Equivalent Granular Equivalent Granular ThicknessThickness

6.04 Apply the concept of 6.04 Apply the concept of Equivalent Granular Thickness to Equivalent Granular Thickness to convert a layered system of convert a layered system of different materials into an different materials into an equivalent thickness of a given equivalent thickness of a given reference material.reference material.The following presentation contains references to The following presentation contains references to Figure 6.04bFigure 6.04b, , Table 6.02Table 6.02 , “ , “GBE Example 1GBE Example 1”, all of ”, all of

which are posted under subsection 2.6 of the which are posted under subsection 2.6 of the course notes on the instructor’s website. Viewer course notes on the instructor’s website. Viewer

discretion is advised as some scenes contain discretion is advised as some scenes contain material of a mathematical nature.material of a mathematical nature.

Why is the Why is the EquivalentEquivalent GranularGranular ThicknessThickness concept necessary?concept necessary?

a pavement design consists of the a pavement design consists of the specification of thicknesses of layers specification of thicknesses of layers of different materialsof different materials an infinite number of combinations of an infinite number of combinations of these parameters are possiblethese parameters are possible what is needed is one unit or what is needed is one unit or parameter that characterizes the parameter that characterizes the pavement’s strengthpavement’s strength

Basic TheoryBasic Theory Layered Elastic Theory is used to Layered Elastic Theory is used to derive layer equivalency factors for derive layer equivalency factors for each layer of a pavementeach layer of a pavement knowing the thickness and Modulus knowing the thickness and Modulus of Elasticity of each pavement layer, of Elasticity of each pavement layer, an equivalent thickness of a standard an equivalent thickness of a standard reference material is calculatedreference material is calculated this equivalent thickness is used to this equivalent thickness is used to characterize the pavement’s strengthcharacterize the pavement’s strength

And now…And now…

Some Mental High- Some Mental High-jinksjinks

A layered system A layered system of different of different materials is materials is

converted to…converted to…h

1h

2h

3

M1

M2

M3

Mref

Mref

Mref

H1

H2

H3

31

1

1

refM

M

h

H 13

11 h

M

MH

ref

A layered system A layered system of a reference of a reference

materialmaterial

thereforthereforee

He

333

232

131 h

M

Mh

M

Mh

M

MH

refrefrefe andand

In Ontario…In Ontario…The elastic modulus for The elastic modulus for new hot mix new hot mix asphaltasphalt is assumed to be is assumed to be 400,000 400,000 psipsi (2.758 GPa) (2.758 GPa)

The elastic modulus for The elastic modulus for new granular new granular ‘A’‘A’ is assumed to be is assumed to be 50,000 psi50,000 psi (0.345 GPa)(0.345 GPa)The elastic modulus for The elastic modulus for new granular new granular subbasesubbase is assumed to be is assumed to be 15,000 15,000 psipsi (0.103 GPa) (0.103 GPa)

The Standard, Reference The Standard, Reference Material is Material is NEW GRANULAR NEW GRANULAR

‘A’‘A’Therefore, in Ontario, the layer Therefore, in Ontario, the layer equivalency factor for new asphalt hot equivalency factor for new asphalt hot mix is…mix is…

0.2850000

400000 33

This means that 100 mm of new hot This means that 100 mm of new hot mix asphalt has equivalent strength to mix asphalt has equivalent strength to 200 mm of new Granular ‘A’200 mm of new Granular ‘A’

In Ontario, granular ‘A’ is used for the In Ontario, granular ‘A’ is used for the granular base layer in conventional granular base layer in conventional pavement designpavement designTherefore the layer equivalency factor Therefore the layer equivalency factor for granular base is…?for granular base is…?right, right,

1.01.0!!What would the layer equivalency What would the layer equivalency factor for new granular subbase in factor for new granular subbase in Ontario be?Ontario be?

