SUBGRADE CRITERIA FOR AIRPORT FLEXIBLE PAVEMENT DESIGN

By Dr. Marshall R. Thompson1, Member, ASCE and Manuel O. Bejarano2, Student Member,

ASCE

ABSTRACT

Current mechanistic-empirical airport pavement design procedures use Elastic

Layer Programs (ELP) to predict pavement responses (deflections, stresses,

strains) generated by the gear load. The procedures incorporate subgrade strain

criteria for controlling pavement rutting. WESICE/F.AA and Al vertical

compressive strain criteria were developed from ELP analyses of pavement

sections per the revised CBR equation. The limited scope of pavement test

sections and performance data required extrapolation to other subgrade, loading

and climatic conditions. The large and varying rutting criteria used to interpret the

test section performance data are not consistent with the more rigorous criteria

generally associated with high type airport pavements.

A subgrade stress ratio (SSR = repeated deviator stress /soil strength) approach

is presented in this paper. The University of Illinois (U of IL) SSR criteria ensure

the pavement exhibits -stable" subgrade permanent deformation performance_

Subgrade rutting is controlled by limiting SSR to acceptable levels, depending on

traffic The WES/CE/FAA strain criteria expressed in SSR terms are below about

0.4 These SSRs are very conservative and result in increased pavement thickness.

Permissible SSRs for airport subgrades are probably in the range of 0.5 to 0.7.

Load pulse characteristics (stress level and duration) of multiple-wheel gear

configurations and stress history effects (sequence of stress level applications) on

subgrade permanent deformation accumulation need to be further considered in

implementing the SSR concept.

1 Professor Emeritus, Dept of Civil Eng, Univ. Of Illionis at Urbana-Champaign, Newmark Civil Engineering Lab, 205 N. Mathews Ave., Urbana, IL 6180122 Graduate Research Assistant, Dept of Civil Eng, , Univ. of Illinois at Urbana-Champaign, Newmark Civil Eng. Lab , 205 N Mathews Ave , Urbana, IL 61801

INTRODUCTION

Current mechanistic-based airfield pavement design procedures such as

the US Army WES (Barker and Brabston, 1975), Asphalt Institute (1987),

Army/Air Force Technical Manual (Departments of the Army, and the Air Force,

1989), and LEDFAA (FAA, 1995) use Elastic Layer Programs (ELP) to predict

the structural response of flexible pavements to applied aircraft gear loads. These

pavement responses (strain, stress, deflection) are related to pavement

performance (asphalt concrete (AC) fatigue cracking and pavement rutting) using

transfer functions. The most common existing transfer function relates pavement

life (number of load repetitions) to subgrade vertical compressive strain. Subgrade

strain is the controlling factor for most WES/CE'LEDFAA designs. However,

pavement sections designed using these criteria tend to be conservative and

limited insight is gained concerning the mechanisms of pavement distress

development. It is necessary to improve these subgrade criteria to produce more

functional, reliable and cost-effective airfield flexible pavements. This paper

presents and analyzes current subgrade strain criteria for airfields, introduces the

Suberade Stress Ratio (SSR) as an alternative, and demonstrates the influence of

new aircraft large gear configurations (e.g., the Boeing 777 tridem) on the

repeated loading behavior of cohesive soils.

CURRENT SUBGRADE DESIGN CRITERIA

The WES Subgrade Design Criteria

In the early 1970's the US Army Waterways Experimental Station (WES)

began the development of a pavement design procedure based on elastic layered

theory. Barker and Brabston's report (1975) presents the procedure. The WES

procedure was implemented as a design manual for the Departments of the Army

and the Air Force (1989). The Federal Aviation Administration (FAA) computer

program LEDFAA (FAA, 1995) is a modification of the WES program and is the

design procedure for pavements serving the Boeing 777. In general, the WES

procedure incorporates subgrade strain criteria for controlling pavement rutting. It

assumes that surface rutting is mainly due to subgrade shear deformation implying

that negligible permanent deformation accumulates in the pavement layers above

the subgrade. Subgrade rutting is controlled by limiting the vertical compressive

strain at the top of the subgrade. The subgrade strain criteria were developed from

ELP analyses of idealized conventional pavement sections subjected to typical

aircraft gear loads. In the development of the subgrade design criteria Barker and

Brabston (1975) indicated that:

".., it was desired to use a group of pavement sections which covered a range

of design conditions. The design parameters which were to be varied were the

subgrade modulus, the design aircraft and the number of load repetitions. The

variations and number of pavement sections required preclude the direct use of

test section data However, since the present CE and FAA thickness design criteria

represent a statistical treatment of test section data, it was possible to use the CE

and FAA procedures to generate idealized pavement sections. For various

loadings of aircraft with single-wheel, dual-wheel, or dual-tandem gears, this

procedure was used to generate pavement sections which would perform

satisfactorily at 1,200, 6,000, and 25,000 annual departures on 3-, 6-, 10-, and 20-

CBR subgrades."

