Nwamarah Uche

DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR PREDICTION OF FATIGUE AND RUTTING STRAIN

Digitally Signed by: Content manager’s

DN : CN = Weabmaster’s name

O= University of Nigeria, Nsukka

OU = Innovation Centre

Nwamarah Uche

Faculty of Engineering

Department of Civil Engineering

DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR PREDICTION OF FATIGUE AND RUTTING STRAINS IN

STABILIZED LATERITIC BASE OF LOW VOLUME

EKWULO, EMMANUEL OSILEMMEPG/Ph.D/10/57787

9

: Content manager’s Name

Weabmaster’s name

a, Nsukka

Department of Civil Engineering

DEVELOPMENT OF LAYERED ELASTIC ANALYSIS PROCEDURE FOR IN CEMENT -

LOW VOLUME ROADS

EKWULO, EMMANUEL OSILEMME

10

CHAPTER 2

LITERATURE REVIEW

2.1 Pavement Design History

Pavement design is a complex field requiring knowledge of both soil and paving

materials, and especially, their responses under various loadings and environmental

conditions. Pavement design methods can vary, and have evolved over the years in

response to changes in traffic and loading conditions, construction materials and

procedures. Design methods have progressed from rule-of-thumb methods, to

empirical methods and at present, towards a mechanistic approach.

In the United States, the majority of pavement designers use the AASHTO

(American Association of State Highway and Transportation Official ) Guide for

design of Pavement Structures (AASHTO, 1993). The AASHTO Guide was

developed from empirical performance equations based on observations from the

AASHTO Road Test conducted in Illinois from October, 1958 to November, 1960.

Many significant changes in loading conditions, construction materials and methods,

and design needs have occurred since the time of AASHTO Road Test, prompting

development of new mechanistic-empirical design procedures. This procedure

allows the designer to consider current site conditions such as realistic loading,

climatic factors such as temperature and moisture, material properties and existing

pavement condition in the design of a new pavement, rehabilitation of an existing

pavement, or evaluation of an existing pavement. This approach is described in more

details in the Guide for mechanistic-empirical Design of New and Rehabilitated

Pavement Structures (NCHRP, 2004). Additionally, mechanistic-empirical design

procedure was developed such that improvement could be made as technology

advances.

11

Empirical methods of analysis are derived from experimental data and practical

experience. The mechanistic-empirical (M-E) design approach considers the three

necessary elements of rational design (Yoder and Witczak, 1975). The element of

rational design include (1) an assumed failure or distress parameter predictive

theory (2) evaluation of material properties in relationship to the theory selected and

(3) relationship determination between the performance level desired and the

appropriate parameter magnitude. The mechanistic-empirical design approach

applies engineering mechanics principles to consider these rational design elements.

The initial phase of the mechanistic design approach consist of proper structural

modeling of pavement structures (NCHRP, 2004). Pavement is modeled as multi-

layered elastic or viscoelastic on elastic or viscoelastic foundation. These models are

used in analysis to predict critical pavement responses (deflections, stresses and

strains) due to traffic loading and environmental conditions for selected trial or

initial design. The accuracy of the chosen model is validated by data from controlled-

vehicle tests or other types of tests where actual loading and environmental

conditions are simulated. Where predicted values agree with measured values, the

level of confidence in the model increases with increase data available for validation.

Once an accurate structural response model is developed, the responses are input

into distress models to determine pavement damage throughout the specific design

period. Failure criteria are then evaluated, and an iterative process continues until a

final design is reached.

2.2 Flexible Highway Pavements

The beginning of flexible pavement construction history to early 1900’s in United

States when experience dominated pavement design and construction. Through the

experience gained over the years, many design methods were developed for

determining critical features like thickness of the asphalt surface. As of 1990, there

12

were millions of miles of paved roads in the US, 94% of which are topped by asphalt

(Huang, 1993). A typical flexible pavement cross section consists of an asphalt

concrete surface, base and subbase resting on the natural subgrade.

Since the beginning of road building, three types of flexible pavement construction

have been used: conventional flexible pavement, full-depth asphalt and contained

rock asphalt mat (CRAM). As knowledge increased and other technologies

developed, a composite pavement made up of hot mix asphalt concrete (HMA) and

Portland cement concrete (PCC) beneath the HMA came into being with the most

desirable characteristics. However, the CRAM construction is still relatively rare and

composite pavement is very expensive, and hence seldom used in practice (Huang,

1993).

Various empirical methods have been developed for analyzing flexible pavement

structures. However, due to limitations of the analytical tools developed in the 1960s

and 1970s, the design of flexible pavements is still largely empirically-based. The

empirical method limits itself to a certain set of environmental and material

conditions (Huang, 1993), if the condition changes, the design is no longer valid. The

mechanistic-empirical method relates some inputs such as wheel loads to some

outputs, such as stress or strain. The mechanistic method is more reliable for the

extrapolation from measured data than empirical methods. However, the

effectiveness of any mechanistic design method relies on the accuracy of the

predicted stresses and strains. Due to their flexibility and power, three-dimensional

(3D) finite element methods are increasingly being used to analyze flexible

pavements.

2.3 Pavement Design and Management

Pavement engineering may be defined as the process of designing, construction,

maintenance, rehabilitation and management of pavement, in order to provide a

13

desired level of service for traffic. In the design stage of pavement design, engineers

make a number of assumptions about the construction methods and level of

maintenance for the pavement.

Flexible pavements are classified as a pavement structure having a relatively thin

asphalt wearing course, with layers of granular base and subbase being used to

protect the subgrade from being overstressed. This type of pavement design is based

on empiricism or experience, with theory playing only a subordinate role in the

procedure. However, the recent design and construction changes brought about

primarily by heavier wheel-loads, higher traffic levels, and recognition of various

independent distress modes contributing to pavement failure (such as rutting,

shoving and cracking) have led to the introduction and increased use of stabilized

base and Subbase material. The purpose of stabilizer material is to increase the

structural strength of the pavement by increasing rigidity. Roadway rehabilitation

using asphalt without the need for excavation of old, cracked and oxidized asphalt

pavements with water-weakened, or non-uniform support bases and subbases has

often been attempted, usually with variable success. It was concluded (Johnson and

Roger, 1992) that keeping water out of the road base and sub-base is a major solution

to prevent premature road failures.

The purpose of a pavement is to carry traffic safely, conveniently and economically

over its design life, by protecting the subgrade from the effects of traffic and climate

and ensuring that materials used in the pavement do not suffer from deterioration.

The pavement surface must provide adequate skid resistance. The structural part of

the pavement involves material sections that are suitable for the above purpose. The

design process consists of two parts: the determination of the pavement thickness

layer that have certain mechanical properties, and the determination of the

composition of the material that will provide these properties. The main structural

14

layer of the pavement is the road base, whose purpose is to distribute traffic loads so

that stresses and strains developed by them in the subgrade and subbase are within

the capacity of the materials in these layers.

Asphalt pavements are designed and constructed to provide an initial service life of

between 15 to 20 years (Gervais et al, 1992), however, this design life is rarely met,

largely because of more traffic, heavier axle loads, material problems, higher tire

pressure and extreme environmental conditions. These factors usually result in two

major modes of distress: surface cracking and rutting which, if allowed to progress

too far, will require major rehabilitation or complete reconstruction. Research work

over the past several decades had led to many recommended solutions. New asphalt

mixes, use of larger crushes aggregates, textile sheets, thicker asphalt layer, polymer

modification and reinforcement of various types have been tried in the field to

minimize pavement cracking or rutting.

In asphalt pavement, the term “reinforcement” generally means the inclusion of

certain material with some desired properties within other materials which lack

these properties. Within the entire pavement structure, the asphalt concrete layer

receives most of the load and non-load induced tensile stresses. However, it is

known that asphalt concrete lacks the ability to resist such stresses which makes it an

ideal medium for which reinforcement can be considered. If reinforcement is to be

considered, two basic features need to be considered (Haas, 1984):

1. Intended function of the reinforcement

i. reducing rutting

ii. reducing cracking

iii. reducing layer thickness

iv. extending pavement life/reducing maintenance

15

2. Reinforcement alternative

i. Types and possible locations in the pavement structure

ii. Major variables (pavement layer and reinforcement properties, traffic

loads and volume etc.

2.4 Flexible Pavement Design Principles

Before the 1920s, pavement design consisted basically of defining the thickness of

layered materials that would provide strength and protection to a soft subgrade.

