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Training on Sustainable Road Development 8 July – 9 August 2002

AN ENGINEERING MANUAL FOR

HIGHWAY PAVEMENT DESIGN YONGYUTH TAESIRI PORANIC JITAREEKUL Road and Pavement Design Branch Department of Highways, Bangkok, Thailand

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TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION 1

Typical Pavements in Thailand 1

CHAPTER 2: SUBGRADE EVALUATION 3

The California Bearing Ratio (CBR) 3

The Modulus of Subgrade Reaction (k) 6

Elastic Parameters 7

CHAPTER 3: PAVEMENT MATERIALS 9

Unbound Granular Material 9

Cemented Materials 10

Asphalt 11

Cement Concrete 12

Elastic Parameters 12

Typical Values of Modulus for Pavement Materials in Thailand 17

CHAPTER 4: THICKNESS DESIGN OF FLEXIBLE PAVEMENT I 19

The Asphalt Institute Method 19

Road Note 29 Method 27

CHAPTER 5: THICKNESS DESIGN OF FLEXIBLE PAVEMENT II 35

Stresses and strains in flexible pavement structure 35

Analysis of strains in flexible pavements 36

Odemark’s Method 40

Distress Prediction 41

Mechanistic Procedures 45

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CHAPTER 6: THICKNESS DESIGN OF RIGID PAVEMENT 47

The Portland Cement Association Method (PCA Method) 47

Road Note 29 Method 62

Details of Joints 64

Reinforcement Design Procedure 65

REFERENCES 67

APPENDIX: EXAMPLE PROBLEMS 69

Design CBR value 69

Flexible Pavement Design (Asphalt Institute (1970) Method) 70

Analytical Design of Flexible Pavement 73

Rigid Pavement Design (PCA Method) 75

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CHAPTER 1

INTRODUCTION Most natural soils are not strong enough to accept significant trafficking by commercial (heavy) vehicle such as trucks and heavy buses. A pavement is the means whereby the high loads and stresses generated under the wheels of vehicles are reduced to levels that are low enough to be accepted by the subgrade (natural soil) without distress. Where the pavement largely consists of materials such as crushed rocks or gravel which lack tensile strength the pavement is known as a flexible pavement. This is the most common type of pavement in Thailand. Where the pavement is made from cast-in-place portland cement concrete it is known as a rigid pavement Usually, the pavement is made up of a series of layers or courses of various materials one upon the other. The strength of each layer is greater than that of the layer below, and smaller than that of layer above. These layers of materials are referred to as a pavement structure. The pavement structure is designed based on the intensities of traffic produced by heavy vehicle and the strength of subgrade soil. Typical Pavements in Thailand The national highways under the responsibilities of Thailand Department of Highways have the total length of about 50,000 kilometers which all are paved. Approximately, 95 percent of these paved roads are Asphalt Pavements which use asphalt mixtures as a surface and the remainders are Portland Cement Concrete Pavements which use rigid concrete slab as the road surface. The typical cross sections of pavement structure constructed in Thailand are illustrated in Fig 1.1.

Surface CourseBinder Course

Base Course

Subbase Course

Selected Materials

Subgrade

Wearing Course

Pavement Structure

Figure 1.1 Structure of pavements in Thailand

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The definitions and functions of each layer in pavement structure are:

1. The wearing course. This layer lies directly under the vehicle wheels. By itself, it is a non-structural layer. That is it does not contribute to the strength of the pavement such as sprayed seal. The main functions of wearing course are to prevent skidding and wear.

2. The surface course. This course is the uppermost structural component of the

pavement and is constructed with a hot asphalt mixture. The main functions of the surface course are to provide resistance to wear and shearing stress due to traffic loads, to provide a smooth and non-skid surface with comfortable riding and to prevent rain water from permeating into the pavement. Material for surface course is generally dense-graded asphalt mixture. This course may also often acts as wearing course.

3. The binder course. The binder course is lied upon the base course to level its

irregularity, and to uniformly distribute the load transmitted from the surface course. It is normally made up of a hot mix asphalt.

4. The base course. This is the principal load-bearing layer in the pavement. It plays an

important role in distributing the traffic load safely to the subgrade. In Thailand, most common base materials are compacted crushed rocks or gravel. Cement-stabilized base materials are also used. Sometimes, the functions of wearing course, surface course, binder course and base may be combined in a single material such as Full-Depth asphalt and Rigid concrete base

5. The subbase course. This layer has the functions exactly the same as the base course

but is usually of weaker and cheaper material than the base material because of economic reason. The subbase materials are usually made of locally available economical materials.

6. The selected materials. This layer is generally present where the pavement is heavily

loaded or where the subgrade is very weak. It can also serve as a working platform on which the construction of the subbase can proceed. Typically it is made up of locally marginal materials such as soil aggregate. In Thailand, selected materials are divided into two types, namely: selected material “A” and selected material “B”.

7. The subgrade. This is the natural soil underlying the pavement. This soil refers to the

soil about one meter under the pavement. In embankment case, it is the part at depth of approximately one meter below the finished level of the embankment. In case of cut, the subgrade is the part one meter below the excavated surface. The subgrade also includes stabilized or treated soil that replaces unsuitable natural soil. The finished subgrade is referred to as the subgrade level.

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CHAPTER 2

SUBGRADE EVALUATION The support provided by the subgrade is the most important factor in determining pavement design thickness. The purpose of subgrade evaluation is to estimate a value of subgrade support to use in design. The measures of subgrade support described in this manual are:

• California Bearing Ratio • Modulus of Subgrade Reaction (k) • Elastic Parameters

The use of these measures for designing various pavement types is given in Table 2.1 Table 2.1. Use of subgrade support measures

Measure of subgrade support Pavement Type CBR k Elastic Parameters Flexible Pavement Rigid

X X

X

X

The California Bearing Ratio (CBR) In Thailand, the strength of the subgrade is commonly expressed as a CBR value (California Bearing Ratio). However, CBR is not a fundamental soil property but it is merely an arbitrary material ranking obtained using simple laboratory or in-situ tests. The CBR value is determined by sampling subgrade soils to design the thickness of the pavement. Determination of the design CBR value requires preliminary investigations, such as soil tests and CBR tests.

(1) Preliminary Investigation

Preliminary investigations include investigations of topography, geology, groundwater and surface conditions, conditions of cut and embankment, and literature investigations of the past geological surveys, as well as sampling tests of subgrade soils and fill material taken from borrow pits. When sample testing at borrow pits, an emphasis should be placed on the uniformity of the soils and their suitability as subgrade soils. For existing roads or cut subgrades, emphasis should be placed on the actual conditions of subgrade soils in the survey area and changes in properties after disturbance. These soil tests should be conducted as many times as possible prior to the sampling of the soil for the CBR test. The procedure for the sampling of soils for the soil test is as follow:

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1) Sampling of soils from borrow pits

Samples of fill material from the site of the intended borrow excavation are taken from various depths through auger boring. The samples should be immediately sealed in the container to prevent any change in their water content and sent to the laboratory for testing.

2) Samples from subgrade at cut sections

Samples of subgrade soil at cut sections are taken by auger boring from various depths more than one meter below the anticipated level of the subgrade, wherever soil conditions change. The samples are treated in the same way as soils from borrow pits.

(2) CBR test

CBR tests are conducted on the disturbed and re-compacted samples in the following order.

1) Sampling

When pavement is designed prior to the construction of the subgrade embankment, fill materials should be sampled during a dry season of the year. Samples of the fill material are taken in a disturbed condition from at least 50 cm below the exposed surface of the borrow pit and should be packed in container that can prevent any changes in moisture content and then sent to the laboratory for testing.

For cut sections, samples of disturbed subgrade soil are taken from at least 50 cm below the subgrade level. When the subgrade soil within a depth of one meter below the subgrade level varies in type or condition, sample for all soil strata should be taken and tested. For pavement constructed on existing gravel road, sampling of the subgrade soil is conducted in the same way as cut sections. Sample should be taken at the spacing of about 250 – 500 m along the alignment of the purposed route. There is no general rule for sampling spacing. Spacing can be increase or decrease depending on the soil condition. If the results of the preliminary investigations show a varieties of subgrade soils, closer sampling spacing are needed than in uniform subgrade soils.

2) Testing

After removing gravel with a diameter of 19 mm or bigger, soil test specimen should be prepared by being compacted into a mold in five layers, giving 12, 25 and 56 blows to each layer, in a state of optimum water content. The CBR value is measured after the compacted specimens have been immersed in water for four days. The details of CBR testing procedure are described in ASSHTO T-193.

3) Determining of the design CBR value

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3.1) Determining of CBR values for each location

If the results of preliminary investigations and CBR tests show a vertical non-homogeneity of the subgrade soils, the average CBR values of the soil within a one meter depth from the subgrade level should be taken as the CBR value of the location. The average CBR values are determined by the following formula:

33/1

nn3/1

223/1

11avg 100

CBRh...CBRhCBRhCBR

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +++= (2.1)

where, CBRavg = average CBR value of the specific location CBRi = CBR value of soil at depth number 1, 2, 3, …,n h1, h2,…, hn = Thickness of soil layers No. 1, 2, 3, …, n (cm.) h1+h2+…+hn = 100 cm.

