SPECIAL REPORT 96-21

Modeling of Mn/ROAD Test Sections

with the CRREL Mechanistic

Pavement Design Procedure

Susan R. Bigl and Richard L. Berg September 1996
Abstract: The U.S. Army Cold Regions Research and

Engineering Laboratory is developing a mechanistic

pavement design procedure for use in seasonal frost

areas. The procedure was used to predict pavement

performance of some test sections under construction

at the Mn/ROAD facility. Simulations were conducted in

three phases, investigating the effects on predictions of

water table position, subgrade characteristics, asphalt

model, and freeze season characteristics. The procedure predicted significantly different performance by

the different test sections and highly variable results

depending on the performance model applied. The

simulated performance of the tests sections also was

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greatly affected by the subgrade conditions, e.g., density, soil moisture, and water table depth. In general,

predictions for the full-depth asphalt sections indicate

that they will not fail due to cracking, but two of the

three criteria for subgrade rutting indicate failure before

the five- or 10-year design life of the sections. Conventional sections are predicted not to fail due to subgrade

rutting; however, sections including the more frostsusceptible bases in their design are predicted to fail

due to asphalt cracking relatively early in their design

life, and sections with non-frost-susceptible bases are

predicted to fail towards the end of the design life.
Special Report 96-21

Modeling of Mn/ROAD Test Sections

with the CRREL Mechanistic

Pavement Design Procedure

Susan R. Bigl and Richard L. Berg September 1996

Prepared for

MINNESOTA DEPARTMENT OF TRANSPORTATION

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was prepared by Susan R. Bigl, Research Physical Scientist, Civil and

Geotechnical Research Division, Research and Engineering Directorate, U.S. Army

Cold Regions Research and Engineering Laboratory (CRREL), Hanover, New

Hampshire, and by Dr. Richard L. Berg, formerly a Research Civil Engineer at

CRREL.

This work was funded through Agreement 64632, Task Order 1 with the Minnesota

Department of Transportation (Mn/DOT) and a Construction Productivity Advancement Research (CPAR) project, Construction of Roads in Seasonal Frost Areas,

between Mn/DOT and CRREL.

The authors thank George Cochran of the Minnesota Road Research Project and Dr.

Vincent Janoo of CRREL for technically reviewing the manuscript of this report.

The contents of this report are not to be used for advertising or promotional

purposes. Citation of brand names does not constitute an official endorsement or

approval of the use of such commercial products.

ii
CONTENTS

Page

Preface ............................................................................................................ ii

Executive summary ........................................................................................ iii

Introduction .................................................................................................... 1

Computer models ............................................................................................ 1

FROST ....................................................................................................... 1

TRANSFORM ........................................................................................... 6

NELAPAV ................................................................................................. 9

CUMDAM ................................................................................................. 13

Mn/ROAD pavement performance studies .................................................... 14

Phase 1 ....................................................................................................... 15

Phase 2A..................................................................................................... 25

Phase 2B ..................................................................................................... 27

Phase 3 ....................................................................................................... 28

Discussion and recommendations .................................................................. 33

Conclusions .................................................................................................... 35

Literature cited ................................................................................................ 35

Appendix A: Heave, frost, and cumulative damage of flexible sections ....... 37

Appendix B: Heave, frost, and cumulative damage of rigid sections ............ 41

Abstract........................................................................................................... 43

ILLUSTRATIONS

Figure

1. Flow chart of mechanistic design procedure ...................................... 2

2. Example of pavement profile divided into finite elements................. 2

3. Distribution of seasonal freezing index with time at Buffalo,

Minnesota ...................................................................................... 5

4. Comparison of predicted values from the Schmidt and Ullidtz

asphalt modulus equations ............................................................ 7

5. Stress dependence of resilient modulus in 1206 clay subgrade

material .......................................................................................... 10

6. Pavement structure of Mn/ROAD test sections simulated ................. 15

7. Predicted moduli of Mn/ROAD materials .......................................... 19

8. Example output from FROST for Mn/ROAD test section ML5-F4

with a 1.8-m water table ................................................................ 20

9. Seed moduli output by TRANSFORM for Mn/ROAD test section

ML5-F4 with a 1.8-m water table ................................................. 21

10. Deflection and strain calculated by NELAPAV for Mn/ROAD

test section ML5-F4 with a 1.8-m water table .............................. 22

iii
Page

11. Cumulative damage for case f4w6 with optimum density

1206 subgrade ............................................................................... 23

12. Cumulative damage for case f2w9 ..................................................... 23

13. Cumulative damage for case f4w6 with 1232 subgrade ..................... 23

14. Cumulative damage for case r5w6 ..................................................... 24

15. Frost and thaw penetrations predicted by FROST for freeze

seasons in Phase 2B environmental sensitivity study ................... 27

16. Resilient modulus vs. degree of saturation of never-frozen 1206

subgrade material illustrating the effect of dry density................. 28

17. Distribution of freezing indices and water table depths in 21-year

Phase 3 series ................................................................................ 30

18. Predicted results from simulation of full-depth section during

freeze season 1983–1984 .............................................................. 31

19. Predicted results from simulation of full-depth section during

freeze season 1985–1986 .............................................................. 31

20. Distribution of cumulative damage during seasons............................ 32

TABLES

Table

1. Classification of soil for corresponding modulus equation ................ 7

2. General form of resilient modulus equations used in

TRANSFORM .............................................................................. 8

3. Poisson’s ratio for the material layers ................................................ 9

4. Models currently available in NELAPAV.......................................... 10

5. Format of a NELAPAV input file ...................................................... 11

6. Cumulative damage models used ....................................................... 12

7. Layer composition and thicknesses of pavement structure in test

sections simulated ......................................................................... 14

8. Test sections and conditions analyzed................................................ 16

9. Material parameters input to FROST for Mn/ROAD test section

simulations .................................................................................... 17

10. Modulus equations used for Mn/ROAD test section simulations ...... 18

11. Constants for equations to determine gravimetric unfrozen

moisture content ............................................................................ 20

12. Maximum frost heave and frost penetration in modeled

simulations .................................................................................... 21

13. Predicted applications to failure from Phase 1 simulation series of

flexible pavement test sections ..................................................... 22

14. Applications to failure from simulations of rigid test sections........... 24

15. Predicted applications to failure from simulations of flexible

test sections run in Phase 2A series .............................................. 26

16. Performance predictions for F3 test section with water table at 2.4 m ... 28

17. Results of 21-year freezing index/water table series .......................... 29

18. Midwinter thaw index summations ................................................... 33

19. Average percentage of total yearly damage accumulated during

four seasons ................................................................................... 33

iv
EXECUTIVE SUMMARY

The U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) is

developing a mechanistic pavement design procedure for use in seasonal frost areas.

It consists of four computer programs that compute soil and pavement moisture and

temperature conditions (FROST), resilient modulus and Poisson’s ratio (TRANSFORM), stresses and strains in the pavement system (NELAPAV), and cumulative

damage (CUMDAM). Damage predictions are based on several equations that

employ horizontal strain at the base of an asphalt layer, vertical strain at the top of the

subgrade, or horizontal stress at the base of a concrete layer. The procedure was used

to predict pavement performance of some of the Mn/ROAD test sections. Laboratory

tests on the Mn/ROAD materials (Bigl and Berg 1996a, Berg et al. 1996) provided the

input parameters necessary for the modeling effort. Simulations were conducted in

three phases, investigating the effects on predictions of water table position, subgrade

characteristics, asphalt model, and freeze season characteristics.

Phase 1, conducted in the spring of 1991, included an initial simulation series that

modeled temperatures from a year close to the mean freezing index. These boundary

conditions were applied to eight flexible and three rigid sections. Phase 2, an effort in

the summer of 1992, had two primary objectives. Phase 2A included three series

modeling the eight flexible sections with the mean freeze season and changing the

method employed to calculate the asphalt and subgrade moduli. Phase 2B investigated

the variability in predictions when temperatures from freeze seasons with maximum

and minimum freezing indices are applied to a single flexible section. Phase 3, an

effort in the summer of 1993, expanded the investigation of the effects of freeze season

characteristics. This series modeled 21 different freeze seasons applied to one fulldepth and one conventional flexible section.

The procedure predicted significantly different performance by the different test

sections and highly variable results depending on the performance model applied. The

simulated performance of the test sections was also greatly affected by the subgrade

conditions, e.g., density, soil moisture and water table depth. In general, predictions

for the full-depth asphalt sections indicate that they will not fail due to cracking, but

two of the three criteria for subgrade rutting indicate failure prior to the 5- or 10-year

design life of the sections. Conventional sections are predicted not to fail due to

subgrade rutting, but sections including the more frost-susceptible bases in their

design are predicted to fail due to asphalt cracking relatively early in their design life,

and sections with non-frost-susceptible bases are predicted to fail towards the end of

their design life.

v
INTRODUCTION

This is one of four reports related to the fullscale pavement test facility, Mn/ROAD, constructed by the Minnesota Department of Transportation (Mn/DOT) adjacent to Interstate 94 in

Otsego, Wright County. One report describes the

results of laboratory tests conducted to determine

the physical and freeze-thaw related characteristics of the on-site subgrade and two of the pavement system materials used in the test sections

(Bigl and Berg 1996a). Another report discusses

resilient modulus tests conducted on the above

materials (Berg et al. 1996). This report provides

an initial description of the computer programs

used in a mechanistic pavement design procedure

under development by CRREL, and then describes

a computer modeling effort that utilizes the results of the material testing program in the procedure to predict the performance of some Mn/

ROAD test sections. The final report of the series

summarizes information in the first three reports

(Bigl and Berg 1996b).

The mechanistic pavement design procedure is

being developed for use in seasonal frost areas

and considers seasonal variations in pavement

strength such as:

1. Large increases in base and subgrade strengths

when frozen.

2. Loss of base and subgrade strengths during

the spring when thawing and excess water

weakens the layers.

3. Loss of asphaltic concrete strength during

the summer months when asphalt moduli

decrease with higher temperatures.

Availability of data from the Mn/ROAD facility will allow us to verify and refine various aspects of the model.

COMPUTER MODELS

The mechanistic design procedure consists of

the four programs FROST, TRANSFORM,

NELAPAV, and CUMDAM (Fig. 1). FROST predicts the amount of frost heave and thaw settlement of the pavement structure and conditions

throughout the depth of the structure (temperature, water content, pore water pressure, ice content, density) at a given time increment. TRANSFORM uses the output from FROST as input and

divides the pavement structure into “layers” based

on moisture or temperature conditions. Each layer

is then assigned a resilient modulus, Poisson’s

ratio and density value. NELAPAV, a nonlinear

layered elastic program, calculates stresses, strains

and deflections at specified locations within a pavement profile when a load is applied to the surface.

CUMDAM calculates the incremental and cumulative damage the pavement undergoes using several available damage models. The behavior is

normally modeled for a one-year period, with output on a daily basis. By assuming that the results

from a single year will be repeated annually, the

number of applications to failure is estimated.

FROST

FROST is a one-dimensional coupled heat flow

and moisture flow model that computes frost heave

and thaw settlement of a pavement or soil profile

Modeling of Mn/ROAD Test Sections

with the CRREL Mechanistic

Pavement Design Procedure

SUSAN R. BIGL AND RICHARD L. BERG
with time. It also calculates temperature, moisture

stress, water content, ice content, and density

through the depth of the profile at each time increment. FROST was originally developed by Berg

et al. (1980) in a cooperative study funded by the

Corps of Engineers, the Federal Highway Administration, and the Federal Aviation Administration. Additional details beyond those described

here are given in Guymon et al. (1993). The model

assumes one-dimensional vertical heat and moisture flux and is based on a numerical solution

technique termed the nodal domain integration

method. The nodal domain integration method allows use of the same computer program to solve a

problem by either the finite element method, the

integrated finite difference method, or any other

mass lumping numerical method. For this study,

we chose to use the integrated finite difference

computational method.

Figure 2 shows how FROST uses nodes, which

are exact points, to divide the column of material

into horizontal elements. Material properties are

assigned to each element.

The program was developed for use on problems of seasonal freezing and thawing of nonplastic soils, and is based on the following primary assumptions, with additional assumptions

reported in Guymon et al. (1993):

1. Darcy’s law applies to moisture movement

in both saturated and unsaturated conditions.

Figure 1. Flow chart of mechanistic design procedure.

Figure 2. Example of pavement profile divided

into finite elements.

Input

• Geometry

• Initial Conditions

• Boundary Conditions

• Material Characteristics

FROST

Output/Input

• Heave

• Frost/thaw Penetration

Additional Material

Characteristics TRANSFORM

Nodal Temperature,

Moisture & Density

• Load Configuration

• Evaluation Locations NELAPAV

Strains; Stresses

• Traffic

• PCC Parameters CUMDAM

• Physical and Elastic

 Properties of Sublayers

• Geometry

Cumulative

Damage

2
2. The porous media are nondeformable as far

as moisture flux is concerned; i.e., consolidation is negligible.

3. All processes are single valued; i.e., hysteresis is not present in relationships such as

the soil water characteristic curve.

4. Water flux is primarily as liquid; i.e., vapor

flux is negligible.

The governing equation used in FROST to describe soil moisture flow is derived by substituting the extended Darcy moisture-flow law into

the one-dimensional continuity equation for an

incompressible fluid flowing through porous

media, i.e.,

∂

∂

∂

∂

∂θ

∂

ρ

ρ

∂θ

x ∂

K h

xt t H

u i

w

 i



 



 = + (1)

where KH = unsaturated hydraulic conductivity

(permeability) (cm/hr)

h = total hydraulic head (cm water)

x = depth (cm)

θu = volumetric unfrozen water content (%)

ρi = density of ice (g/cm3)

ρw = density of water (g/cm3)

θi = volumetric ice content (%)

t = time (hr).