Pavements were designed against subgrade shear failure. Engineers used their

experience based on successes and failures of previous projects. As experience

evolved, several pavement design methods based on subgrade shear strength were

developed. Ever since, there has been a change in design criteria as a result of

increase in traffic volume. As important as providing subgrade support, it is equally

important to evaluate pavement performance through ride quality and other surface

distress that increase the rate of deterioration of pavement structure. For this reason

performance became the focus of pavement designs. Methods based on serviceability

(an index of the pavement service quality) were developed based on test track

experiments. The AASHTO Road Test in 1960s as a seminal experiment from which

the AASHTO design guide was developed. Methods developed laboratory test data

or test track experiments in which model curves are fitted to data are typical

example of empirical methods. Although they may exhibit good accuracy, empirical

methods are valid for only the materials and climate conditions for which they were

developed.

Meanwhile, new materials started to be used in pavement structures that provide

better subgrade protection, but with their own failure modes. New designs criteria

were required to incorporate such failure mechanisms such as fatigue cracking and

permanent deformation in the case of asphalt concrete. The Asphalt Institute method

16

(Asphalt Institute, 1982, 1991) and the Shell method (Claessen et al, 1977; Shook et al,

1982) are examples of procedures based on asphalts concrete’s fatigue cracking and

permanent deformation failure modes. These methods were the first to use linear

elastic theory of mechanics to compute structural response in combination with

empirical models to predict number of loads to failure for flexible pavements. The

problem in the use of the elastic theory is that pavement material do not exhibit the

simple behaviour assumed in isotropic linear elastic theory. Nonlinearities, time and

temperature dependency, and anisotropy are some of the complicated features often

observed in pavement materials. Therefore to predict pavement performance

mechanistically, advanced modeling is required. The mechanistic design approach is

based on the theories of mechanics and relates pavement structural behaviour and

performance to traffic loading and environmental influences. Progress has been

made on isolated cases of mechanistic performance prediction problem, but the

reality is that fully mechanistic methods are not yet available for practical pavement

design (Schwartz and Carvalho, 2007).

Mechanistic-empirical approach is a hybrid approach. Empirical methods are used to

fill in the gaps that exist between the theory of mechanics and the performance of

pavement structures. Simple mechanistic responses are easy to compute with

assumptions and simplifications (that is homogenous material, small strain analysis,

static loading as typically assumed in linear elastic theory), but they themselves

cannot be used to predict performance directly: some type of empirical model is

required to carryout the appropriate correlation. Mechanistic-empirical methods are

considered an intermediate step between empirical and fully mechanistic methods.

2.5 Pavement Design Procedures

Studies in pavement engineering have shown that the design procedure for highway

pavement is either empirical or mechanistic. An empirical approach is one which is

17

based on the results of experiments or experience or both. This means that the

relationship between design inputs and pavement failure were arrived at through

experience, experimentation or a combination of both. The mechanistic approach

involves selection of proper materials and layer thickness for specific traffic and

environmental conditions such that certain identified pavement failure modes are

minimized. The mechanistic approach involves the determination of material

parameters for the analysis, at conditions as close as possible to what they are in the

road structure. The mechanistic approach is based on the elastic or visco-elastic

representation of the pavement structure. In mechanistic design, adequate control of

pavement layer thickness as well as material quality are ensured based on theoretical

stress, strain or deflection analysis. The analysis also enables the pavement designer

to predict with some amount of certainty the life of the pavement (Schwartz and

Carvalho, 2007).

2.5.1 Empirical Design Approach

An empirical design approach is one that is based solely on the result of experiment

or experience. Observations are used to establish correlations between the inputs and

the outcomes of a process, for example pavement design and performance. These

relationships generally do not have firm scientific basis, although they must meet the

tests of engineering reasonability. Empirical approaches are often used as an

expedient when it is too difficult to define theoretically the precise cause and effect

relationships of a phenomenon.

The principal advantages of empirical design approaches are that they are usually

simple to apply and are based on actual real-world data. Their principal

disadvantage is that the validity of the empirical relationships is limited to the

conditions in the underlying data from which they were inferred. New materials,

construction procedures, and changed traffic characteristics cannot be readily

incorporated into empirical design procedures.

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The first empirical method for flexible pavement design date to the mid 1920s when

the first soil classification were developed. One of the first to be published was the

Public Roads (PR) soil classification system (Huang, 2004). In 1929, the California

Highway Department developed a method using the California Bearing Ratio (CBR)

strength test (Porter, 1950; Huang, 2004). The CBR method relates the material’s CBR

value to the required thickness to provide protection against subgrade shear failure.

The thickness computed was defined for the standard crushed stone used in the

definition of the CBR test. The CBR test was improved by the US Corps of Engineers

(USCE) during the World War II and later became the most popular design method.

In 1945 the Highway Research Board(HRB) modified the PR classification. Soils were

grouped in seven categories (A-1 to A-7) with indexes to differentiate soils within

each group. The classification was applied to estimate subbase quality and total

pavement thickness (Huang, 2004).

Several methods based on subgrade shear failure developed after CBR method.

Huang (2004) used Terzaghi’s bearing capacity formula to compute pavement

thickness, while Huang (2004) applied logarithmic spirals to determine bearing

capacity of pavements. However, with increasing traffic volume and vehicle speed,

new materials were introduced in the pavement structure to improve performance

and smoothness and shear failure was no longer the governing design criterion.

The first attempt to consider a structural response as a qualitative measure of the

pavement structural capacity was measuring surface vertical deflection. A few

methods were developed based on the theory of elasticity for soil mass. This method

estimated layer thickness based on a limit for surface deflection. The first published

work on this method was the one developed by the Kansa State Highway

Commission, in 1947 (NCHRP, 2007), in which Boussinesg’s equation was used and

the deflection of subgrade was limited to 2.54mm. Later in 1953, the U.S. Navy

19

applied Burmister’s two-layer elastic theory and limited the surface deflection to

6.35mm. Other methods were developed over the years, incorporating strength tests.

More recently, resilient modulus has been used (Huang, 2004) to establish

relationships between the strength and deflection limits for determining thickness of

new pavement structures and overlays. The deflection methods were most appealing

to practitioners because deflection is easy to measure in the field. However, failures

in pavements are caused by excessive stress and strain rather than deflection

(NCHRP, 2007). In the early 1950s, experimental tracks started to be used for

gathering pavement performance data. Regression models were developed linking

the performance data to design inputs. The biggest disadvantage of regression

methods is the limitation on their application. As is the case for any empirical

method, regression methods can be applied only to the conditions similar to those

for which they were developed. The empirical AASHTO method (AASHTO, 1993),

based on the AASHTO Road Test from the late 1950s, is the most widely used

pavement design method today. The AASHTO design equation is a regression

relationship between the number of load cycles, pavement structural capacity, and

performance measured in terms of serviceability. The concept of serviceability was

introduced in the AASHTO method as an indirect measure of the pavement’s ride

quality. The serviceability index is based on surface distress commonly found in

pavements.

The AASHTO (1993) method has been adjusted several times over the years to

incorporate extensive modifications based on theory and experience that allowed the

design equations to be used under conditions other than those of the AASHTO Road

Test.

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2.5.2 CBR Design Methods

The almost universal parameter used to characterize soils for pavement design

purpose is the California Bearing Ratio (CBR). This empirical index test was

abandoned in California over 50 years ago but, following its adoption by the US.

Corps of Engineers in World War II, it was gradually accepted World-wide as the

appropriate test (Brown, 1997). Given that the test is at best, an indirect measurement

of undrained shear strength and the pavement design requires knowledge of soil

resilience and its tendency to develop plastic strains under repeated loading, the

tenacity exhibited by generation of highway engineers in regard to the CBR is

somewhat surprising. Jim Porter, a Soil Engineer for the State of California,

introduced the “Soil Bearing Test” in 1929 commented nine years later, that the

bearing values are not direct measure of the supporting value of materials (Porter,

1938). In recognition that the CBR design curves give a total thickness of pavement to

prevent shear deformation in the soil, Turnbull (1950) noted that the CBR is an index

of shearing strength. The shear strength of soil is not of direct interest to the road

engineer, the soil should operate at stress levels within the elastic range (Brown,

1997). The pavement engineer is therefore more concerned with the elastic modulus

of soil and the behaviour under repeated loading.