Where the subgrade soil is stabilized, the effective depth of the treated soil is the total depth of treated soil minus 20 cm. For the bottom 20 cm of the treated soil, the CBR value is considered to be equals that of the natural soil. The maximum CBR value of a stabilized soil is limited to 20.

The average CBR value is normally adopted for subgrade of which the upper part has higher CBR value. It is useless to adopt the average CBR value if the weak layer presents on top of the stronger layer as the pavement structure is directly affected by the weak layer. In such case, the CBR value of weak layer should be adopted, or should be replaced by the better materials.

3.2) Determination of CBR for each section

Based on the preliminary investigations, the road should be divided into sections in which the subgrade soil is fairly uniform. In each section, the design CBR is determined statistically from all CBR values measured in that section. According to Asphalt Institute Manual (1970), the design CBR is defined as the CBR value that 90 percent of all test values in the section are equal to or greater than. This is determined in the following steps:

3.2.1. Arrange all test values in numerical order. 3.2.2. For each different test value, beginning with the lowest one, compute

the percentage of the total number of values that is equal to, or greater than that value.

3.2.3. Plot the results on cross section paper: abscissa = subgrade CBR value; ordinate = percent of subgrade CBR values equal to or greater than. Then, draw a smooth best-fit curve through the plotted points.

3.2.4. Read from the curve the subgrade CBR value at 90 percent. This is the Design CBR value.

Sometimes, a few tested CBR values are very high or very low as compared to other values. These odd values may be omitted in determining the design CBR

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values, depending on judgement. The statistic method can be used to judge whether the extreme values can be ignored. The method is as follow:

(a) Calculate γ which is defined as:

For checking extreme large maximum value,minmax

1maxmax

CBRCBRCBRCBR

−−

=γ − (2.2a)

For checking extreme small minimum value,minmax

min1min

CBRCBRCBRCBR

−−

=γ + (2.2b)

where, γ = a statistic indicator CBRmax = the highest CBR value among the tested values CBRmax-1 = the second highest CBR value CBRmin = the lowest CBR value CBRmin+1 = the second lowest CBR value

(b) From Table 2.2, check the γ value. If calculated γ is greater than the valued

given in the table, the extreme CBR value should be ignored, if not that CBR value should be included in determining design CBR.

Table 2.2 Value of γ used in determining whether to ignore extreme CBR

values Number of

Sample γ Number

of Sample γ Number

of Sample γ

3 4 5 6 7 8

0.941 0.765 0.642 0.560 0.507 0.468

9 10 11 12 13 14

0.437 0.412 0.392 0.376 0.361 0.349

15 16 17 18 19 20

0.338 0.329 0.320 0.313 0.306 0.300

It should be noted that if the result indicates that the extreme CBR should be neglected, it does not mean that that value is wrong but it is just merely not statistically significant.

The Modulus of Subgrade Reaction (k) The modulus of subgrade reaction is used as an input in rigid pavement design. It can be used to evaluate the supporting power of subgrade, sub-base and base and can be determined in-situ from a plate loading test. The method is standardized in ASSHTO T-235. In summary, a loaded is applied on a circular plate of 30 inches (762 mm) in diameter. To avoid bending, a series of stacked plate, increasing in diameter from top to bottom, are used. Deflection of the plate due to loading are measured by three dial gauges located at the outside edge about 120° apart. The load is applied at a constant rate until a pressure of 10 psi (69 kPa) is reached. The pressure is kept constant until the deflection increases not more than 0.001 inch (0.025 mm) per minutes. The average of the three dial readings is adopted to determine the deflection. The modulus of subgrade reaction is defined as:

Δ

=pk (2.3)

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where, p = pressure applied by the plate (10 psi) Δ = deflection of plate in inches. Because the k value is determined from the field, the moisture content and densities can not be controlled to simulate the worst condition expected during the design life. The k value can be adjusted to the value corresponding to the condition other than those during the field test. Laboratory specimens can be produced, one having the moisture contents and densities similar to those in the field, the other having a different moisture content and densities to simulate the desired condition. The specimens are then subjected to a creep consolidation test under a pressure of 10 psi (69 kPa), and deformation d at various times are recorded until the increase in deformation becomes negligibly small. The adjusted k value is calculated by:

freq

fadj k

dd

k = (2.4)

where, kf = k value measured from the specimen prepared at the field condition

df = deflection measured from the specimen prepared at the field condition dreq = deflection measured from the specimen prepared at the required

condition. The plate loading test is time-consuming and expensive. Usually k value is estimated by correlation to simpler tests such as CBR. Fig 2.1 shows the approximate relationship between k value and other soil properties. It should be aware that the modulus of subgrade reaction (k) is not the elastic modulus of the subgrade (E). The k value is the magnitude of pressure that causes a unit deformation to soil while E value is the ratio between stress and strain of the material. Elastic Parameters In analytical design approach (discussed in Chapter 6), the subgrade materials are usually assumed to be elastic and isotropic. The elastic parameters required in the analysis include Elastic Modulus (E) and Poisson’s Ratio (ν). The elastic modulus of the subgrade can be determined from laboratory testing condition as described in ASSHTO T-292 or can be determined from the field by non-destructive testing method such as Falling Weight Deflectometer (FWD). However, the modulus of subgrade materials is often approximated from the CBR value using empirical relationships purposed by various researchers, for example:

Shell E (MPa) = 10 × CBR (%) (2.5a) Poulsen & Stubstad (1980) E (MPa) = 10 × [CBR (%)]0.73 (2.5b) Powell et al (1984) E (MPa) = 17.6 × [CBR (%)]0.64 (2.5c)

The Shell’s relationship is most widely used. The modulus estimated by these equations have been found to vary in the range of 5CBR to 20CBR (Sparks and Potter, 1992) Poisson’s ratios for subgrade are usually assumed to be 0.45 for cohesive soil and 0.35 for cohesionless materials.

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Note: 1 psi = 69 kPa, 1 pci = 271.3 kN/m3) Figure 2.1. Approximate interrelationships of soil classifications and bearing values (After

PCA, 1984)

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CHAPTER 3

PAVEMENT MATERIALS Typically, materials used in pavement construction in Thailand can be classified into four main categories. They are:

(a) Unbound Granular Material (b) Cemented Materials (c) Asphalt (d) Cement Concrete

The choice of materials for any particular application is based on considerations of structural requirements, economics, durability and construction conveniences. Requirements of the materials which are widely employed for road construction in Thailand are presented in this Chapter. Unbound Granular Material Granular materials consist of crushed rocks or gravels which have a grading that make them mechanically stable, workable and able to be compacted. In flexible pavement construction, granular materials are used for base, subbase and selected materials.

Base and Subbase Materials According to Thailand Department of Highways standard, the materials to be used as base and subbase materials should have the properties conforming to the values listed in Table 3.1.

Table 3.1 Requirements of Unbound Base and Subbase Materials Requirements Properties Standard Base Course Subbase Course

Los Angeles Abrasion Soundness Liquid Limit Plastic Index CBR*

ASTM C131 AASHTO T-104 AASHTO T-89 AASHTO T-90 AASHTO T - 193

≤ 40 % ≤ 9 % ≤ 25 % ≤ 6 % ≥ 80 %

≤ 60 % not specified ≤ 35 % ≤ 6 % ≥ 25 %

* Test at the density of not less than 95 % of modified maximum dry density The allowed gradations of base and subbase materials are listed in Table 3.2. For base materials, materials must fall into gradation A or B only

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Table 3.2 Gradations for Base and Subbase % Passing (by weight) Sieve Size (mm) A* B* C D E

50 25 9.5 2.00 0.425 0.075

100 - 30-65 15-40 8-20 2-8

100 - 40-75 20-45 15-30 5-20

- 100 50-85 25-50 15-30 5-15

- 100 60-100 40-70 25-45 5-20

- 100 - 40-100 20-50 6-20

* Base Materials

Selected Materials Requirements of the selected materials are given in Table 3.3. Table 3.3. Quality requirements for selected materials

Requirements Properties Standard Selected Material

“A” Selected Material

“B” Maximum Size Passing Sieve No. 200 Liquid Limit Plastic Index CBR* Swelling Durability Index (for Shale)

AASHTO T-27 AASHTO T-27 AASHTO T-89 AASHTO T-90 AASHTO T-193 AASHTO T-193 ASSHTO T-210

50 mm ≤ 30 % ≤ 40 % ≤ 20 % ≥ 10 % ≤ 3 % ≤ 30 %

50 mm ≤ 35 %

not specified not specified

≥ 6 % ≤ 3 %

not specified * Test at the density of not less than 95 % of modified maximum dry density Cemented Materials Cemented materials are those produced by additions of cement, lime or other hydraulically binding agent to granular materials in sufficient quantities to produce a bound layer with significant tensile strength. When base or subbase materials conforming to the values listed in Table 3.1 and 3.2 are not locally available, soil can be stabilized by cement and used as the base or subbase materials. In such cases the stabilized soil should satisfy the requirements listed in Table 3.4. Table 3.4. Quality requirements for soil cement base/subbase

Materials % Passing Sieve No.