The WES development of the design criteria included the following

assumptions:

Traffic is represented in number of operations of the fully loaded design

aircraft.

Loads are essentially static, and the load in each tire is circular and uniform.

The pavement is a linear elastic layered system with full friction between

interfaces.

The bottom layer is of infinite thickness.

The deformation characteristics of the pavement materials are represented by

the modulus of elasticity and Poisson's ratio as determined in a repeated load

test.

The AC modulus and Poisson's ratio were selected as 1380 MPa (200 ksi) and

0.5 respectively.

Granular base and subbase layer were subdivided in sublayers. The modulus

of each sublayer was determined based on the sublayer thickness and the

modulus of the material below the sublayer.

The subgrade modulus is related to CBR by the equation Es (NiPa) = 10.3

CBR (Es (psi)=1500 CBR).

Strains were computed using the elastic layer program CHEVIT (Barker &

Brabston, 1975). The WES report does not indicate how many pavement sections

and aircraft gear loadings were analyzed. The WES strain criteria are presented in

Figure 1 and are algebraically expressed by the equation:

N = 1000 x ( 0 . 000247+0 .000245 x log10( Es)

εv )0. 0658 x Es 0 .559

where N = Allowable repetitions

ev = Vertical strain at the top of the subgrade

Es = Modulus of the subgrade, psi

The design criteria were validated using WES test data presented by

Ahlvin et al., (1971) The Multiple Wheel Heavy Gear Load (NIWHGL) tests

weere conducted on pavement sections with an AC layer 7.5 cm. (3 in.) thick and

a crushed stone base 15 cm. (6 in.) thick. The subbase layer was a non plastic

gravel-sand with thicknesses ranging from 15 to 83 cm. (6 to 33 in.) placed over a

4-CBR subgrade. The subgrade was 91 cm (36 in.) of a heavy clay (known as

Vicksburg Buckshot Clay -- VBC) placed on top of the natural soil (a lean clay).

Traffic loadings included single-wheel, dual tandem (i.e., B-747) and 12-wheel (i

e, C-5) gear loads.

Figure 1. WES/CB/FAA Subgrade Strain Criteria

The failure criteria for the WES-N1WHGL tests were one inch heave above

the pavement surface or severe surface cracking. Failure criteria established in this

manner may be indirectly or not related with subgrade shear structural failure.

One inch heave may be due to large subgrade shear displacement and severe

disruption of the different pavement layers (Lane et al., 1993). Surface rutting was

not considered to be a critical factor in judging pavement failure. However,

measured surface rutting at failure in the WES-MWHGL test sections were not

constant and varied with pavement thickness and gear load (Chou, 1977). Rut

depths at failure were in the range of 13 to 90 mm. (0.5 to 3.5 in.) (Ahlvin et al.,

1971). Results of the full-scale tests are presented in Table 1. From these data, the

relationship in Figure 2 was developed. Barker and Brabston (1975) noted that

none of the test data extended to higher traffic levels. They concluded that the test

data do not represent a complete verification of the subgrade criteria but that an

extrapolation of the criteria to higher traffic levels is justifiable.

Table 1 Summary of MWHGL Test Section Data (Barker & Brabston, 1975)

Figure 2. Verification of the WES/CET:VA Subgrade Strain Criteria

Pavement failure (as related to subgrade strain criteria) is based on cumulative

damage according to Miner's hypothesis. In the Army/Air Force Design manual

(19S9) and the LEDFAA program (FAA, 1995) the damage factor is calculated as

the ratio of applied traffic repetitions (n) of a single aircraft to allowable load

repetitions to failure (N) of the aircraft. The subgrade cumulative damage factor

(CDF) is the sum of the damage factors for the various aircraft, thus the final

pavement design represents variations in applied loads (mixed traffic conditions).

Failure is predicted when the CDF reaches a value of one. (Barker & Brabston,

1975; Barker & Gonzalez, 1991; FAA, 1995).