The CBR method of pavement design is an empirical design method and was first

used by the California Division of Highways as a result of extensive investigations

made on pavement failures during the years 1928 and 1929 (Corps of Engineers,

1958). To predict the behaviour of pavement materials, the CBR was developed in

1929. Tests were performed on typical crushed stone representative of base course

materials and the average of these tests designated as a CBR of 100 percent. Samples

of soil from different road conditions were tested and two design curves were

produced corresponding to average and light traffic conditions. From these curves

the required thickness of Subbase, base and surfacing were determined. The

21

investigation showed that soils or pavement material having the same CBR required

the same thickness of overlying materials in order to prevent traffic deformation. So,

once the CBR for the subgrade and those of other layers are known, the thickness of

overlying materials to provide a satisfactory pavement can be determined. The US

corps of Engineers adopted the CBR method for airfield at the beginning of the

Second World War, since then, several modifications of the original design curves

have been made (Oguara, 2005). Some of the common CBR design methods include

the Asphalt Institute (Asphalt Institute, 1981) method, the National Crushed Stone

Association (NCSA) design method (NCSA, 1972), the Nigerian (CBR) design

procedure (Highway Manuel, 1973) etc.

2.5.2.1 The Asphalt Institute CBR Method

Although the Asphalt institute has developed a new thickness design procedure

based on the mechanistic approach (Asphalt Institute, 1981), the original asphalt

institute thickness design procedure is based on the concept of full depth asphalt,

that is using asphalt mixtures for all courses above the subgrade or improved

subgrade. Traffic analysis is in terms of 80kN equivalent single axle load in the form

of a Design Traffic Number, DTN. The DTN is the average daily number of

equivalent 80kN single-axle estimated for the design period. The CBR, Resistance

value or Bearing value from plate loading test is used in subgrade strength

evaluation. Figure 2.1 shows the Thickness chart for Asphalt pavement structure.

The recommended minimum total asphalt pavement thickness (TA) is presented in

Table 2.1

2.5.2.2 The National Crushed Stone Association CBR Method

The National Crushed Stone Association (NCSA) empirical design method (NCSA,

1972) is based on the US Corps of Engineers pavement design. Traffic analysis is

based on the average number of 80kN single-axle loads per lane per day over a

22

pavement life expectancy of 20 years. The method incorporates a factor of traffic in

the design called Design Index (DI). Six design index categories are defined as

presented in Table 2.2. In the absence of traffic survey data, general grouping of

vehicles can be obtained from spot checks of traffic and placed in one of the three

groups as follows:

Group 1: Passenger cars, panel and pickup trucks

Group 2: Two-axle trucks loaded or larger vehicles empty or carrying light

Loads.

Group 3: All vehicles with more than three loaded axles

Subgrade strength evaluation is made in terms of CBR and compaction requirement

is provided to minimize permanent deformation due to densification under traffic.

Presented in Figure 2.2 is the NCSA design chart.

Figure 2.1: Thickness Requirement for Asphalt Pavement Structure (Source: Oguara, 2005)

23

Table 2.1.: Minimum Asphalt Pavement Thickness(TA) (Source: Oguara, 2005)

Traffic DTN Minimum TA(mm)

Light Less than10 100

Medium 10 - 100 125

Heavy 100 – 1000 More than

1000

150 175

Table 2.2: NCSA Design Index categories (Source: Oguara, 2005)

Design Index

General Character Daily ESAL

DI-1 Light traffic (few vehicles heavier than passenger cars, no regular use by Group 2 or 3 vehicles)

5 or less

DI-2 Medium-light traffic (similar to DI-1, maximum 1000 VPD including not over 5% Group 2, no regular use by Group 3 vehicles

6-20

DI-3 Medium traffic (maximum 3000VPD, including not over 10% Group 2 and 3, 1% Group 3 vehicles)

21-75

DI-4 Medium – heavy traffic (maximum 6000VPD, including not over 15% Group 2 and 3, 1% Group 3 vehicles)

76-250

DI-5 Heavy traffic (maximum 6000VPD, may include 25% Group 2 and 3, 10% Group 3 vehicles)

251-900

DI-6 Very heavy traffic (over 6000VPD, may include over 25% Group 2 or 3 vehicles)

901-3000

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2.5.2.3 The Nigerian CBR Method

The Nigerian (CBR) design procedure is an empirical procedure which uses the

California Bearing Ratio and traffic volume as the sole design inputs. The method

uses a set of design curves for determining structural thickness requirement. The

curves were first developed by the US Corps of Engineers and modified by the

British Transportation and Road Research Laboratory (TRRL, 1970), it was adopted

by Nigeria as contained in the Federal Highway Manual (Highway Manuel, 1973).

The Nigerian (CBR) design method is a CBR-Traffic volume method, the thickness of

the pavement structure is dependent on the anticipated traffic, the strength of the

foundation material, the quality of pavement material used and the construction

procedure. This method considers traffic in the form of number of commercial

vehicles/day exceeding 29.89kN (3 tons). Subgrade strength evaluation is made in

terms of CBR. The selection of pavement structure is made from design curves

shown in Figure 2.3.

Figure 2.2: NCSA Design Chart (Source: Oguara, 2005)

25

The thickness of the pavement layers is dependent on the expected traffic loading.

Recommended minimum asphalt pavement surface thickness is considered in terms

of light, medium and heavy traffic as follows:

Light traffic - 50mm

Medium - 75mm

Heavy - 100mm

Figure 2.3: The Nigerian CBR Design chart (Source: Oguara, 2005)

26

2.5.2.4 The AASHTO Pavement Design Guides

The AASHTO Guide for Design of Pavement Structures is the primary document

used to design new and rehabilitated highway pavements. The Federal Highway

Administration's 1995-1997 National Pavement Design Review found that some 80

percent of states use the 1972, 1986, or 1993 AASHTO Guides (AASHTO, 1972;

1986; 1993), of the 35 states that responded to a 1999 survey by Newcomb and

Birgisson (1999), 65% reported using the 1993 AASHTO Guide for both flexible and

rigid pavement designs.

All versions of the AASHTO Design Guide are empirical methods based on field

performance data measured at the AASHO Road Test in 1958-60, with some

theoretical support for layer coefficients and drainage factors. The overall

serviceability of a pavement during the original AASHO Road Test was quantified

by the Present Serviceability Rating (PSR; range = 0 to 5), as determined by a panel

of highway raters. This qualitative PSR was subsequently correlated with more

objective measures of pavement condition (e.g., cracking, patching, and rut depth

statistics for flexible pavements) and called the Pavement Serviceability Index (PSI).

Pavement performance was represented by the serviceability history of a given

pavement - i.e., by the deterioration of PSI over the life of the pavement. Roughness

is the dominant factor in PSI and is, therefore, the principal component of

performance under this measure.

2.5.3 Mechanistic Design Approach

The mechanistic design approach represents the other end of the spectrum from the

empirical methods. The mechanistic design approach is based on the theories of

mechanics to relate pavement structural behavior and performance to traffic

loading and environmental influences. The mechanistic approach for rigid

pavements has its origins in Westergaard's (Westergaard, 1926) development

27

during the 1920s of the slab on subgrade and thermal curling theories to compute

critical stresses and deflections in a PCC slab. The mechanistic approach for flexible

pavements has its roots in Burmister's (Burmister, 1945) development during the

1940s of multilayer elastic theory to compute stresses, strains, and deflections in

pavement structures.

A key element of the mechanistic design approach is the accurate prediction of the

response of the pavement materials - and, thus, of the pavement itself. The

elasticity-based solutions by Boussinesq, Burmister, and Westergaard were an

important first step toward a theoretical description of the pavement response

under load. However, the linearly elastic material behavior assumption underlying

these solutions means that they will be unable to predict the nonlinear and inelastic

cracking, permanent deformation, and other distresses of interest in pavement

systems. This requires far more sophisticated material models and analytical tools.

Much progress has been made in recent years on isolated pieces of the mechanistic

performance prediction problem. The Strategic Highway Research Program during

the early 1990s made an ambitious but, ultimately, unsuccessful attempt at a fully

mechanistic performance system for flexible pavements. To be fair, the problem is

extremely complex; nonetheless, the reality is that a fully mechanistic design

approach for pavement design does not yet exist. Some empirical information and

relationships are still required to relate theory to the real world of pavement

performance.