67.03.050000

15000 33

i.e., 300 mm of new granular subbase i.e., 300 mm of new granular subbase would be equivalent in strength to 200 would be equivalent in strength to 200 mm of new granular ‘A’mm of new granular ‘A’

MTO Tabulated GBE’s MTO Tabulated GBE’s (After: "Pavement Design and Rehabilitation Manual", 1990)(After: "Pavement Design and Rehabilitation Manual", 1990)

The MTO has published Granular Base The MTO has published Granular Base Equivalencies (GBE’s) for three design Equivalencies (GBE’s) for three design

situations:situations:

New ProjectsNew ProjectsResurfacing ProjectsResurfacing ProjectsReconstruction ProjectsReconstruction Projects

These are listed in Table 6.02 in the These are listed in Table 6.02 in the course notes.course notes.

New ProjectsNew Projects these are the maximum values to be these are the maximum values to be

assumed for new pavement designsassumed for new pavement designs

Resurfacing ProjectsResurfacing Projects these are the values to be assumed for these are the values to be assumed for

existing pavement layers when an existing pavement layers when an overlay is being consideredoverlay is being considered

these are based on average test values these are based on average test values on pavements overlaid by the MTOon pavements overlaid by the MTO

Reconstruction ProjectsReconstruction Projects These are the lowest values for the These are the lowest values for the

materials in a pavement structure (at materials in a pavement structure (at their weakest)their weakest)

GBE’s can be…GBE’s can be… estimated during coring and boring estimated during coring and boring

surveys based on the operator’s surveys based on the operator’s descriptions of each layer material or descriptions of each layer material or based on an estimated percent loss in based on an estimated percent loss in strengthstrength

calculated from measured elastic calculated from measured elastic modulus values for samples of each layer modulus values for samples of each layer of the pavementof the pavement

used to evaluate the strength of an used to evaluate the strength of an existing pavement, determine overlay existing pavement, determine overlay requirements or design a new pavementrequirements or design a new pavement

Example: Example: Given the bore hole Given the bore hole log data below, evaluate the GBE log data below, evaluate the GBE

of this pavement.of this pavement.LayeLaye

rr MaterialMaterial M M (psi)(psi)

ThickneThickness (mm)ss (mm)

11Old HL (30% Old HL (30% loss in GBE)loss in GBE) 4545

22Old HL Old HL (crumbles)(crumbles) 9090

33Old Granular Old Granular BaseBase

30,0030,0000

170170

44Old Granular Old Granular SubbaseSubbase 8,0008,000 340340

55Silty Sand Silty Sand SubgradeSubgrade -- --

Equiv. Equiv. FactorFactor

HHe e

(mm)(mm)

1.71.7

1.01.0

0.840.84

0.540.54

--

76.576.5

9090

142.8142.8

183.6183.6

--

TABLE 6.02

GRANULAR BASE EQUIVALENCY FACTORS

(After: "Pavement Design and Rehabilitation Manual", 1990)

NEW PROJECTS                Equivalency

Material Factor New or Recycled HL 2.00

Granular A in Base 1.00Granular B in Subbase 0.67

Cement Treated Material in Subbase (with Gr. A base) 1.40Cement Treated Material in Base (no subbase) 1.80

Bituminous Treated Material in Base (with Gr. A subbase) 1.50Cold Mix 1.80

OGDL (Open Graded Drainage Layer) 1.00

RESURFACING PROJECTS                Equivalency

Material Factor Crushed RBM* (in base) 1.00

Bituminous Treated Crushed RBM* 1.50Crushed RBM* Blended with New Granular A 1.00

Pulverized Bituminous Surface Mixed with Existing Base 1.00Old HL 1.25

Old Granular Base 0.75Old Granular Subbase 0.50

RECONSTRUCTION PROJECTS                Equivalency

Material Factor Granular A Layer 1.00

Old HL 1.00Old Granular Base 0.60

Old Granular Subbase 0.40

Note: For design purposes OFC and Surface Treatment, because of their thickness, are assumed to have no structural value and

act only as a surface wearing course.

*RBM - Recovered Bituminous Material

The total GBE for the pavement is The total GBE for the pavement is therefore:therefore:

mmH e 9.4926.1838.142905.76

What was the original GBE for the What was the original GBE for the pavement ?pavement ?

67.03400.11700.2900.2450 He

mmHe 8.6678.227170180900

What % of its original strength has been What % of its original strength has been lost?lost?

%268.667

9.4928.667%

lostGBE