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Report No. MIDOT-15953-2/1
Prepared for:
Mr. Curtis Bleech
Michigan Department of Tranpsortation
Construction and Technology Division/Laboratory
P.O. Box 30049
Lansing, Michigan 48909
Prepared by:
Harold L. Von Quintus, P.E.
ERES Consultants – A Division of Applied Research Associates
26 Stillmeadow
Round Rock, Texas 78664
August 2004
Pavement Structural Analysis of the
Design Recommendations for Reconstructing
I-96 (M-39 to Schaeffer Road)
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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Report No. MIDOT-15953-2/1
Prepared for:
Mr. Curtis Bleech
Michigan Department of Tranpsortation
Construction and Technology Division/Laboratory
P.O. Box 30049
Lansing, Michigan 48909
Prepared by:
Harold L. Von Quintus, P.E.
ERES Consultants – A Division of Applied Research Associates
26 Stillmeadow
Round Rock, Texas 78664
Harold L. Von Quintus, P.E. August 2004
Texas Registration 46169
Pavement Structural Analysis of the
Design Recommendations for Reconstructing
I-96 (M-39 to Schaeffer Road)
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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Executive Summary
I-96 between M-39 and Schaeffer Road, just west of Detroit, Michigan, is planned for
reconstruction in 2005. The Michigan Department of Transportation (DOT) completed a
design for the reconstruction of this segment of I-96 in accordance with the 1993
AASHTO DARWin program.(1)
The objective of this study was to analyze the proposed
flexible pavement layer thickness and material types recommended for this segment
along I-96. Two mechanistic-empirical (M-E) design/analysis methods were used to
analyze the pavement design. One of the M-E design/analysis methods was the same one
used to prepare A Simplified Catalog of Solutions, and the second one is the new M-E
Pavement Design Guide developed under NCHRP 1-37A.(2,3)
Results from these analyses suggest that the proposed pavement structure will be
adequate relative to cracking. In fact, the tensile strain calculated under the standard
design load is less than the value that has been typically assumed for the endurance limit.
The one concern is with rutting and distortion. Both M-E analysis methods predict levels
of rutting that exceed the allowable level of 0.50 inches within the analysis period. Using
a PG 76-22 asphalt in the top two layers (the wearing surface and leveling course) will
reduce the rutting to an acceptable level. Whether a PG 70-22P or PG 76-22 is used
should be defined based on asphalt or mixture modulus testing or some type of torture
test to ensure that the HMA mixtures will be resistant to rutting.
Prior to construction, it should be confirmed that the pavement materials meet or exceed
the assumptions used in design, regardless of the design method. It is also recommended
that sufficient testing be completed during construction to ensure that the design
assumptions are satisfied.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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Table of Contents
Section Page
1. Introduction .................................................................................................................... 1
2. Study/Design Objective ..................................................................................................... 1
3. Project Design Parameters ................................................................................................. 1
3.1 Design Traffic ........................................................................................................ 1
3.2 Subsurface Investigations – Soil Support Design Value ....................................... 5
3.3 Non-Frost Susceptible Material ............................................................................. 7
3.4 Hot Mix Asphalt Mixtures ................................................................................... 11
3.5 Subsurface Drainage System ............................................................................... 13
4. Mechanistic-Empirical Thickness Design-Evaluation Method ....................................... 13
4.1 Pavement Structural Design Assumptions........................................................... 14
4.2 Evaluation Criteria ............................................................................................... 15
4.3 Simplistic M-E Analysis Method......................................................................... 15
4.4 New M-E Pavement Design Guide Software ...................................................... 19
5. Summary of Evaluations.................................................................................................. 21
6. Limitations .................................................................................................................. 22
7. References .................................................................................................................. 23
Appendices:
A Summary of Truck Traffic Equivalent Single Axle Load Applications Computed
for the Base Year 2005 .................................................................................................... 25
B Summary of Repeated Load Resilient Modulus Tests Extracted from the LTPP
Database for the Michigan Sites ...................................................................................... 32
C Layer Properties and Pavement Responses Computed for the I-96 Design Cross
Section .................................................................................................................. 36
C.1 HMA Modulus Determination............................................................................. 36
C.2 Unbound Layer Modulus Determination ............................................................. 38
C.3 EVERSTRS Output for Fatigue Cracking Analysis ............................................ 40
C.4 EVERSTRS Output for HMA Rutting Analysis ................................................. 42
D Analysis of the Proposed Design Cross Section of I-96 Using the New M-E
Pavement Design Guide Software ................................................................................... 43
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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1. Introduction
I-96 between M-39 and Schaeffer Road, just west of Detroit, Michigan, is planned for
reconstruction in 2005. The Michigan Department of Transportation (DOT) completed a
design for the reconstruction of this segment of I-96 in accordance with the 1993
AASHTO DARWin program.(1)
Figure 1 shows the pavement design (material types and
layer thickness) resulting from that design procedure.
Mr. Curtis Bleech with the Michigan DOT requested that an analysis of that pavement
structural design be completed using a mechanistic-empirical method for a 20 and 40-
year analysis period. The purpose of this document is to present the analyses completed
for evaluating the design pavement cross sections (material types and layer thickness)
recommended for the reconstruction of I-96 (refer to figure 1).
2. Study/Design Objective
The objective of this study was to analyze the flexible pavement layer thickness and
material types recommended for the segment along I-96 between M-39 and Schaeffer
Road using two mechanistic-empirical (M-E) design/analysis methods. One of the M-E
design/analysis methods was the same one used to prepare A Simplified Catalog of
Solutions, and the second one is the new M-E Pavement Design Guide developed under
NCHRP 1-37A.(2,3)
3. Project Design Parameters
3.1 Design Traffic
The traffic parameters that were used to determine the design number of 80-kN (18-kip)
Equivalent Single Axle Loads (ESALs) in accordance with the 1993 AASHTO Design
Guide are summarized below and were provided by the Michigan DOT.
� Average Annual Daily Commercial Traffic in 2005 = 9,600
� Initial Annual ESALs, both directions = 2,382,720
� Directional Distribution Factor = 0.56
� Lane Distribution Factor = 0.70
� Compound Commercial Traffic Growth Rate = 2.0%
Pavement Structural Analysis of the
Design Recommendations for Reconstructing I-96 (M-39 to Schaeffer Road)
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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� 20-Year ESALs, one-way traffic = 22,694,400
� 40-Year ESALS, one-way traffic = 56,400,000
Figure 1 Pavement design resulting from the 1993 AASHTO Design Guide for
the reconstruction of I-96.
HMA TOP COURSE
HMA LEVELING COURSE
HMA BASE COURSE
AGGREGATE BASE
SAND SUBBSASE
SILTY CLAY SOIL
HMA Top Course (PG 70-22P);
1.5 inches; Air Voids = 7.5%;
Vbe=10.5%
HMA Leveling Course (PG 70-
22P); 2.5 inches; Air Voids =
7.5%; Vbe=10.5%
HMA Base Course (PG 70-22);
10 inches; Air Voids = 7.5%;
Vbe= 9.5%
OGDC Aggregate Base Course;
16 inches (21AA-MOD)
Crushed Stone Base
Sand Subbase, Class IIA; 8 inches
Low Plasticity, Firm Silty Clay
Soil
Geotextile Separator-Fabric
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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The truck traffic inputs for the new M-E Pavement Design Guide software, however, are
the actual truck volume distribution and axle load distributions. Table 1 shows the truck
traffic distribution that was used in this pavement design study. The Truck Traffic
Classification (TTC) group for this urban freeway was assumed to be 3.(3)
Figures 2–4
show the axle load spectra for the single, tandem and tridem axles, respectively.
Table 1 Truck Traffic Volume Distribution for the Base Year, 2005.
Truck Type Normalized Volume Distribution, %
4 0.90
5 11.6
6 3.6
7 0.2
8 6.7
9 62.0
10 4.8
11 2.6
12 1.4
13 6.2
Using the default normalized truck volume and axle weight distributions determined from
an analysis of the Long Term Pavement Performance (LTPP) traffic data and the
AASHTO equivalency factors, the number of 18-kip (80-kN) ESALs were estimated for
the base year for this section of I-96.(3)
Appendix A summarizes the computations for the
ESALs using the normalized axle load distributions that are expected for this urban
freeway. The number of ESALS was computed to be 4,411,425 in 2005 for both
directions, which is almost twice the value used in the 1993 AASHTO design procedure
(2,382,720 ESALs). The reason for this difference is not known, but indicates that the
global default distribution values embedded in the new M-E Pavement Design Guide
software may not be applicable to the truck traffic in Michigan, or at least should be
confirmed prior to full-scale use.
A lane distribution factor of 0.70 and a directional distribution of 0.56 were used to
compute the design-lane ESALs for 2005 – a value of 1,729,279. As noted above, the
ESALs determined from the volume and axle load normalized distributions
recommended for use in the new M-E Pavement Design Guide are greater than those
used in the design study completed by the Michigan DOT. The average number of 18-
kip (80-kN) ESALS per truck application determined using the normalized distributions
was computed to be 1.259 (refer to Appendix A).