2.5.4. Mechanistic –Empirical Design Approach

The development of mechanistic-empirical design approaches dates back at least

four decades. As its name suggests, a mechanistic-empirical approach to pavement

design combines features from both the mechanistic and empirical approaches. The

induced state of stress and strain in a pavement structure due to traffic loading and

environmental conditions is predicted using theory of mechanics. Empirical models

28

link these structural responses to distress predictions. Huang (1993) notes that

Kerkhoven and Dormon (1953) were the first to use the vertical compressive strain

on top of the subgrade as a failure criterion to reduce permanent deformation. Saal

and Pell (1960) published the use of horizontal tensile strain at the bottom of the

asphalt bound layer to minimize fatigue cracking. The concept of horizontal tensile

strain at the bottom of the asphalt bound layer was first used by Dormon and

Metcaff 1965) for pavement design. The Shell method (Claussen et al, 1977) and the

Asphalt Institute method (Shook et al, 1982; Asphalt Institute, 1992) incorporated

strain-based criteria in their mechanistic-empirical procedures. Several studies over

the past fifteen years have advanced mechanistic-empirical techniques. Most of the

works, however, were based on variants of the same two strain-based criteria

developed by Shell and the Asphalt Institute. The Washington State Department of

Transportation (WSDOT), North Carolina Department of Transportation(NCDOT)

and Minnesota Department of Transportation(MNDOT), to name but a few,

developed their own Mechanistic-Empirical procedures (Schwartz and Carvalho,

2007). The National Cooperative Highway Research Program (NCHRP) 1-26 project

report, Calibrated Mechanistic Structural Analysis Procedures for Pavements (1990),

provided the basic framework for most of the efforts made by state DOTs. WSDOT

(Pierce et al., 1993; WSDOT, 1995).

2.5.5 Layered Elastic System

The analysis of stresses, strains and deflections in pavement systems have been

largely derived from the Boussinesq equation originally developed for a

homogeneous, isotropic and elastic media due to a point load at the surface.

According to Boussinesq, the vertical stress σZ at any depth z below the earth’s

surface due to a point load P at the surface is given by (Oguara, 2005):

29

σZ = 2

.Z

Pk (2.0)

Where,

k = ( )[ ] 2

52

1

1

2

3

z

r+π (2.1)

and

r is the radial distance from the point of load application.

For stress on a vertical plate passing through the centre of a loaded plate:

σZ = ( )

+−

23

22

3

1zr

zP (2.2)

Where,

P is the unit load on a circular plate of radius r ( or of a tyre of known contact area

and pressure). Here the vertical stress is dependent on the depth z and radial

distance r and is independent of the properties of the transmitting medium.

Considering radial strains which is dependent on Poisson’s ratio µ, from equation

(2.2) and µ = 0.5, the Boussinesq equation for deflection, ∆ at the centre of a circular

plate is given as:

∆ = ( )

( ) 21

22

2

2

3

zrE

rP

+ (2.3)

This may be written as

∆ = FE

aP )( (2.4)

Where, F = ( )[ ] 2

12

1

1.

2

3

zr+

(2.5)

30

The term F reflects the depth-radius ratio. The value of F when taken at the contact

surface equals 1.5 and 1.18 for flexible and rigid plate respectively.

For flexible plate, the deflection at the centre of the loaded circular plate of radius

“a” is therefore given as:

∆ = E

Pa5.1 (2.6)

and for a rigid plate, the deflection is given as:

∆ = E

Pa18.1 (2.7)

From equations (2.6) and (2.7), the modulus of elasticity E of a soil or pavement can

be computed by measuring the deflection under a known load and contact area

(Oguara, 2005). The fact that pavement deflection can be directly related to Hook’s

law that says stress σ is proportional to strain Є, or to the modulus of elasticity of the

material, has brought forth the use of elastic layered systems – a mechanistic

approach in design of pavements (Oguara, 1985)

The response of pavement systems to wheel loading has been of interest since 1926

when Wetergaard used elastic layered theory to predict the response of rigid

pavements (Westergaard, 1926). It is generally accepted that pavements are best

modeled as a layered system, consisting of layers of various materials (concrete,

asphalt, granular base, subbase etc.) resting on the natural subgrade. The behaviour

of such a system can be analyzed using the classical theory of elasticity (Burmister,

1945). The Layered Elastic Analysis (LEA) is a mechanistic-empirical procedure

capable of determining pavement responses (stress and strain) in asphalt pavement.

The major assumptions in the use of layered elastic analysis are that;

31

i. the pavement structure be regarded as a linear elastic multilayered system

in which the stress-strain solution of the material are characterized by the

Young’s modulus of Elasticity E and poison’s ratio µ.

ii. Each layer has a finite thickness h except the lower layer, and all are infinite

in the horizontal direction.

iii. The surface loading P can be represented vertically by a uniformly

distributed vertical stress over a circular area.

In three-layered pavement system, the locations of the various stresses are as shown

in Figure 2.4 (Yoder and Witczak, 1975). The horizontal tensile strain at the bottom of

the asphalt concrete layer and vertical compressive strain at the top of the subgrade

are given by equations 2.8 and 2.9 respectively;

Єr1 = 1

11

1

11

1

1

EEE

zrr σµ

σµ

σ−− (2.8)

Єz1 = ( )32

3

1rz

Eσσ − (2.9)

Where,

1zσ = vertical stress at interface 1 (bottom of asphalt concrete layer)

2zσ = vertical stress at interface 2

1rσ = horizontal stress at the bottom of layer 1

2rσ = horizontal stress at the bottom of layer 2

3rσ = horizontal stress at the top of layer 3

31 EandE are Modulus of elasticity of layer 1 and 3 receptively.

µ = Poisson’s ratio of the layer

32

2.5.6 Finite Element Model

The Finite Element Method (FEM) is a numerical analysis technique for obtaining

approximate solutions to engineering problems. In the finite element analysis of

asphalt pavements, the pavement and subgrade is descritized into a number of

elements with the wheel load at the top of the pavement. The FEM assumes some

constraining values at the boundaries of the region of interest (pavement and

subgrade) and is used to model the nonlinear response characteristic of pavement

materials.

2.5.7 Mechanistic-Empirical Design Inputs

Inputs for M-E pavement design include traffic, material and subgrade

characterization, climate factors and performance criteria. Layered elastic models

require a minimum number of inputs to adequately characterize a pavement

structure and its response to loading. Some of the inputs include modulus of

elasticity (E) and Poisson’s ratio (µ) of material, pavement thickness(h) and the

P

µ1 = 0.5, h1, E1

µ2 = 0.5, h2, E2

µ1 = 0.5, h3, E2

a

σz1

σr1

σz2

σr2

σr3

Interface 1

Interface 2

Figure 2.4: Three-Layer Pavement System Showing Location of Stresses

33

loading (P). In the Mechanistic-Empirical(M-E) pavement design guide (AASHTO,

1993), three levels of material inputs are adopted as shown in Table 2.3. Level 1

material input is obtained through direct laboratory testing and measurements. This

level of input uses the state of the art technique in characterization of materials as

well as characterization of traffic through collection of data from weigh-in-motion

(WIM) stations; Level 2 uses correlations to determine the required material inputs,

while Level 3 uses material inputs selected from typical defaults values. Tables 2.4

and 2.5 shows typical input values for some pavement materials. The outputs

expected in layered elastic analysis are the pavement responses; stresses, strains and

deflections.

Table 2.3: Inputs levels in layered elastic Design

Material Input

Level 1

Input

Level 2

Input

Level 3

Asphalt Concrete Measured

Diametric Modulus

Estimated

Diametric Modulus

Default

Diametric Modulus

Portland Cement

Concrete

Measured

Elastic Modulus

Estimated

Elastic Modulus

Default

Elastic Modulus

Stabilized Materials Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

Granular Materials Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

Subgrades Measured

Resilient Modulus

Estimated

Resilient Modulus

Default

Resilient Modulus

34

Table 2.4: Default Resilient Modulus (Mr) Values for Pavement Materials

General Level of Subgrade Support

AASHTO Soil Classification Broad Mr range and Mean Mr at Optimum Moisture

Content

Very Good Coarse grained: Gravel and gravely soils; A-1-a, A-1-b

172 to 310MPa Mean = 269MPa

Good Coarse grained: Sand and Sandy soils A-2-4, A-3

138 to 275MPa Mean = 207MPa

Fair Fined grained: Mixed silt and clay A-2-7, A-4, A-2-5, A-2-6

103 to 207MPa Mean = 179MPa

Poor Fine grained: Low compressibility A-5, A-6

69 to 172MPa Mean = 124MPa

Very Poor Fine grained: High compressibility A-7-5, A-7-6

34 to 103MPa Mean = 69MPa

Crushed Stone 138 to 241MPa Mean = 172MPa

NOTE: Subgrade properties for the above soil classes are as follows Very Poor: (PI = 30, No. 200 = 85%, No. 4 = 95%, D60 = 0.02mm) Poor: (PI = 15, No. 200 = 75%, No. 4 = 95%, D60 = 0.04mm) Fair: (PI = 7, No. 200 = 30%, No. 4 = 70%, D60 = 1.0mm) Good: (PI = 5, No. 200 = 20%, No. 4 = 61%, D60 = 3.0mm) – Meets most agencies spec for subbase materials. Very Good: (PI = 1, No. 200 = 5%, No. 4 = 47%, D60 = 8.0mm) Meets most agencies spec for base material.