200

Maximum Size

LL (%)

PI (%)

Target Unconfined

Compressive Strength* (7 days)

Soil Cement Base Soil Cement Subbase

< 25 % < 40 %

< 50 mm < 50 mm

< 40 < 40

<15 < 20

1750 kPa 689 kPa

* Samples are compacted according to modified compaction standard.

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Asphalt Asphalt can be described as a combination of bitumen and aggregates which are mixed together, spread and compacted while hot, to form a pavement surface. The strength of asphalt is derived from friction between the aggregate particles, the viscosity of the bitumen under operating conditions and the cohesion within the mass resulting from the bitumen itself and the adhesion between the bitumen and aggregate. Typical standard proportions of asphalt mixtures used in Thailand are given in Table 3.5. Table 3.5 Standard proportion of mixture Type of Mixture Surface course Surface course Binder Course Thickness (mm) 25 – 35 40 - 70 40 – 80 Nominal size (mm) 9.5 12.5 19.0 Sieve size (mm) % Passing by weight

37.5 25.0 19.0 12.5 9.5 4.75 2.36 1.18 0.600 0.300 0.150 0.075

- - - 100 90-100 55-85 32-67 - - 7-23 - 2-10

- - 100 80-100 - 44-74 28-58 - - 5-21 - 2-10

- 100 90-100 - 56-80 35-65 23-49 - - 5-19 - 2-8

Asphalt content (% by weight) 4.0 – 8.0 3.0 – 7.0 3.0 – 6.5 Asphalt Penetration 60-70 The mix design of the asphalt mixture is determined by the Marshall test. The Marshall design standards is given in Table 3.6. Table 3.6. Marshall design standards Type of Mixture Surface Course Surface Course Binder Course Nominal Size (mm) 9.5 12.5 19.0 Number of Blows 75 75 75

N 8006 8006 8006 Stability lb 1800 1800 1800

Flow 0.25 mm (1 inch) 8-16 8-16 8-16 Percentage of air void (%) 3-5 3-5 3-5 Percentage of Void in Mineral Aggregate (%)

15 14 13

N/0.25mm 712 712 712 Stability/Flow (min.) lb/0.01in. 160 160 160

Percent strength Index (min.) 75 75 75

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Cement Concrete Cement concrete is referred to as a homogeneous mixture of cement, fine and coarse aggregate, water and chemical admixtures. The cementitious portion of concrete is generally Portland cement concrete. In Thailand, concrete is used as a base in rigid pavement. The Thailand Department of Highways standard required a 28-day characteristic compressive strength of not less than 32.5 MPa. However, the 28-day concrete flextural strength is a principal design factor. The suitable values for road pavement construction is typically 3.0 – 5.0 MPa. A typical relationships for converting 28-day compressive strength to 28-day flextural strength for concrete with crushed aggregate is:

ccf f75.0f = (3.1) where, fc = 28-day concrete compressive strength (MPa) fcf = 28-day concrete flextural strength (MPa) Elastic Parameters If the analytical design method (discussed in Chapter 6) is to be used for designing flexible pavement, pavement materials have to be characterized based on their mechanical properties. In theoretical pavement analysis, the elastic model has been commonly used to calculate stresses, strains and deflections in pavement structure. For the sake of employing the elastic theory in the analysis, the elastic parameters for each layer must be assigned as the input data. Two materials parameters are need in the theory, namely: the coefficient of elasticity or commonly known as Young’s modulus (E) and Poisson’s ratio (ν).

Asphalt Concrete In reality asphalt concrete is visco-elastic in nature due to the bitumen in the mixture. However, at the normal operate rates and magnitude of loading and temperature, asphalt may be considered as an elastic isotropic material. The modulus and Poisson’s ratio of asphalt are affected by many factors, such as:

- Proportion of coarse angular particle in the mix - Density - Age - Efficiency of mixing - Bitumen content - Bitumen class - Bitumen viscosity - Percentage of air void in the mix - Rate of loading, and - Temperature

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Of which, the most important factor in determining the modulus of asphalt is temperature. The temperature environment of asphalt must be taken into account during pavement analysis and design. Because of the many factors which may affect the result, the modulus of asphalt used in the design should be determined by testing sample of proposed mix under condition of temperature and loading similar to those expected in the field. The laboratory methods for the determination of modulus and Poison’s ratio include Flextural Testing, Indirect Tensile Test or Direct Compression Testing. The test specimens are subjected to the cyclic load, the stresses and strains induced by each load application are recorded for modulus calculation. When suitable laboratory testing facilities are not available the nomographs published by Shell (1978) can be used to obtain reasonable estimate of modulus. However, they cannot be used to select values of Poisson’s ratio. This nomograph shown in Fig 3.1 is developed by Van der Poel and can be used to estimate the modulus (stiffness) of the bitumen at the required temperature and loading rate. Once the Van der Poel nomograph has been used to estimate the modulus of bitumen, the nomograph developed by Bonnaure et al is used to estimate the modulus of asphalt the asphalt mix. This nomograph is shown in Fig 3.2. The average modulus of asphalt which have been obtained by laboratory testing of typical asphalt mix used in Thailand are shown in Fig 3.3.

2000400060008000

100001200014000

10 20 30 40 50

Temperature (Degree celsius)

Res

ilien

t Mod

ulus

(MPa

)

Figure 3.3 Average modulus of typical asphalt concrete mix in Thailand vs temperature

(Adapted from Silarom, 2001)

Granular Materials The elastic parameters of granular materials are generally measured in a triaxial cell under condition of repetitive loading by an apparatus called repeated load triaxial cell. The recoverable portion of the axial deformation response is used in determining the modulus. In the field, the modulus of pavement materials can also be determined from a back calculation of measured bowls of deflection produced by Falling Weight Deflectometer. AUSTROADS (1992) gives the elastic parameters of various granular materials used in pavement construction in Australia as shown in Table 3.7. However, the researches indicate that modulus of granular materials is dependent to stress level, moisture and density conditions. The published data should be adopted with caution.

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Figure 3.1. Nomograph for determining the modulus of bitumens

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Figure 3.2. Nomograph for predicting the modulus of asphalt mixes

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Table 3.7 Elastic parameters of granular materials (After AUSTROADS, 1992) High Quality Crushed Rock

Base Quality Crushed Rock

Sub-Base Gravel

Property Over Granular Material

Over Stiff Cemented Material

Over Granular Material

Over Stiff Cemented Material

Over Granular Material

Over Stiff Cemented Material

Range of E (MPa) Typical E (MPa) Range of ν Typical ν

150 – 550

500* 350

0.25 – 0.40

0.35

200 – 700

500* 350

0.25 – 0.40

0.35

150 – 500

400* 300

0.25 – 0.40

0.35

200 – 500

400* 300

0.25 – 0.40

0.35

150 – 400

300* 250

0.25 – 0.40

0.35

150 – 450

300* 250

0.25 – 0.40

0.35

* Where material is compacted using Modified Compaction, other value for Standard Compaction.

Cemented Materials Cemented materials are commonly regarded as linear elastic and isotropic. The modulus is assumed to be uniform. The Poisson’s ratio may be shown to have relatively little influence on pavement thickness and can be assumed to be 0.20 (AUSTROAD, 1992) The modulus of cemented materials can be measured by third point loading of flexture beam specimens. This method is favored as the test conditions are considered to simulate the stress/strain magnitude occurred in a pavement layer. Alternatively, direction tension testing may be employed, with the modulus determined from the linear portion of the stress – strain plot. The back calculation from deflection bowls generated by Falling Weight Deflectometer is also a practical method to obtain the modulus of cemented materials in the field. Modulus of cemented materials can be related to a simpler parameter such as Unconfined Compressive Strength (UCS) of the materials. Relationships have been developed. Some of them are:

2

10000)MPa(E46.4)MPa(UCS ⎟

⎠

⎞⎜⎝

⎛= (ASSHTO) (3.2a)

3500)]MPa(UCS[1814)MPa(E 88.0 += for cemented crushed rock (3.2b) 1100)]MPa(UCS[2240)MPa(E 88.0 += for cemented natural gravel (3.2c)

(Queensland Main Road, 1982) If reliable information is not available, published values should be consulted. AUSTROADS (1992) suggested the elastic parameters of cemented materials as listed in Table 3.8. It should be noted that since the modulus of cemented materials are dependent on a number of factors, such as additive content and densities, the published values should be used with caution.