The Asphalt Institute (AI) Subgrade Design Criterion

Witczak (1972) proposed vertical subgrade strain criteria for the design of

Full-Depth Asphalt Pavements. Witczak's failure criteria are to limit the vertical

strain on top of the subgrade (evaluated at a critical temperature of the asphalt

concrete layer) for a given number of strain applications. The theoretical study

was developed from an analysis of the revised CE CBR design thickness equation

(Ahlvin et al , 1971) for flexible pavements subjected to MWHGL aircraft traffic.

Witczak indicated that the revised CBR equation translates into allowable strains

(greater than those calculated by the earlier CBR equation) approaching

asymptotic values for high levels of traffic. Therefore, for multiple wheel aircraft,

flexible pavement thickness requirements approach a constant value for a large

number of load repetitions

A DC-8-63F aircraft was used to analyze the effect of subgrade type and

repetition level on permissible maximum vertical subgrade strain. It was

concluded that for all practical purposes aircraft type and subgrade modulus

yielded insignificant differences in the permissible maximum vertical strain –

strain repetition relationship.

In Witczak's criteria, a permissible vertical strain of 1460 microstrain is used

at lx106 repetitions at a limiting AC modulus of 690 NIPa (100 ksi) Suggested

thickness reduction percentages of 95, 85, 70 and 50 approximate thickness

requirements for repetitions of 105, 104, 10' and 102, respectively. Environmental

effects are considered by a thickness adjustment factor: "a factor of 1.0 is applied

for high annual air temperature conditions and 0.9 for cooler environments."

SUBGRADE STRAIN CRITERIA COMMENTS

In highway flexible pavement mechanistic-based design procedures, it has

been customary to express subgrade design criteria in the form:

εv = L(1/N)"

where N = Permissible number of ESAL's

εv = Subgrade compressive vertical strain

L, m = Empirically developed parameters

Typical highway criteria (National Cooperative Highway Research Program

Report, 1990) show that the "L" parameter ranges from 1.0x 10-2 to 2 8x 10.2 and

in some procedures "L" varies with design reliability. The "m" parameter varies

between 0.22 and 0.28. The philosophy of the subgrade vertical strain criteria is to

control pavement rutting (in the range of 10 to 20 mm. (0.4 to 0.6 in.)) by limiting

subgrade resilient strain for a specific number of load repetitions

Laboratory test data (Townsend & Chisolm, 1976) on the %/BC subgrade

(presented in Figure 3 for 1000 load repetitions) show that subgrade resilient

strains are not uniquely related to permanent strain accumulation for a given

number of load repetitions. For a given resilient strain, low strength soils

experience larger permanent deformation than higher strength soils. In the WES

criteria, the allowable number of strain repetitions is a function of the resilient

strain and subgrade modulus.

Figure 3. Soil Strength Effect on Permanent Strain – Resilient Strain Relations

Analyses of the WES database by the BAA/PSA Projects and

summarized by Lane et al., (1993) show that the allowable number of strain

repetitions — subgrade vertical strain relationship is relatively independent of

soil modulus. Early work by Witczak (1972) reached the same conclusion. The

BAAIPSA Projects derived vertical strain equation (correlation coefficient of

0.814) is numerically expressed as:

εv =

a

C0 .174

where

εv = Subgrade compressive vertical strain.

C = Coverages.

a = Constant depending on the reliability level. For 50, 75, 90 and 95

percent the constant is 0.00582, 0.00533, 0.00503 and 0 00470

respectively

A major limitation of current subgrade strain criteria for airport

pavement design is the very limited scope of the field performance data and

subgrade soil types utilized in their development. The vertical strain criteria have

been primarily extrapolated from WES test section results. The WES pavement

test sections were not representative of current FAA minimum requirements and

the traffic levels in the MWHGL tests are not representative of current busy

runway or taxiway traffic operations. New loading configurations such as the B-

777 tridem gear were obviously not included in the M\VHGL tests. Thus, tridem

loading test section pavement performance data are not available Tridem-gear

wheel load interactions or any other complex gear configuration generate unique

subgrade stress pulses (stress levels and duration). B-777 tridem gear loading

impacts are currently considered by the use of a provisional a value (the "Load

Repetition Factor" in FAA AC No. 150/5320-6D) of 0.72.