The total hydraulic head h equals the sum of the

pore pressure head (hp = u/ρw), where u is the pore

water pressure, plus the elevation head (he = –x),

where x is measured vertically downward. The ice

sink term, ρi ∂θi /ρw ∂t, exists only in freezing or

thawing zones, and in these zones, eq 1 is coupled

to the heat transport equation. The ice sink term

assumes that θi

 is a continuous function of time.

In FROST, the soil water characteristics are

represented using a relationship in the form of

Gardner’s (1958) equation:

θ

θ

u α

o

w p

=

A h +1 (2)

where θu = volumetric unfrozen water content (%)

θo = soil porosity (%)

hp = pore pressure head (cm of water)

Aw = Gardner’s multiplier for the moisture characteristics

α = Gardner’s exponent for the moisture

characteristics.

For each soil to be modeled, point values of θu

and hp are determined in a laboratory moisture

retention test (Ingersoll 1981). Gardner’s eq 2 is

then fit to the data using a least squares approach

to determine the best fit parameters Aw and α. Test

results for the Mn/DOT materials are given in the

first report of this series (Bigl and Berg 1996a).

Unsaturated hydraulic conductivity is also approximated in FROST using a Gardner’s equation:

K k

A h

H s

K p

=

+

β

1 (3)

where KH = unsaturated hydraulic conductivity

(cm/hr)

ks = saturated hydraulic conductivity

(cm/hr)

hp = pore pressure head (cm of water)

AK = Gardner’s multiplier for hydraulic

conductivity

β = Gardner’s exponent for hydraulic

conductivity.

Point values of KH and hp for each soil are determined in the laboratory by an unsaturated hydraulic conductivity test (Ingersoll 1981), and, again,

Gardner’s eq 3 is fit to the data using a least

squares approach to determine the best fit parameters AK and β. See Bigl and Berg (1996a) for the

test results on the Mn/ROAD materials.

Within the partially frozen zone, FROST reduces the unsaturated hydraulic conductivity using an empirical constant, termed the E-factor,

combined with the ice content according to the

following equation:

K Kh E E i F Hp i = ( ) × ≥ , − 10 0 θ θ (4)

where KF = the adjusted hydraulic conductivity

in a partially frozen element (cm/hr)

E = an empirical constant, dimensionless

θi = volumetric ice content (%).

For this study, the E-factor was determined within

the FROST program using an empirically derived

equation based on the saturated hydraulic conductivity, ks, in centimeters/hour:

E k = − ( ) +

5

4

3 6 2

s . (5)

3
Frost heave is estimated from the total amount

of ice segregation in the frozen zone by:

θθ θθ si on =− − ( ) (6)

where θs = volumetric segregated ice content (%)

θo = porosity (%)

θn = residual unfrozen water content (%).

If θs is greater than 0, ice segregation has occurred

and the frost heave is computed by multiplying θs

by the zone thickness. The θn parameter establishes the pore water stress at the freezing front

for the solution of the moisture transport equation. In this study, θn was obtained by assuming a

moisture tension of –800 cm of water and solving

eq 2. The use of the –800 cm of water condition

stems from that being the highest tension measured in various field studies. Thaw settlement

from ice melting is the reverse process of that

described above for ice segregation.

To conduct the calculations described above,

FROST requires the following input for each material: 1) Gardner’s coefficients for soil moisture

characteristics, 2) Gardner’s coefficients for hydraulic conductivity characteristics, 3) porosity and

density of the soil, 4) thermal conductivity and

volumetric heat capacity of the dry soil, and 5) the

E-factor.

FROST also requires the following input for

initial and boundary conditions: 1) element lengths,

2) upper- and lower-boundary pore water pressures, 3) upper- and lower-boundary temperatures,

4) initial temperature, pore pressure and ice content distributions with depth, 5) surcharge pressure, 6) freezing point depression and 7) modifier

of the upper node during thaw.

In all cases, the pavement structure was simulated as a column with its upper boundary at the

pavement surface and extending down to 400 cm

(13.1 ft) using 99 elements. The length of elements within the expected zone of freezing

(down to 110 cm or 3.6 ft) was about 2 cm (0.8

in.). These lengths were adjusted for individual

cases to provide nodes positioned exactly at the

depths where the interface between materials

are located in the Mn/ROAD test sections. The

deeper soil was modeled with element lengths

of 4 cm between 110 and 230 cm (3.6–7.6 ft), 10

cm between 230 and 340 cm (7.6–11.2 ft), and

20 cm from 340 cm (11.2 ft) to 400 cm (13.1 ft).

The upper boundary pore water pressure was

chosen to be computer-generated, as follows.

When the profile is completely thawed and downward vertical drainage occurs, the surface pore

water boundary condition is modeled by

∂

∂

h

x = 0 (7)

which means that the velocity flux across this

boundary is zero. The upper-boundary condition

is set to 0 cm of water when the upper-boundary

temperature is above 0°C and frozen regions remain in the column. When the surface temperature is below 0°C, a specified constant upperboundary pore pressure is used. To be consistent

with previous studies, a value of –300 cm of water

was used.

The lower-boundary pore pressure condition of

FROST is set by specifying discrete pore water

pressures that relate to the water table elevation at

times when these conditions occur. At intermediate times, lower-boundary pore water pressures

are linearly interpolated. For all the Mn/DOT cases,

we set the lower boundary pore pressure to produce a constant water table depth throughout the

simulation. We simulated the water table in each

test section at the depth determined by field measurements to be representative of the on-site conditions. Where the measured water table varied

through a test section, we conducted two simulations using the deepest and shallowest values.

Input for the upper boundary temperature condition consists of a set of specified times and temperatures that are implemented as step changes.

Values were input in 24-hr increments using the

mean daily air temperature. Conditions at Buffalo, Minnesota, were simulated, since this is the

nearest station to the Mn/ROAD facility (16 km;

10 mi) with a reasonably long record of meteorological data. The time period simulated was 1

October 1959 to 14 November 1960. If the severity of a winter is judged by its air freezing index,

the 1959–1960 winter is very near the average

value for the 28-year period ending in 1987. The

distribution of freezing indices at Buffalo during

this time is shown in Figure 3. Starting the simulations on 1 October gave 30 days of computations before the first freeze event, allowing the

4
model to stabilize and gradational moisture and

temperature conditions to develop.

FROST adjusts the air temperature values to

represent the soil surface temperatures using a

procedure similar to the Corps of Engineers nfactor approach for seasonal freezing indices (U.S.

Army 1966). An n-factor is defined as the ratio of

the surface index to the air index, separately calculated for the full freeze and thaw season. In this

study, 0.5 was used for the freezing n-factor (i.e.,

on days when the air temperature was ≤ 0°C), and

1.8 was used for the thawing n-factor.

Bottom boundary temperature conditions consist

of a set of times and temperatures that are linearly

interpolated at intermediate times. Three points

were set during the simulations using estimated

values of a reasonable ground temperature. The start

and end temperatures are estimated to be 9.59°C

(49.3°F), which is 3°C (5°F) higher than the mean

annual air temperature 6.83°C (44.3°F). The third

point was set so that a minimum value of 6.0°C

(42.8°F) would occur at the end of the freeze season.

Initial conditions required to be set for the

FROST program are temperature, moisture stress,

and ice content. The initial temperature of all elements was estimated to be 5°F higher than the

mean annual air temperature. For cases with water table depths less than 3 m (10 ft), the initial

moisture tension/pressure was set at a gradient to

produce a water table (i.e., pressure = 0) at the

specified depth, increasing positively downwards

at 1 cm water/1 cm depth. For simulations with

intermediate water table depths (3.6, 5.6 and 6.1

m; 12, 18, and 20 ft), the initial tension was set to

–200 cm water (an estimate of optimum conditions) from the surface to the depth beneath which

the tension from the theoretical gradient would

increase positively. In simulations with the deepest in-situ water tables (13.7 and 15.2 m or 45 and

50 ft), we set a minimum bottom tension of –300

cm, with tensions decreasing from the bottom to 2

m (6.5 ft), and a constant tension of –200 cm

water from 2 m (6.5 ft) to the surface. Initial volumetric ice content was set at 0.0% for all elements, since the simulations began prior to the

start of the freeze season.

Surcharge (overburden) pressure is a constant

value to simulate the pressure acting on the top

node of the modeled column. In a case where only

soil beneath a pavement surface is being modeled,

this overburden should simulate the pressure of

the pavement on the soil. For the Mn/ROAD test

section simulations, the pavement properties were

included in the modeled column, so the overburden pressure was set at zero.

The freezing point depression is a constant value

that represents the temperature at which in-situ soil

water freezes. This was set in all cases to be 0°C.

A modifier is included that adjusts the overburden pressure acting on the upper node during thaw

periods. This value can be set between 0.0, to

represent old, cracked pavements, and 1.0, to represent brand new pavements. We used 1.0 for the

Mn/ROAD cases.

Figure 3. Distribution of seasonal freezing index with time at Buffalo,

Minnesota.

1960 1970 1980 1990

3000

2000

1000

0

1600

1200

800

400

0

Freezing Index

(°C-days) (°F-days)

Buffalo, MN

5
Standard procedures of FROST calculations

were selected as follows. The fully implicit method

was used for the moisture time domain solution,

and the Crank-Nicolson method for the heat transfer time domain solution. Simulations were run

with a time step of 0.2 hours, which is the time at

which boundary conditions are adjusted; updates

of the thermal and hydraulic properties were set to

occur once per hour.

FROST produces what can be a very large output file. The first part of the file is a listing of the

initial profile conditions, including all the input

material properties. The next section is an incremental (usually daily) listing of the conditions

generated for each node, including temperature,

pore water pressure, water content, ice content,

density, and porosity. The final section of the output file is a summary of the predicted frost heave

and frost/thaw penetration data.

TRANSFORM

TRANSFORM was developed at CRREL by

Chamberlain et al. (in prep.) and was modified

extensively by Wendy Allen and Gregor Fellors,

both of CRREL, for this study. The TRANSFORM

program uses FROST daily output files as input

and produces files of layered pavement systems

where each layer is assigned a resilient modulus,

Poisson’s ratio, density and thickness. Output files

from TRANSFORM are in the format to be used

as input files to NELAPAV, the layered elastic

program used to compute stresses and strains in

the pavement system. NELAPAV requires a single

file containing both load and structural data for

each day of the simulation.

TRANSFORM first reads from a separate file a

series of material type identifiers and their associated parameters needed for calculating the moduli

of the materials in the frozen and thawed condition (see below). Then, TRANSFORM reviews

the initial part of the FROST output file to determine the material type identifier for each element.

From the incremental (daily) listings of the

FROST output file, TRANSFORM next reads the

following conditions for each element: temperature, water content, ice content, material density,

and porosity. A modulus value is then calculated

for each element.

Moduli of surface paving materials were calculated as follows. PCC concrete had the modulus

set at a constant value of 3.4 × 107 kPa (5,000,000

lb/in.2). In the initial two simulation series, the

resilient modulus, Mr

 , of asphalt concrete layers

were calculated by the equation (Schmidt 1975):

M T r (. . ( ) lb/in.2 6 285 1 931 10 10 2= − × −

TT T 3 280 10 1 888 10 . . 42 53 −× −× − −

+× +× − − 1 175 10 1 502 10 74 85 . . T T

− × − 2 022 10 10 6 . ) T (8)

where T is the temperature of the element (°C).

For pavement temperatures greater than 50°C, the

asphalt modulus was set to 1.7 × 105 kPa (25,000

lb/in.2); for temperatures less than –29°C, it was

set to 3.3 × 107 kPa (4,840,000 lb/in.2). In a third

series of simulations, a second model was used

for predicting asphalt moduli when the temperature was above 1°C (Ullidtz 1987):

Mr (lb/in.2) = [15,000

–7900 log (T)] × 145.04. (9)

At below 1°C, the Schmidt (1975) relationship

was used. Predictions of the two asphalt models

are compared in Figure 4.

In the layers that represent an unstabilized base

course, subbase or subgrade material, TRANSFORM calculates the modulus using regression

equations developed from results of laboratory

resilient modulus testing conducted on frozen and

thawed soil samples (Berg et al. 1996). Each soil

element is first classified using the criteria in Table

1 to determine which type of modulus equation is

appropriate. The modulus is then calculated using

one of the equations shown in general form in

Table 2. The equations relate the frozen resilient

modulus to temperature (through unfrozen water

content), and the unfrozen resilient modulus to

degree of saturation, stress condition, and to density for the class 6 special base course and the

1206 subgrade. The specific parameters for the

Mn/ROAD materials will be discussed in a later

section.

The following parameters, which are specific

to each material, are used in the regression equations (Table 2): 1) FC1 and FC2, regression coefficients for the resilient modulus in the frozen

condition, 2) TC1, TC2, TC3, and TC4, regres6
sion coefficients for the resilient modulus in the

thawed condition, 3) f(σ)m, an approximation of

the mean stress condition, and 4) α and β, unfrozen water content constants.

Several forms of the unfrozen water content

function were investigated for predicting the frozen moduli of the Mn/ROAD materials, as reported in Berg et al. (1996). The form used for the

Phase 1 simulation series of this study is the normalized gravimetric unfrozen water content, calculated as shown in Table 2. A second, normalized volumetric form of the unfrozen water content

function was used in Phases 2 and 3 simulation

series. It is calculated by multiplying the gravimetric unfrozen water content by the dry density

in Mg/m3.

TRANSFORM uses an approximation of the

f(σ) stress term in its equations to predict moduli

of unfrozen soils. Since this term is constant for

each soil, the unfrozen moduli calculated by

TRANSFORM are not dependent on stress. The

approximation used was the mean stress condition applied during the laboratory resilient modulus testing.

Because some materials have a significant discontinuity between the minimum frozen and

Figure 4. Comparison of predicted values from the Schmidt and Ullidtz

asphalt modulus equations.

Table 1. Classification of soil for corresponding modulus equation.

Classification Definition

1 Frozen: the ice content is greater than or equal to 0.005, the temperature not equal to 0°C, and the

pore pressure less than 0.

2 Partially thawed: the ice content is greater than or equal to 0.005 and the pore pressure is greater

than or equal to 0.