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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0
10000
20000
30000
40000
50000
60000
70000
0 10 20 30 40 50
Single Axle Load, kips
Nu
mb
er
of
Mo
nth
ly S
ing
le A
xle
Lo
ad
s
Figure 2 Monthly single axle load distribution or spectra for the base year for
the segment of I-96 from M-39 to Schaeffer Road.
0
5000
10000
15000
20000
25000
30000
35000
0 20 40 60 80 100
Tandem Axle Load, kips
Nu
mb
er
of
Mo
nth
ly T
an
de
m A
xle
Lo
ad
s
Figure 3 Monthly tandem axle load distribution or spectra for the base year for
the segment of I-96 from M-39 to Schaeffer Road.
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0
500
1000
1500
2000
2500
3000
3500
0 20 40 60 80 100 120
Tridem Axle Load, kips
Nu
mb
er
of
Mo
nth
ly T
rid
em
Ax
le L
oa
ds
Figure 4 Monthly tridem axle load distribution or spectra for the base year for
the segment of I-96 from M-39 to Schaeffer Road.
For the simplistic M-E analysis procedure, the design values recommended for use by the
Michigan DOT were used in the design computations and checks because of the different
types of trucks typically used in Michigan, as compared to other agencies from traffic
data included in the LTPP database. Re-analyzing the Weighing-In-Motion (WIM) data
for selected Michigan sites was beyond the scope of work for this thickness design study.
3.2 Subsurface Investigations – Soil Support Design Value
The logs of sixty-nine 5-fott (1.5-meter) borings were provided to determine the types of
soils along this project. The soils along this portion of I-96 consist of varying thickness of
fill or topsoil over a low plasticity, firm silty clay.
The effective resilient modulus of the foundation soil is a design parameter required by
the 1993 AASHTO Design Guide and M-E design procedures. The resilient modulus is
determined from repeated load triaxial tests, and can have a significant impact on the
flexible pavement layer thickness. Resilient modulus tests were unavailable for the soils
along this roadway. The Michigan DOT used a design resilient modulus of 3,000 psi
(20,684 kPa) in the AASHTO design. This design resilient modulus is based on
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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Michigan’s experience and should be conservative for the existing foundation soil that
will not be removed during the reconstruction of this segment along I-96.
Repeated load resilient modulus tests of similar soils, however, are available in the LTPP
database for various sites in Michigan. Figure 5 shows the average test results for this
type of soil, which are similar to those estimated from correlations developed by Von
Quintus, et al.(4)
Thus, the repeated load resilient modulus test results shown in figure 5
were used to estimate the design resilient modulus for the foundation soil for both M-E
design procedures.
0
1
2
3
4
5
6
7
8
9
10
0 5 10
Cyclic Deviator Stress, psi
Re
silie
nt
Mo
du
lus
, k
si Confinement = 2 psi
Confinement = 4psi
Confinement = 6 psi
Figure 5 Average repeated load resilient modulus test results recovered from
the LTPP database for silty clay soils, similar to those encountered
along I-96.
The correlations noted above only represent a best-guessed value for design. The design
values used in the M-E design procedures are greater than the value suggested for use by
the Michigan DOT (3,000 psi or 20,684 kPa) in the AASHTO DARWin program. The
difference in these design resilient modulus values will be discussed in greater detail in a
latter section of this report.
To confirm the design resilient modulus values for the in place soils, however, it is
suggested that repeated load resilient modulus tests be performed in the laboratory on
undisturbed or re-compacted test specimens. If repeated load resilient modulus tests are
not possible, deflection basins can be measured along the existing roadway and the elastic
modulus back-calculated for the subgrade soils using the procedure used by Von Quintus
et al, for LTPP.(5,6)
If modulus values are back-calculated from deflection basins along I-
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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96, they should be adjusted using the correction factors recommended by Von Quintus, et
al.(6)
Based on the boring logs provided, the subgrade soils encountered along the section of I-
96 are believed to have a frost susceptibility classification of moderate or medium using
the Corps of Engineers classification system (refer to figure 6).(7)
It is suggested that a
non-frost susceptible material be placed above the subgrade to minimize the potential for
frost heave over time. Thus, a minimum of 36 inches (914 mm) of non-frost susceptible
materials were included in the pavement cross-sections analyzed in this study.
Results from the subsurface investigations did not indicate ground water at the time of
drilling. Seasonal variation in ground water is expected for this area. Thus, subsurface
drains were assumed in the design computations for determining the required layer
thickness. It is understood that subsurface drains and a geotextile fabric-separator are
included in the planned reconstruction.
3.3 Non-Frost Susceptible Material
For this climatic area, the Michigan DOT requires that 36 inches (914 mm) of non-frost
susceptible material be placed above any frost-susceptible soil based on historical data
and experience. The thickness of non-frost susceptible material requirement was
assumed for this design study and not re-evaluated, as noted above.
Two unbound aggregate materials are available for use in the reconstruction of this
segment along I-96: a class IIA sand subbase and a 21AA-MOD crushed stone aggregate
base. Resilient modulus tests were completed and are available for similar materials from
the FHWA-LTPP database for test sections in Michigan. This laboratory data was used to
estimate the resilient modulus for each of these materials, similar to the method used to
develop Pavement Structural Design Study – A Simplified Catalog of Solutions.(2)
A
geotextile fabric should be used as a separator layer between the crushed aggregate base
and sand subbase.
Sand Subbase Material
It is understood that the existing sand material encountered in the borings along I-96 will
be replaced with Class IIA material for the flexible pavement design option. Resilient
modulus tests on the sand proposed for use were unavailable. However, repeated load
resilient modulus tests performed on materials classified as sand subbases were
previously extracted from the LTPP database.
Figures 17 to 20 in Appendix B graphically present the distribution of the resilient
modulus measured at specific stress states. It is important to note that the distributions
appear to be normal for those groups with a sufficient number of tests. This normal
distribution of resilient modulus values at specific stress states is also applicable to other
unbound materials that have a sufficient number of resilient modulus tests.
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Table 2 summarizes the median resilient modulus values included in Appendix B for
sandy soils and sand subbase materials. As tabulated, the median resilient modulus for
the sand subbase material is about 18,500 psi (127,553 kPa) for all tests, as well as the
tests for samples recovered from only the LTPP sites located in Michigan.
Figure 6. Average rate of heave versus percentage finer than 0.02 mm for natural
soil gradations.(6)
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Figure 7 shows the average test results for a Class IIA sand subbase material in Michigan
that were extracted from the LTPP database. These average test results were used to
determine the design resilient modulus for both M-E design procedures.
Table 2 Median resilient modulus measured on the sand subbases and sand
subgrades recovered from all of the LTPP sites and from those sites
that are located in Michigan.
Median Resilient Modulus, psi (MPa)
(Refer to figures 17 to 20 in Appendix B) Material/
Layer
Stress State
All LTPP Sites LTPP Sites in Michigan
Sand
Subbase
Confinement = 10 psi
Cyclic Stress = 9 psi
18,400 (126.9)
(N=62)*
18,700 (128.9)
(N=10)
Sand
Subgrade
Confinement = 2.0 psi
Cyclic Stress = 1.8 psi
7,700 (53.1)
(N=440)
8,300 (57.2)
(N=7)
* N = number of resilient modulus tests within each group.
0
5
10
15
20
25
30
35
0 50 100 150
Bulk Stress, psi
Re
silie
nt
Mo
du
lus
, k
si
Confinement = 3 psi
Confinement = 5 psi
Confinement = 10 psi
Confinement = 15 psi
Confinement = 20 psi
Figure 7 Average repeated load resilient modulus test results extracted from
the LTPP database for a sand subbase that is expected to be similar to
the material placed along I-96.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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Crushed Stone Aggregate Base Material
The crushed stone aggregate base material planned for use along I-96 is a material that
meets the Michigan DOT’s specification for a 21 AA-MOD material. Table 3 lists the
gradation for this aggregate base material. The resilient modulus tests completed on
unbound aggregate base materials were extracted from the LTPP database for similar
aggregate base materials. However, no resilient modulus tests have been completed on
aggregate base materials that have a similar gradation to the one listed in table 3. Most of
the base material tested within the LTPP program represents a more dense material.
Figure 8 shows the average test results from repeated load resilient modulus tests for
aggregate base materials that are as close as possible – but have slightly more material
passing the smaller sieve sizes. These average values included in figure 8 were used in
the study for the crushed stone aggregate base material.
Table 3 Gradation requirements for the 21 AA-MOD crushed aggregate base
planned for use along I-96.