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Table 3.8. Elastic parameters of cemented materials (After AUSTROADS, 1992)

Property Crushed Rock 2-3 % Cement

Base Quality Natural Gravel 4–5% Cement

Subbase Quality Natural Gravel 4-5% Cement

Range of E (MPa) Typical E (MPa) Range of ν Typical ν

3000 – 8000 5000

0.1 – 0.3 0.2

3000 – 7000 5000

0.1 – 0.3 0.2

1500 – 3000 2000

0.1 – 0.3 0.2

Typical Values of Modulus for Pavement Materials in Thailand Average values for some typical pavement materials used in Thailand can be assumed from Table 3.9. These values are from the laboratory test and back calculation of Falling Weight Deflectometer test carried out on various existing highways. Table 3.9 Average values for some typical pavement materials used in Thailand (After

Thailand Department of Highways, 2001)

Pavement Materials Asphalt Grade/ Cement Content

Elastic Modulus at 35°C MPa

Asphalt Materials Surface Treatment Cold Mixed Asphalt Asphalt Concrete AC surfacing on stabilized based layers Unbound Granular Base Crushed rock base Steel slag Crushed gravel base Natural gravel base Cement-modified base Mod. Crushed rock Mod. Gravel Stabilized soil cement Stabilized laterite Subbase Materials Sand Clay

AC 60/70 or 80/100

Cutback RC 3000 or 800 Asphalt Emulsion AC 25/35 or 40/70

2 % 2 % 4 %

0 0 0

3000 2000

250 – 650 300 – 400 150 – 500 120 – 300

200 – 400 150 – 300 100 – 400 300 – 600

100 – 150 10 × CBR(%)

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CHAPTER 4

THICKNESS DESIGN OF FLEXIBLE PAVEMENTS I

EMPIRICAL METHODS Methods for the design of flexible pavements may be classified into two categories, namely empirical method and analytical or mechanistic method. The empirical method is based on past experience and may include laboratory or field tests of the subgrade and pavement materials. These tests are generally for classification of the materials and also give quantitative information about their mechanical properties. Empirical methods of pavement design have played an important role in determining the thickness of pavement structure for many years. The major advantage of the empirical method is that the design procedure is relatively easy and fast to perform. Furthermore, the parameters used in the design by empirical approaches are usually not complicated to determine such as CBR for example. The Thailand Department of Highways has employed the empirical design method for more than three decades. Empirical methods are satisfactory so long as the materials and conditions of loading for which they were developed do not change. However, traffic volumes and loadings have tended to increase significantly in recent years. In addition, the new materials, such as soil cement, may not be allowed as they were not recognized in the design manual. The extension of design manual to cater new loads and new materials may be accomplished only by the extensive of field observation data from the full-scale experimental roads. On contrary, the analytical methods do not suffer from above handicaps. An introduction to analytical design method will be described in the next Chapter. This Chapter presents a couple of empirical design methods: The Asphalt Institute (1970) Method and the TRRL’s Road Note 29 method. The Asphalt Institute Method This method has been employed as a design procedure of pavement structure in Thailand for more than 30 years. The procedure is empirical in nature and relatively easy to perform. The soil parameter used in thickness design is a CBR while the traffic parameter is given in the Design Traffic Number. The thickness – to – traffic relationship were developed based on analyses of data from the ASSHO road test, the WASHO road test, British road test, and the experiences of highway agencies and other sources. The pavement structure recommended by Asphalt Institute’ Manual is in the form of Full-Depth Asphalt. A Full-Depth asphalt pavement is an asphalt pavement in which asphalt-aggregate mixtures are employed for all courses above the subgrade or improved subgrade. A Full-Depth asphalt pavement is laid directly on the prepared subgrade. According to Asphalt Institute manual, the mathematical symbol, TA, denote Full-Depth or Total Asphalt. Although Asphalt Institute recommended the use of Full – Depth asphalt structure, the asphalt thickness can be reduced by the substitution of other granular layers. The properties of these

20

materials and method to transform the asphalt thickness to the thickness of granular layers are also given in the design manual. Some important parts of the flexible pavement design procedure published in Asphalt Institute (1970) design manual are cited as follow.

Traffic Analysis Traffic on highways varies both in number of vehicles and in the magnitude of loading. Pavement is usually subjected to a range of traffic loadings, and each magnitude of load produces its own level of damage to the pavement. The method recommended in Asphalt Institute manual (1970) converts the number of loads of different magnitude to an equivalent number of loads of a standard magnitude, equivalent in the sense that they will cause the same amount of pavement damage. The Asphalt Institute has defined the term of Design Traffic Number (DTN) as the common factor in the design. The determination of this factor will be discussed later. Some special terms employed in Asphalt Institute method in relation to traffic analysis are:

1. Design Lane; the lane on which the greatest number of equivalent 18,000-pound single-axle loads is expected. Normally, this will be either lane of a two-lane roadway or the outside lane of multi-lane highways.

2. Design Period; the number of years from the initial application of traffic until the first major resurfacing or overlay is anticipated. This term should not be confused with pavement life. By adding asphalt overlay is required, pavement life may be extended indefinitely, or until geometric considerations or other factors may make the pavement obsolete.

3. Design Traffic Number (DTN); the average daily number of equivalent 18,000-pound single-axle loads estimated for the design lane during the design period.

4. Initial Daily Traffic (IDT); the average daily number of vehicles expected to used the roadway, in both directions, during the first year.

5. Equivalent 18,000-pound Single-Axle Load; the effect on pavement performance of any combination of axle loads of varying magnitude, equated to the number of 18,000-pound (8 tons or 80 kN) single-axle loads required to produce an equivalent effect.

6. Traffic Classification; Light: Traffic conditions resulting in a Design Traffic Number less than ten (DTN < 10) Medium: Traffic condition resulting in 10 < DTN < 100 Heavy: Traffic condition resulting in DTN > 100

Determination of Design Traffic Number (DTN)

1. Estimate the average daily number of vehicles expected during the first year following the opening of the completed roadway to traffic. This is called Initial Daily Traffic (IDT). Estimating the initial and future traffic volumes and loading may be obtained from the traffic survey data that has been collected for some period of times.

2. Estimate the percent heavy truck, A, in the traffic stream from traffic count and classification data. However, when such data are lacking, estimates may be made from in formation given in Table 4.1.

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Table 4.1 Estimated Ranges in percent heavy trucks in the United States Description of Highway Percent Heavy Truck*

City Street (Local) Urban Highways Primary Interstate Local Rural Roads Interurban Highways Primary Interstate

5 % or less

5% - 15% 5% - 10%

15 % or less

5 % – 20 % 10 % - 25 %

* These values are from the United States condition. Other countries may require further considerations.

It should be noted that the heavy trucks defined herein are heavy commercial vehicles (buses or trucks), normally 2-axle 6-tire vehicles or larger.

3. Determine the percent heavy trucks, B, in the design lane. This may be estimated from Table 4.2. Normally most truck operates in the outermost traffic lanes, and may be considered equally divided in both directions. There are exceptions to this, however, for special circumstances where heavy truck-haul traffic will be in one direction, such as mining area, with empty trucks using the return lanes. On multilane highways, most of the heavy trucks usually are in outside lanes.

Table 4.2 Percentage of total truck traffic in design lane (After AI, 1970)

Number of Traffic Lanes (Two Directions)

Percentage of Trucks in Design lane

2 4

6 or more

50 45 (35 – 48) 40 (25 – 48)

4. Estimate the average daily number of heavy trucks expected on the design lane (one

direction only) as follows:

Number of heavy trucks = 100

B100

A)IDT( ×× (4.1)

where IDT, A and B are as described in previous steps above.

5. Estimate the average gross weight of the heavy trucks from weight study data. The standard weights of trucks in Thailand are 21 tons for 3-axle 10-tire vehicles (Heavy trucks) and 12 tons for 2-axle 6-tire vehicles (Medium Trucks and Heavy Busses).

6. Determine the design standard axle load. In Thailand, the design standard axle load equal to the legal single-axle load limit (8.2 tons or 18,000 pound)

7. With the above information, establish the Initial Traffic Number (ITN) using the Traffic Analysis Chart as shown in Fig 4.1. This chart is based on following formula:

)Nlog(05.1)Wlog(33.1)Slog(40.368.10)ITNlog( +++−= (4.2)

where, S = single-axle load limit (1000 lbs) W = weight of heavy vehicles (lbs) N = number of heavy vehicles

22

Figure 4.1 Traffic analysis chart

23

8. When the resultant ITN is 10 or less, and when a relatively large number of

automobiles and light trucks are expected to use the roadway, a correction of ITN is required. The correction is made by the use of Fig 4.2.

Figure 4.2 Chart for adjusting Initial Traffic Number (ITN) for daily volume of

automobiles and light trucks 9. Establish the Design Period. For new construction, the Design Period normally will be

15 – 20 years. 10. Estimate the Annual Growth Rate of traffic from the traffic survey data. 11. For the selected Design Period and Annual Growth Rate, select the Initial Traffic

Number (ITN) adjustment Factor from Table 4.3.

Table 4.3 Initial Traffic Number (ITN) Adjustment Factors* (After AI, 1970) Annual Growth Rate, %, (r)

Design Period,

Years, (n) 2 4 6 8 10 2 3 4 6 8 10 12 14 16 18 20 25 30 35

0.05 0.10 0.21 0.32 0.43 0.55 0.67 0.80 0.93 1.07 1.21 1.60 2.03 2.50

0.05 0.10 0.21 0.33 0.46 0.60 0.75 0.92 1.09 1.28 1.49 2.08 2.80 3.68

0.05 0.10 0.22 0.35 0.50 0.66 0.84 1.05 1.28 1.55 1.84 2.74 3.95 5.57

0.05 0.10 0.22 0.37 0.53 0.72 0.95 1.21 1.52 1.87 2.29 3.66 5.66 8.62

0.05 0.10 0.23 0.39 0.57 0.80 1.07 1.40 1.80 2.28 2.86 4.92 8.22 13.55

* Factor = r20

1)r1( n −+

24

12. Multiply the ITN (step 7 or 8) by the Adjustment Factor (step 11 above) to obtain DTN20 for use in the Thickness Design Charts.