Another limitation of the WES criteria is the varying rutting criteria used to

interpret the results of the WES-NMIHGL pavement tests. Rut depths associated

with the WES criteria are in the range of 13 to 89 mm. (0.5 to 3.5 in.). Large rut

depths are not tolerable for high type airport pavements. British experience

demonstrates that rut depths of 25 to 40 mm (1.0 to 1_5 in ) represent the limits

for surface serviceability with little or no heave occurring at those limits (Lane et

al., 1993).

PERMANENT DEFORMATION PRINCIPLES

To limit pavement surface rutting to acceptable levels, careful attention

must be directed to each pavement component The AC surface, the granular

base/subbase and the subgrade layers contribute to the total accumulation of

pavement surface rutting (Thompson & Nauman, 1993)

Mechanistic-based rutting distress models use stress-, strain-, or

deflection-related parameters to estimate permanent deformation accumulation

under repeated loading. One approach to establish rutting models for flexible

pavement is to correlate structural response determined from a selected standard

structural analysis model with field distress measurements. The forms of

laboratory-based soils distress models are helpful in establishing the general

parameters that best define the structural response-field distress measurement

relationships (Thompson & Nauman, 1993).

Subgrade rutting potential is related to the stress level, soil strength and

number of load repetitions. The Log permanent strain — Log load repetitions

model has been an appropriate, versatile and practical approach. The model

(Monismith et al., 1975) is expressed as follows:

Log ep = a + b Log N or εp = ANb

Where N = Number of load repetitions

εp = Permanent strain

a, b = Experimentally determined factors

A = AntiLog of "a" and an experimental constant dependent on

material and stress level condition

A permanent strain accumulation rate prediction model (Majidzadeh

et al., 19S1) is expressed as:

εp/N=AN"

where N = Number of load repetitions

e, = Permanent strain

A = An experimental constant dependent on material and stress level

condition.

m = Experimental constant depending on material type. Note that m = b-1

in the aforementioned model

Data considered in the National Cooperative Highway Research Program

[NCHRP] Report 1-26 (1990) indicated that for tine-grained soils, the "b" term is

generally in the range of 0.10 to 0.20. The "A" term is more variable and depends

on soil type, repeated stress state, and factors influencing soil strength. Stress state

is generally expressed in terms of repeated stress state (co = ci - c3), principal

stress ratio (clIc3), and deviator stress ratio (o0ra3). Comprehensive studies

(Majidzadeh et al., 1976; Knutson et al., 1977; Thompson Nauman, 1993) on the

"A" term reveal that many soils show a "threshold stress level" above which

permanent deformation accumulates rapidly under repeated loading and below

which the rate of cumulative deformation from additional stress applications is

considerably less. In most cases the threshold stress level is about 50 percent of

the soil strength. The stress ratio (repeated deviator stress/soil strength) approach

is considered in this paper. Figure 4 shows pattern of permanent deformation as a

Function of the SSR for the VBC. Low "A" values are noted for reduced stress

ratios, and large "A" values are noted for increased SSRs, as seen in Figure 5

Therefore, factors influencing load-related stress state and strength of in situ soils

are very important considerations

Figure 4. Patterns of Permanent Deformation in Terms of SSR

Figure 5. Variation of A values with SSR

A major difficulty in predicting subgrade permanent deformation is the

effect of stress history. Stress application sequence and load pulse duration

influence the repeated loading behavior of cohesive soils. Unpublished laboratory

results (U of IL) for a lean clay show that a stress sequence of gradually

increasing SSR may cause less permanent deformation than a sequence where the

high SSR is initially applied. This may indicate the inadequacy of using the CDF

approach for predicting permanent deformation in cohesive soils. Poulsen and

Stubstad (1978) suggest that an appropriate approach is to relate permanent

deformation to the number of load repetitions of the heaviest load class expected

in the design period. In the same U of IL study, stress sequence did not

significantly influence the soil's resilient modulus Load pulse duration effects are

discussed later in this paper.

SUBGRADE STRESS RATIO CRITERIA

Subgrade Stress Ratio (SSR) is defined as the ratio of the subgrade

deviator stress to the unconfined compressive strength (peak stress or stress at 5 %

strain) of the subgrade soil. The philosophy of the SSR concept is to ensure that

the pavement system exhibits a "stable" subgrade permanent deformation

performance as shown in Figure 6. Total anticipated surface rutting can be limited

to acceptable levels. High stress levels (above "threshold stress level -) are

associated with increased and perhaps unstable subgrade permanent deformation.