Sieve Size 37.5 mm 25.0 mm 12.5 mm 2.36 mm 0.60 mm 0.075 mm
Percent
Passing, % 100 80-100 40-70 15-35 5-20 <8
0
5
10
15
20
25
30
35
40
0 50 100 150
Bulk Stress, psi
Re
silie
nt
Mo
du
lus
, k
si
Confinement = 3 psi
Confinement = 5 psi
Confinement = 10 psi
Confinement = 15 psi
Confinement = 20 psi
Figure 8 Average repeated load resilient modulus test results extracted from
the LTPP database for a 21AA crushed aggregate base.
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3.4 Hot Mix Asphalt Mixtures
Three hot mix asphalt (HMA) mixtures are planned for use along I-96; an HMA wearing
course, an HMA leveling course, and an HMA base course (refer to figure 1). The elastic
modulus of the HMA is an input parameter for both the M-E analysis methods used in
this design study. Dynamic modulus tests are unavailable for the mixtures planned for
use along I-96, and are not included in the LTPP database. Thus, the Witczak dynamic
modulus regression equation embedded in the new M-E Pavement Design Guide was
used to calculate the modulus for each HMA mixture.
Figures 9 to 11 show the average modulus at the mid-depth of each HMA layer. These
monthly values at various depths were used in the new M-E Pavement Design Guide
software. However, an equivalent annual modulus for each layer was used with the
simplistic M-E analysis method. These resulting equivalent annual modulus values are
provided in Appendix C.
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15
Month of Year
Dyn
am
ic M
od
ulu
s, ksi
Figure 9 Monthly average dynamic modulus values calculated at the mid-depth
of the HMA wearing surface and leveling layers.
The HMA mixtures are assumed to have minimum fracture characteristics. Figure 12
graphically illustrates the minimum tensile strains at failure as a function of the resilient
modulus measured using indirect tensile testing methods in accordance with the
procedure recommended by Von Quintus, et al.(12)
The fatigue cracking criteria used in
the design study corresponds to the relationship in figure 12. The evaluation of fatigue
cracking for the HMA layers was completed in accordance with the steps outlined by
Von Quintus, et al., and Von Quintus and Killingsworth.(10,12)
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0
500
1000
1500
2000
2500
3000
3500
0 5 10 15
Month of Year
Dyn
am
ic M
odu
lus, ksi
Figure 10 Monthly average dynamic modulus values calculated at the mid-depth
of the upper portion of the HMA base layer.
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15
Month of Year
Dyn
am
ic M
od
ulu
s, ksi
Figure 11 Monthly average dynamic modulus values calculated at the mid-depth
of the lower portion of the HMA base layer.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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1
10
100
10 100 1000 10000
Total Resilient Modulus, psi
Ten
sile S
train
at
Failu
re, m
ils/in
.
Figure 12 Relationship between minimum tensile failure strains and indirect
tensile resilient modulus.(12)
3.5 Subsurface Drainage System
A subsurface drainage system was included in the proposed design for I-96. The
subsurface drainage system ensures that the non-frost susceptible sand subbase and soils
will not become saturated for extended periods of time. This recommendation and design
feature is based on information recovered from boring logs and reported by Michigan
DOT for the supporting soils in adjacent areas along I-96.
4. Mechanistic-Empirical Thickness Design-Evaluation Method
Two M-E analysis procedures were used to evaluate the design resulting from the
AASHTO DARWin program (refer to figure 1). One is defined as the simplistic M-E
procedure and the other is the new M-E Pavement Design Guide. Appendix C includes
the response computations for the simplistic M-E procedure, while Appendix D provides
the results of the evaualtion using the new M-E Pavement Design Guide software. This
section of the report provides a summary of the results from the simplistic and new M-E
analysis procedures.
The structural deterioration of flexible pavements is associated with cracking of the HMA
surface, and/or development of ruts in the wheel path. The methodology used in this
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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study, applies the cumulative damage concept in the prediction of these two modes of
distress. Use of the cumulative damage concept permits accounting, in a rational manner,
for damage caused by each load application.
Seasonal and other variations in material properties and modulus of each layer with
different loads can be considered in these predictions of damage. Evaluations of design
life for candidate pavement structures are based on computations of damage caused by
each truck type and load (or an 18-kip ESAL) for different seasons of the year, and
summing the results to obtain the total damage to the pavement structure. For this design
study, however, dynamic modulus tests results were unavailable for all HMA mixtures
planned for use along I-96. As noted above, the dynamic modulus for the HMA mixtures
were calculated using the Witczak regression equation included in the new M-E
Pavement Design Guide software. An equivalent annual modulus for similar HMA
mixtures was used in the design study. The equivalent annual modulus values are
included in Appendix C.
4.1 Pavement Structural Evaluation Assumptions
The pavement layer thickness and material types were based on mechanistic-empirical
techniques, in accordance with the following assumptions and design features.
• The pavement structural response model used to calculate pavement responses
for the simplistic M-E analysis method was based on elastic layer theory -
EVERSTRS.
• The proposed pavement structure was evaluated using the design criteria for
fatigue cracking (limiting the tensile strain at the bottom of the HMA layers),
HMA rutting (limiting the vertical strain at the mid-depth of each HMA
layer), and subgrade distortion (limiting the vertical strain at the top of the
foundation soil).
• Structural design life = 20 years.
• Tire load = 4,500 lbs. (20 kN) per tire.
• Tire pressure = 120 psi (827 kPa).
• Sand Subbase; Assumed to be non-frost susceptible and determined from
repeated load resilient modulus tests included in the LTPP database, figure 7;
Poisson’s ratio = 0.40.
• Aggregate Base (21AA-MOD); Determined from repeated load resilient
modulus tests included in the LTPP database, figure 8; Poisson’s ratio = 0.35.
• The combined equivalent annual elastic layer modulus for the HMA surface,
leveling, and base mixtures = 892,000 psi (127.6 MPa) for the simplistic M-E
analysis method, refer to Appendix C; Poisson’s ratio = 0.30. For the new M-
E Pavement Design Guide, the dynamic modulus default values for a
Superpave mix with a PG 70-22 asphalt was used (figures 9-11). The asphalt
grades included as defaults in the new M-E Design Guide software are only
for the standard grades.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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4.2 Evaluation Criteria
The objective of this study was to evaluate the flexible pavement structure shown in
figure 1 using M-E criteria over two analysis periods: 20 and 40 years. The failure of a
pavement system under the cumulative damage concept is assumed to occur when the
damage index reaches a fixed amount, generally 1.0. It should be understood that a
damage index of 1.0 does not necessarily imply a functional failure, but is instead that
level of damage selected as sufficient to warrant maintenance and/or rehabilitation.
Failure of flexible pavements is defined as alligator cracking over 10 to 20 percent of the
area subjected to wheels or one-half inch (12.7 mm) of foundation rutting.
For this study, a damage index of 1.0 means the pavement has been subjected to a
sufficient number of wheel loads (Nf) to cause 10 to 20 percent alligator cracking of
moderate to high severity or 0.5 inches (12.7 mm) of foundation distortion. In addition, a
value of 0.40 inches (10 mm) of distortion (rutting, ∆HMA) in the HMA layers was also
used in the evaluation. These values of 10 to 20 percent cracking and 0.5 inches (12.7
mm) of foundation distortion were selected, because previous studies of in-service
pavements have indicated that these levels will usually trigger some type of pavement
rehabilitation.
4.3 Simplistic M-E Analysis Method
Fatigue Cracking Evaluation
Two fatigue cracking models were used with the simplistic M-E analysis method.
Equation 1 and figure 13 were used to determine the allowable number of load
applications for fatigue cracking analysis of the pavement structure.
( ) ( )( ) ( ) 854.0291.300432.0
−−= ECFatigueN tf ε (1)
Where:
( )MC 10= (2)
−
+= 69.084.4
bea
be
VV
VM (3)
εt = Tensile strain at the bottom of the HMA layer, in./in.
E = HMA elastic or dynamic modulus, psi.
C = Correction factor to account for volumetric properties
Vbe = Percent effective asphalt content by volume in HMA mixture, %
Va = Percent air voids in the HMA mixture, %
Equation 1 is based on 20 percent fatigue cracking, and is the equation embedded in the
new M-E Pavement Design Guide software, but without the global calibration factors.
The global calibration factors were not used because they were determined based on the
cracking predictions using the modulus values of each layer within specific time intervals
and seasons. The simplistic M-E method uses equivalent annual modulus values for each
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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layer, which are presented and discussed in Appendix C. Figure 13 presents the
allowable number of load applications for 10 percent cracking. Table 4 summarizes the
allowable or permissible tensile strain at the bottom of the HMA layer for both the 20 and
40-year traffic levels using both fatigue cracking relationships.
The tensile strain at the bottom of the HMA layers was computed with EVERSTRS for
the AASHTO design, which is also included in table 4 (refer to Appendix C). As shown,
the computed tensile strain is less than the permissible HMA tensile strains for both
fatigue cracking models. In fact, the computed tensile strain of 49.7 micro-strains is
below the assumed endurance limit for HMA. Typical values being used for the
endurance limit are in the range of 65 to 75 micro-strains. Thus, fatigue cracking should
not be a problem for the proposed structure.