Thickness Design of Pavement Structure The total thickness of hot mix asphalt concrete pavement structure, TA, required for given traffic and subgrade conditions can be determined from the Thickness Design Chart in Fig 4.3. The parameters used in design are DTN and subgrade CBR. The Design Chart is based on following formula:

4.0A

CBR)DTNlog(97.319.9T +

= (4.3)

Thickness Design Chart is based on a 20-year design period. For a Design Period of less, or more, than 20 years, an adjustment must be made to reflect the fewer, or additional, equivalent 18,000-pound single-axle loads. This adjustment is made by multiplying the ITN by the proper factor from Table 4.3. The ITN obtained, then, is the average daily number of equivalent 18,000-pound single-axle load applications for the selected Design Period adjusted to an equivalent DTN for a 20-year Design Period. The design CBR value is determined as described in Chapter 2. Moreover, the following minimum thicknesses of total asphalt pavement structure, TA, are recommended as given in Table 4.4. Table 4.4: Minimum TA

Design Traffic Number (DTN) Minimum TA, Inches Less than 10 10 – 100 100 – 1000 More than 1000

4 5 6 7

* 1 inch = 25.4 mm.

25

Figure 4.3 Thickness design chart

26

The used of Untreated Granular Bases The thickness, TA, of asphalt layer obtained from the Thickness Design Chart is the Full-Depth asphalt. That is the whole pavement structure consists of only a thick asphalt layer placed on top of subgrade. However, as the asphalt is quite expensive, therefore, in order to reduce the construction expense, Asphalt Institute allows the use of untreated granular materials to replace a portion of the Full-Depth asphalt layer. The principle is to convert thickness of asphalt into thicknesses of granular materials which can equally spread the wheel load onto the subgrade. The Asphalt Institute recommended the use of a Substitution ratio (Sr) for making an approximate thickness conversion from asphalt layer to untreated granular base. It is recommended that:

1. 2.0 units thickness of high-quality untreated granular base material be required for each 1.0 unit thickness of asphalt layer for which it may be substitute. In this case, Sr = 2.0.

2. 2.7 units thickness of low-quality untreated base material be required for each 1.0 unit thickness of asphalt layer for which it may be substituted. In this case, Sr = 2.7.

High-quality and low-quality untreated base materials are prescribed in Table 4.5: Table 4.5 High-quality and Low-quality untreated base materials (After AI, 1970)

Test Requirements Test Low-quality High-quality CBR, minimum or R-value, minimum Liquid Limit, maximum Plasticity Index, maximum Sand Equivalent, minimum Passing No. 200 sieve, maximum

20 55 25 6 25 12

100 80 25 NP 50 7

Thailand Department of Highways, based on its experience, adapts the Asphalt Institute suggestions in the design of pavement structures. The Sr values for various granular materials currently employed by the Department are summarized in Table 4.6. Table 4.6 Substitution Ratio for various untreated granular materials used by Thailand

Department of Highways Materials Substitution Ratio (Sr)

Crushed Rock Base (CBR ≥ 80 %) Aggregate Subbase (CBR ≥ 25 %) Selected Material “A” (CBR ≥ 10 %) Selected Material “B” (CBR ≥ 6 %)

2.0 2.7 3.0 3.5

Minimum Thickness of Asphalt Pavement Layer Only a limited portion of a Full-Depth asphalt pavement is allowed to be converted to untreated granular base. The maximum thickness that may be converted depended on the minimum thickness of asphalt pavement layer required above it to support the anticipated traffic. The chart in Fig 4.4 may be used as a guide for establishing this minimum thickness.

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The chart takes into consideration the amount and weight of traffic loadings, expressed as DTN, and the strength properties of untreated granular base.

Figure 4.4 Minimum thickness of asphalt pavement layers over untreated granular bases Road Note 29 Method In 1970, The Road Research Laboratory (TRRL) in Britain published a design manual for new pavement construction called “Road Note 29”. The design method contained in the manual is of CBR – type. The thickness of the subbase is related to the CBR – value of the subgrade and to the total number of standard axle loads. The thicknesses of the other layers are related to the quality of the materials in the pavement itself as well as to the traffic loading by a series of curves. The design charts and tables contained in Road Note 29 are derived from the results of the TRRL’s many full-scale road tests under British conditions of climate, materials, traffic loading etc. The flexible pavement design method described in Road Note 29 is summarized as follow:

Traffic Analysis For the purpose of structural design, the loads imposed by private cars do not contribute significantly to the structural damage caused to road pavements by traffic. Therefore, only the number of commercial vehicles and their axle-loadings are considered. Normally, the heavy commercial vehicles operate on the outermost lane (the slow lane). Hence, the procedure provides designs applicable to this lane. These designs will be used over the whole carriageway width. The traffic information will be available from traffic survey data from which the traffic at time of construction can be estimated and expressed in terms of number of commercial vehicles per day in each direction and the annual growth rate.

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For various initial intensities of commercial traffic, Fig 4.5 gives the cumulative number of commercial vehicles carried by each slow lane for design lives up to 40 years. Fig 4.5 (a), (b), (c) and (d) are for annual growth rates of 3, 4, 5 and 6 percent respectively. (a) Growth rate 3% (b) Growth rate 4% (c) Growth rate 5 % (d) Growth rate 6 % Figure 4.5. Relations between cumulative number of commercial vehicles carried by design

lane and design life

29

If the initial traffic intensities are greater than 2500 commercial vehicles per day in each direction (the maximum shown in Fig 4.5), the cumulative number of commercial vehicles carried by the design lane can be estimated by extrapolation from the given curves. However, if the traffic data lead to the cumulative total of more than 90 million commercial vehicles to be carried by the design lane during the design period, a value of 90 millions should be adopted because the road is likely to be saturated. The number of commercial vehicles carried by the design lane is then converted to a number of axles. The average number of axles per commercial vehicle varies with the type of road as shown in Table 4.7. The number of commercial axles has to be expressed as equivalent number of 18,000-pound axles (standard axle). Table 4.7 also gives the number of standard axles per commercial axle and the factor that must be applied to the cumulative number of commercial vehicles on the design lane to derive the cumulative number of standard axles for use in the design. Table 4.7 Conversion factors to be used to obtain the equivalent number of standard axles

from the number of commercial vehicles.

Type of Road

Number of axles per

commercial vehicle,

(a)

Number of standard axles per

commercial axle, (b)

Number of standard axles per

commercial vehicle, (a) × (b)

Motorways and trunk roads designed to carry over 1000 commercial vehicles per day in each direction at time of construction

2.7

0.4

1.08 Roads designed to carry between 250 and 1000 commercial vehicles per day in each direction at time of construction

2.4

0.3

0.72 All other public roads 2.25 0.2 0.45

Thickness Design of Pavement Structure Road Note 29 presented the charts for determining the minimum thickness of various layers of pavement structure as shown in Fig 4.6 – Fig 4.8. The main factors used in the design are the cumulative number of standard axles, subgrade CBR and type of materials employed. After determining the traffic and design period, the subgrade, the subbase, the base and the surface are each considered in turn. Subgrade The strength of the subgrade is a principal factor in determining the thickness of the pavement. The strength of the subgrade is assessed on the CBR scale. CBR determination is described in Chapter 2. Road Note 29 recommended that the water table should be prevented from rising to within 600 mm of the finished subgrade level. This may be done by sub-soil drainage or by raising the finished subgrade level by means of an embankment.