3 Thawed, with negative pore pressure: the ice content is less than 0.005 and the pore pressure is

less than 0.

4 Thawed, with positive pore pressure: the ice content is less than 0.005 and the pore pressure is

greater than 0.

5 Recently frozen layer: the temperature is less than 0°C and was recently thawed. This layer

retains its modulus prior to freezing until the frozen equation predicts a higher modulus or until

the temperature rises.

6 Recovering thawed layer: for 120 days subsequent to having been frozen, a thawed layer has its

modulus reduced according to a ratio that diminishes over time.

–20 –10 0 10 20 30 40 50

107

106

105

104

Temperature (°C)

Schmidt

Ullidtz

Resilient Modulus

7 × 107

7 × 106

7 × 105

7 × 104

(kPa) (lb/in.2)

7
thawed predicted moduli, algorithms were added

to TRANSFORM for providing a smoother transition in calculated moduli between the frozen

and thawed condition. When the soil goes from an

unfrozen to a frozen state, the modulus is held

constant at its unfrozen value until either of two

changes occur: 1) the soil becomes cold enough

that the modulus as calculated by the frozen equation exceeds the pre-frozen modulus, or 2) the soil

warms. When the soil warms, the modulus is set

at the value calculated by the frozen equation and

continues to follow the frozen curve until the soil

is completely thawed. After complete thawing,

the soil undergoes a 120-day “recovery period.”

During this time, the modulus value increases according to a power relationship with about onehalf of the recovery taking place in the first 25

days about 75% recovery in 75 days and 100%

recovery in 120 days.

After calculating the predicted modulus of an

element, TRANSFORM also assigns it a Poisson’s

ratio using the criteria shown in Table 3.

After a modulus value has been assigned to all

elements from a particular time step, adjacent eleTable 2. General form of resilient modulus (Mr) equations used in

TRANSFORM.

Condition Equation

Frozen M FC f w r FC ( ) () lb/in. u g

2 2 = 1 −

Partially thawed M TC f f r TC TC TC ( ) ( ) () () lb/in. m 2 34 2 = γσ 1 100

Thawed, negative pore pressure M TC f S f f r TC TC TC ( ) () () () lb/in. m 2 34 2 = γσ 1

Thawed, positive pore pressure M TC f f r TC TC TC ( ) ( ) () () lb/in. m 2 34 2 = γσ 1 100

Notes:

FC1, FC2 = regression coefficients for the frozen condition

f(w

u–g) = wu–g

/wo

w

u–g = grav. unfrozen water content (decimal) = α β

100 0

T

T

wo = unit water content (1.0)

α, β = unfrozen water content constants

T = temperature, °C

T0 = 1.0°C

TC1 – TC4 = regression coefficients for the thawed condition

f(S) = S/So

S = degree of saturation (%)

So = 1.0 %

f(γ) = γ

d

/ γ

o

γd = dry density (Mg/m3)

γ

o = 1.0 Mg/m3

σ = stress (lb/in.2)

f (σ)m = a mean value of either f

1

(σ) = J1/σo

or f

2 (σ) =(J2 /τoct)/σo

or f

3 (σ) = τoct/σo

σo = 1.0 lb/in.2

J1 = bulk stress (lb/in.2) = 3σ3 + σd

J2 = 2nd stress invariant (lb/in.2) = 3 3

2 σ + 2 σ3σd

τoct = octahedral shear stress (lb/in.2) ( 2 3/ ) σd

Table 2. General form of resilient modulus (Mr) equations used in

TRANSFORM.

8
ments within the same material type are combined

into a single layer if the modulus of the deeper

element is less than ±20% different from the modulus of the upper sublayer. A “weighted average”

modulus of the two elements is then determined,

with the weighting based on their relative lengths.

The modulus of the next lower finite element is

then compared with the modulus of the upper element. The checking and combining process continues until an element modulus is outside of the

20% limitation or if a layer of a different material

or a different frozen/unfrozen state is encountered.

In this manner, a particular material layer in the

pavement profile may be divided into several

sublayers. During the process of combining elements with similar modulus values, the thickness

of each sublayer is also determined, as well as a

weighted average of its other properties such as

temperature, density and Poisson’s ratio.

Typically, the pavement profile that was divided into 99 finite elements for the FROST program is combined by TRANSFORM into 5 to 20

sublayers with similar resilient modulus values.

During the winter and spring a larger number of

sublayers is more prevalent than in the summer

months. TRANSFORM creates an additional “infinite” layer beneath the modeled column for passing to NELAPAV, which has its properties set the

same as those for the bottom modeled sublayer.

Additional items must be input to (or generated

from) TRANSFORM in order for it to create input files for NELAPAV. They include 1) loading

information such as the total load on a specified

loaded radius, or load pressure, 2) location and

depth information related to the points where the

stresses and strains are to be computed, and 3) a

model number telling NELAPAV which form of

the modulus equation to use for each material.

In the program, a 4082-kg (9000-lb) load was

applied to a radius of 15.0 cm (5.91 in.), which

approximates the area of a standard set of dual

wheels or a falling weight deflectometer (FWD)

testing plate. In all cases, stresses and strains were

computed beneath the center of the load. For flexible pavements, the stress state at two points were

analyzed: at the bottom of the pavement layer,

and at the top of the subgrade. For rigid pavements, stress was computed only at the bottom of

the pavement. In all cases the point of computation was 0.01 in. from the interface between materials.

NELAPAV

NELAPAV is an acronym for Nonlinear Elastic Layer Analysis for PAVements. It computes

stresses, strains, and displacements at any point in

an n-layered pavement system. The mainframe

computer version of the program was developed

by Lynne Irwin of Cornell University and Gregor

Fellers of CRREL in 1980. The microcomputer

version was developed by Irwin and Daniel Speck

at Cornell University in 1984 and 1985 (Irwin and

Speck 1986). The program is an adaptation of the

Chevron Layered Elastic Systems program

(CHEVLAY).

Irwin and Speck (1986) describe the computational approach used by NELAPAV and define

the following terms. The term state of a point in a

Table 3. Poisson’s ratio for the material layers.

Poisson’s ratio Condition

Asphalt

0.30 Layer temperature is less than –2.0°C

0.35 Layer temperature is greater than or equal to –2.0°C and less than or

equal to 1°C

0.40 Layer temperature is greater than 1°C and less than or equal to 8°C

0.45 Layer temperature is greater than 8°C

Concrete

0.15 Constant for all conditions

Soil

0.33 Thawed, volumetric ice content is less than 0.005

0.35 Frozen, volumetric ice content is greater than or equal to 0.005

9
layered system is used to refer to the set of

stresses, strains, and displacements occurring

at that point for a particular loading condition.

A set of layer moduli (Mr1,..., Mrn) is said to be

compatible at radius r with a given set of nonlinear models (f1,...,fn) if each Mr agrees

(within a specified tolerance) with the modulus determined by the model fi evaluated at

the middepth of layer i and at radius r.

The fundamental assumption of NELAPAV

may be stated as follows: “The state of a point

p = (r,z) in a layered system is primarily determined by the modulus of elasticity of each of

the layers in the system at the radius, r, of the

point.” Once this assumption has been made,

the state of any point in the layered system

may be determined by computing a set of compatible moduli at the radius of the point and

then evaluating the resulting layered system at the

point, holding the moduli constant.

NELAPAV operates as a “front-end” to

CHEVLAY in that it calls the basic CHEVLAY

routines iteratively in order to come up with a set

of compatible moduli for the layered system at the

radius of each of the desired calculation points.

The tolerances for compatibility used in this study

0 10 20

104

105

Resilient Modulus

w = 16.1%

γ = 105 lb/ft d 3

2 1

2

4

7

σ (lb/in. ) 3

7 x 10 4

7 x 10 5

(kPa) (lb/in. ) 2

(lb/in. ) 2

Deviator Stress

0 70 140 (kPa)

Figure 5. Stress dependence of resilient modulus in 1206

clay subgrade material (from Berg et al. 1996).

Table 4. Models currently available in NELAPAV (from Yang 1988).

Model

 no. Name Specification

0 Linear Mr = constant

1 Bulk stress M k k r = 1θ 2

2 Deviator stress M

k kk k

kk k k r d d

d d

= +− <

+− ≥







2 31 1

24 1 1

( )

( )

σ σ

σ σ

3 Second stress invariant M kJ k

r oct = 1 2 2 ( ) τ

4 Octahedral shear stress M k k

r oct = 1τ 2

5 Vertical stress M k k r v = 1σ 2

6 Major principal stress M k r k = 1 1σ 2

7 First stress invariant M kJ J k k k k r p oct c =+ + 1 10

2

1

2 2 1 3 4 ( )( ) τ

octahedral shear stress

and anisotropic

consolidation ratio

Notes:

θ = bulk stress

k1, k2, k3, k4 = constants

σd = deviator stress

σv = vertical stress

σ1 = major principal stress

J10 = first stress invariant due to overburden only

J1p = first stress invariant due to overburden and load

kc = anisotropic consolidation ratio

10
were a 2.0% maximum change in Mr from

one iteration to the next and a total of 10

iterations.

NELAPAV allows the use of nonlinear

(i.e., stress-dependent) modulus values in

the analysis. Modulus values for thawing

and unfrozen fine-grained soils are highly

nonlinear as illustrated in Figure 5. Table

4, from Yang (1988), illustrates the various types of linear and nonlinear models

currently available for use in NELAPAV;

however, models 2 and 7 are not currently

incorporated in the rest of the CRREL

design procedure. In the CRREL version

of NELAPAV, model 1 has been changed

to the semi-log form:

M ke k r ( ) = 1 2θ (10)

where k1 and k2 are constants and θ is bulk

stress. For this study, we utilized models

0, 1, 3, and 4, the specifics of which will

be described in a later section.

One shortcoming of NELAPAV is that

it allows only one circular load to be applied at the surface. This is not a major

problem in this analysis because we are

dealing with roadway pavements rather

than airport pavements, which experience

much more complex tire configurations.

Table 5 is a brief listing of the information included in a NELAPAV input file

(Irwin and Speck 1986). It may contain

up to 25 layers, with the following values

for each: model number (from Table 4),

seed modulus, Poisson’s ratio, total density, lateral earth pressure coefficient, thickness,

and the constants required for the equations from

Table 4.

NELAPAV requires a seed modulus to begin

its predictions of modulus for the various material

layers. The value used for the seed modulus is the

resilient modulus calculated in and passed from

TRANSFORM. The constants required for computations are also passed from TRANSFORM.

The k2 value is a constant assigned on the basis of

material type. The k1 constant varies with the moisture/density level of the layer, and is calculated by

multiplying together all the nonstress terms in the

predictive equation for the material (Table 2).

During this study, K0, the coefficient of lateral

earth pressure, was assigned to the layers as follows: a value of 1.5 was used for paving materials

and frozen soil; a value of 1.0 was used for all

unfrozen soil layers. We now feel that this system

is too simplified, and are modifying the section of

TRANSFORM that assigns K0.

For each layer, NELAPAV expects to receive a

value for the total density, which is adjusted to a

buoyed density below the water table. In this study,

however, we used dry density instead of total density, and neglected to adjust to a buoyed density

below the water table. A short sensitivity study,

conducted when these problems were discovered,

Table 5. Format of a NELAPAV input file (from Irwin and

Speck 1986).

Subject input parameters

Header problem description

Units input units

Load load, pressure, load radius

Layered system n

M1 E1 seed ν1 γ1 K0,1 h1 k1,1 k2,1 k3,1 k4,1 t

1

M2 E2 seed ν2 γ2 K0,2 h2 k1,2 k2,2 k3,2 k4,2 t

2

.

.

.

Mn En seed νn γn K0,n hn k1,n k2,n k3, n k4,n t

n

Tolerance maximum iterations, tolerance

Calculation points r1, z1

r2, z2

.

.

.

rm, zm

Notes:

n = number of layers

Supplied for each layer

M = model number (see Table 4)

E seed = seed modulus (lb/in.2)

ν = Poisson’s ratio

γ = density (lb/ft3)

K0 = lateral earth pressure coefficient

h = thickness (in.)

k1.. k4 = constants to be used in models (see Table 4)

t = mean temperature (°C)

rm, zm = radius, depth at which to make calculations (in.)

11
Table 6. Cumulative damage models used.

A. Flexible Pavement Horizontal Strain Criteria

1) The Asphalt Institute (MS-1, 1982):

NC E a ta = × [ ] − − − 18 4 4 325 10 3 3 291 0 854 . (. ) . . ε

where Na = number of load applications to 45% cracking

C = a function of the volume of the voids and the volume of asphalt, 10z

z = 4.84 [(Vb/Vv + Vb) – 0.69]

Vb = volume of the asphalt, percent (11%)

Vv = volume of the voids, percent (5%)

εt = tensile strain at the bottom of the asphalt layer, in./in.

Ea = modulus of the asphalt layer, lb/in.2

2) Witczak (1972) (i.e., Asphalt Institute MS-11):

N abq c d

a t = (/ ) 1 ε

where a = 1.86351 × 10–17

b = 1.01996

c = 4.995

d = 1.45

q = pavement temperature, °F

3) The Corps of Engineers (U.S. Army 1988):

N E a = 10 2 68 5 2 66 − − t a ( . log . log ) ε

4) Coetzee and Connor (1990):

NaEb c a t a = ε

where when Ea ≥ 1,500,000 lb/in.2: a, b, c = 3.364 × 106, –7.370, –4.470

and when Ea < 1,500,000 lb/in.2: a, b, c = 6.565 × 106, –5.764, –3.640

B. Flexible Pavement Subgrade Strain Criteria

1) The Asphalt Institute (1982):

N m l s = 10 1 − v [ / (log log )] ε

where Ns = allowable traffic based on subgrade strain

m = a constant (0.25)

l = a constant (2.8 × 10–2)

εv = vertical strain at the top of the subgrade, in./in.