Figure 13 Relationship between HMA tensile strain and allowable wheel load
applications for the alligator cracking failure criteria.(8)
Distortion Evaluation – Unbound Layers
Equation 4 and figure 14 were used to determine the allowable number of load
applications for distortion analyses of the unbound layers in the pavement structure.
( ) ( ) ( )( ) 082.4955.01110259.1−−
= SoilvRf MxDistortionN ε (4)
0.0001
0.0010
0.0100
1,000 10,000 100,000 1,000,000 10,000,000
Wheel Load Applications
Asp
halt
Co
ncre
te T
en
sile S
train
, in
/in
1,000,000 psi
600,000 psi
300,000 psi
100,000 psi
Asphalt Concrete Modulus
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Where:
MR = Resilient modulus of the foundation soil, psi.
εv(Soil) = Vertical strain at the top of the foundation soil, in./in.
Table 4 summarizes the allowable or permissible vertical strain at the top of the sand
subbase and foundation soil for both the 20 and 40-year traffic levels. The vertical strains
at the top of the sand subbase and foundation soil were computed with EVERSTRS for
the AASHTO design, which are also included in table 4 (refer to Appendix C). As
shown, the computed vertical strains are significantly less than the permissible vertical
strains for both layers. Thus, distortion in the unbound layers should not be a problem for
the proposed structure.
Table 4 Limiting criteria that were used to evaluate the design layer thickness
(refer to figure 1) for a 20 and 40-year analysis periods.
Limiting or Permissible
Values Design Criteria
20-Year
Analysis
40-Year
Analysis
Computed
Responses
(See Note 1)
Design 80-kN (18-kip) ESALs 22,694,400 56,000,000 ---
Equation 1;
20% Cracking 0.000100 0.000075 Tensile strain at the
bottom of the HMA
layers, in./in. Figure 13;
10% Cracking 0.000070 0.000053
0.0000497
Vertical Strain in the HMA layers,
in./in. 0.000091 0.000068 0.00009196*
Vertical strain at the top of the non-
frost susceptible sand material, in/in. 0.000284 0.000227 0.0000993
Vertical strain at the top of the
foundation soil, in./in. 0.000235 0.000187 0.0000889
Permissible maximum surface
deflection, in. 0.0175 0.0158 0.0108
Unbound layer modulus ratios Material and Thickness
Dependent, but <3.0 ---
Note 1: Pavement responses determined at the equivalent annual or summer modulus values for the
standard 18-kip ESAL. The pavement responses were computed with the EVERSTRS elastic layered
program (refer to Appendix C).
*Note 2: Those cells shaded or highlighted with bold numbers indicate the computed values that exceed
the permissible values listed.
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Figure 14 Relationship between subgrade vertical strain and allowable wheel
load applications for the foundation deformation failure criteria.(9)
Rutting Evaluation – HMA Layers
Equation 5 was used to calculate the expected rutting within the HMA layers (∆HMA) of
the pavement structure and the permissible vertical strain in the HMA so that the rut
depth in the HMA layers does not exceed 0.40 inches (10 mm).
( ) ( ) ( ) ( ) ( ) ( )( )( )HMAHMAvfabeHMA tcNVVTx ε4289.05213.00057.15896.271037.5 −
=∆ (5)
Where:
T = Mid-depth temperature of the HMA layer thickness increment, in.
εv(HMA) = Vertical strain at the mid-depth of the HMA layer thickness increment,
in./in.
cf = Confinement factor
tHMA = Thickness of the HMA increment, inches
Table 4 summarizes the allowable or permissible vertical strain at the mid-depth of the
HMA surface layers for both the 20 and 40-year traffic levels. The vertical strains at the
mid-depth of the HMA surface layers were computed with EVERSTRS for the AASHTO
design, which are also included in table 4 (refer to Appendix C). As shown, the
0.0001
0.0010
0.0100
1,000 10,000 100,000 1,000,000 10,000,000
W heel Load Applications
Su
bg
rad
e V
ert
ica
l C
om
pre
ss
ive
Str
ain
, in
/in
20,000 psi
10,000 psi
6,000 psi
3,000 psi
2,000 psi
Subgrade Modulus
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computed vertical strain is greater than the permissible vertical strain. The rutting
calculated with equation 5 is 0.48 inches (12 mm) for the 20-year traffic and 0.70 inches
(18 mm) for the 40-year traffic. Thus, the simplistic M-E method suggests that rutting in
the HMA layers is expected to require the pavement to be rehabilitated within the
analysis period.
Other Evaluation Criteria
Two other criteria were used for the simplistic M-E thickness design check or evaluation.
One is based on limiting the maximum surface deflection and the other is based on
limiting the modulus ratio between two adjacent unbound pavement layers (figure 15).
The long-term in place modulus of unbound base and subbase layers are dependent on the
modulus of the supporting layer because of potential de-compaction in the lower portion
of these layers. The Corp of Engineers developed criteria to limit the modulus of
unbound aggregate layers based on the thickness of that layer and the modulus of the
supporting layer.(9)
This limiting modulus ratio criteria (figure 15) was used in
determining the limiting modulus of the unbound aggregate base and subbase layers. The
elastic layer modulus used in the design computations with EVERSTRS for the unbound
layers are less than those that would result from using figure 15, because the actual stress
sensitivity was used in determining those values.
The permissible surface deflection is listed in table 4 for the two traffic levels or analysis
periods. This permissible deflection criteria has been used by Von Quintus and
Killingsworth and others in analyzing the performance of in-service pavements.(10,11)
Table 4 also includes the maximum surface deflection computed with EVERSTRS (refer
to Appendix C). As shown, the computed value is less than the permissible value.
4.4 New M-E Pavement Design Guide Software
The new M-E Pavement Design Guide software was used to evaluate the proposed
pavement cross section designed using the AASHTO DARWin program. The inputs
used in the program were the best available data and the global default values were used
when insufficient data were available. Appendix D includes a summary of the inputs
used and predicted distresses over time. A 30-year analysis period was used in the
problem rather than 40 years, because the program became unstable above 30 years.
In summary, the proposed flexible pavement and HMA mixtures are not expected to
exhibit significant levels of distress, with the exception of rutting. The new M-E
Pavement Design Guide software predicts greater levels of rutting in the unbound
materials, especially in the foundation soil. One reason for this result is that most of the
sites used in the calibration process for the new software have resilient modulus values
for the subgrade and unbound base layers much greater than those used in this design-
evaluation study.
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Figure 15 Limiting modulus criteria of unbound aggregate base and subbase
layers.(9)
1 10 100
Modulus of Layer n + 1, 10 psi
1
10
100M
odulu
s o
f Layer
n, 10 p
si
3
BASE COURSES
(Meter = Inch x .0254) SUBBASE COURSES
THIC
KNESS
10"
6"
4"
4"
6"
5"7"
8"
105 psi = 698 MPa
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5. Summary of Evaluations
Table 5 provides a summary of all distresses predicted with the different M-E analysis
methods used in this study. In summary, the pavement design cross section proposed for
the reconstruction of I-96 is adequate relative to cracking. The one concern is with
rutting and distortion.
The new M-E Pavement Design Guide software predicts most of the distortion in the
unbound layers and foundation soil, while the simplistic M-E analysis method predicts
that most of the rutting will occur in the HMA layers. As noted in the previous section, it
is believed that the rutting is being over predicted in the foundation soil with 14 inches of
HMA and 16 inches of a crushed aggregate base. In addition, this segment of I-96 has a
much higher traffic level than most of the LTPP sections that were used in the calibration
of the new M-E Pavement Design Guide have much less traffic. For this reason, it is
believed that most of the rutting will be in the HMA mixtures.
Table 5 Summary of distresses predicted for the two analysis periods using the
two M-E analysis methods.
Simplistic M-E Method New M-E Pavement
Design Guide Software Predicted Distress
20-Year 40-Year 20-Year 40-Year
Damage
Index
0.324
(0.101)*
0.801
(0.249)* 0.028 0.047
Fatigue
Cracking Area
Cracking, %
2
(0)*
6
(1)* 8.4 11.9
Top-Down Cracking, ft./mi. NA NA 267 274
Thermal Cracking, ft./mi. NA NA 40 211
PG 70-22 0.48 0.70 0.77 0.86 Total Rutting,
inches PG 76-22 0.36 0.54 NA NA
PG 70-22 0.48 0.70 0.21 0.26 Layer Rutting
or Distortion,
inches Unbound
Layers Minimal Minimal 0.56 0.60
IRI, in./mi. NA NA 120 134 *Note 1: The values in () for fatigue cracking are for the predictions using figure 13, while the
other fatigue cracking numbers are based on equation 1.
