BY DEFLECTION BASIN PARAMETERS

Deflection basin parameter ranges Behaviour

SCI BDI state Max. deft. SD (mm) ( x 10-6 ) (mm) (mm)

Very stiff < 0,2 < 50 <0,01 < 0,01

Stiff 0,2 - 0,4 50-400 0,01 - 0,2 0,01 - 0,1

Flexible 0,4 - 0,6 400-750 0,2 - 0,4 0,1 - 0,15

Very > 0,6 flexible

>750 > 0,4 > 0,15

BCI (mm)

<0,01

0,01-0,05

0,05 -0,08

>0,08

deflection basin parameters in each behavior state , as shown in Table 2, can be used to define the behavior state accurately. Previously, this distinction of behavior states was based on maximum deflection only, but it is now suggested that at least two of the other deflection basin parameters listed in Table 2 be used for this purpose. Steps 4, 5, and 6 of Figure 1 form part of the normal mechanistic design procedure whereby the design inputs in terms of moisture condition, state of cracking of treated materials, layer thicknesses and elastic moduli are needed before the typical linear elastic models can be used for the analysis.

A design-curve approach is suggested, where with the use of relations established through prior analyses of the typical pavement types in the flexible state, steps 4, 5, and 6, can be greatly simplified . This design-curve approach will also render superfluous detailed knowledge of the design inputs (as shown in step 5) that is required for a fundamental linear elastic analysis. Instead, the evaluation phase follows from the meas­urement phase of the deflection basins. The purpose is there­fore to make use of the ELT to simplify this analysis procedure by determining EL T directly from measured deflection basin parameters.

DETERMINATION OF ELT

The ELT, as developed further by Molenaar and Van Gurp (2), is calculated as follows:

L - 1 [ Ei(l EL T = a L h.1 E, (l

where

_ vJ)] 113

- vf)

a = 0.9 for flexible pavements, h; thickness of layer i (m), E; elastic modulus of layer i (N/m2),

Es = elastic modulus of subgrade (N/m2),

v; = Poisson ratio of layer i, vs = Poisson ratio of subgrade layer with value equal to

0.35, and L = number of layers.

The general formula for the EL T is related to the effective elastic modulus of the subgrade. This means that the latter has to be determined before the ELT can be determined. Molenaar and Van Gurp (2) established a relationship between deflection measured at 2 m and subgrade elastic moduli as measured under the falling-weight deflectometer (FWD) for

500

zoo -E ::I..

z ~ 100 f-u LU ...J ... LU

D 5 0

20

71

FLEXIBLE PAVEMENTS

SUBGRAOE MO OULU S I MPo I

FIGURE 2 Relation of subgrade elastic modulus to deflection in four- and five-layered flexible pavements.

bitumen-base pavements. This same procedure can be used to determine the subgrade effective elastic modulus for the typical South African flexible pavements analyzed (6). Rela­tionships were also established between deflection measured at offsets of 915, 610, and 500 mm and subgrade elastic mod­uli. In Figure 2, these relations are shown for four- or five­layered flexible pavement structures.

By thus measuring deflections with the RSD or even the NITRR deflectograph at those offsets on the deflection basin, it is possible to determine the subgrade modulus. It is rec­ommended that at least three of these relations (as illustrated in Figure 2) be used to arrive at an average value of subgrade effective elastic modulus.

By measuring deflections with the RSD or even the NITRR deflectograph at those offsets on the deflection basin , it is possible to determine the subgrade modulus. It is recom­mended that at least three of these relations be used to arrive at an average value of subgrade effective elastic moduli .

Three subgrade effective elastic moduli (50, 70, and 150 MPa), which are typical of the subgrades of South African pavements, were selected as a basis to determine the equiv­alent thickness for the typical flexible multilayered pavements that were analyzed. In Figure 3, however, it is shown that the deflection basin parameter F1 (shape factor, see Table 1), if related to ELT, cannot be used to discern such a difference in subgrade effective elastic modulus . In Figure 4, on the other hand, it is shown how the deflection basin parameter SD (slope of deflection, see Table 1) can be used to discern the difference in effective elastic moduli of the subgrade for mul­tilayered flexible pavement structures.