Subgrade rutting is controlled by limiting SSR to acceptable levels (usually in the

range of 0.5 to 0.7 depending on traffic). The SSR concept includes deviator stress

and soil strength terms that show considerable seasonal and spatial variability.

SSRs are affected by changes in the deviator stress, strength reduction, or a

combination of both. SSR will increase with AC modulus reduction, increases in

soil moisture content/saturation level, and cyclic freeze-thaw in the subgrade. The

SSR concert has been implemented for the design of full-depth asphalt concrete

pavements (Thompson, 1987), conventional flexible pavements (Thompson,

1992) and surface treatment pavements (Thompson, 1994). These procedures

have been successfully used by the Illinois Department of Transportation for the

design of highway flexible pavements. Kelly and Thompson (1988) proposed the

use of the SSR concept for the design/evaluation of flexible pavements for the

Heavyweight F-15 fighter aircraft' They indicated the DOD CBR based designs

provided low SSRs (conservative - require thicker pavements).

Figure 6. Stable and Unstable Permanent Deformation Behavior WES/CE/FAA

AND U OF IL CRITERIA COMPARISONS

WES/CDFAA vertical compressive strain criteria were evaluated using the

U of IL SSR concept. Subgrade deviator stress and unconfined compressive

strength for the strain criteria were calculated assuming that:

ERi = Es in ksi

op = ev E, ER, (ksi) — 086

Qu(Psi) = 03G7

where

Es = Modulus of the subgrade as defined in the WES/CE/FAA procedure.

ERi = Resilient modulus of the subgrade at the breakpoint according to Thompson

& Robnett (1979).

σD = Deviator stress on top of the subgrade.

Ev = Allowable elastic strain (WES/CEIFAA criteria).

Qu = Unconfined compressive strength of the soil estimated according to

Thompson & Robnett (1979).

The WES:CR/FAA strain criteria expressed in SSR terms are shown in

Figure 7. The strain criteria fall below the 40 percent SSR for low number of

annual strain repetitions and below 35 percent SSR for high number of annual

strain repetitions. These SSRs are very conservative and result in increased

pavement thickness. The Illinois DOT SSR highway pavement criteria permit an

SSR of 50% for a 20 year design and high traffic volumes and for low traffic

volume roads the SSR can go up to 70% For airports where the number of strain

repetitions are low, permissible SSRs are probably in the range of 50 to 70%.

However, in considering SSR criteria, it is important to evaluate additional factors

that may contribute to changes in permanent deformation accumulation such as

stress distribution, load pulse duration, and stress history effects associated with

multiple-wheel gear configurations (dual-tandem, tridem, etc.).

AIRCRAFT INDUCED SUBGRADE STRESS PULSE DURATION

The effect of load pulse duration on fine-grained subgrade soil behavior

(modulus, permanent deformation) is not well established. Subgrade stress is

determined by aircraft landing gear configuration, wheel load/tire pressure,

pavement cross section, and subgrade condition. Limited ELP analyses of

conventional pavement sections designed using LEDFAA (FAA, 1995) and 16 in.

full-depth asphalt pavement sections on soil (Es = 20.7 MPa (3 ksi)) and firm (Es =

62.0 MPa (9 ksi)) subgrades demonstrated the effect of the aforementioned

variables on subgrade stress distribution. In general, longer gear configurations (e

g., tridems) produce flatter and increased duration stress pulses. Based on

normalized stress (deviator stress/maximum deviator stress) time curves, the pulse

duration increase at 10 % normalized stress from a dual-tandem to a tridem gear

configuration may range from 30 to 50 %. Aircraft speed determines subgrade

stress pulse duration. Lew aircraft speeds of 16 to 32 kph (10 to 20 mph) and

static in some cases are expected. Analyses of the aforementioned pavement

sections indicated that for these aircraft speeds a haversine stress pulse with a

duration of about one second is realistic for repeated load testing of subgrade

soils. Aircraft velocity effects can be considered by testing the pavement

materials/soils using approximately the same repeated stress states (magnitude and

duration) as those expected in the field.

Pulse duration effects on the resilient modulus and permanent deformation

characteristics of cohesive subgrade soils were considered in a preliminary U of

IL study. Repeated unconfined compressive loading tests at two load pulse

durations were performed on a cohesive soil at two water contents and several

stress levels. The limited testing program was conducted with a CL soil (99%

passing 0200, 55%<24.1 clay, LL 40, PI 18, Max. DD 18.7 kN/m3 (119 pcfl,

OMC 14%) subjected to repetitive haversine pulses with load pulse durations of

60 and 600 milliseconds.