Note 2: The cells that are shaded or highlighted in the table exceed the allowable or permissible
distress magnitudes at the end of each analysis period.
An additional structure was analyzed to reduce the rutting in the HMA layers. The only
difference between the proposed AASHTO-designed flexible pavement and other
structure is that a PG 76-22 was included in the top two HMA layers (wearing surface
and leveling course). The comparison of the predicted rutting for the two asphalts is
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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shown in figure 16 and included in table 5. Using the stiffer asphalt will reduce rutting to
an acceptable level, even for the 40-year analysis period.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Age, Years
Ru
t D
ep
th, in
ch
es
PG 76-22 PG 70-22
Figure 16 Comparison of predicted rutting for HMA mixtures with a PG 70-22
and a PG 76-22.
As shown in figure 1, a PG 70-22 asphalt is planned for use in the top two HMA layers.
Whether the dynamic modulus regression equation will adequately estimate the stiffness
values for the PG 70-22P mixtures is questionable. Whether a PG 70-22P or PG 76-22 is
used should be defined based on asphalt or mixture modulus testing or some type of
torture test to ensure that the HMA mixtures will be resistant to rutting. Without any
additional mixture testing, it is suggested that a PG 76-22 asphalt be included in the top
two mixtures. In addition, it should be confirmed that the pavement materials meet or
exceed the assumptions used in design. It is also recommended that sufficient testing be
completed during construction to ensure that the design assumptions are satisfied prior to
construction.
6. Limitations
All work performed under this study was conducted in accordance with generally
accepted pavement engineering practices using data and project information provided by
the Mr. Curtis Bleech. No other warranty, express or implied, is made. The generalized
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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pavement thickness design recommendations presented herein were based upon the
assumed subsurface and material conditions identified in the report. Sufficient testing
should be completed during construction for quality control purposes and to confirm the
design values assumed for this design study.
7. References
1. AASHTO, 1993 AASHTO Design Guide for Pavement Structures, American
Association of State Highway and Transportation Officials, 1993.
2. Von Quintus, Harold L., Pavement Structural Design Study – A Simplified Catalog of
Solutions, Report No. 3065, Fugro-BRE, Inc. December 2001.
3. NCHRP 1-37A, Mechanistic-Empirical Design Method for the Structural Design of
New and Rehabilitated Pavement Structures, Final Report for NCHRP 1-37A,
National Cooperative Highway Research Program, Washington, DC, 2004.
4. Von Quintus, Harold and Amber Yau, Evaluation of Resilient Modulus Test Data in
LTPP Database, Report No. FHWA/RD-01-158, Federal Highway Administration,
Office of Infrastructure Research and Development, Washington, DC, 2001.
5. Von Quintus, Harold and Amy Simpson, Documentation of the Back-Calculation o f
Layer Parameters for LTPP Test Sections, Volume II: Layered Elastic Analysis for
Flexible and Rigid Pavements, Final Report LTPP DATA, Work Order 9, Task 2
Contract No. DTFH61-96-C-00003, Federal Highway Administration, U.S.
Department of Transportation, January 1999.
6. Von Quintus, Harold and Brian Killingsworth, Design Pamphlet for the
Backcalculation of Pavement Layer Moduli, Publication No. FHWA-RD-97-076,
Federal Highway Administration, Washington, D.C., June 1997.
7. Soils and Geology – Pavement Design for Frost Conditions, TM5-818-2, Department
of the Army Technical Manual, Headquarters, Department of the Army, July 1965.
8. Finn, F.N., K. Nair, C. Monismith, Minimizing Premature Cracking of Asphalt
Concrete Pavements, NCHRP Report No. 195, National Cooperative Highway
Research Program, National Research Council, Washington, DC, June 1973.
9. Barker, W. R. and W. N. Brabston, Development of a Structural Design Procedure
for Flexible Airport Pavements, FAA Report No. FAA-RD-74-199, U.S. Army
Engineer Waterways Experiment Station, Federal Aviation Administration,
September 1975.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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10. Von Quintus, H. L. and Brian Killingsworth, Analyses Relating to Pavement Material
Characterizations and Their Effects on Pavement Performance, Publication No.
FHWA-RD-97-085, Federal Highway Administration, January 1998.
11. Rauhut, J.B. R.L. Lytton, and M.I. Darter, Pavement Damage Functions for Cost
Allocation, Volume 1: Damage Functions and Load Equivalence Factors, Publication
No. FHWA/RD-84-018, Federal Highway Administration, Washington, DC, 1984.
12. Von Quintus, H.L., J.A. Scherocman, C.S. Hughes and T.W. Kennedy, Asphalt-
Aggregate Mixture Analysis System-AAMAS, NCHRP Report No. 338, National
Cooperative Highway Research Program, National Research Council, Washington,
DC, March 1991.
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Appendix A
Summary of Truck Traffic Equivalent Single Axle Load Applications
Computed for the Base Year 2005
Appendix A includes a copy of the spreadsheet used to compute the number of 80-kN
(18-kip) equivalent single axle loads for the base year using the default distributions that
are included in the new M-E Pavement Design Guide for an urban freeway similar to I-
96.
As shown on the attached spreadsheet, the total number of annual ESALs for 2005 is
4,411,425 for both directions. Using a directional distribution factor of 0.56 and a lane
distribution factor of 0.70, the total number of annual ESALs in the design lane is
1,729,279. The average truck equivalency factor for this truck traffic stream is 1.259
ESAL per truck application.
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Appendix B Summary of Repeated Load Resilient Modulus Tests Extracted from
the LTPP Database for the Michigan Sites.
Distribution of Average resilient Modulus for GSGB (Sand).
RES_MOD_AVG
50
100
150
200
250
Quantiles
maximum
quartile
median
quartile
minimum
100.0%
99.5%
97.5%
90.0%
75.0%
50.0%
25.0%
10.0%
2.5%
0.5%
0.0%
226.00
226.00
200.12
151.70
138.00
127.00
112.00
103.30
73.72
72.00
72.00
Moments
Mean
Std Dev
Std Error Mean
Upper 95% Mean
Lower 95% Mean
N
Sum Weights
126.7581
24.4612
3.1066
132.9700
120.5461
62.0000
62.0000
Figure 17 Resilient modulus (in MPa) measured on sand base and subbase
materials recovered from all sites in the LTPP program for a
confining pressure of 10 psi (69 kPa) and a cyclic stress of 9 psi
(62kPa). The resilient modulus values given above are in MPa.
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Distribution of Average resilient Modulus for GSGB (Sand) for Michigan sites.
RES_MOD_AVG
100
120
140
160
180
200
Quantiles
maximum
quartile
median
quartile
minimum
100.0%
99.5%
97.5%
90.0%
75.0%
50.0%
25.0%
10.0%
2.5%
0.5%
0.0%
181.00
181.00
181.00
178.10
143.75
129.00
115.75
114.10
114.00
114.00
114.00
Moments
Mean
Std Dev
Std Error Mean
Upper 95% Mean
Lower 95% Mean
N
Sum Weights
133.2000
21.1019
6.6730
148.2955
118.1045
10.0000
10.0000
Figure 18 Resilient modulus (in MPa) measured on sand base and subbase
materials recovered from all Michigan sites included in the LTPP
program for a confining pressure of 10 psi (69 kPa) and a cyclic stress
of 9 psi (62 kPa). The resilient modulus values given above are in
MPa.
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Distribution of Average resilient Modulus Subgrade Sand.
RES_MOD_AVG
100
200
Quantiles
maximum
quartile
median
quartile
minimum
100.0%
99.5%
97.5%
90.0%
75.0%
50.0%
25.0%
10.0%
2.5%
0.5%
0.0%
191.00
147.36
111.87
84.00
67.00
53.00
43.00
36.00
28.00
23.00
18.00
Moments
Mean
Std Dev
Std Error Mean
Upper 95% Mean
Lower 95% Mean
N
Sum Weights
57.6341
21.3246
1.0166
59.6321
55.6360
440.0000
440.0000
Figure 19 Resilient modulus (in MPa) measured on sand recovered from the
subgrade at all sites in the LTPP program for a confining pressure of
2.0 psi (13.8 kPa) and a cyclic stress of 1.8 psi (12.4 kPa). The resilient
modulus values given above are in MPa.
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Distribution of Average resilient Modulus for Sugrade Sand for Michigan sites.
RES_MOD_AVG
50
100
150
200
Quantiles
maximum
quartile
median
quartile
minimum
100.0%
99.5%
97.5%
90.0%
75.0%
50.0%
25.0%
10.0%
2.5%
0.5%
0.0%
191.00
191.00
191.00
191.00
63.00
57.00
50.00
42.00
42.00
42.00
42.00
Moments
Mean
Std Dev
Std Error Mean
Upper 95% Mean
Lower 95% Mean
N
Sum Weights
73.4286
52.3477
19.7856
121.8422
25.0150
7.0000
7.0000
Figure 20 Resilient modulus (in MPa) measured on sand recovered from the
subgrade at all Michigan sites included in the LTPP program for a
confining pressure of 2.0 psi (13.8 kPa) and a cyclic stress of 1.8 psi
(12.4 kPa). The resilient modulus values given above are in MPa.