Nevertheless, with the deflection basin parameter SCI (sur­face curvature index, see Table 1) it was possible to subdivide these flexible pavements into two separate sets of relations . Those with granular bases had a greater sensitivity to ELT than bitumen-base pavements. This is illustrated in Figure 5,

72

L;::

a: 0 I-u Lt w Q.. ct J: (/)

2

MEASURED Fl ----0,5

0,2

BITUMEN BASE

<t u

E 5 = 50,70,150 MPa

0,1..._ __ _._ ___ _._ _ __.'-'----'----~--~ 0,1 0,2 0,5 2 5 10

EQUIVALENT LAYER THICKNESS ( ELTl (ml

FIGURE 3 Relation of equivalent layer thickness to deflection basin shape factor.

E5

= 150 70 50 MPa

500

0 200 MEASURED SO

V'I ----z 0 i'.= 100 u w ..J "-w a 50 "- ~I 0

w Q..

~ I 0 ..J

20 (/)

10.__ _ __. _ _ _ _.1.-c----'-L-----:~-----=~-----:'.. 0,1 0,2 0,5 I 2 5 10

EQUIVALENT LAYER THICKNESS lELTI (m I

FIGURE 4 Relation of equivalent layer thickness to slope of deflection.

in which the three subgrade effective elastic moduli of the two base types in the flexible behavior state are shown.

The subgrade effective elastic 1no<lulus l:an therefore be determined from Figure 2. Using that subgrade effective elas­tic modulus, it is thus possible to use the measured deflection basin parameters in Figures 3, 4, or 5 to calculate the ELT.

ANALYTICAL PROCEDURE

In the mechanistic design procedure (5), permanent defor­mation is related to subgrade vertical strain (e"), and fatigue cracking in the bitumen bases is related to the maximum horizontal asphalt strain (eHA). As stated earlier, the purpose is to use a design-curve approach in order to simplify the analysis procedure. This is achieved by relating the previously determined EL T directly to these strains.

-E E

"' 0

"'

-E ::I..

tJ V1

100

TRANSPORTATION RESEARCH RECORD 1207

I ' 1-------GRANULAR BASES -

Es = 5 0 M Pa 1--+.--\I-~"\

Es= 70 MP a l=:l=::::::l~=11tt-:---I

E 5 =I !50 MPa +-+---

100,3 I 2 EQUIVALENT LAYER THICKNESS IELTI \ml

FIGURE 5 Relation of equivalent layer thickness to surface curvature index.

In Figure 6 it is shown how it is possible to relate EL T directly to subgrade vertical strain ( ev,) for the various subgrade support conditions for flexible pavements. When the ELT is related to maximum horizontal asphalt strain (eHA), it is appli­cable only to flexible bitumen-base pavements. The relations for the various subgrade support conditions are illustrated in Figure 7. This means that the granular-base pavements, which have relatively thin asphalt surfacings (on average 30-50 mm in the dry regions of South Africa), cannot be analyzed in this fashion. This emphasizes the fact that the ELT concept was developed to calculate compressive strain in the subgrade and does not necessarily give a good indication of horizontal strain in the asphalt layers (10) . The ELT determined earlier using Figures 3, 4, or 5 is now used in Figures 6 and 7 to determine the sub grade vertical strain ( evs) or the maximum horizontai asphait strain (eHA).

Remaining life can be determined for subgrade vertical strain ( ev,) by using the typical fatigue life curves of the South African mechanistic design procedure (5, 9). In Figure 8 these curves are shown for the typical road categories according to the NITRR design traffic classes ( 4). The subgrade vertical strain (ev,), as determined from Figure 6, can therefore directly be used as input with Figure 8 to calculate the remaining life. All that is needed is to establish the road category. In the calculation of the remaining life of bitumen bases, Figure 9 can be used as in the South African mechanistic design pro­cedure (5, 9). In this case, however, it is necessary to know the stiffness of the base layer.