Table 2.5: Typical Poison’s Ratio Values for Pavement Materials (NCHRP, 2004; WSDOT, 2005)

Material µ Range Typicalµ

Clay (saturated) 0.4 - 0.5 0.45

Clay (unsaturated) 0.1 - 0.3 0.2

Sandy clay 0.2 - 0.3 0.25

Silt 0.3 - 0.35 0.325

Dense sand 0.2 - 0.4 0.30

Coarse-grained sand 0.15 0.15

Fine-grained sand 0.25 0.25

Bedrock 0.1 - 0.4 0.25

Crushed Stone 0.1 – 0.45 0.30

Cement Treated Fine-grain

Materials

0.15 – 0.45 0.40

35

2.5.8 Traffic Loading

An important factor affecting pavement performance is the number of load

repetitions and the total weight a pavement experiences during its lifetime.

Although it is not too difficult to determine a wheel or an axle load for an individual

vehicle, it becomes quite complicated to determine the number and types of wheel/

axle loads that a particular pavement will be subjected to over its design life.

Furthermore, it is not the wheel load but rather the damage to the pavement caused

by the load that is of primary concern. The most common approach is to convert

damage from wheel loads of various magnitude and repetitions (“mixed traffic”) to

damage from an equivalent number of “standard” or “equivalent” loads. The most

commonly used equivalent load is the 18,000lb (80kN) Equivalent single axle Load

ESAL. As a result of variation in traffic loading, many pavement design agencies

have developed multiplying factors called “load equivalency factors” as a means of

reducing the variation in traffic loading to single load conditions. The most widely

used load equivalency factor are those developed at the AASHTO Road Test

(AASHTO, 1972). A “load equivalency factor” represents the number of ESALs for

the given weight-axle combination. The AASHTO (2002) Guide for the Design of New

and Rehabilitated Pavement Structures adopts the load spectra approach in M-E design

of pavements. In essence, the load spectra approach uses the same data that ESAL

approach uses only it does not convert the loads to ESALs – it maintains the data by

axle configuration and weight.

For Nigerian traffic condition, traffic analysis could be based on the number of axle

loads of commercial vehicles expressed in terms of an equivalent 80kN single axle

load. There are no load equivalency factors developed in Nigeria, therefore, the

AASHTO equivalency factors could be used in design. Traffic analysis procedure

36

suggested by Oguara (1985) involves the determination of the number of 80kN

equivalent standard axle load (ESAL) as follows:

ESAL = FV TxN∑ (2.10)

TF = ∑V

F

N

ExNA (2.11)

Where,

NV = number of commercial vehicles

NA = Number of axles

TF = Truck or commercial vehicle factor

EF = Load equivalency factors

The truck factors could be calculated from specific truck/ commercial vehicle axle

and weight data. Shook et al, (1982) presented typical truck factors for different

classes of highways and vehicles in the United States. AASHTO (1993)

recommended the estimation of design ESAL from traffic volume. This involves

converting the daily traffic volume into an annual ESAL amount. Pavements are

typically designed for the critical lane or “design lane”, which accounts for traffic

distribution (Pavement interactive, 2008). The ESALs per year is given by:

ESALs per year = (Vehicle/day) x (Lane Distribution Factor) x (days/yr.) x

(ESALs/vehicle) (2.12)

The design ESAL is given by:

ESAL = ESALs per year x ( )

g

gn

11 −+ (2.13)

Where,

n = design period

g = annual growth rate.

37

The Nigerian Highway manual recommended a procedure for estimation of traffic

repetitions (Nanda, 1981) using Table 2.6.

Table 2.6: Vehicle Classification (Nanda, 1981)

Class Description (Nanda, 1981)

Typical ESALs per Vehicle

1 Passenger cars, taxis, landrovers, pickups, and

mini-buses.

Negligible

2 Buses 0.333

3 2-axle lorries, tippers and mammy wagons 0.746

4 3-axle lorries, tippers and tankers 1.001

5 3-axle tractor-trailer units (single driven axle,

tandem rear axles)

3.48

6 4-axle tractor units (tandem driven axle,

tandem rear axles)

7.89

7 5-axle tractor-trailer units(tandem driven axle,

tandem rear axles)

4.42

8 2-axle lorries with two towed trailers 2.60

2.5.9 Material Properties

The ability to calculate the response of pavement structure due to vehicle load

depends on a proper understanding of the mechanical properties of the constituent

materials. In M-E pavement design, material characterization requires the

determination of the material stiffness as defined by the elastic modulus and

Poisson’s ratio. The elastic modulus can either be determined or correlated with

conventional test. In many cases where there is need for laboratory testing, the

method of testing the modulus should reproduce field conditions as accurately as

possible. Generally, the dynamic modulus, diametric resilient modulus, and indirect

tensile test are used for asphalt concrete and stabilized materials; the resilient

modulus test is mainly used for granular materials.

38

2.5.9.1 Elastic Modulus of Bituminous Materials

The dynamic modulus test can be used to determine the linear viscoelastic properties

of bituminous materials. The dynamic modulus is derived from the complex

modulus E* defined as a complex number that relates stress to strain for a linear

viscoelastic material subjected to sinusoidal loading at a given temperature and

loading frequency (Yorder and Witczak, 1975). The dynamic complex modulus test

accounts not only for the instantaneous elastic response without delayed effects, but

also the accumulation of cyclic creep and delayed elastic effects with the number of

cycles. The dynamic modulus test does not allow time for any delayed elastic

rebound during the test, which is the fundamental difference from the resilient

modulus test. The test is conducted as specified in ASTM D3497-79 on unconfined

cylindrical specimen100mm diameter by 200mm high using uniaxialy applied

sinusoidal stress pattern. Strains are recorded using bonded wire strain gauges and

a-channel recording system.

By definition, the absolute value of the complex modulus *E is commonly referred

to as dynamic modulus.

E* = φε

σ

φε

σ

SinCos 0

0

0

0 + (2.14)

Where,

σ0 = stress amplitude (N/mm2)

ε0 = recoverable strain amplitude (mm/mm)

Ф = the phase lag angle (degrees)

For and elastic material, Ф = 0,, hence the dynamic modulus is calculated using

equation 2.15(Yoder and Witczak, 1975)

E* = 0

0*ε

σ=E (2.15)

39

Thus the elastic or dynamic modulus of bituminous materials may be determined by

dividing the peak stress σ0 to strain amplitude ε0 from dynamic modulus test.

The elastic modulus of bituminous materials can also be determined by means of the

diametric resilient modulus device developed by Schmidt (Schmidt, 1972) which is a

repetitive load test on cylindrical specimen 100mm diameter by 63mm high,

fabricated either by marshal apparatus or Hveen Kneading compactor. The repeated

load is applied across the diameter, placing the specimen in a state of tensile stress

along the vertical diameter. Linear Variable Differential Transducers (LVDT)

mounted on each side of the horizontal specimen axis measure the lateral

deformation of the specimen under the applied load. One of the major difference

between a resilient modulus test and a dynamic complex modulus test for asphalt

concrete mixtures is that the resilient modulus test has a loading of one cycle per

second (1 Hz) with a repeated 0.1 second sinusoidal load followed by a 0.9 second

rest period, while the dynamic modulus test applies a sinusoidal loading without

rest period.

Knowledge of the dynamic load and deformations allow the resilient modulus to be

calculated. Frocht (1948) gave expressions for the stresses σx and σy across the

diameter ”d” perpendicular to the applied load P as:

Horizontal Diametral Plane:

+

−=

22

22

4

4

..

2

xd

xd

dt

Px

πσ (2.16)

−

+−= 1

4..

222

2

xd

d

dt

Py

πσ (2.17)

τxy = 0 (2.18)

40

Vertical Diametral Plane:

dt

Px

..

2

πσ = (2.19)

−

++

−−=

dydyddt

Py

1

2

2

2

2

..

2

πσ (2.20)

τxy = 0 (2.21)

where,

t is the specimen thickness and x and y are the distance from the origin along

the x and y-axis.

Thus, if the horizontal deformation across a cylindrical specimen resulting from an

applied vertical load is known the modulus of elasticity can be calculated.

2.5.9.2 Prediction Model for Dynamic and Elastic Modulus of Asphalt Concrete

To perform a dynamic modulus test is relatively expensive. Efforts were made by

asphalt pavement researchers to develop regression equation to estimate the

dynamic modulus for a specific hot mix design. One of the comprehensive asphalt

concrete mixture dynamic modulus models is the Witczak prediction model

(Christensen et al, 2003). It is proposed in the AASHTO M-E Design Guide and the

calculations were based on the volumetric properties of a given mixture.