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Appendix C Layer Properties and Pavement Responses Computed for the I-96
Design Cross Section
Appendix C includes a summary of the methods used to determine the elastic modulus
values for each layer and a copy of the pavement responses that were used to evaluate the
pavement structure. These responses were calculated with EVERSTRS for the standard
design axle load – 18-kip single axle load.
C.1 HMA Modulus Determination
As noted in the report, the dynamic modulus regression equation was used to estimate the
average modulus of each HMA mixture for each month of an average year. The first part
of Appendix C includes the spreadsheet used to determine the monthly modulus values
and the equivalent annual layer modulus for the HMA mixtures used in the fatigue
cracking analysis. For the rutting analysis and predictions made with the simplistic M-E
method, the elastic modulus for the three summer months was used.
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C.2 Unbound Layer Modulus Determination
The second part of Appendix C includes a summary of the procedure and responses used
to determine the resilient modulus for each unbound layer. In other words, select an
elastic modulus for the unbound materials and soils to ensure that the theory
(EVERSTRS) and laboratory provide consistent values at the same stress state for use in
the fatigue analysis.
One of the important steps in this process is to include the at-rest stresses with those
computed from EVERSTRS. Table 6 provides a summary of the information and data
that were used to compute the overburden pressures and at-rest stresses in each unbound
layer.
Table 6 Data used to calculate the overburden pressure and at-rest stresses in
each unbound layer of the design cross section (refer to figure 1).
Layer/Material Type Dry Density,
pcf
Moisture
Content, %
At-Rest Earth Pressure
Coefficient, ko
HMA; average of all three
layers 150 --- ---
21 AA-MOD Crushed
Aggregate Base 130 7.0 0.9
Class II-A Sand Subbase 136 7.0 0.9
Low Plasticity, Firm Silty
Clay 116 13.0 0.5
Table 7 summarizes the EVERSTRS computations from two iterations of using trial
elastic modulus values for each unbound layer. The two iterations demonstrate the need
to check the values used in the elastic layer program to ensure that the theory and
laboratory values provide consistent results. As summarized in table 7, the first iteration
used the design resilient modulus suggested for use by the Michigan DOT and the
maximum layer modulus ratio to estimate the elastic modulus of all other unbound layers
(refer to figure 15). The trial or “guessed” resilient modulus values are not consistent
with the values that would be measured in the laboratory from repeated load tests (figures
5,7, and8). However, the modulus values used in the second iteration are, for all practical
purposes the same values that would be measured in the laboratory at the same stress
states. The values from the second iteration were used in the fatigue cracking analysis.
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Table 7 Comparison of the trial elastic layer modulus used in EVERSTRS with those measured from repeated load
resilient modulus tests in the laboratory at the same stress state.
At-Rest Stress @ ¼
Layer Depth, psi
Stresses Computed w/EVERSTRS @
¼ Layer Depth, psi Total Stress State, psi
Iteration No. &
Unbound Layer
Trial E-
Value, ksi ZZ
XX &
YY ZZ XX YY
Confining
Stress
Deviator
Stress
Bulk
Stress
Lab E-
Value, ksi
Silty Clay* 3 -4.55 -2.28 -0.30 -0.04 -0.04 2.32 2.53 --- 5.1 Sand Subbase 9 -2.68 -2.41 -0.50 0.37 0.39 2.02 --- 7.24 6.8 1
Aggregate Base 20 -1.54 -1.39 -1.21 0.42 0.51 0.88 --- 4.60 6.5
Silty Clay* 5.2 -4.55 -2.28 -0.41 -0.07 -0.07 2.69 2.61 --- 5.2 Sand Subbase 7.0 -2.68 -2.41 -0.64 0.02 0.04 2.37 --- 8.08 7.2 2
Aggregate Base 7.5 -1.54 -1.39 -0.97 -0.11 -0.07 1.46 --- 5.47 7.5
*NOTE: The stress state was determined at the ¼ depth within each unbound layer, with the exception for the foundation or subgrade soils. The stress state was
determined 18-inches into the subgrade. These depths are consistent with the values recommended for use by Von Quintus, et al. (10)
The at-rest stresses were
computed using the information and data included in table 6.
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C.3 EVERSTRS Output for Fatigue Cracking Analyses
The following is a summary of the output from the EVERSTRS program for the design
cross section using the layer modulus values determined in the previous section of
Appendix C. The other pavement responses are also included in this ouput for
determining the damage index for fatigue cracking and foundation distortion, and
whether the design cross section will be provide adequate performance over the two
analysis periods. These responses are based on equivalent annual modulus values.
CLayered Elastic Analysis by EverStress for Windows
Title: Michigan I-96 Reconstruction No of Layers: 5 No of Loads: 2 No of X-Y Evaluation Points: 2
Layer Poisson's Thickness Moduli(1)
* Ratio (in) (ksi)
1 0.3 14 892
2 0.35 16 7.5
3 0.35 8 7
4 0.45 240 5.2
5 0.4 * 50
Load No X-Position Y-Position Load Pressure Radius
* (in) (in) (lbf) (psi) (in)
1 0 0 4500 120 3.455
2 13 0 4500 120 3.455 Location No: 1 X-Position (in): .000 Y-Position (in): .000
cNormal Stresses
Z-Position Layer Sxx Syy Szz Syz Sxz Sxy
(in) * (psi) (psi) (psi) (psi) (psi) (psi)
13.999 1 49.55 56.79 -1.15 0 0.13 0
18 2 -0.11 -0.07 -0.97 0 0.1 0
32 3 0.02 0.04 -0.64 0 0.05 0
38.1 4 -0.12 -0.11 -0.56 0 0.03 0
56 4 -0.07 -0.07 -0.41 0 0.02 0
cNormal Strains and Deflections
Z-Position Layer Exx Eyy Ezz Ux Uy Uz
(in) * (10^-6) (10^-6) (10^-6) (mils) (mils) (mils)
13.999 1 36.83 47.39 -37.06 -0.246 0 10.163
18 2 34.26 40.87 -121.13 -0.235 0 9.642
32 3 33.55 35.68 -94 -0.224 0 8.197
38.1 4 35.04 36.79 -87.08 -0.233 0 7.643
56 4 28.26 29.03 -67.77 -0.186 0 6.268
cPrincipal Stresses and Strains
Z-Position Layer S1 S2 S3 E1 E2 E3
(in) * (psi) (psi) (psi) (10^-6) (10^-6) (10^-6)
13.999 1 -1.15 49.55 56.79 -37.06 36.83 47.39
18 2 -0.98 -0.1 -0.07 -123.34 36.47 40.87
32 3 -0.64 0.03 0.04 -94.71 34.26 35.68
38.1 4 -0.56 -0.12 -0.11 -87.81 35.77 36.79
56 4 -0.41 -0.07 -0.07 -68.11 28.6 29.03
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Location No: 2
X-Position (in): 6.500 Y-Position (in): .000
cNormal Stresses
Z-Position Layer Sxx Syy Szz Syz Sxz Sxy
(in) * (psi) (psi) (psi) (psi) (psi) (psi)
13.999 1 51.24 59.38 -1.19 0 0 0
18 2 -0.1 -0.07 -1.01 0 0 0
32 3 0.03 0.04 -0.65 0 0 0
38.1 4 -0.12 -0.11 -0.57 0 0 0
56 4 -0.07 -0.07 -0.42 0 0 0
cNormal Strains and Deflections
Z-Position Layer Exx Eyy Ezz Ux Uy Uz
(in) * (10^-6) (10^-6) (10^-6) (mils) (mils) (mils)
13.999 1 37.87 49.74 -38.54 0 0 10.299
18 2 36.9 42.51 -126.58 0 0 9.756
32 3 34.99 36.22 -96.23 0 0 8.26
38.1 4 36.26 37.23 -88.89 0 0 7.695
56 4 28.82 29.22 -68.58 0 0 6.299
cPrincipal Stresses and Strains
Z-Position Layer S1 S2 S3 E1 E2 E3
(in) * (psi) (psi) (psi) (10^-6) (10^-6) (10^-6)
13.999 1 -1.19 51.24 59.38 -38.54 37.87 49.74
18 2 -1.01 -0.1 -0.07 -126.58 36.9 42.51
32 3 -0.65 0.03 0.04 -96.23 34.99 36.22
38.1 4 -0.57 -0.12 -0.11 -88.89 36.26 37.23
56 4 -0.42 -0.07 -0.07 -68.58 28.82 29.22
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C.4 EVERSTRS Output for HMA Rutting Analyses
The output from the EVERSTRS program summarized below was used to calculate the
expected rutting in the HMA layers using the average summer modulus values.