Preliminary laboratory testing data support the following observations.

Subgrade stress pulse duration has some effect on permanent deformation, and

limited effect on resilient modulus. Increased pulse duration increases permanent

deformation. The effect is greater at increased subgrade stress levels, and

decreased subgrade soil strength conditions. The difference in permanent

deformation accumulation rate due to variations in stress ratio and stress pulse

duration is most pronounced in the first 100 lead repetitions. Longer pulse

duration yields higher permanent strain per cycle in the first cycles. Afterwards,

the rate of accumulation is essentially the same for both stress pulse durations. On

the other hand, an increased pulse duration decreases resilient modulus with a

greater difference at reduced subgrade stress levels and increased subgrade soil

strengths. The B-777 tridem aircraft gear induces larger subgrade stresses and

pulse durations than conventional tandem gear configurations Thus, current

flexible pavements may experience increased rutting

SUMMARY

The development and utilization of current subgrade design criteria are

presented. Current mechanistic-based airfield pavement design procedures use

ELP to predict airfield pavement responses (deflection, stresses, strains) generated

by a gear load. Computed vertical strains are limited to prevent pavement rutting

using subgrade strain criteria (permissible subgrade compressive strain -- number

of load repetitions). WES/CE/FAA and Al vertical compressive strain criteria

were developed from ELP analyses of pavement sections obtained from the

modified CBR equation (includes the a term) that incorporates the results of the

NINVIIGL study. The limited scope of pavement test sections and performance

data required extrapolation to other subgrade, loading and climatic conditions.

The large and varying rutting criteria used to interpret the test section performance

data are not consistent with the more rigorous criteria generally associated with

high type airport pavements.

The U of IL SSR criterion is presented as an alternative. Subgrade rutting

potential depends on stress level, soil strength, stress history, and load repetitions.

Patterns of permanent deformation are related to SSR. The "A" term from the Log

permanent strain Log load repetitions or power model is a function of SSR. Large

and unstable permanent deformation patterns are associated with large SSRs. The

SSR criterion ensures that the pavement exhibits a "stable" subgrade permanent

deformation. Total anticipated surface rutting can be limited to acceptable levels.

Subgrade rutting is controlled by limiting SSR to levels usually in the range of 0.5

to 0.7 depending on traffic. The WES/CE/FAA vertical compressive strain criteria

expressed in SSR terms fall below 0.4. These SSRs are very conservative and

result in increased pavement thickness. Permissible SSRs for airport subgrades are

probably in the range of 0.5 to 0.7.

A limited U of IL laboratory study considered the effect of stress history and

pulse duration on the repeated loading behavior of a cohesive soil. Preliminary

analyses indicate that a stress sequence of gradually increased SSR may cause less

permanent deformation than a sequence where the high SSR is initially applied.

Suess sequence did not significantly influence soli resilient moduli. Subgrade

stress pulse duration has some effect on permanent deformation, and limited effect

on resilient modulus. In general, for a given subgrade stress level and soil

strength, an increased pulse duration increases permanent deformation and

decreases resilient modulus. Tridem aircraft gear configurations induce larger

stress pulse durations than conventional tandem gear configurations. Therefore,

current flexible pavements may experience increased rutting rates due to increased

subgrade stress and subgrade stress pulse duration.

In conclusion, improved subgrade design criteria are required to produce more

functional, reliable and cost-effective airfield pavements and to provide better

insights concerning the mechanism of pavement distress development. The SSR

concept appears promising. Load pulse characteristics (stress level and duration)

of multiple-wheel gear configurations and stress history effects (sequence of stress

level applications) on subgrade permanent deformation accumulation need to be

further considered in implementing the SSR concept for mechanistic-empirical

based airport flexible pavement design.

ACKNOWLEDGMENTS / DISCLAIMER

This paper was prepared from a study conducted in the Center of Excellence for

Airport Pavement Research. Funding for the Center of Excellence is provided in

part by the Federal Aviation Administration under Research Grant Number 95-C-

001 The Center of Excellence is maintained at the University of Illinois at

Urbana-Champaign who works in partnership with Northwestern University and

the Federal Aviation Administration. Ms. Patricia Watts is the FAA Program

Manager for Air Transportation Centers of Excellence and Dr. Satish Agrawal is

the FAA Technical Director for the Pavement Center.