2) The Corps of Engineers (U.S. Army 1987):

N A B s v = 10000 ( / ) ε

where A = 0.000247 + 0.00245 log Es

B = 0.0658 Es

0.559

Es = subgrade resilient modulus, lb/in.2

12
Table 6 (cont’d).

C. Rigid Pavement Horizontal Stress Criteria

1) The Corps of Engineers (U.S. 1990):

Nh df adon) /bdon = − 10 [( ]

where: Nh = allowable traffic based on horizontal stress

df = Rcon/σh

Rcon = flexural strength of the concrete, lb/in.2

σh = horizontal stress at the base of the concrete, lb/in.2

adon = 0.2967 + 0.002267 SCI

bdon = 0.3881 + 0.000039 SCI

SCI = surface condition index of the pavement when failed

showed that this did not significantly affect the

resultant strain calculations.

The solution computed by NELAPAV is an

approximation of the exact solution. In reality, the

stress state changes from point to point. Therefore, the modulus of a nonlinear material varies

both vertically and horizontally. While NELAPAV

recomputes the set of compatible moduli to determine the states of points at different radii, it is

bound by the assumption that the moduli are constant everywhere in the layers. An exact theory

for nonlinear materials would allow the modulus

to vary horizontally within the layer in accordance

with the nonlinear model.

Output from NELAPAV is one file for each

day. The files include: 1) a repeat of the input

information, 2) compatible moduli of the layers

resulting from calculations, and 3) stress conditions for all points specified. For this study, the

points specified were located 0.01 in. above the

bottom of the asphalt or PCC and 0.01 in. below

the top of the subgrade.

CUMDAM

The program CUMDAM calculates cumulative

damage to the pavement structure, and was developed at CRREL. No report has been prepared that

discusses its function and operation. In general

form, the procedure used for CUMDAM’s calculations is the linear summation of cycle ratios,

referred to as Miner’s rule, which may be stated as:

n

N

D

i

i i

= i

∑ = 1 (11)

where ni = number of applications at strain level i

Ni = number of applications to cause failure at strain level i, based on damage

model predictions

D = total cumulative damage.

In this relation, failure can occur when D equals

or exceeds 1.0. Thus, for a section to last its design life, the value of D should not accumulate to

1.0 until the design period expires.

The value ni

 relates to the design traffic, or

applications, in 8165-kg (18,000-lb) equivalent

standard axle loadings (ESALs). For the first two

simulation series in this study, anticipated traffic

was considered to be 2,815,000 ESALs during a

5-year period. Since our incrementation was on a

daily basis, we applied this as a constant loading

of 1542 ESALs per day. In the final simulation

series the anticipated traffic was revised upwards

to 3,300,00 ESALs over five years, applied at a

rate of 1808 ESALs per day.

CUMDAM includes several damage models

previously developed by others for determining

Ni

 the number of applications to failure at a particular strain/stress condition (Table 6). Of the

damage models for flexible pavements, four are

based on horizontal strain at the bottom of the

asphalt layer, and relate to damage effects that

result in pavement cracking. These models were

developed by the Asphalt Institute (1982), Witczak

(1972), the Corps of Engineers (U.S. Army 1988),

and Coetzee and Connor (1990). Three other damage models for flexible pavements are based on

13
the vertical strain at the top of the subgrade, and

these relate to rutting damage in the pavement.

They were developed by the Asphalt Institute

(1982), the Federal Aviation Administration (Bush

1980), and the Corps of Engineers (U.S. Army

1987). For rigid pavements, CUMDAM uses the

damage model developed by the Corps of Engineers (U.S. Army 1990), which is based on the

horizontal stress at the base of the PCC.

The program assumes that all applications will

affect the point being modeled. That is, the damage is not reduced according to a pass-to-coverage algorithm to simulate the lateral wander of the

axle within the travel lane.

It is recognized that some of the equations are

being applied outside of the original assumptions

used in their development; however, they are representative of cumulative damage models currently

available and are used for the initial analysis until

more appropriate equations can be developed.

The CUMDAM program first reads the strain/

stress conditions from the daily NELAPAV output files and calculates the allowable applications

predicted by the various models under those conditions. It then divides the design applications by

the allowable applications, producing a daily incremental damage value. The incremental values

are summed to produce a cumulative damage value

and these are printed to individual files for each

model type. A file summarizing the daily strain

and deflection information is also produced.

MN/ROAD PAVEMENT

PERFORMANCE STUDIES

Performance predictions using the Mechanistic

Pavement Design Procedure were conducted in

three major efforts:

Phase 1, conducted in the spring of 1991, included an initial simulation series that modeled

temperatures from a year close to the mean freezing index. These boundary conditions were applied to eight flexible and three rigid sections.

Table 7. Layer composition and thicknesses of pavement structure in test sections simulated.

Test Layer 1 Layer 2 Layer 3

Section Comp* Thick † Comp Thick Comp Thick

Flexible

5-yr design

F-1 AC 14.6 (5.75) CL4 83.8 (33.0)

F-2 AC 14.6 (5.75) CL6 10.2 (4.0) CL4 71.1 (28.0)

F-3 AC 14.6 (5.75) CL5 10.2 (4.0) CL3 83.8 (33.0)

F-4 AC 22.2 (8.75)

10-yr design

F-14 AC 27.3 (10.75)

F-19 AC 19.7 (7.75) CL3 71.1 (28.0)

F-21 AC 19.7 (7.75) CL5 58.4 (23.0)

F-22 AC 19.7 (7.75) CL6 45.7 (18.0)

Rigid

5-yr design

R-5 PCC 19.7 (7.5) CL4 7.6 (3.0) CL3 68.5 (27.0)

R-6 PCC 19.7 (7.5) CL4 12.7 (5.0)

10-yr design

R-11 PCC 24.1 (9.5) CL5 12.7 (5.0)

*Composition:

AC—asphalt concrete; PCC—portland cement concrete; CL3—class 3 special;

CL4—class 4 special; CL5—class 5 special; CL6—class 6 special

†Thickness, cm (in.)

14
Phase 2, an effort in the summer of 1992, had

two primary objectives. Phase 2A included three

series modeling the eight flexible sections with

the mean freeze season and changing the method

employed to calculate the asphalt and subgrade

modulus. Phase 2B investigated the variability in

predictions when temperatures from freeze seasons with maximum and minimum freezing indices are applied to a single flexible section.

Phase 3, an effort in the summer of 1993, expanded the investigation of the effects of freeze

season characteristics. This series modeled 21 different freeze seasons applied to one full-depth and

one conventional flexible section.

Phase 1

Pavement sections

The Mn/ROAD mainline facility has 23 test

sections, including both flexible and rigid pavement systems, that are designed to fail after either

5 or 10 years. Included in the test matrix are pavement systems with various thicknesses and qualities of base and subbase materials. The base/subbase materials have a “special” Mn/DOT grading

designation for the test facility and range from

class 3, a well-graded sand, through classes 4 and

5, which have decreasing percentages of fines, to

class 6, a well-graded gravel with sand. The subgrade at the site classifies as a sandy lean clay, a

CL in the Unified Soil Classification System and

an A-6 in the AASHTO Classification System

(Bigl and Berg 1996a). Of the four subgrade

samples tested at CRREL, two exhibited high heaving in the frost susceptibility test, while the other

two ranked as having a medium heave rate.

The mechanistic procedure was applied to 11

test sections, which were distributed among the

designs as follows: four 5-year flexible, two 5-

year rigid, four 10-year flexible, and one 10-year

rigid. Figure 6 and Table 7 show the pavement

structures of the test sections simulated. Seven of

the test sections had variable water table depths

along their lengths, and these were simulated at

the two extreme water table positions. Table 8

lists the test sections and water table conditions

simulated as well as the nomenclature used to

denote the various cases. The case nomenclature

includes the Mn/DOT test section number and the

water table depth (in ft) preceded by a “w.” For

example, f1w9 refers to Mn/ROAD test section

ML5-F-1 with a water table 2.7 m (9 ft) below the

pavement surface and r11w6 refers to section

ML10-R-11 with a water table 1.8 m (6 ft) below

the pavement surface. All but one case involved

the high-heaving subgrade (sample 1206) beneath

the pavement structure. The final simulation included the lower-heaving subgrade (sample 1232)

under the 5-year full-depth section (ML5-F4),

termed case f4w6ss, or “second subgrade.”

Figure 6. Pavement structure of Mn/ROAD test sections simulated.

Asphalt Concrete

Class 4

Portland Cement Concrete

Class 5

Class 3

Class 6

F-1 F-2 F-3 F-4

0

10

20

30

40

50

0

20

40

60

80

100

120

(cm) (in.)

Depth Below Pavement Surface

5 Year (ML 5-)

F-14 F-19 F-21 F-22 R-5 R-6 R-11

10 Year (ML 10-) 5 Year 10 Year

Flexible Rigid

15
Table 8. Test sections and conditions analyzed.

Water table

Mn/ROAD Depth Simulation

test section m (ft) case Other variations

FLEXIBLE

5-year

ML5-F-1 2.7 (9) f1w9

ML5-F-2 2.7 (9) f2w9

ML5-F-2 6.1 (20) f2w20

ML5-F-3 2.4 (8) f3w8

ML5-F-3 6.1 (20) f3w20

ML5-F-4 1.8 (6) f4w6

ML5-F-4 1.8 (6) f4w6ld Low density subgrade

ML5-F-4 1.8 (6) f4w6ss No. 1232 subgrade

10-year

ML10-F-14 15.3 (50) f14w50

ML10-F-19 5.5 (18) f19w18

ML10-F-21 5.5 (18) f21w18

ML10-F-21 13.7 (45) f21w45

ML10-F-22 13.7 (45) f22w45

RIGID

5-year

ML5-R-5 1.8 (6) r5w6

ML5-R-5 3.7 (12) r5w12

ML5-R-6 1.2 (4) r6w4

ML5-R-6 3.7 (12) r6w12

10-year

ML10-R-11 1.8 (6) r11w6

ML10-R-11 3.7 (12) r11w12

Material properties

Material properties input to the FROST program are shown in Table 9. The soil water characteristics are based on a best fit to the moisture

retention test data using the Gardner’s eq 2. Soil

residual moisture contents were calculated using

eq 2 with a pressure of –800 cm water. The soil

permeability characteristics result from fitting the

Gardner’s eq 3 to unsaturated hydraulic conductivity test results.

As part of this study, Mn/DOT class 3 special,

class 6 special, and two subgrade materials had

been tested to determine the information for input

to the model. Results of the soil characterization

tests are given in Bigl and Berg (1996a). The class

4 special and class 5 special materials were not

tested, so their behavior had to be approximated

using data from previously tested materials that

most closely matched their specified size gradations. A subbase from taxiway A at the Albany,

New York, airport most closely matched the class

4 special subbase specifications; dense-graded

stone, which had been tested during a cooperative

study in Winchendon, Massachusetts, most closely

matched the class 5 special material. Results of

the characterization tests of the substitute materials are also given in Bigl and Berg (1996a) and in

Cole et al. (1986, 1987).

The densities of the Mn/ROAD materials, which

had been characterized with compaction testing,

were set at the optimum values. For the substitute

materials, the densities were set at the values determined from in-place samples taken from the

site. To demonstrate the influence of proper compaction, one simulation (case f4w6ld) involved

setting the density of the 1206 subgrade to a reduced value less than optimum (1.69 Mg/m3

, 105.5

lb/ft3

). Optimum density was set at 1.89 Mg/m3

(117.9 lb/ft3), determined with a compactive effort of 2360 kJ/m3 (55,000 ft-lb/ft3

).

16
Table 9. Material parameters input to FROST for Mn/ROAD test section simulations.

(PCC) (DGS) (TAS) (1206) (1232)

Parameter Asphalt Concrete Class 6 Class 5 Class 4 Class 3 Subgrade SubgradeSoil density (g/cm3) 2.3 2.3 2.09 1.89 2.16 2.11 1.89 1.99

Specific heat of soil (cal/g °C) 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

Thermal cond. of soil (cal/cm hr °C) 17.5 17.5 17.0 17.0 17.0 17.0 17.0 17.0

Soil porosity (cm3/cm3) 0.14 0.14 0.331 0.337 0.206 0.251 0.374 0.320

Soil water characteristics:

A

w 0.3090 0.3090 1.0001 0.4961 0.152 0.1735 0.00240 0.00226

α 0.3190 0.3190 0.4444 0.3660 0.269 0.3239 0.7134 0.6790

Residual water content (cm3/cm3) 0.039 0.039 0.01614 0.05008 0.10741 0.09994 0.2916 0.2638

Saturated hydraulic cond. (cm/hr) 2.10 1.05 6.0 5.54 2.8 4.5 0.14 0.0087Permeability characteristics:

Ak 0.0349 0.0349 3.723 × 10–8 3.912 6.58 × 10–5 1647.1 0.000571 0.001886

β 2.6450 2.6450 5.6733 1.3930 2.962 0.7207 2.6395 1.8129

17
Table 10. Modulus equations used for Mn/ROAD test section simulations.

A. Frozen condition

Std.