CLayered Elastic Analysis by EverStress for Windows
Title: Michigan I-96 Reconstruction No of Layers: 5 No of Loads: 2 No of X-Y Evaluation Points: 2
Layer Poisson's Thickness Moduli(1)
* Ratio (in) (ksi)
1 0.3 4 700
2 0.35 10 615
3 0.35 24 7.5
4 0.45 240 5.2
5 0.4 * 50
Load No X-Position Y-Position Load Pressure Radius
* (in) (in) (lbf) (psi) (in)
1 0 0 4500 120 3.455
2 13 0 4500 120 3.455 Location No: 1
X-Position (in): .000 Y-Position (in): .000
cNormal Stresses
Z-Position Layer Sxx Syy Szz Syz Sxz Sxy
(in) * (psi) (psi) (psi) (psi) (psi) (psi)
1 1 -85.01 -89.89 -116.84 0 1.14 0
3 1 -28.04 -28.95 -82.96 0 3.21 0
5.2 2 -11.11 -9.67 -46.35 0 4.85 0
7.7 2 4.15 6.63 -22.69 0 5.49 0
11.5 2 27.58 31.48 -5.29 0 3.59 0
cNormal Strains and Deflections
Z-Position Layer Exx Eyy Ezz Ux Uy Uz
(in) * (10^-6) (10^-6) (10^-6) (mils) (mils) (mils)
1 1 -32.84 -41.9 -91.96 0.235 0 12.081
3 1 7.9 6.21 -94.09 0.134 0 11.881
5.2 2 13.82 16.98 -63.54 0.041 0 11.708
7.7 2 15.89 21.33 -43.02 -0.052 0 11.579
11.5 2 29.94 38.5 -42.21 -0.196 0 11.426
cPrincipal Stresses and Strains
Z-Position Layer S1 S2 S3 E1 E2 E3
(in) * (psi) (psi) (psi) (10^-6) (10^-6) (10^-6)
1 1 -116.88 -89.89 -84.97 -92.03 -41.9 -32.77
3 1 -83.15 -28.95 -27.86 -94.44 6.21 8.25
5.2 2 -47.01 -10.45 -9.67 -64.98 15.26 16.98
7.7 2 -23.77 5.23 6.63 -45.4 18.26 21.33
11.5 2 -5.68 27.97 31.48 -43.06 30.79 38.5
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Appendix D Analysis of the Proposed Pavement Design Cross Section for I-96 Using
the New M-E Pavement Design Guide Software
Appendix D includes a listing of the inputs used in the new M-E Pavement Design Guide
software. In addition, graphical summarizes of all predicted distresses follow the inputs.
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Limit Reliability
65
170 90
2500 90
10 90
1000 90
0.35 90
0.6 90
9600
2
56
70
45
Project: I-96, Wayne County, Michigan
General Information Description:
This is an analysis of a flexible pavement design that
was completed using the 1993 AASHTO DARWin
procedure.
Design Life 30 years
Base/Subgrade construction: September, 2003
Pavement construction: September, 2003
Traffic open: October, 2003
Type of design Flexible
Analysis ParametersAnalysis type Probabilistic
Performance CriteriaInitial IRI (in/mi)
Terminal IRI (in/mi)
AC Surface Down Cracking (Long. Cracking) (ft/500):
AC Bottom Up Cracking (Alligator Cracking) (%):
AC Thermal Fracture (Transverse Cracking) (ft/mi):
Permanent Deformation (AC Only) (in):
Permanent Deformation (Total Pavement) (in):
Location: I-96; Wayne County, Michigan
Project ID: CS 82122
Section ID: M-39 to Schaefer Road
Principal Arterials - Interstate and Defense Routes
Date: 8/26/2004
Station/milepost format: Miles: 0.000
Station/milepost begin: 11.72
Station/milepost end: 12.05
Traffic direction: East bound
Default Input LevelDefault input level Level 3, Default and historical agency values.
Traffic Initial two-way aadtt:
Number of lanes in design direction:
Percent of trucks in design direction (%):
Percent of trucks in design lane (%):
Operational speed (mph):
Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 Class 13
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Traffic -- Volume Adjustment Factors
Monthly Adjustment Factors (Level 3, Default MAF)
Vehicle Class
Month
January
February
March
April
May
June
July
August
September
October
November
December
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Midnight 1.2% Noon 3.5%
0.9% 1:00 am 0.6% 1:00 pm 4.2%
11.6% 2:00 am 0.5% 2:00 pm 6.1%
3.6% 3:00 am 0.5% 3:00 pm 7.3%
0.2% 4:00 am 0.6% 4:00 pm 7.1%
6.7% 5:00 am 2.3% 5:00 pm 9.8%
62.0% 6:00 am 8.0% 6:00 pm 6.4%
4.8% 7:00 am 7.9% 7:00 pm 4.0%
2.6% 8:00 am 7.4% 8:00 pm 3.0%
1.4% 9:00 am 4.5% 9:00 pm 2.8%
6.2% 10:00 am 3.9% 10:00 pm 2.3%
11:00 am 4.1% 11:00 pm 2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
2.0%
18
10
12
1.62 0.39 0.00 0.00
2.00 0.00 0.00 0.00
1.02 0.99 0.00 0.00
1.00 0.26 0.83 0.00
2.38 0.67 0.00 0.00
1.13 1.93 0.00 0.00
1.19 1.09 0.89 0.00
4.29 0.26 0.06 0.00
3.52 1.14 0.06 0.00
2.15 2.13 0.35 0.00
8.5
12
120
120
51.6
49.2
49.2
Vehicle Class Distribution Hourly truck traffic distribution
(Level 3, Default Distribution) by period beginning:
AADTT distribution by vehicle class
Class 4
Class 5
Class 6
Class 7
Class 8
Class 9
Class 10
Class 11
Class 12
Class 13
Traffic Growth Factor
Vehicle
Class
Growth
Rate
Growth
Function
Class 4 Compound
Class 5 Compound
Class 6 Compound
Class 7 Compound
Class 8 Compound
Class 9 Compound
Class 10 Compound
Class 11 Compound
Class 12 Compound
Class 13 Compound
Traffic -- Axle Load Distribution FactorsLevel 3: Default
Traffic -- General Traffic InputsMean wheel location (inches from the lane
marking):
Traffic wander standard deviation (in):
Design lane width (ft):
Number of Axles per Truck
Quad
Axle
Class 4
Class 5
Class 6
Vehicle
Class
Single
Axle
Tandem
Axle
Tridem
Axle
Class 7
Class 8
Class 9
Class 10
Class 11
Class 12
Class 13
Axle Configuration
Average axle width (edge-to-edge) outside
dimensions,ft):
Dual tire spacing (in):
Axle Configuration
Single Tire (psi):
Dual Tire (psi):
Average Axle Spacing
Tandem axle(psi):
Tridem axle(psi):
Quad axle(psi):
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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42.13
-83.21
628
10
Climate icm file:
Detroit-Michigan
Latitude (degrees.minutes)
Longitude (degrees.minutes)
Elevation (ft)
Depth of water table (ft)
-10 -16 -22 -28 -34 -40 -46
Structure--Design Features
Structure--Layers Layer 1 -- Asphalt concrete
Material type: Asphalt concrete
Layer thickness (in): 1.5
General Properties
General
Reference temperature (F°): 70
Volumetric Properties as Built
Effective binder content (%): 10.5
Air voids (%): 7.5
Total unit weight (pcf): 148
Poisson's ratio: 0.35 (predicted)
Parameter a: -1.63
Parameter b: 0.00000384
Thermal Properties
Thermal conductivity asphalt (BTU/hr-ft-F°): 0.67
Heat capacity asphalt (BTU/lb-F°): 0.23
Asphalt Mix
Cumulative % Retained 3/4 inch sieve: 0
Cumulative % Retained 3/8 inch sieve: 20
Cumulative % Retained #4 sieve: 35
% Passing #200 sieve: 6.5
Asphalt Binder
Option: Superpave binder grading
A 10.2990 (correlated)
VTS: -3.4260 (correlated)
High temp.
°C
Low temperature, °C
46
52
58
64
70
76
82
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-10 -16 -22 -28 -34 -40 -46
Layer 2 -- Asphalt concreteMaterial type: Asphalt concrete
Layer thickness (in): 2.5
General Properties
General
Reference temperature (F°): 70
Volumetric Properties as Built
Effective binder content (%): 10.5
Air voids (%): 7.5
Total unit weight (pcf): 148
Poisson's ratio: 0.35 (predicted)
Parameter a: -1.63
Parameter b: 0.00000384
Thermal Properties
Thermal conductivity asphalt (BTU/hr-ft-F°): 0.67
Heat capacity asphalt (BTU/lb-F°): 0.23
Asphalt Mix
Cumulative % Retained 3/4 inch sieve: 0
Cumulative % Retained 3/8 inch sieve: 30
Cumulative % Retained #4 sieve: 40
% Passing #200 sieve: 6
Asphalt Binder
Option: Superpave binder grading
A 10.2990 (correlated)
VTS: -3.4260 (correlated)
High temp.