The contents of this paper reflect the views of the authors who are responsible

for the facts and accuracy of the data presented within The contents do not

necessarily reflect the official views and policies of the Federal Aviation

Administration. This paper does not constitute a standard, specification, or

regulation

APPENDIX

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for Airfields (Elastic Layered Method), Technical Manual TM 5-825-2- I/AFM

886, Chapter 2, Section A Federal Aviation Administration, (1995), Advisory

circular No. 150/5320-16, Airport Pavement Design for the Boeing 777 Airplane,

U S Department of Transportation.

Kelly H F and Thompson M R , (1988), Mechanistic Design Concepts for Hex. -

vweigh: F-15 .aircraft on Flexible Pavements, Journal of Transportation

Engineerinz, ASCE, Vol 114, No. 3.

Knutson, R. M., Thompson, M.R., Mullin, T., and Tayabji, S. D., (1977), Material

Evaluation Study - Ballast and Foundation Materials Research Program FRA-

ORS:D-77-02. Federal Railroad Administration.

Lane, R., Woodman, G., and Barenberg, E.J., (1993), Pavement Design

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D. C.

Majidzadeh, K., et al., (1981), Implementation of a Pavement Design System,

Final Report, Research Project EEE 579, Ohio State University, Columbus, Ohio.

Monismith, C.L., Ogawa, N. and Freeme, C.R., (1975), Permanent Deformation

Characteristics of Subgrade Soils due to Repeated Loading, Record 537,

Transportation Research Board, Washington D.C.

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Mechanistic Structural Analysis Procedures for Pavement, Volume 1 - Final

Report and Volume 2 - Appendices, National Cooperative Highway Research

Program, Transportation Research Board, National Research Council, University

of Illinois at Urbana-Champaign.

Poulsen, J., and Stubstad, R.N., (1978), Laboratory Testing of Cohesive

Subgrades Results and Implications Relative to Structural Pavement Design and

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of Asphalt Pavements, Ann Arbor, Michigan.

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Granular Base Moduli for Mechanistic Pavement Design

Erol Tuturnluer1, Associate Member and

Marshall R. Thompson2, Member

Abstract

Simple stress dependent granular material models are proposed to predict the

aggregate cross-anisotropic responses observed in flexible airport pavements. A

cross-anisotropic representation has different material properties (i.e., elastic

modulus and Poisson's ratio) assigned in the horizontal and vertical directions.

Repeated load triaxial tests with vertical and lateral deformation measurements

are used for establishing these anisotropic properties. Flexible pavement responses

predicted under one wheel of the Boeing 777-200A aircraft using the anisotropic

model are found to be higher than LEDFAA response variables. A sensitivity

analysis shows, in general, that as aggregate base horizontal and shear stiffnesses

increase, the critical pavement responses decrease to some extent.

Introduction

Current mechanistic design methods, such as LEDFAA (FAA - AC, 1995),

Corps of Engineers (TM 5-825-2-1/AFNI 88-6,1989), and the Asphalt Institute

(AI MS-1, 1982), use Elastic Layer Programs (ELP5) to predict airfield pavement

resilient responses generated by the gear load. In these procedures, the granular

layer moduli are established as some multiple of the subgrade modulus,

irregardless of the thickness and the modulus of Asphalt Concrete (AC) surface

course overlying the granular layer(s) or wheel loading conditions. Furthermore,

ELP analyses of conventional flexible pavements indicate significant tensile

stresses in the lower portions of the aggregate base, a material with limited/no

tensile strength. The implications of these current granular material modeling

concepts/procedures have been considered in studies conducted at the FAA Center

of Excellence (COE) for Airport Pavement Research at the University of Illinois.

11 Assistant Professor22 Professor Emeritus. Department of Civil Engineering, University of Illinois 205 N. Mathesws, urbana, IL 61801-2352

The stress-dependent modulus behavior of aggregates (stress hardening) is

well documented (Thompson and Elliot, 1985; Tutumluer, 1995) and

crossanisotropic behavior is observed in granular materials (Tutumluer, 1995;

Tutumluer and Thompson, 1997). The cross-anisotropic representation assigns

different material properties (i.e., elastic modulus and Poisson's ratio) in the

horizontal and vertical directions. COE studies show that simple stress dependent

granular material models can be used to predict the aggregate cross-anisotropic

responses. Nonlinear characterization models have been established from repeated

load triaxial test data with both vertical and lateral deformation measurements.