Material Equation (Mr in lb/in.2)* n r2 error

Clay subgrade sample 1206 (565)

Frozen M fw r = − − 1 049 2 344 ,() u g . 207 0.99 0.275

Frozen M fw r = − − 1 052 2 929 ,() u v . 207 0.99 0.262

Clay subgrade sample 1232 (566)

Frozen M fw r = − − 846 2 161 ( ) u g . 244 0.98 0.423

Frozen M fw r = − − 848 2 633 ( ) u v . 244 0.98 0.394

Class 3 special “stockpile”

Frozen M fw r = − − 5 488 1 076 ,() u g . 210 0.97 0.507

Frozen M fw r = − − 5 542 1 249 ,() u v . 186 0.97 0.467

Class 4 special (taxiway A subbase)

Frozen M fw r = − − 1 813 1 733 ,() u g . 85 0.93 0.885

Frozen M fw r = − − 1 652 2 813 ,() u v . 69 0.91 0.916

Class 5 special (dense graded stone)

Frozen M fw r ug . = ,() − − 8 695 1 2814 28 0.95 0.511

Frozen M fw r uv . = ,() − − 9 245 1 489 28 0.97 0.432

Class 6 special “stockpile”

Frozen M fw r ug . = ,() − − 19 427 0 795 260 0.98 0.338

Frozen M fw r uv . = ,() − − 19 505 0 897 260 0.98 0.341

Notes:

n = number of test points

r2 = coefficient of determination

Mr = resilient modulus

f(S) = S/ So σ = stress (lb/in.2)

S = degree of saturation (%) f

1(σ) = J1/σo

So = 1.0 % f

2(σ) = (J2/τoct/σo

f(γ) = γ

d/

γ

o f

3(σ) = τoct/σo

γd = dry density (Mg/m3) σo = 1.0 lb/in.2

γo = 1.0 Mg/m3 J1 = bulk stress (lb/in.2)

f(wu–g) = wu–g/wo J1 = 3 σ3+ σd

wu–g = gravimetric unfrozen water content J2 = 2nd stress invariant (lb/in.2)

wo = unit water content (1.0) J2 = 3σ3

2 + 2 σ3σd

f(wu–v) = wu–v/wo τoct = octahedral shear stress (lb/in.2)

wu–v = volumetric unfrozen water content τoct = ( 2 3/ )σd

*Output from equations can be converted to kilopascals by multiplying by 6.895.

Saturated hydraulic conductivities were set at

the laboratory-determined value, except in the case

of the 1206 clay subgrade. In that case, we multiplied the laboratory value by 10 to approximate

the hydraulic behavior after formation of frostinduced shrinkage cracks.

The modulus equations used in TRANSFORM

for the Phase 1 modeling are the normalized gravimetric form shown in Table 10a and the unfrozen

form shown in Table 10b. The associated unfrozen water constants utilized in the frozen form of

the equations are given in Table 11. Development

18
Table 10 (cont’d).

B. Unfrozen condition

Std.

Material Equation (Mr in lb/in.2)* n r2 error

Clay subgrade sample 1206 (565)

Never Frozen M fS f f r . . 3 . = , , () () () − − 1 597 000 2 63 14 42 0 257 γ σ 655 0.82 0.251

Clay subgrade sample 1232 (566)

Never Frozen M fS f r . . = × . () () − − 1 518 1030 13 85

3

0 272 σ 451 0.95 0.328

Class 3 special “stockpile”

Thawed M fS f r . . = , () () − 283 300 1 003

2

0 206 σ 408 0.86 0.520

Class 4 special (taxiway A subbase)

Thawed M fS f r . . = × . () () − 8 946 108 3 026

2

0 292 σ 149 0.86 0.168

Class 5 special (dense graded stone)

Thawed M fS f r . . = , () () − 382 400 0 8759

2

0 1640 σ 64 0.77 0.164

Class 6 special “stockpile”

Thawed M fS f f r ... = , () () () − 1 391 0 507 4 04

1

0 608 γ σ 492 0.79 0.232

Thawed M fS f e f r . . . () = , () () − 5 257 0 486 4 05 γ 0 0193 1 σ 492 0.76 0.249

of these equations is discussed in Berg et al. (1996).

Figure 7 shows the predicted moduli for the Mn/

ROAD materials using mean values for stress and

density, where applicable.

It should be noted that the thawed modulus

equation used for class 6 special material is an

exception to general form given in Table 2. In this

case, we used a semi-log form (eq 10), rather than

the log-log form, which eliminated problems that

occurred from negative stresses generated by the

model.

It should also be noted that after the Phase 1

simulations were completed, we discovered that

resilient modulus tests on the 1206 subgrade in

the unfrozen condition were probably in error due

to a miscalibrated testing system. As a result, the

unfrozen subgrade moduli predicted in Phase 1

modeling are likely to be substantially higher than

-12 -10 -8 -6 -4 -2 0 2

Temperature (°C)

10

10

10

108

6

4

2

1206

1232

Class 3

Class 4

Class 5

Class 6

Resilient Modulus

7 x 10 8

7 x 10 6

(kPa) (lb/in. ) 2

7 x 10 2

7 x 10 4

Degree of Saturation (%)

100 80 60 40 20

1232 1206

Class 3

Class 4 Class 5

Class 6

10

10

10

10

106

5

3

4

2

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

7 x 10 2

a. Frozen condition. b. Thawed condition.

Figure 7. Predicted moduli of Mn/ROAD materials.

19
exist in the field, resulting in less damage than

would have been obtained with more reasonable

moduli.

The model numbers for the program NELAPAV

(Table 4) were set as follows. Model 0, the linear

model, was used at all times for paving materials

and for soils in the frozen state. With model 0, the

seed modulus is accepted as the modulus of the

material layer. Model numbers were assigned to

unfrozen soils as follows: Model 1—class 6; Model

3—class 3 and class 4; Model 4—both clay

subgrades.

In all of the cumulative damage studies on the

flexible pavements, it was assumed that the pavement properties were constant from one pavement

test section to another. Some of the test sections

we simulated will have pavement properties different from others because of the experimental

design of the paved surface. Some variations in

the asphalt pavement properties could be considered in subsequent modeling efforts, but we maintained the same asphalt pavement properties in all

of these simulations.

Results—flexible sections

Output from FROST for the 5-year

full-depth simulation (f4w6) is shown

in Figure 8. The top graph shows the

daily mean air temperature for the period from 1 October 1959 to 14 November 1960. The center portion illustrates the predicted frost heave and

the bottom graph contains the predicted frost and thaw penetration as

functions of time. Frost output graphs

for all the flexible cases are compiled

in Appendix A. Table 12 contains

maximum frost heave and maximum

frost penetration depths for each of

the cases simulated (Table 8). Simulations with shallower water table

depths had greater amounts of heave

and less frost penetration compared

to simulations with a deeper water

table location. Sections that included

the substitute for the class 4 special

subbase (taxiway A subbase) had

higher amounts of heave than those

with other combinations of subbase

materials.

Table 11. Constants for equations to determine gravimetric unfrozen moisture

content, wu–g.

Equation constants*

Soil α β

Subgrade

1206 11.085 –0.274

1232 8.121 –0.303

Class 3 special

stockpile 1.497 –0.709

Class 4 special

Taxiway A 3.0 –0.25†

Class 5 special

Dense stone 2.0 –0.40†

Class 6 special

Stockpile 0.567 –1.115

* wu–g, decimal form = α β

100 0

T

T

† Values for these materials are estimated

Figure 8. Example output from FROST for Mn/ROAD test section ML5-F4 with a 1.8-m (6-ft) water table. Simulation starts

on 1 October.

20
Figure 9 presents the moduli being calculated

by TRANSFORM and passed as seed moduli to

NELAPAV for the f4w6 case. The plotted moduli

are the minimum values for each day, with the

subgrade (top) being located within 0.3 m (1 ft) of

the asphalt and subgrade (bottom) being the rest

of the modeled section (to 4.0 m or 13.1 ft). Note

that the predicted asphalt moduli during the summer months are smaller than those of the subgrade,

which results in high horizontal strains at the base

of the asphalt layer during the summer months. In

later simulations (Phase 2 and 3), we used other

models to determine the asphalt modulus.

Figure 10 shows the deflection and strains computed by NELAPAV for the f4w6 case. The horizontal strain at the base of the asphalt is low

through the winter with a few small peaks during

short-term thaw periods, then exhibits high peaks

during spring thaw and summer. It appears to be

closely tied to the asphalt temperature/modulus

during the spring thaw. The vertical strain at the

top of the subgrade is also low during the winter

with three sharp peaks during thaw events. The

vertical strain also rises during spring and summer, closely tracking the pavement surface temperature. The deflection plotted is from the base

of the asphalt, but is assumed to be similar to the

surface deflection. It also shows peaks during midwinter thaws, and a maximum peak during the

spring prior to drainage of excess moisture. Generally, deflections in the summer are greater than

winter values.

Table 12. Maximum frost heave and frost

penetration in modeled simulations

Frost Frost

Cases heave penetration

cm (in.) cm (in.)

5-YEAR

Flexible

f1w9 0.25 (0.10) 137.9 (54.3)

f2w9 1.19 (0.47) 121.9 (48.0)

f2w20 0.33 (0.13) 142.0 (55.9)

f3w8 0.08 (0.03) 134.1 (52.8)

f3w20 0.00 142.0 (55.9)

f4w6 1.37 (0.54) 118.1 (46.5)

f4w6 ld 1.32 (0.52) 118.1 (46.5)

f4w6 ss 0.03 (0.01) 137.9 (54.3)

Rigid

r5w6 1.04 (0.41) 121.9 (48.0)

r5w12 0.00 137.9 (54.3)

r6w4 4.72 (1.86) 103.9 (40.9)

r6w12 0.00 134.1 (52.8)

10-YEAR

Flexible

f14w50 0.00 134.1 (52.8)

f19w18 0.00 142.0 (55.9)

f21w18 0.00 134.1 (52.8)

f21w45 0.00 134.1 (52.8)

f22w45 0.00 134.1 (52.8)

Rigid

r11w6 1.42 (0.56) 118.1 (46.5)

r11w12 0.00 134.1 (52.8)

ld = low density (1.69 Mg/m3 or 105.5 lb/ ft3)

ss = second subgrade (1232)

Figure 9. Seed moduli

output by TRANSFORM

for Mn/ROAD test section

ML5-F4 with a 1.8-m (6-

ft) water table. Subgrade

(top) is within the upper

0.3 m (1 ft) of subgrade

beneath the asphalt. Subgrade (bottom) is beneath

that layer to the bottom

of the modeled section.

21
Figure 10. Deflection and strain calculated by NELAPAV

for Mn/ROAD test section ML5-F4 with a 1.8-m (6-ft)

water table. Horizontal strain is at the base of the pavement. Vertical strain is at the top of the subgrade.

Table 13. Predicted applications to failure (× 1000) from Phase 1 simulation series of flexible

pavement test sections.

Horizontal criteria Vertical criteria

Asp. Inst. Asp. Inst. Corps of Coetzee/ Asp. Inst. Corps of

Cases MS-1 MS-11 Engineers Connor MS-1 Engineers FAA

5-YEAR

F1W9 86 498 88 4,380 136,942 5,653 11,879

F2W9 522 1,244 550 42,703 32,477 1,345 1,526

F2W20 722 1,534 764 66,450 155,909 8,226 9,855

F3W8 957 1,706 958 92,419 116,287 2,653 9,611

F3W20 1,068 1,801 1,055 105,202 222,462 7,889 20,632

F4W6 28,585 75,751 90,926 >107 3,715 15 152

F4W6ld 1,905 20,209 7,036 >107 165 >107 >107

F4W6ss 72 1,180 96 >107 >107 >107 >107

10-YEAR

F14W50 103,272 485,198 605,194 > 107 8,602 10 251

F19W18 396 6,148 966 75,751 2,962,263 56,680 457,585

F21W18 3,394 30,456 12,751 2,010,107 562,830 84,382 42,478

F21W45 3,404 30,358 12,794 2,010,107 611,772 92,571 48,188

F22W45 7,614 57,315 31,147 8,040,429 73,190 22,415 3,388

Notes:

ld = low density (1.69 Mg/m3 or 105.5 lb/ft3)

ss = second subgrade (1232)

Traffic simulated at rate of 562,830 ESAL applications/yr

Table 13 lists the applications to failure predicted from the 1-year simulation period applied to the flexible sections. The values listed

in Table 13 were determined by taking the reciprocal of the one year (365-day) cumulative

damage value produced by the CUMDAM program and multiplying by the number of applications received by the sections during that

time period (562,830 per year). This application rate was based on an initial estimate that

the traffic across the test sections would be

2,815,000 ESALs in 5 years, or 5,630,000

ESALs in 10 years. Note that the values listed

in Table 15 are thousands of ESAL applications. Subsequent to conducting the Phase 1

series, a revised estimate is that the 5-year sections will receive 3,300,000 ESAL applications

in five years, (i.e., are designed to fail after

3,300,000 ESAL applications); the 10-year sections will fail at 6,600,000 ESAL applications.

Individual values listed in Table 13 vary

anywhere from very much below to very much

above the failure values described. By comparing values horizontally across the table for any

case, it can be seen that different models esti22
mate substantially different pavement lives for the

same strain conditions.

A close review of the values in Table 13 illustrates a variety of interesting occurrences:

1. Cases with Mn/ROAD test section ML5-F-4

that employed the lower density subgrade

(f4w6ld) or the “1232” subgrade (f4w6ss) predicted the pavement to fail much more quickly

than when the higher (optimum) density 1206

subgrade was used. This is due to the fact that

the higher density “1206” subgrade used in

most simulations maintained a resilient modulus during the summer months in excess of

276,000 kPa (40,000 lb/in.2

), but the modulus

values for the same period were about 96,000

kPa (14,000 lb/in.2) for f4w6ld and about 6900

kPa (1000 lb/in.2) for f4w6ss. The “low density” predicted moduli are the closest to the

values measured during the summer months

with an FWD.

2. Variations in water table position in the

same test section result in different predicted

lifespans, especially if the water table is less

than 3 m (10 ft) deep at one location and more

than 6 m (20 ft) deep at another. Both the

ML5-F-2 and ML5-F-3 test section simulations illustrate a shorter predicted life with a

shallow water table depth. For the shallow

water table conditions, greater availability of

water results in higher thaw weakening (reduced modulus values) in the spring.

3. Most of the sections are predicted to fail

due to cracking of the pavement caused by

tensile stresses at the bottom of the pavement

much before they will fail due to rutting caused

by excessive deformation of the subgrade. It

is only the simulations of the full-depth sections (ML5-F-4, case f4w6, and ML10-F-14,

f14w50) that indicate rutting failures may occur before excessive fatigue cracking.

Figures 11 to 13 illustrate examples of the

relation between accumulating damage and

time. Additional plots of heave, frost penetration, and cumulative damage for all the flexible sections are compiled in Appendix A.