Stiffness can be determined by using typical tabulated val­ues (5) or by using the typical nomograph approach to deter-

Horak

z <t 0:: I-(/)

::l..

"' > I.II

I I I I I ! I F LEXIBLE PAV EMEN TS

I I I ' I 1\ I Ii I 0 0 0 t----t---w-t-'\l-'lot--+--+--+-.,.._-----1

'" ~ " \. '

\ \ \ I

500 \. \ ' "

I\ E5 • 150 MPo ~

E5 •70MPa

100'---...__,__~_._ ....... __._...._ ____ ~ 0,3 I 2 EQUIVALENT LAYER THICKNESS !EL Tl !ml

FIGURE 6 Relation of subgrade vertical strain to equivalent layer thickness for flexible pavements.

mine stiffness modulus values of bituminous mixes (2, 11). By using the previously determined maximum horizontal strain (EHA) as input, the equivalent traffic can be determined for the related bitumen base stiffness. The recommended shift factors shown in Table 3 should be applied to the calculated remaining fatigue life.

ELT can, however, be related directly to fatigue life (3) as calculated above. It was shown previously how deflec­tion basin parameters can be used to identify the pavement behavior state accurately. ELT can be used to indicate whether a pavement structure with cemented subbases or bases is in the flexible behavior state. According to the definition given by Freeme (5), such flexible pavements with the cemented layers are in the cracked phase, exhibiting equivalent granular behavior. In Figure 10, ELT for the precracked life of pave­ments with cemented subbases and bases is shown in terms of standard 80-kN axle repetitions. A distinction can be made on the basis of the variance of the elastic modulus of the sub grade. However, an EL T value of at least 1. 1 m is required for a subgrade modulus of 70 MPa to have any significant precracked life for the cemented layers. Although the mechanistic rehabilitation procedure (5) makes provision for the application of crack growth factors, this does not change the fact that the major portion of the structural life of typical South African pavement structures with cemented layers is in the cracked phase.

In flexible pavement structures, typical fatigue life curves, such as those shown in Figure 11, can be used. In this figure the subgrade support condition applies for a subgrade effec­tive elastic modulus(£,) of70 MPa. The relation for subgrade vertical strain (Evs) holds good for all flexible pavements, but the relation for maximum horizontal asphalt strain ( EHA) holds only for flexible bitumen-base pavements.

soo.--------------~

~ 1001-----.---i-T----Jf-~------l <(

er 1-Vl

I

:1_

<(

I \jJ

I

BITUMEN BASES

I

f0'---'---'--1.--'--'-- --- ---'---' 0 ,3 2

EQUIVALENT LAYER THICKNESS I ELT l lml

FIGURE 7 Relation of equivalent layer thickness to maximum horizontal asphalt strain for bitumen-base pavements.

CONCLUSIONS AND RECOMMENDATIONS

73

Deflection basin parameters, as measured with the RSD or the NITRR deflectograph, can be used to enhance and sim­plify the South African mechanistic design procedure. The mechanistic design procedure can be simplified by using a design-curve approach, achieved in this instance by using the EL T concept.

The deflections, as measured on the reverse curvature of the deflection basin, correlate well with subgrade effective elastic modulus. The subgrade effective elastic modulus deter­mined using such relations forms the basis for calculation of the EL T. It also has intrinsic significance in terms of identi­fying statistically uniform sections of subgrade support con­ditions in a typical initial assessment of a pavement length.

The EL T concept is applicable to the approximation of structural capacity of flexible pavements. Deflection basin parameters correlate well with a value such as ELT in general, as calculated for flexible pavements. For some deflection basin parameters it is even possible to discern between granular­and bitumen-base pavements. Using such measured deflection basin parameters, it is possible to determine ELT for the previously determined subgrade effective elastic moduli.