°C
Low temperature, °C
46
52
58
64
70
76
82
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-10 -16 -22 -28 -34 -40 -46
Layer 3 -- Asphalt concreteMaterial type: Asphalt concrete
Layer thickness (in): 10
General Properties
General
Reference temperature (F°): 70
Volumetric Properties as Built
Effective binder content (%): 9.5
Air voids (%): 7.5
Total unit weight (pcf): 148
Poisson's ratio: 0.35 (predicted)
Parameter a: -1.63
Parameter b: 0.00000384
Thermal Properties
Thermal conductivity asphalt (BTU/hr-ft-F°): 0.67
Heat capacity asphalt (BTU/lb-F°): 0.23
Asphalt Mix
Cumulative % Retained 3/4 inch sieve: 10
Cumulative % Retained 3/8 inch sieve: 40
Cumulative % Retained #4 sieve: 50
% Passing #200 sieve: 5.5
Asphalt Binder
Option: Superpave binder grading
A 10.2990 (correlated)
VTS: -3.4260 (correlated)
High temp.
°C
Low temperature, °C
46
52
58
64
70
76
82
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Value
0.153
7.5
1.18
0.015
Value
4.86
7.5
0.365
17.5
Layer 4 -- Crushed gravelUnbound Material: Crushed gravel
Thickness(in): 16
Strength Properties
Input Level: Level 3
Analysis Type: ICM inputs (ICM Calculated Modulus)
Poisson's ratio: 0.35
Coefficient of lateral pressure,Ko: 0.5
Modulus (input) (psi): 7500
ICM Inputs
Gradation and Plasticity Index
Plasticity Index, PI: 0
Passing #200 sieve (%): 7
Passing #4 sieve (%): 30
D60 (mm): 10
Calculated/Derived Parameters
Maximum dry unit weight (pcf): 130 (user input)
Specific gravity of solids, Gs: 2.65 (derived)
Saturated hydraulic conductivity (ft/hr): 302 (derived)
Optimum gravimetric water content (%): 7 (user input)
Calculated degree of saturation (%): 78 (calculated)
Soil water characteristic curve parameters: Default values
Parameters
a
b
c
Hr.
Layer 5 -- A-2-4Unbound Material: A-2-4
Thickness(in): 8
Strength Properties
Input Level: Level 3
Analysis Type: ICM inputs (ICM Calculated Modulus)
Poisson's ratio: 0.35
Coefficient of lateral pressure,Ko: 0.5
Modulus (input) (psi): 7000
ICM Inputs
Gradation and Plasticity Index
Plasticity Index, PI: 0
Passing #200 sieve (%): 10
Passing #4 sieve (%): 72
D60 (mm): 0.1
Calculated/Derived Parameters
Maximum dry unit weight (pcf): 135 (user input)
Specific gravity of solids, Gs: 2.65 (derived)
Saturated hydraulic conductivity (ft/hr): 0.000866 (derived)
Optimum gravimetric water content (%): 7 (user input)
Calculated degree of saturation (%): 78 (calculated)
Soil water characteristic curve parameters: Default values
Parameters
a
b
c
Hr.
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Value
57.5
1.18
0.648
2240
Value
57.5
1.18
0.648
2240
Layer 6 -- CLUnbound Material: CL
Thickness(in): 12
Strength Properties
Input Level: Level 3
Analysis Type: ICM inputs (ICM Calculated Modulus)
Poisson's ratio: 0.45
Coefficient of lateral pressure,Ko: 0.5
Modulus (input) (psi): 5200
ICM Inputs
Gradation and Plasticity Index
Plasticity Index, PI: 15
Passing #200 sieve (%): 65
Passing #4 sieve (%): 93
D60 (mm): 0.1
Calculated/Derived Parameters
Maximum dry unit weight (pcf): 116 (user input)
Specific gravity of solids, Gs: 2.73 (derived)
Saturated hydraulic conductivity (ft/hr): 3.25e-005 (derived)
Optimum gravimetric water content (%): 13 (user input)
Calculated degree of saturation (%): 87.4 (calculated)
Soil water characteristic curve parameters: Default values
Parameters
a
b
c
Hr.
Layer 7 -- CLUnbound Material: CL
Thickness(in): Semi-infinite
Strength Properties
Input Level: Level 3
Analysis Type: ICM inputs (ICM Calculated Modulus)
Poisson's ratio: 0.45
Coefficient of lateral pressure,Ko: 0.5
Modulus (input) (psi): 5200
ICM Inputs
Gradation and Plasticity Index
Plasticity Index, PI: 15
Passing #200 sieve (%): 65
Passing #4 sieve (%): 93
D60 (mm): 0.1
Calculated/Derived Parameters
Maximum dry unit weight (pcf): 116 (user input)
Specific gravity of solids, Gs: 2.73 (derived)
Saturated hydraulic conductivity (ft/hr): 3.25e-005 (derived)
Optimum gravimetric water content (%): 13 (user input)
Calculated degree of saturation (%): 87.4 (calculated)
Soil water characteristic curve parameters: Default values
Parameters
a
b
c
Hr.
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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0.00432
3.9492
1.281
-3.4488
1.5606
0.4791
5
1
1
1.673
1.35
7
3.5
0
1000
1
1
0
6000
1
1
0
1000
0.0463
0.00119
0.1834
0.00384
0.00736
0.00115
0.387
0.009995
0.000518
0.00235
18.36
Distress Model Calibration Settings - Flexible AC Fatigue Level 3 (Nationally calibrated values)
k1
k2
k3
AC Rutting Level 3 (Nationally calibrated values)
k1
k2
k3
Standard Deviation Total
Rutting (RUT):
0.1587*POWER(RUT,0.4579)+0.001
Thermal Fracture Level 3 (Nationally calibrated values)
k1
Std. Dev. (THERMAL): 0.2474 * THERMAL + 10.619
CSM Fatigue Level 3 (Nationally calibrated values)
k1
k2
Subgrade Rutting Level 3 (Nationally calibrated values)
Granular:
k1
Fine-grain:
k1
AC CrackingAC Top Down Cracking
C1 (top)
C2 (top)
C3 (top)
C4 (top)
Standard Deviation (TOP) 200 + 2300/(1+exp(1.072-2.1654*log(TOP+0.0001)))
AC Bottom Up Cracking
C1 (bottom)
C2 (bottom)
C3 (bottom)
C4 (bottom)
Standard Deviation (TOP) 32.7 + 995.1 /(1+exp(2-2*log(BOTTOM+0.0001)))
CSM Cracking
C1 (CSM)
C2 (CSM)
C3 (CSM)
C4 (CSM)
Standard Deviation (CSM) CTB*1
IRIIRI Flexible Pavements with GB
C1 (GB)
C2 (GB)
C3 (GB)
C4 (GB)
C5 (GB)
C6 (GB)
Std. Dev (GB)
IRI Flexible Pavements with ATB
C1 (ATB)
C2 (ATB)
C3 (ATB)
C4 (ATB)
Pavement Structural Analysis August 2004 Report No. 15953-2/1 ARA-ERES Consultants
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The following graphs represent the distress predictions with the new M-E Pavement Design Guide software.
Surface Down Cracking - Longitudinal
0
300
600
900
1200
1500
1800
2100
2400
2700
3000
0 36 72 108 144 180 216 252 288 324 360 396
Pavement Age (month)
Longitudin
al C
rackin
g (ft
/mi)
Surface
Depth = 0.5"
Surface at Reliability
Design Limit
Bottom Up Cracking - Alligator
0
10
20
30
40
50
60
70
80
90
100
0 36 72 108 144 180 216 252 288 324 360 396
Pavement Age (month)
Allig
ato
r C
rackin
g (%
)
Maximum Cracking
Bottom Up Reliability
Maximum Cracking Limit
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Thermal Cracking: Total Length Vs Time
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 36 72 108 144 180 216 252 288 324 360 396
Pavement Age (month)
Tota
l Length
(ft/m
i)
Thermal Crack Length
Crack Length at Reliability
Design Limit
Permanant Deformation: Rutting
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 36 72 108 144 180 216 252 288 324 360 396
Pavement Age (month)
Rutt
ing D
epth
(in
) SubTotalAC
SubTotalBase
SubTotalSG
Total Rutting
TotalRutReliability
Total Rutting Design Limit
AC Rutting Design Value = 0.35
Total Rutting Design Limit = 0.6
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IRI
0
20
40
60
80
100
120
140
160
180
200
0 36 72 108 144 180 216 252 288 324 360 396
Pavement Age (month)
IRI
(in
/mi) IRI
IRI at Reliability
Design Limit
Recommended