These material models have been successfully implemented into a finite element

program, GT-PAVE, developed by Tutumluer (1995).

A conventional airport flexible pavement is analyzed in this paper using

isotropic ILLI-PAVE (Raad and Figueroa, 1980) and anisotropic GT-PAVE finite

element programs and assigning representative properties for a dense-graded

crushed stone base (FAA P-209). The GT-PAVE values for AC strain, subgrade

strain, and subgrade deviator stress under one wheel of a BOEING 777-200A are

in general higher than predicted by the LEDFAA./JULEA ELP program.

Moreover, both GT-PAVE and ILLI-PAVE aggregate moduli are considerably

different than those assigned in the ELP procedures. Such discrepancies in

predicted moduli are apparently due to improved material characterization that

considers the nonlinear stress dependent aggregate behavior in the finite element

programs. A sensitivity analysis of anisotropic granular base model parameters is

also performed using the GT-PAVE program for critical pavement responses.

Anisotrooic Properties from Triaxial Tests

Thick granular layers commonly used in airport flexible pavements provide

load distribution that is essential to the integrity of the pavement. Initially, an

apparent anisotropy is induced in granular layers during construction by aggregate

placement and then loading from the compaction equipment. Heavy aircraft wheel

loads further cause significant amounts of directional stiffening of the granular

materials in the vertical direction. An anisotropic approach can adequately

accommodate this kind of directional variation of granular material stiffnesses.

The important effects of load induced directional stiffening and dilative behavior

of granular materials have been successfully modeled in recent studies using a

cross-anisotropic approach (Tutumluer, 1995; Tutumluer and Thompson, 1997). •

The repeated load triaxial compression test is currently the most commonly

used method to measure the resilient (elastic) deformation characteristics of

unbound aggregates for use in pavement design. The resilient modulus test is

performed on a cylindrical specimen of granular materials subjected to repeated

axial compressive (deviator) stresses. To simulate the lateral stresses caused by

the initial in situ pressure and that from applied wheel loadings, the specimen is

subjected to a constant all-around confining pressure. An advantage of the triaxial

test is that the axial and radial (or vertical and horizontal) strains can be

determined relatively easily. Determination of lateral strains in a triaxial specimen

is essential for characterizing the anisotropic elastic properties of granular bases.

Anisotropic resilient response - elastic response obtained from the repeated

load triaxial tests due to the pulse deviator stress - can be defined from triaxial test

data with measured vertical and lateral deformations as follows:

Vertical Resilient Modulus

Horizontal Resilient Modulus

Resilient Shear Modulus

Where the horizontal resilient modulus (MRh) is newly defined for anisotropic

elasticity, and σd, (= σ1-σ3) and σ3 are deviator stress and confining pressure,

respectively. Since for a cylindrical triaxial sample there is co-axiality between

the material and principal stress axes, the horizontal and vertical directions, as

referred to in the above definitions, are used in the same context with the radial (r)

and vertical (z) directions under axial symmetry.

Anisotropic Material Characterization

The five cross-anisotropic material properties needed to define an anisotropic

material under conditions of axial symmetry were given by Zienkiewicz and

Taylor (1989) as: moduli in vertical and radial directions, MRZ and MR': shear

modulus in vertical direction. GR; Poisson's ratio for strain in the vertical

direction due to a horizontal direct stress vz : and Poisson's ratio for strain in any

horizontal direction due to a horizontal direct stress, v,. Pickering ( 1 970) studied

the bounds of the elastic parameters in a cross-anisotropic material. In addition to

the requirement of each of the three moduli being greater than zero, the Poisson's

ratios in horizontal and vertical directions were shown to be related to each other

for a positive strain energy (Pickering, 1970).

A new improved way of modeling granular materials using cross-anisotropic

nonlinear elasticity was proposed recently at the University of Illinois to predict

the dilative granular material behavior as observed from laboratory triaxial test

results (Tutumluer and Thompson, 1997). Granular material response was shown

to be reasonably characterized by using stress dependent models which express

the modulus as nonlinear power functions of stress states. The characterization

models include in the formulation the two triaxial stress conditions, i.e., the bulk

stress 8 (= G1+2G3) and the deviator stress od, to account for the effects of both

confinement and shear loading, respectively (Uzan, 1992).

Repeated load triaxial test results, which included vertical and lateral

deformation measurements performed on a variety of aggregate types, were