Witczak’s prediction equation is presented in equation 2.22a

[ ])22.2(

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0)(001767.0029232.0249937.1log

)log393532.0log313351.0603313.0(

34

2

38384

4

2

200200

*

ae

PPPP

VV

VVPPPE

f

abeff

beff

a

η−−−

+−+−+

+−−−−+−=

Where

*E = Dynamic modulus, in 105 Psi

41

η = Bituminous viscosity, in 106 Poise (at any temperature, degree of aging)

f = Load frequency, in Hz

Va = Percent air voids content, by volume

Vbeff = Percent effective bitumen content, by volume

P34 = Percent retained on 19mm sieve, by total aggregate weight(cumulative)

P38 = Percent retained on 9.51mm sieve, by total aggregate weight(cumulative)

P4 = Percent retained on 4.76mm sieve, by total aggregate weight(cumulative)

P200 = Percent retained on 0.074mm sieve, by total aggregate weight(cumulative)

Asphalt concrete elastic modulus can also be predicted using equation 2.22.

Researches have indicated that the dynamic modulus values of asphalt concrete

measured at a loading frequency of 4Hz is comparable with the elastic modulus

values (FDOT, 2007; TM 5-822-13/AFJMAN 32-1018, 1994). The elastic modulus can

then be predicted by modifying equation 2.22b as follows:

[ ])22.2(

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0)(001767.0029232.0249937.1log

)log393532.07919691.0(

34

2

38384

4

2

200200

be

PPPP

VV

VVPPPE

abeff

beff

a

η−−

+−+−+

+−−−−+−=

Where

E = Elastic modulus, in 105 Psi

η = Bituminous viscosity, in 106 Poise (at any temperature, degree of aging)

Va = Percent air voids content, by volume

Vbeff = Percent effective bitumen content, by volume

P34 = Percent retained on 19mm sieve, by total aggregate weight(cumulative)

P38 = Percent retained on 9.51mm sieve, by total aggregate weight(cumulative)

P4 = Percent retained on 4.76mm sieve, by total aggregate weight(cumulative)

P200 = Percent retained on 0.074mm sieve, by total aggregate weight(cumulative)

42

2.5.9.3 Elastic Modulus of Soils and Unbound Granular Materials

The elastic properties of subgrade soils and unbound granular materials for base and

subbase courses can be measured directly by the Resilient Modulus test using a

triaxial test device capable of applying repeated dynamic loads of controlled

magnitude and duration. The resilient (recoverable) deformation over the entire

length of the specimen could be measured with LVDT. The specimen size is

normally 100mm in diameter by 200mm high. The Resilient modulus is calculated by

dividing the repeated axial stress σd (equal to the deviator stress) by the recoverable

strain εr.

For unbound granular materials, the resilient modulus MR, which is stress

dependent, is given as (Shook et al, 1982):

MR = K1.θ.K2 (2.23)

Where, K1 and K2 are material constants experimentally determined and

θ = the sum of principal stresses.

If repeated load test equipment is not available, the Resilient Modulus of subgrade

may be estimated from CBR values by using the relationship developed by

Heukelom and Klomp, (1962) as:

MR(MPa) = 10.3 CBR (2.24a)

MR(psi) = 1500CBR (2.24b)

For subgrade soaked CBR value between 1 and 10%

For unbound base material layers, the resilient modulus may be assumed to be a

function of the thickness of the layer h and the modulus of the subgrade reaction

MRs (Emesiobi, 2000) as shown in equation (2.25)

43

MR = 0.2 x h0.45 x MRs (2.25)

Where,

h is in millimeters and MR must lie between 2 and 4 times MRs.

The AASHTO Guide for design of pavement structures (AASHTO, 1993)

recommends a standard method of calculating subgrade modulus. This method

involves calculating a weighted average subgrade resilient modulus based on the

relative pavement damage. Because lower values of subgrade resilient modulus

result in more pavement damage, lower values o subgrade resilient modulus is

weighted more heavily. The relative damage equation used in the 1993 AASHTO

Guide is:

fu = (1.18 x 108)32.2−

RM (2.26)

Where,

fu = relative damage factor

MR = resilient modulus in psi

Therefore, over an entire year, the average relative damage is given by:

n

uuuu

fnff

f

+++=

...21 Where, n = 12.

When triaxial test equipment for resilient modulus is not available, the U.S Army

Corps of Engineers (Hall and Green, 1975) recommends the estimation of resilient

modulus for unbound granular material using equation 2.27.

MR(psi) = 5409(CBR)0.71 (2.27)

Researches have also revealed some useful relationship between CBR and resilient

modulus “E” of stabilized laterite (Ola, 1980) as follows;

For soaked specimen,

E(psi) = 250(CBR)1.2 (2.28)

44

For unsoaked specimen

E(psi) = 540(CBR)0.96 (2.29)

2.5.9.4 Non-linearity of Pavement Foundation

The non-linearity of pavement foundation has been demonstrated both from insitu

measurement of stress and strain (Brown and Bush, 1972; Brown and Pell, 1967)

using field instrumentation, and through back-analysis of surface deflections bowls

measured with the Falling Weight Deflectometer. These non-linearity characteristics

have also been extensively studied using repeated load triaxial facilities and various

models proposed for use in pavement analysis. Some of these are quite sophisticated.

For granular materials, the use of stress dependent bulk and shear modulus provides

a much more sounder basis for analysis than the simple “k-θ” model in which the

resilient modulus is expressed as a function of the mean normal stress and usually, a

fixed value of Poisson’s ratio is adopted, typically 0.3.

For fine grained soils, emphasis has been placed on the relationship between resilient

modulus and deviator stress following the early work done by Seed et al (1962). For

saturated silty- clay, Brown et al (1987) suggested the following model based on a

series of good quality laboratory tests;

Gr =

m

r

or

q

P

C

q

'

(2.30)

Where Gr = Resilient shear modulus

qr = Repeated deviator stress

P0’ = Mean normal effective stress

C, m = Constant for the particular soil

For partially saturated soils with degree of saturation in excess of 85%, the same

equation was valid with P0’ being replaced by the soil suction.

45

2.5.9.5 Poisson’s Ratio

The Poisson’s ratio µ is defined as the ratio of lateral strain εL to the axial strain εa

caused by a load parallel to the axis in which the strain is measured (Oguara, 1985).

Values of Poisson’s ratio are generally estimated, as most highway agencies use

typical values as design inputs in elastic layered analysis. Table 2.7 gives typical

Poisson’s ratio values by various agencies.

Table 2.7: Poisson’s Ratio Used by Various Agencies (Oguara, 2005)

Material Original Shell Oil Company

Revised Shell Oil Company

The Asphalt Institute

Kentucky Highway Department

Asphalt Concrete 0.5 0.55 0.40 0.40

Granular Base 0.5 0.53 0.45 0.45

Subgrade 0.5 0.35 0.45 0.45

If deformations are monitored from either static or dynamic test, an approximate µ

value could be obtained from equation (2.28):

µ =

∆−

0

11

2

1

V

V

aε (2.31)

Where,

V = volume of the material

2.5.9.6 Climatic Conditions

The mechanical parameters of both bounded and unbound layers in pavement

structures are seasonally affected. It is therefore important to understand their

seasonal variations in order to be able to predict their effect on pavement

performance. In mechanistic design, two climatic factors, temperature and moisture

are considered to influence the structural behaviour of the pavement, for instance,

temperature influences the stiffness and fatigue of bituminous materials and is the

major factor in frost penetration. Moisture conditions influence the stiffness and

strength of base course, subbase course and subgrade.

46

In most pavement design procedures, the effect of the environment is accounted for

by including them in the material properties. The mean annual air temperature

MAAT or mean monthly air temperature MMAT have been generally used in

pavement design analysis. Because the effect of freezing and thawing is very serious

in temperate regions, more attention has been directed towards design of pavement

to resist spring thaw effects. These efforts have several times led to loss of subgrade

supporting capacity, a phenomenon called spring break up.

In Mechanistic design, the effect of environmental factors is included in the analysis.

The moisture and temperature variation for each sub-layer within the pavement, or a

representative temperature need to be determined. In the Asphalt institute design

method, pavement temperature can be determined by (Witczak, 1972):

MMPT = MMAT( ) ( )

+

+−

++ 6

4

34

4

11

zz (2.32)

Where,

MMPT = mean monthly pavement temperature

MMAT = mean monthly air temperature

Z = depth below pavement surface (inches)

Pavement design is usually predicated on a subgrade which is assumed to be near-

saturation. The design may be based on subgrade with lower moisture content if

available field measurement indicates that the subgrade will not reach saturation.