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Subbase The required thickness of subbase is determined from the cumulative number of standard axles to be carried and the CBR of the subgrade using Fig 4.6. In the case that CBR of the subgrade is less than 2 percent (the lowest value given in Fig 4.6), an additional 150 mm of subbase, above the requirement for CBR 2 percent, should be used. For cumulative traffic of less than 0.5 million standard axles, the minimum CBR of the subbase should be 20 percent. For cumulative traffic in excess of 0.5 million standard axles, the minimum CBR of the subbase should be 30 percent. For stabilized subbase, it can be assumed the CBR of 30 percent. If the CBR of the subgrade is in excess of the minimum requirement for the subbase, no subbase is required. Where subbase is required the minimum thickness that should be laid are 80 mm where the cumulative traffic is less than 0.5 million standard axles and 150 mm where the traffic is in excess of that value. Base Road Note 29 suggested the base materials as summarized in Table 4.8 below. Table 4.8. Base materials as recommended by Road Note 29

Base Materials Type of Road Road designed to carry less than 2.5 million standard axles

Crushed Rock

Road designed to carry between 2.5 million to 11 million standard axles

Soil Cement

Road designed to carry in excess of 11 million standard axles

Lean Concrete, Wet-mix or dry Bound Macadam Base

The thicknesses required for each of the base materials are determined by the use of Fig 4.7 or Fig 4.8, in terms of cumulative number of standard axles to be carried. To use the charts, it should be noticed the difference in English and American terminology. “Roadbase” would be “Base course” in American and “Basecourse” would be “Binder course”. Surfacing Course The thickness of surfacing in terms of the cumulative number of standard axles to be carried can be determined by Fig 4.7 and Fig 4.8 depending on the type of base material used. Road Note 29 recommended the surfacing course material to be varied with the cumulative traffic to be carried and the details are given in Table 4.9. The surfacing is intended to be laid in two courses, except where the cumulative traffic is less than 0.5 million standard axles. The thicknesses of surfacing course are indicated in Table 4.9. For cumulative traffic of over 11 million standard axles the minimum thickness of surface course plus binder course is 100 mm. For additional surfacing thickness over 100 mm shown in Fig 4.7 and Fig 4.8

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Table 4.9. Bituminous surfacing materials as recommended by Road Note 29 Traffic

Over 11 millions 2.5 – 11 millions 0.5 – 2.5 millions Less than 0.5 million Surface course Minimum Thickness 40 mm Rolled asphalt (BS 594) Binder course Minimum thickness 60 mm Rolled asphalt (BS 594) Dense bitumen macadam or dense tarmacadam

Binder course Rolled asphalt (BS 594) Dense bitumen macadam or dense tarmacadam

Surface course Minimum thickness 20 mm Rolled asphalt (BS 594) Dense tar (BTIA) Cold asphalt (BS 1690) Medium textured tarmacadum (BS 802) Dense bitumen macadam (BS 1621) Open textured bitumen macadam (BS 1621) Binder course Rolled asphalt (BS 904) Dense bitumen macadam or Dense tarmacadam Single-course tarmacadam (BS 802) Single-course bitumen macadam (BS 1621)

Two-course (a)Surface course Minimum thickness 20 mm Cold asphalt (BS1690) Coated macadam (BS 802, BS 1621, BS 1241 or BS 2040) (b) Binder course Coated macadam (BS 802, BS 1621, BS 1241 or BS 2040) Single course Rolled asphalt (BS 594) Dense tar surfacing (BTIA) Medium textured tarmacadum (BS 802) Dense bitumen macadam (BS 1621) 60 mm of single-course tarmacadam (BS 802) 60 mm of single-course bitumen macadam (BS 1621)

32

Figure 4.6. Thickness of subbase.

33

Figure 4.7. Lean concrete, soil cement and cement-bound granular base courses: minimum thickness of surfacing and base course

34

Figure 4.8. Wet-mix and dry-bound macadam base course: minimum thickness of surfacing and base course.

35

CHAPTER 5

THICKNESS DESIGN OF FLEXIBLE PAVEMENTS II

AN INTRODUCTION TO ANALYTICAL METHOD The theoretical approach for designing flexible pavements, which is so called Analytical or Mechanistic Method has captured the interest of pavement engineers since 1960s. This method uses fundamental physical properties and theoretical model of each pavement material to predict the stresses, strains and deflections due to load on the pavement. The thicknesses and composition of pavement materials are designed so that the stresses, strains and deflections do not exceed the capabilities of any of the materials. Some of the advantages of the analytical method as compared to empirical methods are as follows.

• The analytical method is more theoretical. It is based on mechanistic responses on pavement materials to the applied loads. Provided that the material properties and material model are correct, the pavement can be designed correctly and confidently anywhere and any environment condition.

• Pavements can be designed according to any available materials. In the empirical approach, the procedures are limited only to certain pavement materials for which they were developed.

• The analytical approach can cater any magnitude of wheel loads and frequencies while the empirical method is valid only for the wheel loads and traffic intensities that it has experienced during the experimental processes.

• For certain traffic condition, a pavement can be designed into various patterns. This helps the engineers to select the most optimum one. The empirical method is limited only one or two patterns of pavement structure.

• Since the damage of pavement can be predicted, therefore the maintenance strategies can be easily obtained.

• By the advent of computer, the analysis and design can be performed quickly. The main disadvantage is that the analytical approach is still required a great deal of researches in order to develop the relationships between loads and pavement responses as well as the models to predict pavement distresses based on these responses. Moreover, because of complexity of the method, computer is necessary. Stresses and strains in flexible pavement structure When a pavement is loaded by the external wheel loads, the stresses and strains that occur at various positions consist of:

1. Vertical Stresses/Strains 2. Shear Stresses/Strains 3. Radial (Horizontal) Stresses/Strains

36

Shear stresses/strains relate to the stability of the pavement. Generally, if the pavement and its embankment is proper constructed and not overloaded, the pavement structure will not fail by shear failure. Moreover, the modern pavement design concept focuses on the riding quality rather than preventing shear failure. Hence, for design purpose, only vertical and horizontal stresses/strains are considered. The researches have found that pavement materials are capable of being subjected to very high stresses while can not tolerate excessive strains. Consequently, in analytical pavement design, the strains are commonly considered as design criteria. Analysis of strains in flexible pavements One of the major steps in analytical design of flexible pavement is the analysis of strains beneath the pavement structure.

Homogeneous Mass The simplest way to analysis the stresses and strains in flexible pavement under wheel loads is to consider it as a homogeneous half-space. A half-space has an infinitely large area and an infinite depth with a top plane on which the loads are applied. Boussinesq (1885) proposed the first theory to determine the stresses, strains and deflections due to concentrated load applied on an elastic half-space. The concentrated load can be integrated into circular load area. Fig 5.1 shows a homogeneous half-space subjected to a circular load with a radius a and a uniform pressure q. The half-space has an elastic modulus E and a Poisson ratio ν. A small cylindrical element with center at a distance z below the surface and r from the axis is shown. Due to symmetry, there are only three normal stresses, σz, σr, and σt. These stresses are functions of q, r/a and z/a and can be determined by the charts shown in Fig 5.2 to Fig 5.5.

zσz

σr σt

τzr

τrz

2aq

E, ν

Figure 5.1 Components of stresses under axisymmetric loading After the stresses are obtained from the charts, the strains can be obtained by:

)]([(E1

trzz σ+σν−σ=ε (5.1a)

)]([(E1

ztrr σ+σν−σ=ε (5.1b)

37

)]([(E1

rztt σ+σν−σ=ε (5.1c)

If the contact area consists of two circles, the stresses and strains can be determined by superposition.

Layered System Boussinesq’s theory can not solve the problems with more than one material such as pavement systems. In such case, Burmister’s layered theory is more appropriate. Burmister (1943) developed solutions for a two-layer system and then extended them to a three-layer system. Based on this theory, the solutions are eventually developed to be applied to a multi-layered system with any number of layers. The basic assumptions to be satisfied are:

1. Each layer is homogeneous, isotropic, and linearly elastic with an elastic modulus E and a Poisson ratio ν.

2. The material is weightless and infinite in horizontal extent. 3. Each layer has a finite thickness h, but the lowest layer is infinite in thickness. 4. A uniform pressure q is applied on the surface over a circular area of radius a. 5. Continuity conditions are satisfied at the layer interfaces.

The solutions for multi-layer system are so complex that computer is necessary. Consequently, a number of computer programs has been developed and used for structural analysis of flexible pavement (such as CIRCLY, KENLAYER, BISAR, ELSYM5, MICHPAVE ILLIPAVE etc.) These programs are generally based on multi-layered elastic theory or finite element theory. However, the multi-layered elastic theory based programs are more widely used because of their simplicity.

38

Figure 5.2. Vertical stresses due to circular loading

Figure 5.3. Tangential stresses due to circular loading.

39

Figure 5.4. Radial stresses due to circular loading.

Figure 5.5. Vertical deflection due to circular loading

40

Odemark’s Method To determine pavement responses in multi-layered system by using the elastic theory is quite complicated. Alternatively, Odemark (1949) suggested the approximate solution to determine the stresses, strains and deflections of multi-layered system. Odemark’s procedure is based on the assumption that the stresses and strains below a layer depend on the stiffness of that layer only. If the thickness, modulus and Poisson’s ratio of a layer are changed, but the stiffness remains unchanged, the stresses and strains below the layer should also remain unchanged. This stiffness of a layer is proportional to:

2

3

1Ehν−

(5.2)

where h is the thickness of the layer. The transformation shown in Fig 5.6 should not affect the stresses or strains in layer 2 if:

22

23e

21

131

1

Eh

1Eh

ν−=

ν− or 3

21

22

2

11e

11

EE

hhν−

ν−×= (5.3)

where he is the equivalent thickness

h1 E1 ν1he E2 ν2

E2 ν2 E2 ν2

Figure 5.6 Odemark’s transformation of a layered system The system after transformation in Fig 5.6 is then a half-space material which Boussinesq’s equations can be used, but only for stresses, strains and displacement below the interface. Odemark’s method is not mathematically correct. In order to obtain results that close to the theory of elasticity, a correction factor, f, should be introduced. Moreover, if the Poisson’s ratio is assumed to be the same for all layers, equation 5.3 can be written as:

32

11e E

Ehfh ×= (5.4)

Reasonably good results agreement with the theory of elasticity is obtained with a correction factor of 0.8, except for the first interface where a factor of 0.9 is used for two-layer system and 1.0 for a multi-layer system. If the thickness of layer one, h1, is less than the radius of the loaded area, a, then a factor of 1.1(a/h1)0.3 will bring the horizontal tensile strain at the bottom of layer one closer to that obtained from the theory of elasticity. For a multi-layered system the equivalent thickness of the upper n – 1 layers with respect to the modulus of layer n, may be calculated from:

41

∑−

=

×=1n

1i

3n

i1n,e E

Ehfh , or (5.5a)

3n

1n1n33

3

223

2

11n,e E

Eh...h

EE

hEE

h...fh −− ×

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+×⎥⎥⎦

⎤

⎢⎢⎣

⎡+×

⎟⎟

⎠

⎞⎜⎜

⎝

⎛+×= (5.5b)

Layers below layer n are assumed to have the modulus En in the transformed system. Deflections are calculated as the sum of the compression of the layers plus the deflection of the subgrade. The compression of an individual layer is found as the difference between the deflection at the top and the bottom of the layer in the transformed system. For the top layer the transformed system is a half-space with modulus E1. In addition to the correction factor given previously, the Odemark’s method will give results close to the theory of elasticity provided that:

- moduli are decreasing with depth (Ei/Ei+1 > 2) - the equivalent thickness of each layer is larger than the radius of the loaded area.