Damage related to the horizontal strain criteria has different patterns with time for different models. Damage predicted by the MS-1

(Asphalt Institute) model has some increase

during winter thaw events and during the main

spring thaw, but a majority of its increase is in the

summer period. Damage from the MS-11 (Asphalt Institute) model has a consistent pattern of

rising during winter and spring thaw periods, and

remaining constant during the summer. The patFigure 11. Cumulative damage for case f4w6 with optimum density 1206 subgrade.

Figure 12. Cumulative damage for case f2w9.

Figure 13. Cumulative damage for case f4w6 with 1232

subgrade.

23
tern of damage accumulation from the Corps of

Engineers model is similar to the MS-1 model,

especially when the water table is shallow, causing larger resultant deflections and strains. For

simulations with deeper water tables, smaller

amounts of damage accumulate during the summer.

Damage from models using the vertical strain

criteria follow three general patterns: 1) a sharp

rise during spring thaw period with no accumulation at other times of the year (e.g., Fig. 12), 2) a

series of increases during winter thaw events and

the spring thaw (Fig. 11), and 3) in the cases with

lower modulus subgrades, a gradual increase in

damage during the spring, with sharper increases

in the summer (Fig. 13). This last result is likely

due to the anomalously low asphalt moduli being

predicted by the Schmidt model.

Results—rigid sections

Predicted applications to failure for the concrete (rigid) sections is shown in Table 14, with

the three sections in the table indicating the results of a sensitivity study. In the left-hand section, the flexural strength of the concrete was set

at 4480 kPa (650 lb/in.2) and the surface condition index (SCI) at the point of failure was set at

80. In the central section, the flexural strength

was reduced to 3448 kPa (500 lb/in.2), while the

SCI remained at 80. For predictions in the righthand column, the flexural strength was kept at

Table 14. Applications to failure (× 1000) from simulations of

rigid test sections.

RCON = 650 RCON = 500 RCON = 650

Case SCI = 80 SCI = 80 SCI = 90

5-YEAR

R5W6 52,601 507 45,244

R5W12 65,598 605 56,452

R6W4 157,655 1,505 135,622

R6W12 132,120 1,701 113,933

10-YEAR

R11W6 >5.6 × 108 18,761,000 >5.6 × 108

R11W12 >5.6 × 108 28,141,500 >5.6 × 108

Notes:

RCON = Concrete flexural strength (lb/in.2)

SCI = Surface condition index at failure

Traffic simulated at rate of 562,830 ESAL applications/yr.

4480 kPa and the SCI was increased to

90. A comparison of the cumulative damage with time for the case representing

section ML5-R-5 with a 1.8-m (6-ft) water table (r5w6) using all three combinations of flexural strength and SCI is also

illustrated in Figure 14. Appendix B has

a compilation of graphs depicting the

frost/thaw penetration and cumulative

damage for all rigid sections simulated.

Cases with a flexural strength of 4480

kPa exhibited very little damage, with

the ML10-R-11 section having unmeasurable damage. Reducing the flexural

strength to 3448 kPa greatly increased

the predicted damage for the 5-year sections, but had a lesser effect on damage

in the 10-year section.

The pattern of damage accumulation

with time varied with the test section simulated

Figure 14. Cumulative damage for case r5w6.

24
(App. B). ML5-R-5 experienced rapid increases

in damage during the thaw periods, but also had

an equivalent increase in damage over the summer months. The other sections experienced a

majority of their damage during the thaw periods

and very little damage during the summer.

The low damage predictions result from the

fact that the model predicts damage at the center

of a slab, whereas the majority of damage occurs

at the slab edges. Chou (1989) recommends increasing the stresses computed from the layered

elastic method by a factor of 1.33 to estimate the

coverage levels for roadway pavements.

Phase 2A

To address problems discovered in the Phase 1

modeling series, three additional simulation series were conducted on the eight flexible test sections studied in Phase 1 with the water table located at the shallowest position. A change that

applied to all three series was that the normalized

volumetric unfrozen water content form of the

frozen modulus equations (Table 10a) was used,

rather than the normalized gravimetric form used

in Phase 1.

The first of the new series was essentially a

repeat of the initial series in that it used the Schmidt

model (eq 8) for calculation of the asphalt modulus and the high density 1206 form of the subgrade

for modulus calculations. It differed from the initial series in that the normalized volumetric unfrozen water content form of the frozen modulus

equations was utilized. A mistake in the CUMDAM

program was also remedied—correcting the value

of the subgrade modulus used in the Corps of

Engineers vertical strain damage calculation. Table

15 lists the results of this series in the rows labeled “Schmidt.” In general, predictions of applications to failure in the conventional cross sections were less than in the original series using the

horizontal strain criteria and greater using the vertical strain criteria. In the full-depth sections (F4

and F14), applications to failure were increased in

both the horizontal and vertical strain criteria.

The second series addressed the issue that the

Phase 1 simulations computed summer asphalt

moduli that were lower than considered reasonable. In this series, the Ullidtz model (eq 9) was

used to calculate the asphalt modulus at temperatures greater than 1°C; at colder temperatures, the

Schmidt model was used. This series also used the

high density 1206 form for the subgrade modulus

calculations. Results for this series are shown in

Table 15 in rows labeled “Ullidtz.” In nearly all

cases, this series produced higher predicted applications to failure than the corresponding Schmidt

series.

The third series also used the Ullidtz model to

calculate the asphalt modulus. In addition, it addressed the problem from the Phase 1 simulations

that during the summer the predicted subgrade

moduli based on the high-density 1206, or “normal” form were higher than FWD-measured values. For this series, the unfrozen subgrade modulus, when recovered, was set to be constant at

103,000 kPa (15,000 lb/in.2). This value was chosen as being approximately equal to an average

value back-calculated from FWD measurements

on subgrade during fall 1991.* As a result of this

modulus approximation, the linear model (model

0 in Table 4) was used in NELAPAV for all

subgrade calculations. The applications to failure

from this series are listed in Table 15 as “Ull15K.” In the conventional sections including a

base/subbase, the applications to failure were

slightly lower than those resulting from the previous case with the Ullidtz asphalt model and the

higher-modulus subgrade; in the full-depth sections, they were quite a bit lower.

A comparison of the Ullidtz/15K subgrade series results with the originally designed failure at

3,300,000 applications for the 5-year sections and

at 6,600,000 applications for the 10-year sections

yields the following conclusions:

1. In general, the Mechanistic Pavement Design Procedure predicts the 5-year conventional

sections to fail due to asphalt cracking prior to the

end of the design life, while failure from subgrade

rutting is predicted beyond the design life.

2. Predictions for the 5-year full-depth section

indicate that it will not fail from asphalt cracking,

but two of the three criteria for subgrade rutting

indicate early failure.

3. The two 10-year conventional sections with

class 5 and class 6 special bases (F21 and F22) are

predicted to fail from asphalt cracking at about

the end of the design applications, while subgrade

rutting criteria indicate longer life.

* D. Van Deusen, Mn/ROAD, pers. comm. 1992.

25
Table 15. Predicted applications to failure (× 1000) from simulations of flexible test sections run in Phase 2A

series.

Horizontal criteria Vertical criteria

Asp. Inst. Asp. Inst. Corps of Coetzee/ Asp. Inst. Corps of

Cases MS-1 MS-11 Engineers Connor MS-1 Engineers FAA

5-YEAR

F1W9

Phase 1 86 498 88 4,380 136,942 5,653 11,879

Schmidt 85 414 78 3,557 244,709 3,297 15,665

Ullidtz 651 935 218 17,616 258,179 3,430 17,025

Ull-15K 617 863 201 15,578 213,193 3,133 18,441

F2W9

Phase 1 522 1,244 550 42,703 32,477 1,345 1,526

Schmidt 271 859 259 14,634 210,011 2,840 11,389

Ullidtz 970 1,429 376 37,053 255,832 3,262 15,488

Ull-15K 908 1,303 340 31,925 117,747 1,971 6,649

F3W8

Phase 1 957 1,706 958 92,419 116,287 2,653 9,611

Schmidt 533 1,224 487 32,818 96,046 1,197 7,298

Ullidtz 1,255 1,842 528 58,812 87,260 1,108 6,381

Ull-15K 1,225 1,705 503 54,327 115,098 1,404 10,501

F4W6

Phase 1 28,585 75,751 90,926 >107 3,715 15 152

Schmidt 45,171 121,039 175,884 >107 4,505 314 164

Ullidtz 65,218 123,699 149,292 >107 11,952 317 246

Ull-15K 7,055 26,561 8,219 3,752,200 7,996 331 467

10-YEAR

F14W50

Phase 1 103,272 485,198 605,194 >107 8,602 10 251

Schmidt 126,479 721,577 970,397 >107 11,687 417 336

Ullidtz 209,230 760,581 852,773 >107 17,107 412 359

Ull-15K 19,902 153,779 40,903 >107 26,943 787 2,232

F19W18

Phase 1 396 6,148 966 75,751 2,962,263 56,680 457,585

Schmidt 309 4,335 635 43,328 4,329,462 37,175 632,393

Ullidtz 2,948 14,480 2,278 574,316 4,329,462 37,422 639,580

Ull-15K 2,688 12,367 1,976 469,025 1,125,660 18,173 264,239

F21W18

Phase 1 3,394 30,456 12,751 2,010,107 562,830 84,382 42,478

Schmidt 1,958 16,072 4,701 420,022 865,892 10,452 70,442

Ullidtz 8,515 33,402 9,343 3,752,200 792,718 9,689 61,849

Ull-15K 6,661 23,335 6,513 2,345,125 457,585 8,752 66,686

F22W45

Phase 1 7,614 57,315 31,147 8,040,429 73,190 22,415 3,388

Schmidt 1,750 21,507 5,070 493,711 68,388 1,078 3,077

Ullidtz 8,235 42,964 9,192 3,752,200 85,667 1,278 4,297

Ull-15K 6,186 26,045 5,986 2,084,556 120,520 2,086 9,840

Notes:

Phase 1—previous work, Schmidt— new series with Schmidt asphalt model, Ullidtz—new series with Ullidtz

asphalt model above 1°C, Ull-15K—new series with Ullidtz asphalt model and summer subgrade modulus =

15K lb/in.2 (103,000 kPa). Traffic simulated at rate of 562,830 ESAL applications/yr.

26
4. The 10-year conventional section with class

3 special subbase (F19) may fail due to asphalt

cracking, but not from subgrade rutting.

5. Predictions for the 10-year full-depth section indicate that it will not fail from asphalt cracking, but two of the three criteria for subgrade rutting indicate early failure.

Phase 2B

To investigate the influence of the applied

freeze/thaw season on the predicted performance

of the sections, an environmental effects sensitivity series was conducted using the single conventional flexible test section, F3, which included

class 5 special and class 3 special materials as its

base and subbase courses (Fig. 6) and a water

table at a depth of 2.4 m (8 ft). Prior simulations

had applied upper boundary temperatures from

the season with a freezing index near to the 30-

year mean, 1959–60 (freezing index 1003 °C-days,

1806 °F-days). This new series applied temperatures from three other freeze/thaw seasons, including those with freezing indices equal to the

mean of the three coldest seasons during the period 1959 to 1987 and the maximum and minimum for the 1959–1987 period. These seasons

were maximum—1978–79 (1477 °C-days, 2658

°F-days), minimum—1986–87 (467 °C-days, 841

°F-days), and mean 3 coldest out of 30—1964-65

(1391 °C-days, 2503 °F-days). Results from these

years were compared with F3W8 predictions for

the mean year that had been run in the “Schmidt”

series, since this Phase 2B series also used the

Schmidt model for asphalt modulus calculations

(eq 8) and the high density 1206 form for the

subgrade modulus calculations.

Figure 15 shows the freeze/thaw penetration in

the F3 section predicted by FROST for all four

freeze seasons. In the mean year, multiple small

freeze/thaw events were followed by a long freeze

event that penetrated the subgrade and a spring

warming that remained above freezing. The minimum year had several freeze/thaw events, but they

were less severe—none of them penetrated beyond the base course materials. The maximum

year began with a very severe freeze event that

penetrated to the subgrade and lasted all winter. In

the spring, thawing of this freeze bulb was interrupted by two smaller freeze events, such that

there existed a thawed layer in the subbase between two frozen zones. The year with a freezing

index equal to the mean of the three coldest in 30

(3/30 year) had a freeze season consisting of a

single severe freeze event that penetrated into the

subgrade, which then thawed with no small freeze

events.

Figure 15. Frost and thaw penetrations predicted by FROST for freeze

seasons in Phase 2B environmental sensitivity study. Simulations start on

1 October.

AC

CL5

CL3

0 60 120 180 240 300 0 60 120 180 240 300

0

20

40

60

0

20

40

60

Elapsed Time (days)

Frost/Thaw Depth

0

50

100

150

0

50

100

150

(cm) (in.)

1959–60 1986–87

1978–79 1964–65

Mean Min.

Max. 3/30

Frozen

Unfrozen

27
Table 16 lists the predicted damage in terms of

applications to failure from this environmental series, in which traffic was simulated at 562,830

ESALs per year. Compared with the mean year,

failure due to the horizontal strain criteria (asphalt

cracking) is predicted earlier with the maximum

year and the 3/30 year, and later with the minimum year. However, the spread of values is not

that great, and 3 of the 4 models predict failure

sooner than the design figure of 3,300,000 applications for all four of the seasons modeled. Time

of failure due to the vertical strain criteria (asphalt

rutting) is predicted sooner in the maximum year

than the mean year, and at about the same time

as the mean year with the 3/30 year. No damage

due to subgrade rutting was predicted with the

minimum year in which no frost penetrated the

subgrade.

Phase 3

The third phase of the study modeled two

flexible pavement sections to which 21 years of

environmental conditions were applied. Various

analyses were conducted attempting to correlate

the predicted damage with the characteristics of

the freeze seasons simulated.