EL T correlates well with sub grade vertical strain (Ev,) for flexible pavement structures and can be used to discern the effect of variance of subgrade elastic moduli. On the other hand , clear relations between maximum horizontal asphalt strain ( EHA) and ELT do not exist for granular-base pavements as they do for bitumen-base pavements. This is due to the thin asphalt layer typically used on granular-base pavements

74 TRANSPORTATION RESEARCH RECORD 1207

<t

0:

-~ 104

DESIGN TRAFFIC CLASS EO El E2 E3 I E4

~ ~ <1 a:

_ I 111 11111 I 11111111 I 1111111 LIGHTLY TRAFFICKED ROADS ICJ

I-V1

103

lJJ Cl

1 n 111 111 1111 I I I

"' - MAJOR ROADS IB>

<t a: FREEWAYS IA> <..? CD I ::i V1

102 I

_J

<t u I-a:

I ' I I

I ' I 11 lJJ >

10 I 11 I 11 I I 111. I I .

104 10 5 10 6

EQUIVALENT TRAFFIC, E80

FIGURE 8 Recommended subgrade vertical strain criteria for different road categories.

DESIGN TRAFFIC CLASS -Ea El EZ E3 E4

1000

:>oo

I

I

I

'' w • ! • oo z <t ::i 0 - _J

" :l ..J -w 100 zW - :z: <t 3: 0: 50 I- z (/) .J< I'

WO _J '3" I: u;

I 11 : I z w 10 I- 105 106 10 7

EQUIVALENT TRAFFIC ,EBO

(Use equivalency coeff1cienr n'41

'

FIGURE 9 Recommended fatigue life criteria for thick bitumen bases.

108

in South Africa. There are other design curves (6) whereby the maximum horizontal asphalt strain ( EHA) can be calculated by using deflection basin parameters. These distress deter­minant strains can be calculated from previously determined ELT values.

flexible pavement with regard to the distress determinants (Evs

and eHA) . Use is made of the typical fatigue-life relations of these two distress determinants.

A design-curve approach can also be followed whereby ELT, as determined from deflection basin measurements, is directly related to remaining life. The precrack life of cemented subbase::s and base::s can aisu be:: determined using such a design curve.

The value of EL T can be used in a mechanistic design or an analytical procedure to establish the structural life of a

TABLE 3 SHIFT FACTORS FOR BITUMINOUS BASES

A (Lightly traf-

ficked roads)

2

Road category

B (Major roads)

5

c (Freeways)

10

Overlays are important rehabilitation options. Although the EL T concept does not allow for the analysis of individual layers, the design-curve approach lends itself ideally to use with overlay-design curves developed for these types of pave­ments (6) . Apart from that, the concept of the ELT can be used in the initial assessment of rehabilitation investigations.

ACKNOWLEDGMENT

The author thanks the Chief Director of the National Institute for Transport and Road Research for permission to publish this paper.

Horak

roB

.::= Evs FOR . I

·-- FLEXI BL E - PAVEMENTS I

I

TRH41N!TRR 198501 TR AFFIC CL ASSES

' I - E 4 -10 7 V1 z 0 f:: >=

~ E3

w Cl. w Ct: ' w

. I '

,, ...J x I • <I

0 a: <I 10 6 0

! : I' >-E2

I ' 1 ~s • 70 MPo

z <I >-V1

! I -El

I ! I .. ;•

;,

I I I ~EHA F OR_ I 1 I ' BITUMEN

EO I ! BASE : i I I PAVEMENTS

10 5

~I IP

EQUIVALENT LAYER THICKNESS IELT I lml

FIGURE 10 Initiation of cracking of cemented bases and subbases in terms of equivalent layer thickness.