The Odemark’s method is also known as the Method of Equivalent Thickness (MET) Distress Prediction Calculating stresses and strains is only the first step in the analytical design process. Results of the analysis are used to estimate the service life of the trial pavement section. Usually, the criteria, which are assigned to pavement materials and to the subgrade, are in the form of relationships between the level of strain induce by the single application of a standard axle load and the number of such applications which will result in the condition of the material or the pavement reaching an allowable limit. Generally, it is considered that fatigue cracking and rutting are the two principle modes of distress to be considered for flexible pavement design. These two modes of distress are illustrated in Fig 5.7.

Surface

Base

Subgrade

Surface

Base

Subgrade

(a) Rutting (b) Fatigue Cracking

εc εc

εt

Figure 5.7 Failure modes and critical strains in asphalt pavement

42

The fatigue cracking is caused by the repeated horizontal tensile strain, the maximum of which develops at the bottom of asphalt and bound layers such as cemented material. The crack, once occurs, propagates upwards to the top resulting in gradual deteriorating of the pavement. Rutting is considered to be caused by excessive accumulate vertical compressive strain that occurs at the top of subgrade. Actually, permanent compressive strain can occur in all layers especially in granular materials. However, the analysis of typical pavement has shown that 70 – 90 % of the magnitude of permanent deformation occur in subgrade as it is the weakest as compared with other materials. Moreover, the vertical compressive strain at the top of asphalt and bound material is assumed to be so small that can be neglected provided that good mix design and proper compaction are applied. The service life of the pavement will be controlled by the mode of distress which first falls below the acceptable limit. For example, the service life of a pavement may be taken as the period at the end of which permanent deformation of the pavement becomes unacceptable or the period at the end of which cracking of the asphalt surfacing becomes unsatisfactory. Normally, two design criteria will be used for an analytical method. They are:

1. Maximum horizontal tensile strain on the underside of the asphalt bound layer. This controls the fatigue cracking of the asphalt layer.

2. Maximum vertical compressive strain on the surface of the subgrade. This controls the

permanent deformation of the subgrade that leads, in turn, to permanent deformation of the pavement surface.

Asphalt Fatigue Cracking Criteria To predict the deterioration of asphalt most criteria make use of the maximum tensile strain. This strain is used to calculate the allowable number of load repetitions. Many analytical methods have an asphalt strain criteria based on the results of laboratory tests, where failure was defined as a 50 % decrease of the initial asphalt modulus. The general relationship between the maximum tensile strain in asphalt produced by a specific load and the allowable number of repetitions of that load is:

32 k1

kt1f )E()(kN −−ε= (5.6)

where, Nf = number of load repetition before asphalt falls below allowable limit εt = maximum tensile strain at the bottom of asphalt layer E = elastic modulus of asphalt

The values of k1, k2, and k3 are constant values, which are different from one highway agency to another.

The major difference in various methods is the values of k in strain criteria. For example; In the Asphalt Institute (9th edition) the allowable number of load repetition is given by:

43

854.0291.3t

3f )E()(10325.4C4.18N −−− ×ε××××= (5.7)

M10C =

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+×= 69.0

VVV

84.4Mbv

b

where, Vb = percent by volume of bitumen in the asphalt mix Vv = percent by volume of air void in the asphalt mix με = maximum tensile strain in microstrain In Shell method, the asphalt strain criteria is given by:

( ) 65

0

5t

5bbf 10

EE)(04.24V71.9VPI82.1PI43.36N ×⎟⎟

⎠

⎞⎜⎜⎝

⎛×με×−×+×−=

α− (5.8)

where, PI = penetration index of the bitumen E0 = reference modulus = 50000 MPa for controlled strain testing = 5000 MPa for controlled stress testing

α = -0.36 for controlled strain testing, and –0.28 for controlled stress testing

In AUSTROAD (1992) design method the asphalt strain criteria is given by: 80.15

t5

bf )E()()]08.1V856.0(6918[N −− ×με×+×= (5.9)

Subgrade Rutting Criteria The rutting is normally related to the maximum vertical normal (compressive) strain at the top of the subgrade. The allowable number of load repetitions, N, to limit rutting of the pavement structure is typically given by:

5kc4f )(kN −ε= (5.10)

where, εc = maximum compressive strain at the top subgrade Two criteria have been used to limit rutting: limit the vertical compressive strain on top of the subgrade and other to limit the total accumulated permanent deformation on the pavement surface based on the permanent deformation properties of each individual layer. Equation (5.10) is used by several highway agencies with the values of k4 and k5 shown in Table 5.1 Table 5.1 Subgrade strain criteria used by various highway agencies

Agency k4 K5 Rut Depth (mm.) The Asphalt Institute (9th ed.) 1.365 × 10-9 4.477 12.5 Shell (1985)

50 % reliability 6.15 × 10-7 4.0 12.5 85 % reliability 1.94 × 10-7 4.0 12.5 95 % reliability 1.05 × 10-7 4.0 12.5

TRRL (UK) 6.18 × 10-8 3.95 10.0

44

AUSTROADS (1992) suggested the subgrade strain criteria as 14.7

f8511N ⎟⎟

⎠

⎞⎜⎜⎝

⎛με

=

Cracking of Cement Bound Materials The cracking in cement bound materials is normally related to the maximum horizontal tensile strain at the bottom of the cement bound layer. Several researchers have presented the strain criteria for cracking in cement bound materials, for example:

For a cement-treated crushed rock base with less than 100 mm cover, 8.8

41.0t

fE

28400N ⎟⎟⎠

⎞⎜⎜⎝

⎛

×με=

For more than 100 mm cover, 0.8

45.0t

fE

35000N ⎟⎟⎠

⎞⎜⎜⎝

⎛

×με= (Jameson et al, 1992) (5.11)

where, E = modulus of cemented material

For lightly cementitous gravel, 69.7

zf

UCS266N ⎟⎟⎠

⎞⎜⎜⎝

⎛σ

×= (De Beer, 1989) (5.12)

where, UCS = unconfined compressive strength σz = compressive normal stress

and, R

10MPa160

EMPa164.0N6

26.3

zf ×

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛×

σ=

α

(Ullidtz and Stubstad, 1985) (5.13)

where, α = 1.16 when E < 160 MPa, else 1.0 R = regional factor Concept of Equivalent Single Axle Load The damage due to different axle groups is dependent on the number of tires per axle and the load on the axle. For design purposes, it is generally appropriate to consider axle groups in terms of the follow types:

• single axle with single wheels • single axle with dual wheels • tandem axles both with dual wheels

The relative damage associated with any particular axle load can be expressed in terms of relationship as shown in Table 5.2 Table 5.2 Axle loads which cause equal damage Axle Configuration Single Single Single Dual Tandem Dual

Load (kN) 53 80 135

45

The standard axle is defined as a single axle with dual wheels that carres a load of 8.2 tons (80 kN). Loads on the axle configurations given above that cause the same amount of damage as the standard are given in Table 5.2 For axle group loads other than those in Table 5.2, the damage caused is expressed as the number of standard axles which produce the same damage and is calculated as follow:

Number of standard axles for same damage = n

2.5TablefromLoadeAppropriatGroupAxleonLoad

⎟⎟⎠

⎞⎜⎜⎝

⎛ (5.14)

Where exponent n may vary depending on the type of pavement. Commonly a value of 4 is adopted for the exponent in which case the number of standard axles for the same damage is termed the number of equivalent standard axle. In practice, the number of equivalent standard axles can be determined by multiplying number of commercial axles by an appropriate factor. Analytical Procedure In summary the procedure of analytical design consists of:

• evaluating the input parameters (materials, traffic, environment etc.) • select trial pavement. • analysis the trial pavement to determine the allowable traffic. • comparing this with the design traffic and finally accepting or rejecting the trial

pavement. The design procedure is based on the structural analysis of a multi-layered pavement subject to traffic loading. A typical pavement model is shown in Fig 5.8.