Cross sections/material properties

The two cross sections simulated employed

layer thicknesses from two Mn/ROAD test sections (Table 7). The first, section F4, was a “fulldepth” section consisting of an asphalt layer lying

directly above the lean clay subgrade. The second, section F3, was a “conventional” section,

including class 6 special as the base material (substituted for class 5 special in the actual pavement

structure) and class 3 special as the subbase.

Physical properties used for the materials were

the same as shown in Table 13, with the exception

that a lower density (1.69 Mg/m3; 105.5 lb/ft3)

was used for the 1206 subgrade. Figure 16 illustrates predicted moduli for several densities of the

1206 subgrade. The asphalt modulus was calcuTable 16. Performance predictions for F3 test section with water table at 2.4

m (8 ft). Freeze/ thaw seasons applied as upper boundary temperatures were

mean year—1959–60, maximum year—1978–79, minimum year—1986–87,

average of the 3 coldest out of 30—1964–65.

Applications to failure (× 1000)

Failure criteria Mean Max Min 3/30

Horizontal

Asphalt Institute (MS-1) 533 384 573 397

Asphalt Institute (MS-11) 1,224 1,215 1,117 1,445

Corps of Engineers 487 375 593 368

Coetzee/Conner 32,818 25,284 50,660 23,530

Vertical

Asphalt Institute (MS-1) 96,046 51,120 >107 96,046

Corps of Engineers 1,197 600 >107 1,143

FAA 7,298 4,080 >107 7,625

Note: Traffic simulated at rate of 562,830 ESAL applications/yr.

100 80 60 40

103

104

105

106

Degree of Saturation (%)

Resilient Modulus

115 lb/ft 3

108

105

High

Medium

Low

Density (lb/ft )3

114 - 117

107 - 110

104 - 106

7 x 10 6

7 x 10 5

7 x 10 4

7 x 103

(kPa) (lb/in. ) 2

Figure 16. Resilient modulus vs. degree of saturation of never-frozen 1206 subgrade material illustrating the effect of dry density.

28
Table 17. Results of 21-year freezing index/water table series.

Maximum Applications to failure (millions)

Water table Freezing Freeze/thaw freeze depth Horizontal strain Vertical strain

depth index events in into subgrade Asphalt cracking Subgrade rutting

Year m (ft) °C (°F)-days subgrade (cm) CEH AIH-MS11 CEV AIV-MS1

A. Full depth (F4)

6970 1.5 (4.8) 1191 (2144) 2 91.8 18.20 66.00 0.21 5.38

7071 1.3 (4.2) 1152 (2074) 4 91.8 18.02 52.59 0.34 8.23

7172 1.1 (3.6) 1274 (2294) 2 91.8 15.16 45.02 0.31 7.64

7273 1.2 (4.0) 839 (1510) 2 69.8 18.97 50.69 0.37 7.72

7374 1.3 (4.2) 923 (1661) 2 77.8 17.80 51.48 0.78 10.97

7475 1.4 (4.6) 968 (1743) 3 81.8 17.21 47.93 0.18 5.47

7576 1.3 (4.2) 931 (1675) 3 73.8 16.83 52.26 0.16 4.15

7677 1.6 (5.3) 1256 (2261) 4 107.8 17.92 62.38 0.16 4.87

7778 1.1 (3.7) 1331 (2395) 1 91.8 13.88 60.22 0.10 3.01

7879 1.2 (3.8) 1477 (2658) 3 99.8 17.66 51.36 6.66 17.18

7980 1.2 (3.8) 903 (1625) 5 79.8 16.67 43.10 0.19 5.30

8081 1.2 (4.0) 666 (1199) 3 67.8 17.15 42.63 0.26 7.72

8182 1.8 (6.0) 1227 (2209) 3 107.8 16.29 47.92 0.04 1.44

8283 1.2 (3.9) 589 (1061) 8 63.8 16.73 34.26 0.11 3.71

8384 1.0 (3.3) 1179 (2123) 2 81.8 16.86 48.96 0.12 3.50

8485 1.0 (3.3) 942 (1696) 3 81.8 16.08 44.68 0.15 4.31

8586 1.0 (3.2) 1197 (2154) 2 81.8 17.67 71.27 0.79 11.48

8687 0.9 (3.0) 467 (841) 4 45.8 15.91 33.52 0.48 8.44

8788 1.5 (4.8) 898 (1616) 4 87.8 16.91 48.28 0.34 6.15

8889 1.5 (4.9) 1032 (1858) 4 87.8 17.57 50.53 0.26 7.19

8990 1.4 (4.7) 750 (1350) 7 65.8 16.50 37.45 0.25 6.83

Notes:

CEH = Corps of Engineers (horizontal) CEV = Corps of Engineers (vertical)

AIH-MS11 = Asphalt Institute (MS-11) AIV = Asphalt Institute (MS-1)

ND = no damage

Traffic simulated at rate of 660,000 ESAL applications/yr.

lated with a combination of the Ullidtz model at

above 1°C temperatures and the Schmidt model at

colder temperatures.

Environmental conditions

The series simulated the 21-year time period

1969–70 to 1989–90, using a combination of recorded air temperatures and an estimated position

of the water table. The simulations started on 1

October of the first year and proceeded for 365

days, using mean daily air temperatures recorded

at Buffalo, Minnesota, applied as a step condition

for 24-hr periods. The depth to the water table

was varied based on the total precipitation accumulated at St. Cloud, Minnesota, during the thaw

season prior to the simulated freeze season. An

inverse relationship between precipitation and

water table depth was applied such that the maximum precipitation produced the shallowest water

table at 0.91 m (3 ft) below the surface and the

minimum precipitation produced the deepest water table at 1.82 m (6 ft). The water table was held

constant throughout the simulation at the depth

determined by this relationship. Figure 17 shows

the distribution of estimated water table and freeze

index for this period.

Results

As in previous simulation series, there was a

wide variation in the damage amounts predicted

by the different models (Table 17). In general,

less damage related to horizontal strain was predicted in the full-depth design than in the conventional design. On the other hand, when all other

29
Table 17 (cont’d). Results of 21-year freezing index/water table series.

Maximum Applications to failure (millions)

Water table Freezing Freeze/thaw freeze depth Horizontal strain Vertical strain

depth index events in into subgrade Asphalt cracking Subgrade rutting

Year m (ft) °C (°F) days subgrade (cm) CEH AIH-MS11 CEV AIV-MS1

A B. Conventional (F3)

6970 1.5 (4.8) 1191 (2144) 1 13.4 0.46 2.46 0.82 61.97

7071 1.3 (4.2) 1152 (2074) 1 13.4 0.56 2.63 0.47 34.83

7172 1.1 (3.6) 1274 (2294) 1 17.4 0.56 2.53 0.34 26.17

7273 1.2 (4.0) 839 (1510) 0 0 0.49 1.69 ND ND

7374 1.3 (4.2) 923 (1661) 2 1.4 0.46 2.04 ND ND

7475 1.4 (4.6) 968 (1743) 1 5.4 0.49 2.61 1.46 120.66

7576 1.3 (4.2) 931 (1675) 1 0 0.55 2.71 ND ND

7677 1.6 (5.3) 1256 (2261) 1 25.4 0.43 2.18 0.71 58.36

7778 1.1 (3.7) 1331 (2395) 1 13.4 0.49 2.31 0.51 38.69

7879 1.2 (3.8) 1477 (2658) 1 21.4 0.49 2.72 0.36 27.68

7980 1.2 (3.8) 903 (1625) 1 5.4 0.52 1.87 0.44 33.62

8081 1.2 (4.0) 666 (1199) 0 0 0.50 1.50 ND ND

8182 1.8 (6.0) 1227 (2209) 1 29.4 0.42 2.21 0.46 37.95

8283 1.2 (3.9) 589 (1061) 0 0 0.51 1.34 ND ND

8384 1.0 (3.3) 1179 (2123) 1 5.4 0.49 1.84 1.18 91.16

8485 1.0 (3.3) 942 (1696) 1 5.4 0.48 1.56 0.98 77.74

8586 1.0 (3.2) 1197 (2154) 1 5.4 0.48 2.70 1.64 ND

8687 0.9 (3.0) 467 (841) 0 0 0.44 1.45 ND ND

8788 1.5 (4.8) 898 (1616) 1 9.4 0.45 1.85 0.72 58.30

8889 1.5 (4.9) 1032 (1858) 1 9.4 0.53 1.89 0.45 33.69

8990 1.4 (4.7) 750 (1350) 0 0 0.55 1.65 ND ND

Notes: CEH = Corps of Engineers (horizontal) CEV = Corps of Engineers (vertical)

AIH-MS11 = Asphalt Institute (MS-11) AIV = Asphalt Institute (MS-1)

ND = no damage

Traffic simulated at rate of 660,000 ESAL applications/yr.

1.0

1.2

1.4

1.6

1.8

Water Table Depth

(m)

0 400 800 1200 1600 (°C-days)

Freezing Index

6

5

4

3

0 1000 2000 3000 (°F-days)

(ft)

Figure 17. Distribution of freezing indices and water table depths in 21-year

Phase 3 series.

30
conditions are constant, there was more damage

related to vertical strain in the full-depth design.

When frost did not penetrate the subgrade in the

conventional design, essentially no vertical strain

damage was predicted.

Freeze season characteristics were initially

quantified by analyzing the total freezing index,

the number of times that frost was predicted to

enter the subgrade and the maximum depth of

frost penetration beneath the top of the subgrade

(Table 17). Lower amounts of damage (higher

applications to failure) were predicted by the Asphalt Institute horizontal strain model in seasons

with higher freezing indices and deeper frost penetration in both the full-depth and conventional

cross sections. However, predictions of damage

from the other models did not correlate with any

of the above parameters.

It was noted that two similarly categorized seasons, 1983–84 and 1985–86, which had nearly

identical freezing indexes and water table depths,

as well as the same number of freeze thaw events,

had diversely different damage predictions in the

full-depth section (Table 17a). A large thaw event

in the middle of the 1983–1984 freeze season was

accompanied by severe weakening of the subgrade

both during midwinter and spring thaw, which

resulted in a considerable amount of predicted

damage (Fig. 18). The 1985–86 year experienced

a nearly continuous freeze season with no significant midwinter thaw event (Fig. 19). As a result,

the subgrade modulus underwent thaw weakening

0 100 200 300

Elapsed Time (days)

0.04

0.03

0.02

Horizontal Damage

0.01

Vertical Damage

1.0

0.5

0

103

104

105

106

107

7 × 103

7 × 104

7 × 105

7 × 106

7 × 107

Resilient Modulus (lb/in.2)

Resilient Modulus (lkPa)

0

40

80

120

Depth (in.)

Depth (cm)

Subgrade

Subgrade

AC

Asphalt

a

b

c

CEV CEH

AIH

0

100

200

300

Figure 19. Predicted results from simulation of

full-depth section during freeze season 1985–

1986, starting on 1 October. a) Frost/thaw depth,

b) seed resilient modulus passed to NELAPAV,

and c) cumulative damage (see Table 17).

Figure 18. Predicted results from simulation of

full-depth section during freeze season 1983–

1984, starting on 1 October. a) Frost/thaw depth,

b) seed resilient modulus passed to NELAPAV,

and c) cumulative damage. (Abbreviations—see

Table 17.).

31
only during spring thaw in the 1985–86 season, and

the corresponding total damage accumulation was

much less.

Based on the above observation, we tried a new

approach to quantifying the characteristics of the

freeze seasons. It involved summing the thawing

degree days experienced during the freeze season

in two ways. The first was a total from all events,

and the second was a total from only the thaw

events that exceeded 16°C-days (30°F-days) (Table

18). The quantity 16°C-days was chosen based on

analysis by Mahoney et al. (1985) indicating that

pavements approach their critically weak condition after this amount of thaw has been experienced. Unfortunately, neither of these quantities

correlated with predicted damage amounts. Apparently, a more sophisticated index that perhaps

combines freeze index, severity of midwinter thaw

events, and other parameters is required to correlate with predicted damage.

In analyzing the Phase 3 simulation results, we

examined the distribution of predicted damage

through the four seasons defined as follows: fall—

1 October to start of freeze, winter—freeze season as defined by freezing index, spring—75 days

following end of freeze season, summer—remainder of 365-day simulation. The simulations predicted a wide variation in seasonal damage

amounts for different years, especially in the vertical strain damage in the conventional cross section (Fig. 20). In years when vertical strain damage was predicted for the conventional cross

1970 1975 1980 1985 1990

0.6

0.4

0.2

0

Annual Damage

Fall Winter Spring Summer

a. Conventional section, Asphalt Institute horizontal

strain model MS-11.

b. Conventional section, Asphalt Institute vertical strain

model MS-1.

c. Full depth section, Asphalt Institute horizontal strain

model MS-11.

d. Full depth section, Asphalt Institute vertical strain

model MS-1.

Figure 20. Distribution of cumulative damage during seasons.

1970 1975 1980 1985 1990

0.6

0.4

0.2

0

Fall Winter Spring Summer

1970 1975 1980 1985 1990

0.03

0.02

0.01

0

Fall Winter Spring Summer

1970 1975 1980 1985 1990

0.03

0.04

0.02

0

0.01

Annual Damage

Fall Winter Spring Summer

32
section, a majority occurred in the spring, while

the remainder occurred in the winter (Table 19).

Horizontal strain damage in the conventional cross

section also occurred mainly in the spring, with

additional significant amounts in both the winter

and fall, and very small amounts in the summer.

In the full-depth cross section, horizontal strain

damage occurred primarily in the winter, with

slightly less in the spring, and some additional

damage in the fall. Both vertical strain models

predicted damage in the full-depth section to occur mainly in the winter, with some in the spring.

The Asphalt Institute vertical strain model also

predicted additional amounts of summer damage.