REFERENCES

J. N. Odemark . ln vestigatio11s on the Elastic Propertie. of Soils and tlte Design of Pm1eme11ts A ccording 10 the Theory of Elasticity . Statcns Vaeginsliture , Stockholm , Sweden 1949.

2. A. A . A . Molenaar and Van Gurp. Optimizatio11 of the 711ick11ess Design of Asphalt Co11crete. Proc., 10th Au tralian Road Research Board Confe rence. Vol. 10 No. 2, 1980, pp. 31-44 .

3. A. A. A. Molenaa r. Str11c111ral Performance and Design of Flex­ible Road Constructioris and Asphalt Concrete O verlays. D. Tech. Sc. thcsi , TechnischcHogeschool. Delft , The Netherlands , 1983.

4. Stn1ct11ral Design of.l11terurba11 and R11ml.Road Pavements. TRl-14 , National Jnstitute for T {ansport and Road R esearch, CSIR, Pr -toria, South Africa, 1985. . .

5. C. R. Freeme. Ev<1l11ntio11 of Pavement Belravwur for Ma1or Rehabilitation of Roads. NlT RR Technical Report RP/19/83, CSIR, Pretoria, Republic of South Africa, 1983 .

6. E. Horak . The Use of Surface Dcfiec1ion Basin Measurements in tbc Mccba11istic Analy: is of Flexible Pavement . Proc., 6th /memational C.Onfere11ce 011 the Structural Design of A sphalt Pavements, Ann Arb r, Mich . Vol. l 1987, pp. 990-1001.

7. Horak E. Metisurement and Data Processing of Deflection Basins. NrrRR Technical Report RP/23, CSIR, Pretoria, Republic of South Africa , 1986.

0 <V

~ </')

z 0

f::: I-w Q. w a:: w _J

x <I

z ~

0 <V

Cl a:: <I Cl z <t 1-

10 6

105

</'I 10 4

" u <I a: u w a:: Q.

10 3

·--- r--c ----'-- , ~ ,_.. --

'

Es I . I- 50 MPo I-

70 MPo 150MPo- I

I I 11 : 1

I I I • 11 I

I l I I i I

' I I I

I I ! I I

' !

' I I

i I I I : j I i !

! I ! I I ! !

I

I 11 ! I 1 I . . i I 0 ,20 1,0 5, 0

EQUIVALENT LAYER THICKNESS IELTJ(m)

FIGURE 11 Pavement life for maximum horizontal asphalt strain and subgrade vertical strain criteria in terms of equivalent thickness.

75

8. C. R. Freeme, M. De Beere, and A . W. Viljoen. The Behaviour and Mechanistic Design of Asphalt Pavements. Proc., 6th Inter­national Conference on the Structural Desigri of Asphalt Pave­ments, Ann Arbor, Mich., Vol. 1, 1987, pp. 333-343.

9. C. R . Freeme, J. H . Maree , and A. W. Viljoen. Mechanistic Design of Asphalt Pavemenr~ and Verification of Designs Using the Heavy Vehicle Simulator. Proc., 5th Jmem(ltional Conference 011 tlie Strucwral Design of Asvhalt Pavement. , Pretoria, Repub­lic of South Africa, Vol. 1, CSIR Reprint RR362, 1982, pp. 156- 173.

10. G. J. Jordaan . An Assessment of the Pavement Arialytical and Rehabilitation Desigri Methods: A Method Based on the FWD Measurements arid the Equivalent Layer Concept (The Nether­lands) . NITRR Technical Note T045/85, CSIR, Pretoria, Republic of South Africa , 1985.

11. F . Bonnaure, G . Gest, A . Gravious, and 0. Uge. A New Method of Predicting the Stiffness of Asphalt Paving Mixtures. Proc., Association of Asphalt Paving Techriologists, Dallas, Texas, Vol. 46, 1977, pp. 64-97.

Publication of this paper sponsored by Committee on Flexible Pave­ment Design.