For Nigerian climatic condition, the most damaging environmental factor is rainfall,

which unfortunately has not received as much attention as that of frost or freeze-

thaw action. Although the soaked CBR test has been used to simulate the worst

environmental conditions, this may be over conservative in the dry regions of

Nigeria. The provision of adequate drainage facility and proper compaction of

47

pavement materials will go a long way to alleviate the effect of the environment ,

especially rainfall on pavements (Oguara, 1985).

2.6 Pavement Response Models

Mechanistic-empirical design procedure requires calculation of the critical structural

responses (stresses, strains or displacements) within the pavement layers induced by

traffic and/ or environmental loading. These responses are used to predict damage

in the pavement system which is later related to the pavement distresses (cracking or

rutting). Basically, two types of mechanistic models are commonly used to model

flexible pavements; the layered elastic model (LEA) and the finite element model

(FEM). Both of these models can easily be run on personal computers and only

require data that can be realistically obtained.

2.6.1 Layered Elastic Model

A layered elastic model can compute stresses, strains and deflections at any point in

a pavement structure resulting from the application of a surface load. The layered

elastic model assumes that each pavement layer is homogenous, isotropic and

linearly elastic (Burmister, 1945) and could be used to analyze pavement distress

(Peattie, 1963). The layered elastic approach works with relatively simple

mathematical models and thus, requires some basic assumptions. These assumptions

are:

i. Pavement layers extend infinitely in the horizontal direction.

ii. The bottom layer (usually the subgrade) extends infinitely downwards.

iii. Materials are not stressed beyond their elastic ranges.

Layered elastic models require a minimum number of inputs such as Thickness of

the pavement layers, Material properties (modulus of elasticity and Poisson’s ratio)

and Traffic loading (Weight, wheel spacing, and axle spacing) to adequately

characterize a pavement structure and its response to loading. The outputs of a

48

layered elastic model are the stresses, strains, and deflections in the pavements.

Layered elastic computer programs are used to calculate the theoretical stresses,

strains and deflections anywhere in a pavement structure. Table 2.8 and Figure 2.5

however, show few critical locations that are often used in pavement analysis.

Table 2.8: Critical Analysis Locations in a Pavement Structure

Location Response Reason for Use

Pavement Surface Deflection Used in imposing load restrictions during spring thaw and overlay design

Bottom of HMA Layer Horizontal Tensile Strain Used to predict fatigue in the HMA layer

Top of intermediate Layer (Base or Surface)

Vertical Compressive Strain

Used to predict rutting failure in the base or subbase

Top of Subgrade Vertical Compressive Strain

Used to predict rutting failure in the subgrade

1. Pavement surface deflection 2. Horizontal tensile strain at the bottom of bituminous layer 3. Vertical compressive strain at top of base 4. Vertical compressive strain at top of subgrade

Figure 2.5: Critical Analysis Locations in a Pavement Structure (Pavement Interactive, 2008)

49

2.6.2 Finite Elements Model

The Finite Element Method (FEM) is a numerical analysis technique for obtaining

approximate solutions to engineering problems. In a continuum problem (e.g., one

that involves a continuous surface or volume) the variables of interest generally

posses infinitely many values because they are functions of each generic point in the

continuum. For example the stress in a particular element of pavement cannot be

solved with one simple equation because the functions that describe its stresses are

particular to each location. However, the finite element method can be used to divide

a continuum (the pavement volume) into a number of small discrete volumes in

order to obtain an approximate numerical solution for each individual volume rather

than an exact close-form solution for the whole pavement volume. Fifty year ago the

computations involved in doing this were incredibly tedious, but today computers

can perform them quite readily. In the finite element analysis of flexible pavements,

the pavement and subgrade is discretized into a number of elements with the wheel

load at the top of the pavement. The FEM assumes some constraining values at the

boundaries of the region of interest (pavement and subgrade) and is used to model

the nonlinear response characteristic of pavement materials. The FEM approach

works with more complex mathematical model than the layered elastic approach so

it makes fewer assumptions. Generally, FEM must assume some constraining values

at the boundaries of the region of interest.

2.7 Flexible Pavement M-E Distress Models (Failure Criteria)

The use of mechanistic approach requires models for relating the output from elastic

layered analysis (i.e stress, strain, or deflections) to pavement behaviour (e.g.

performance, cracking, rutting, roughness etc) as elastic theory can be used to

compute only the effect of traffic loads.

50

The main empirical portions of the mechanistic-empirical design process are the

equations used to compute the number of loading cycles to failure. These equations

are derived by observing the performance of pavements and relating the type and

extent of observed failure to an initial strain under various loads. Currently, two

failure criteria are widely recognized; one relating to fatigue cracking and the other

to rutting deformation in the subgrade. A third deflection-based criterion may be of

special applications (Pavement interactive, 2008). Most of the principles in

mechanistic-empirical design of highway pavements are based on limiting strains in

the asphalt bound layer (fatigue analysis) and permanent deformation (rutting) in

the subgrade.

2.7.1 Fatigue Failure Criterion

Fatigue cracking is a phenomenon which occurs in pavements due to repeated

applications of traffic loads. Accumulation of micro damage after each pass on a

bituminous pavements leads to progressive loss of stiffness and eventually, to

fatigue cracking. Repeated load initiate cracks at critical locations in the pavement

structure, i.e. the locations where the excessive tensile stresses and strains occur. The

continuous actions of traffic cause these cracks to propagate through the entire

bound layer. The fatigue criterion in mechanistic-empirical design approach is based

on limiting the horizontal tensile strain on the underside of the asphalt bound layer

due to repetitive loads on the pavement surface, if this strain is excessive, cracking

(fatigue) of the layer will result.

The cracks in the asphalt layer may initiate at the bottom of the layer and propagate

to the top of the layer, or may initiate at the top surface of the asphalt layer and

propagate downwards. In Practice pavements are subjected to a wide range of traffic

and axle loads, to account for the contribution of the individual axle load

applications, the linear summation technique known as Miner’s hypothesis (Miner’s

51

Law) is used to sum the compound loading damage that occurs, so that the total

damage can be computed as follows:

∑=

=i

i f

i

N

nD

1

(2.33)

Where,

D = Total cumulative damage

ni = Number of traffic load application at strain level i

Nf = Number of application to cause failure in simple loading at strain level i

This equation indicates that the determination of fatigue life is based on the

accumulative damage level D. Failure occurs when D > 1 and a redesign may be in

order. When D is considerably less than unity, the section may be under designed.

The relationship shows that pavement sections can fail due to fatigue after a

particular number of load applications (Oguara, 2005).

Studies carried out by various researchers have shown that the relationship between

load repetitions to failure Nf and strain for asphalt concrete material is given as:

Nf =

b

t

a

ε

1 (2.34)

Where

Nf = Number of load applications to failure

tε = Horizontal tensile strain at the bottom of asphalt

bound layer

a and b = Coefficients from fatigue tests modified to reflect

insitu performance

Various equations and curves have been developed based on this relationship. Pell

and Brown (1972) used the following in developing their fatigue curves:

52

Nf =

8.3

11 1108.3

−

t

xε

(2.35)

Figure 2.6 shows typical fatigue curves from Freeme et al for layered elastic analysis

(Freeme et al, 1982).

Many other equations have also been developed to estimate the number of

repetitions to failure in the fatigue mode for asphalt concrete. Most of these rely on

the horizontal tensile strain at the bottom of the HMA layer, εt and the elastic

modulus of the HMA. One commonly accepted criterion developed by Finn et al

(1977) is:

Log Nf =

−

−

− 36 10log854.0

10log291.3947.15 ACt Eε

(2.36)

Where,

Nf = Number of cycles to failure

εt = Horizontal Tensile Strain at the bottom of the HMA layer

EAC = Elastic Modulus of the HMA

The above equation defines failure as fatigue cracking over 10 percent of the wheel

path area.

Figure 2.6: Typical Fatigue Curves (Source: Oguara, 2005)

53

The Asphalt Institute (1982) developed a relationship between fatigue failure of

asphalt concrete and tensile strain at the bottom of the asphalt layer follows:

Nf 854.0291.3 )()(0796.0 −−= EItε (2.37)

Where,

Nf = Number of load repetitions to to prevent fatigue cracking

εt = Tensile Strain at the bottom of asphalt layer

EI = Elastic modulus of asphalt concrete (psi)

2.7.2 Rutting Failure Criterion

Permanent deformation or rutting is a manifestation of both densification and

permanent shear deformation of subgrade. As a mode of distress in highway

pavements, pavement design should be geared towards eliminating or reducing

rutting in the pavement for a certain period. Rutting can initiate in any layer of the

structure, making it more difficult to predict than fatigue cracking.