DISCUSSION AND

RECOMMENDATIONS

The Phase 1 modeling series indicated significantly different performance by the different test

sections and highly variable results depending on

the performance model applied (Table 13). The

simulated performance of the test sections was

also significantly affected by the subgrade conditions, e.g., density, soil moisture and water table

depth. For example, compare the model predictions using the Asphalt Institute MS-1 horizontal

strain criteria. For case f4w6, the full-depth 5-

year section with the 1206 subgrade in its optiTable 18. Midwinter thaw index summations.

Water table Freezing Midwinter thaw index

depth index (Total) (> 30 DD)

Year m (ft) °C(°F)-days °C(°F)-days °C(°F)-days

6970 1.5 (4.8) 1191 (2144) 25.5 (45.9) 0.0

7071 1.3 (4.2) 1152 (2074) 41.0 (73.8) 0.0

7172 1.1 (3.6) 1274 (2294) 50.0 (90.0) 19.4 (35.0)

7273 1.2 (4.0) 839 (1510) 21.5 (38.7) 0.0

7374 11.3 (4.2) 923 (1661) 56.0 (100.8) 22.3 (40.1)

7475 1.4 (4.6) 968 (1743) 35.0 (63.0) 14.2 (25.5)

7576 11.3 (4.2) 931 (1675) 67.0 (120.6) 20.7 (37.2)

7677 1.6 (5.3) 1256 (2261) 44.0 (79.2) 0.0

7778 1.1 (3.7) 1331 (2395) 26.5 (47.7) 0.0

7879 1.2 (3.8) 1477 (2658) 52.0 (93.6) 18.0 (32.4)

7980 1.2 (3.8) 903 (1625) 32.0 (57.6) 0.0

8081 1.2 (4.0) 666 (1199) 41.0 (73.8) 17.5 (31.5)

8182 1.8 (6.0) 1227 (2209) 31.5 (56.7) 21.9 (39.4)

8283 11.2 (3.9) 589 (1061) 92.5 (166.5) 75.0 (135.0)

8384 1.0 (3.3) 1179 (2123) 40.0 (72.0) 34.7 (62.4)

8485 1.0 (3.3) 942 (1696) 40.0 (72.0) 22.9 (41.2)

8586 1.0 (3.2) 1197 (2154) 29.0 (52.2) 0.0

8687 10.9 (3.0) 467 (841) 65.0 (117.0) 40.1 (72.1)

8788 11.5 (4.8) 898 (1616) 79.0 (142.2) 54.2 (97.6)

8889 1.5 (4.9) 1032 (1858) 49.0 (88.2) 0.0

8990 11.4 (4.7) 750 (1350) 70.5 (126.9) 27.0 (48.6)

Table 19. Average percentage of total yearly damage accumulated during four seasons.

Accumulated damage (% of total)

Section/model Fall Winter Spring Summer

Conventional

AIH 22 31 45 2

AIV 0 40 60 0

CEV 0 42 58 0

Full depth

AIH 16 51 32 1

AIV 2 44 16 38

CEV 0 80 20 0

Notes:

AIH = Asphalt Institute horizontal (MS-11)

AIV = Asphalt Institute vertical (MS-1)

CEV = Corps of Engineers vertical

33
mum density condition, the model predicts

28,585,000 applications to failure. In case f4w6ld,

the same test section with a low density value for

the 1206 subgrade, the model predicts 1,905,000

applications to failure. And finally, in case f4w6ss,

with the 1232 subgrade that produced lower resilient modulus values in lab tests, failure is predicted after only 72,000 applications, or in less

than one year.

After the Phase 1 simulations were complete,

the resilient modulus data from the 1206 subgrade

were reviewed. A calibration error of unknown

magnitude was discovered in the resilient modulus equipment used to measure the unfrozen modulus on that material. Modulus testing of the 1206

subgrade in the frozen condition and all testing on

the other materials were conducted on a different

machine, which passed its calibration checks. Comparing frozen and unfrozen resilient modulus test

results from the 1206 subgrade with those from

other materials tested, Figure 7, indicates that the

unfrozen Mr values for the 1206 subgrade may be

about an order of magnitude too high. A lower Mr

for the 1206 subgrade would have resulted in earlier failures than computed in this report where

the 1206 optimum density subgrade was used.

We are currently investigating the unfrozen

1206 subgrade results and will include findings

and revised performance predictions in Berg (in

prep.)

It is obviously extremely important to use the

representative subgrade conditions in the design

simulations. Results are consistent with observations from in-service pavements; e.g., weak areas

fail much more rapidly than strong ones and high

water tables cause failures before similar pavements constructed over lower water tables. Both

the 1206 and 1232 subgrade samples were obtained from the test site and were located less than

one-half mile apart, yet their tested behavior was

quite different.

Another important aspect governing the results

of the Mechanistic Pavement Design Procedure is

the method used to calculate the asphalt concrete

resilient modulus. The use of the Schmidt model,

which produces extremely low summer season

moduli, partially accounts for the short lifespans

predicted in the Phase 1 modeling series. Replacement with the Ullidtz model in part of the Phase

2A modeling series increased the predicted

lifespans of the sections when judged by the horizontal strain criteria (Table 15).

Results from the Phase 2A series that used the

Ullidtz model for asphalt modulus calculations

and a recovered summer subgrade modulus of

103,00 kPa (15,000 lb/in.2), a close approximation of the value backcalculated from FWD measurements on subgrade during fall 1991, yield performance predictions that are as “fine-tuned” as

possible, so far (Table 15 “Ull-15K”). When these

Mechanistic Pavement Design Procedure predictions are compared with the originally designed

failure at 3,300,000 applications for the 5-year sections and 6,600,000 applications for the 10-year

sections, the following statements can be made:

1. Predictions for the full-depth sections, both

5 and 10 year, indicate that they will not fail from

asphalt cracking, but two of the three criteria for

subgrade rutting indicate early failure;

2. Conventional sections are predicted not to

fail due to subgrade rutting; however, sections

with more frost-susceptible bases are predicted to

fail because of asphalt cracking relatively early

in their design life, and sections with non-frostsusceptible bases are predicted to fail towards the

end of their design life.

By modeling 21 years of environmental conditions in the Phase 3 series, we were hoping to find

the characteristics of a “most severe” winter that

could be used for design purposes. The results

were complex and a relation between predicted

failure and characteristics of freeze seasons was

elusive, at best.

Based on the above results, we recommend the

following studies:

1. The class 4 special and class 5 special base

materials should receive the full complement of

laboratory tests so that simulations may be run

using properties of actual materials from the site

rather those of substitute materials.

2. Once performance data are received from

Mn/ROAD, predicted and measured values of

moisture, temperature, and strains should be compared.

3. Use performance data from Mn/ROAD to

revise, refine or develop new damage models for

rutting and fatigue cracking.

4. Use performance data from Mn/ROAD to

refine or develop a new model for the change of

the asphalt modulus with temperature.

34
5. Use data from falling weight deflectometer

tests on Mn/ROAD to estimate pavement performance on an annual basis.

6. The Procedure should be used to estimate

performance of all of the test sections. This study

evaluated less than one-half of the sections.

CONCLUSIONS*

The range of values produced for the various

scenarios is, as noted, extremely wide. This leads

to the conclusion that mechanistic design in its

present stage, while a powerful predictor of

changes in pavement response with changes in

loads or moduli, is at present an uncertain predictor of pavement performance. Data and analyses

from Mn/ROAD are crucial to improving that current uncertain state of performance prediction.

LITERATURE CITED

The Asphalt Institute (1982) Research and development of the Asphalt Institute’s thickness design manual (MS-1), ninth edition. College Park,

Maryland. Research Report No. 82-2.

R. Berg (in prep.) Resilient modulus testing of

materials from Mn/ROAD, phase 2. USA Cold

Regions Research and Engineering Laboratory,

Special Report.

Berg, R.L., S.R. Bigl, J. Stark and G. Durrell

(1996) Resilient modulus testing of materials from

Mn/ROAD, Phase 1. USA Cold Regions Research

and Engineering Laboratory, Special Report 96-

19, Mn/DOT Report 96-21.

Berg, R.L., G.L. Guymon and T.C. Johnson

(1980) Mathematical model to correlate frost heave

of pavements with laboratory predictions. USA

Cold Regions Research and Engineering Laboratory, CRREL Report 80-10.

Bigl S.R. and Berg, R.L. (1996a) Testing of materials from the Minnesota Cold Regions Pavement Research Test Facility. USA Cold Regions

Research and Engineering Laboratory, Special Report 96-20, Mn/DOT Report 96-24.

Bigl S.R. and Berg, R.L. (1996b) Material testing of initial pavement design modeling: Minnesota Road Research Project. USA Cold Regions

Research and Engineering Laboratory, CRREL

Report 96-14, Mn/DOT Report 96-23.

Bush, A. (1980) Non-destructive testing for light

aircraft pavements. USAE Waterways Experiment

Station, Vicksburg, Mississippi, sponsored by the

Federal Aviation Administration.

Chamberlain, E., T.C. Johnson, R.L. Berg and

D.M. Cole (in prep.) Prediction of pavement behavior under loading during freezing and thawing. USA Cold Regions Research and Engineering Laboratory, CRREL Report.

Chou, Y.T (1989) Development of failure criteria

of rigid pavement thickness requirements for military roads and streets, elastic layered method.

USAE Waterways Experiment Station, Vicksburg,

Mississippi, Miscellaneous Paper GL-89-9.

Cole, D., D. Bently, G. Durell and T. Johnson

(1986) Resilient modulus of freeze-thaw affected

granular soils for pavement design and evaluation, Part 1. Laboratory tests on soils from

Winchendon, Massachusetts, test sections. USA

Cold Regions Research and Engineering Laboratory, CRREL Report 86-4.

Cole, D., D. Bently, G. Durell and T. Johnson

(1987) Resilient modulus of freeze-thaw affected

granular soils for pavement design and evaluation, Part 3. Laboratory tests on soils from Albany

county airport. USA Cold Regions Research and

Engineering Laboratory, CRREL Report 87-2.

Coetzee, N.F. and B.G. Connor (1990) Fatigue

characteristics of Alaskan pavement mixes. Transportation Research Record No. 1269, Transportation Research Board, National Research Council,

Washington D.C., p.168–175.

Gardner, W.R. (1958) Some steady-state solutions of the unsaturated flow equation with application to evaporation from a water table. Soil Science, 88: 228–232.

Guymon, G.L., R.L. Berg and T.V. Hromadka

(1993) Mathematical model of frost heave and

thaw settlement in pavements. USA Cold Regions

Research and Engineering Laboratory, CRREL

Report 93-2.

Ingersoll, J. (1981) Method for coincidentally

determining soil hydraulic conductivity and moisture retention characteristics. USA Cold Regions

Research and Engineering Laboratory, Special

Report 81-2.

* This was written by George Cochran, Mn/ROAD, pers.

comm. 1994.

35
Irwin, L. and D. Speck (1986) NELAPAV user’s

guide. Cornell University, Ithaca, New York, Cornell

University Local Road Program Report No. 86-1.

Mahoney, J.P., J.A. Lary, J. Sharma and N.

Jackson (1985) Investigation of seasonal load restrictions in Washington state. Transportation Research Record 1043, Transportation Research

Board, National Research Council, Washington

D.C., p. 58–67.

Schmidt, R.J. (1975) Use of ASTM tests to predict low temperature stiffness of asphalt mixes.

Transportation Research Record 544, Transportation Research Board, National Research Council,

Washington, D.C. p. 35–45.

Ullidtz, P. (1987) Pavement Analysis. In Developments in Civil Engineering, Vol. 19, Amsterdam:

Elsevier Science Publishers.

U.S. Army (1966) Calculation methods for determination of depths of freeze and thaw in soils.

Department of the Army, Washington, D.C. Technical Manual TM 5-852-6.

U.S. Army (1987) Flexible pavement design for

airfields (layered elastic method). Department of

the Army, Washington, D.C. Technical Manual

TM 5-825-2-1, Draft.

U.S. Army (1988) Pavement design for roads,

streets, and open storage areas, elastic layered

method. Department of the Army, Washington,

D.C., Technical Manual TM 5-800-09.

U.S. Army (1990) Rigid pavements for airfields

other than Army (layered elastic method). Department of the Army, Washington, D.C., Technical

Manual TM 5-824-2-1.

Witczak, M. (1972) Design of full depth airfield

pavements. In Proceedings, Third International

Conference on the Structural Design of Asphalt

Pavements, London, England, vol. I, p. 450–67.

Yang, W. (1988) Mechanistic analysis of nondestructive pavement deflection data. Doctorate Dissertation, Cornell University, Ithaca, New York

(unpublished).

36
APPENDIX A: HEAVE, FROST, AND CUMULATIVE DAMAGE OF FLEXIBLE SECTIONS

37
38
39
40
APPENDIX B: HEAVE, FROST, AND CUMULATIVE DAMAGE OF RIGID SECTIONS

41
42
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51

Freeze season characteristics Pavement performance

Mechanistic Pavement Design and Evaluation Procedure

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

For conversion of SI units to non-SI units of measurement consult ASTM Standard E380-93, Standard Practice for Use of the

International System of Units, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa.

19103.

The U.S. Army Cold Regions Research and Engineering Laboratory is developing a mechanistic pavement design procedure

for use in seasonal frost areas. The procedure was used to predict pavement performance of some test sections at the Mn/

ROAD facility. Simulations were conducted in three phases, investigating the effects on predictions of water table position,

subgrade characteristics, asphalt model, and freeze season characteristics. The procedure predicted significantly different

performance by the different test sections and highly variable results depending on the performance model applied. The

simulated performance of the tests sections also was greatly affected by the subgrade conditions, e.g., density, soil moisture,

and water table depth. In general, predictions for the full-depth asphalt sections indicate that they will not fail due to cracking,

but two of the three criteria for subgrade rutting indicate failure before the five- or 10-year design life of the sections.

Conventional sections are predicted not to fail due to subgrade rutting; however, sections including the more frost-susceptible

bases in their design are predicted to fail due to asphalt cracking relatively early in their design life, and sections with nonfrost-susceptible bases are predicted to fail towards the end of the design life.