Current failure criteria are intended for rutting that can be attributed mostly to weak

pavement structure. This is typically expressed in terms of the vertical compressive

strain (εv) at the top of the subgrade layer as:

Nf =

4843.46

18 1010077.1

−

v

xε

(2.38)

Where,

Nf = Number of repetions to faulre

εv = Vertical compressive Strain at the top of the subgrade layer

The above equation defines failure as 12.5mm (0.5inch) depression in the wheel

paths of the pavement.

54

The relationship between rutting failure and compressive strain at the top of the

subgrade is represented by the number of load applications as suggested by Asphalt

Institute (1982) in the following form:

Nr 477.49 )(10365.1 −−= cx ε (2.39)

Where,

Nf = Number of load repetitions to limit rutting

εc = Tensile Strain at the bottom of asphalt layer

Rutting criterion is based on limiting the vertical compressive subgrade strain, if the

maximum vertical compressive strain at the surface of the subgrade is less than a

critical value, then rutting will not occur for a specific number of traffic loadings.

Presented in Table 2.9 are permissible vertical compressive subgrade strains for

various number of load applications by some agencies, Figure 2.7 shows 5 criterion

for limiting vertical compressive subgrade strain (Claessen et al, 1977). The Shell

criterion (Shell Criterion, 1977) corresponds to an average terminal rut depth of

13mm, whereas the Monismith and McLean criterion [Monismith and Mclean, 1971]

is based on a terminal rut depth of 10mm.

Table 2.9: Limiting Vertical Compressive Strain in Subgrade Soils by Various Agencies (Source: Oguara, 2005)

Number of load Repetitions to

Failure Nf

(10-6)

Original Shell

Model

(10-6)

Kentucky

(10-6)

TRRL

(10-6)

Chevron Model

(10-6)

Revised Shell

Model

(10-6)

California

(10-6)

103 2700 790 3122 2400 4979 2700

104 1680 639 1639 1400 2800 1680

105 1050 502 860 800 1575 1050

106 650 364 451 500 885 650

107 420 227 237 300 498 420

108 260 89 124 170 280 260

55

2.8 Layered Elastic Analysis Programs

A number of computer programs based on layered elastic theory (Burmister, 1945)

have been developed for layered elastic analysis of highway pavements. The

program CHEVRON (Warren and Dieckman, 1963) developed by the Chevron

Research Company is based on linear elastic theory. The program can accept more

than 10 layers and up to 10 wheel loads. Huang and Witczak (1981) modified the

program to account for material non-linearity and named it DAMA. The DAMA

computer program can be used to analyze a multi-layered elastic pavement structure

under single or dual-wheel load, the number of layers cannot exceed five. In DAMA,

the subgrade and the asphalt layers are considered to be linearly elastic and the

untreated subbase to be non-linear, instead of using iterative method to determine

Figure 2.7: Rutting Criteria by Various Agencies (Source: Oguara, 2005)

56

the modulus of granular layer, the effect of stress dependency is included by

effective elastic modulus computed according to equation (2.39)

E2 = 10.447h1-0.471h2-0.041E1-0.139E3-0.287K10.868 (2.40) Where, E1, E2, E3 are the modulus of asphalt layer, granular base and subgrade

respectively; h1, h2 are the thicknesses of the asphalt layer and granular base. K1 and

K2 are parameters for K-θ model with k2 = 0.5

ELSYM5 developed at the University of California for the Federal Highway

Administration Washington, is a five layer linear elastic program for the

determination of stresses and strains in pavements (Ahlborn, 1972). The program can

Analyze a pavement structure containing up to five layers, 20 multiple wheel loads.

The KENLAYER computer program developed based on Burmister’s elastic layered

theory by Yang H. Huang at the University of Kentucky in 1985, incorporates the

solution for an elastic multiple-layered system under a circular load. KENLAYER

can be applied to layered system under single, dual, dual-tandem wheel loads with

each layer material properties being linearly elastic, non-linearly elastic or visco-

elastic. It can be used to compute the responses for maximum of 19 layers with an

output of 190 points.

The WESLEA program was developed by U.S. Army Corps of Engineers. The

current version can analyze more than 10 layers with more than 10 loads.

The EVERSTRESS (Sivaneswaran et al, 2001) layered elastic analysis program

developed by the Washington State Department of Transportation at the University

of Washington, was developed from WESLEA layered elastic analysis program. The

program can be used to determine the stresses, strains, and deflections in a layered

elastic system (semi-infinite) under circular surface loads. The program is able to

analyze up to five layers, 20 loads and 50 evaluation points. The program can

57

analyze hot mix asphalt (HMA) pavement structure containing up to five layers and

can consider the stress sensitive characteristics of unbound pavement materials. The

consideration of the stress sensitive characteristics of unbound materials can be

achieved through adjusting the layer moduli in an iterative manner by use of stress-

modulus relationships in equations 2.40 and 2.41

Eb = K1θK2 for granular soils ( 2.41)

Es = K3σdK4 for fine grained soils (2.42)

Where,

Eb = Resilient modulus of granualar soils (ksi or MPa)

Es = Resilient modulus of fine grained soils (ksi or MPa)

θ = Bulk stress (ksi or MPa)

σd = (Deviator stress (ksi or Mpa) and

K1, K2, K3, K4 = Regression constants

K1, and K2, are dependent on moisture content, which can change with the seasons.

K3, and K4 are related to the soil types, either coarse grained or fine-grained soil. K2

is positive and K4 is negative and remain relatively constant with the season.

The BISAR program was developed by the Shell Oil Company. The program was

developed based on linear elastic theory. BISAR 3.0 can be used to calculate

omprehensive stress and strain profiles, deflections, and slip between the pavement

layers via a shearspring compliance at the interface.

The proposed LEADFlex Program differed from the other layered elastic analysis

procedures in that while the other programs are capable of carrying out layered

elastic analysis to determine pavement stresses, strains and deflections using trial

pavement thickness as one of the inputs, the LEADFlex program is a comprehensive

58

program that is capable of computing pavement thickness and predict fatigue and

rutting strains in the asphalt pavement. In the final analysis, the program determines

adequate pavement thicknesses that will limit fatigue cracking of asphalt layer and

permanent deformation of subgrade, hence limit pavement failure.

2.9 Validation with Experimental Data

An appreciable amount of work has been performed to validate proposed models

with experimental data. Researchers Ullidtz and Zhang (2002) calculated

longitudinal and traverse strains at the bottom of asphalt, and vertical strains in the

subgrade using layered elastic theory, method of equivalent thickness, and finite

element methods. The authors assert various degrees of agreement between the

computed values and values from the Danish Road Testing Machine. They stated

that the critical factor is treating the subgrade as a non-linear elastic material.

Another study by Melhem and Sheffield (2000) carried out full instrumentation of

several pavement sections at three(3) stations at the South (SM-2A) and North (SM-

2A) lanes of the Kansas Accelerated Testing Laboratory (K-ATL). Tensile strains at

the bottom of the asphalt layer and compressive strains at the top of the subgrade

were calculated using ELSYM5 based on the multi-layer elastic theory while the

measured strains were determined using strain gauges. The relationship between

measured and calculated strains under FWD loading was compared using linear

regression analysis. The result indicated that coefficient of determination was very

good and concluded that the multilayer elastic theory for asphalt pavement is a good

estimator of pavement responses.

A significant study by Huang, et al. (2002) presented the results of various numerical

analyses performed with various structural models, both two and three dimensions

and considering both static and transient loading. Their calculated values were

compared to experimental values from the Louisiana Accelerated Loading Facility

59

(ALF) from three asphalt test values. The Authors concluded stress and strain

responses obtained with the three-dimensional finite element program ABAQUS

with rate-dependent viscoplastic models for the asphalt and elastoplastic models for

the other layers were close to experiment values.

Work done by the Virginia Tech Transportation Institute (Loulizi, et al., 2004)

compared measured pavement responses using layered linear elastic analysis subject

a single tire and one set of dual tires. The authors used several elastic layer programs

and two finite element approaches. They concluded that responses were

underestimated at high temperatures, but overestimated at low intermediate

temperatures. They recognized the need for more research considering dynamic

loading, layer bonding, and anisotropic material properties.

Pavement responses of horizontal tensile and vertical shear strains in the asphalt

layers were of interest in a study authored by Elseifi, et al. (2006). The field-

measured responses from the Virginia Smart Road were compared against finite

element predicted response incorporating a viscoelastic model using laboratory-

determined parameters. In addition, dimensions and vertical pressure measurements

of each tire tread were used in the simulation. The authors claim an average

predictions error of less than 15% between the calculated and field response values,

and concluded elastic models under-predict pavement response at intermediate and

high temperatures.