1 1

2 2

3 3

Spacing ofdual wheels

Uniform stressequal to tire pressure

1. Tensile strain at bottom of asphalt2. Tensile strain at bottom of cemented material3. Compressive strain at top of subgrade

Asphalt

Granularmaterial

Cementedmaterial

Subgrade

Denotes likely locations of criticalstrains due to applied loading

Figure 5.8 Pavement model for analytical design

Generally, significant features of the elastic model are:

1. Pavement materials are considered to be homogeneous, elastic and isotropic. 2. Responses to loading are calculated using linear elastic theory and usually the

computer program is required.

46

3. Critical responses are assessed for pavement and subgrade materials are:

Asphalt horizontal tensile strain at bottom of layer Unbound Granular vertical compressive strain at the top of the layer Cemented Granular horizontal tensile strain at bottom of layer Subgrade vertical compressive strain at the top of the subgrade

4. Standard axle loading consisting of a load of 8.2 tons. For flexible pavements, the

critical responses within the pavement will occur on the vertical axis directly under one wheel or on the vertical axis located symmetrically between a pair of dual wheels. The effect on responses at these positions of the loads supported by the other pair of dual wheels may be neglected.

5. Dual wheel loading is represented by uniform vertical stress in two circles of equal area separated by the distance about 330 – 350 mm center to center as shown in Fig 5.8.

6. The contact stress is related to the tire pressure and is assumed to be in the range of 550 – 700 kPa

The general steps in analytical design procedure of flexible pavement are listed below:

1. Select trial pavement 2. Determine the elastic parameter of all materials including subgrade. 3. Adopt an appropriate strain criterion for subgrade and other unbound materials. 4. Determine the appropriate fatigue criteria for asphalt. 5. Determine the appropriate fatigue criteria for cemented materials (if any). 6. Determine design number of standard axles. 7. Approximate the standard wheel loading as two circular vertical loads. For the

standard axle load of 8.2 tons (80 kN), load on one circle area equals 20 kN and uniform vertical stress distribution is in the range of 500 – 700 kPa. Radius of each load can be calculated by

8. Determine critical locations in the pavement for the calculation of strains as follow: - Bottom of each asphalt or cemented bound layer - Top of subgrade - Top of each unbound material layer

9. Input above values to computer programs such as CIRCLY, KENLAYER, ELSYM5 etc. and determine the maximum vertical compressive strain at the top of subgrade (and unbound materials, if required) and the maximum horizontal tensile strain at the bottom of asphalt and cemented layers

10. Determine using the selected criteria in steps 3, 4 and 5 the allowable number of Standard Axles for each of the relevant distress models.

11. For each distress mode, compare allowable number of standard axles with the design number of standard axles.

12. If, for all distress modes, the allowable number of standard axles exceeds the design number of standard axles, the pavement is acceptable. If not, it is unacceptable.

13. If the pavement is unacceptable, select a new trial pavement and repeat steps 1 to 12. 14. For comparison purpose, if required, additional pavement configurations are designed

by repeating steps 1 to 13. 15. Compare alternative acceptable designs.

An example of analytical design of flexible pavement is given in an Appendix.

47

CHAPTER 6

THICKNESS DESIGN OF RIGID PAVEMENTS Rigid pavements are constructed of portland cement concrete. Generally, concrete pavements can carry much more load repetitions than flexible pavements do and also have longer service life. However, the capital cost is higher and requires maintenance periodically. This chapter provides guidance on the thickness design of rigid pavements proposed for roads carrying commercial traffic. The methods described here are of Portland Cement Association (PCA) and of The Road Research Laboratory (TRRL) in Britain. The Portland Cement Association Method (PCA Method) Portland Cement Association (1984) published the manual for determining slab thickness adequate to carry traffic loads on concrete highways. The thickness design criteria suggested in the manual are based on general pavement theory, performance and research experience gained from many sources. The selection of an adequate thickness is dependent on the choice of joint system, shoulder type and type of subbase if required. Concrete Pavement Types The design procedures apply to the following types of concrete pavements:

1. Joint Plain (unreinforced) Concrete Pavements (JPCP) are constructed without reinforcing steel. Load transfer at the joints is obtained by aggregate interlock between the cracked faces below the saw cut or groove. For load transfer to be effective, it is necessary that short joint spacings be used. The smooth steel dowel bars are often installed as load transfer devices at each contraction joints. The spacings between the joints must be relatively short to control cracking. Commonly used joint spacings for plain pavements are 4 – 6 m.

2. Joint Reinforced Concrete Pavements (JRCP) contain reinforced steel and dowel bars

for load transfer at the contraction joints. The pavements are constructed with longer joint spacings than used for unreinforced pavements. Between the joints, one or more transverse cracks will usually develop. These joints are held tightly together by the reinforcing steel and good load transfer is provided. Generally, joint spacings for reinforced pavements are not more than 12 m.

3. Continuously Reinforced Concrete Pavements (CRCP) are built with out contraction

joints. Due to the relatively heavy, continuous-steel reinforcement in the longitudinal direction, these pavements develop transverse cracks at close intervals. A high degree of load transfer is developed at these crack faces held tightly together by steel reinforcement.

These types of concrete pavements are illustrated in Fig 6.1.

48

4 - 6 m 4 - 6 m

Transverse jointswith or withoutdowels

7 - 12 m

Wire fabrics

Longitudinal jointwith tie bars

Transverse jointswith dowels

ContinuousReinforcement

(a) JPCP

(b) JRCP

(c) CRCP

No joint

Figure 6.1 Three types of concrete pavements

49

Design Factors Thickness design is determined based on four design factors.

1. Flextural strength of the concrete (modulus of rupture, MR)

The 28-day flextural strength of concrete is commonly used for design. The determination of concrete strength is discussed in Chapter 3

2. Strength of the subgrade

For rigid pavement designed by PCA method, the subgrade strength is assessed in term of Westergaard modulus of subgrade reaction (k). Methods of determining the k value are described in Chapter 2.

3. Design period

The life of concrete pavements may vary from less than 20 years on some projects that carry more traffic than originally estimated or have had design, material, or construction defects to more than 40 years on other projects where defects are absent. However, a design period of 20 years is commonly used in design procedure.

4. Design traffic

The design traffic is characterized by the cumulative number of commercial vehicle axle groups expected in the design lane during the design period, together with the proportions of each type of axle group and the distribution of loads on each type of axle group The details are discussed in the following section.

Traffic Analysis PCA use the concept of cumulative damage to deal with loads of different magnitudes. In brief, the proportion of damage caused by loads of a given magnitude is equal to the ratio of the number of such loads in the design period to the number of such loads which will cause failure as obtained from the performance criteria. The sum of these ratios for all load magnitudes indicates the total distress which will occur. If this sum is less than unity then the pavement thickness being analyzed is assumed adequate. If not, then the trial thickness is inadequate. Only the traffic of heavy vehicles with 6 tires or more is included in the design. The number and weights of heavy axle loads expected during the design period are derived from estimation of:

- ADT (average daily traffic in both directions, all vehicles) - ADTT (average daily truck traffic in both directions) - axle load distribution of trucks

50

Information on ADT and ADTT are obtained from traffic survey and the ADTT may be expressed as a percent of ADT. The number of heavy vehicles on the design lane over the design period is calculated by:

Number of heavy vehicles = GFFactorLane100ADTT%ADT ××× (6.1)

where, Lane factor = proportion of heavy trucks on the design lane (can be estimated

by Table 4.2) GF = cumulative growth factor throughout the design period

= r

1)r1( n −+

r = annual traffic growth rate (%) n = design period (years)

Axle load distribution Data on the axle load distribution of the truck traffic is needed to compute the numbers of single and tandem axles of various weights expected during the design period. These data can be obtained from the highway department’s loadometer stations or weight-in-motion studies on routes representing truck weights and types that are expected. The example of load distribution data is given in Table 6.1. Load Safety Factors In the design procedure, the axle loads determined in the previous section are multiplied by a load safety factor (LSF). PCA recommends the load safety factors as shown in Table 6.2. Subgrade and Subbase The support given to concrete pavements by the subgrade and the subbase where used, is the second factor in thickness design. Subgrade and subbase support is defined in terms of modulus of subgrade reaction (k) values as described in Chapter 2. Where the subbase is used, there will be an increase in k that should be used in the thickness design. If the subbase is an untreated granular material, the approximate increase in k can be drawn from Table 6.3a. For a cement-treated subbase, the design k values can be obtained from Table 6.3b Subbase should not be used merely for the purpose of increasing k value because it is not economical. However, the applications of subbase should be: 1) perform as working platform during construction, 2) provide uniform bearing surface under concrete slab, 3) reduced deflection at joints and 4) prevent “pumping” at joints. Thus, subbase materials should satisfy above requirements. In Thailand, subbase for concrete pavements can be made of unbound granular materials, bound materials or lean mixed concrete or even soil aggregate. Sometimes sand blanket is laid on top for the purpose of preventing pumping.

51

Table 6.1. Example distributions of loads on axle groups for rigid pavement design (Route Bangkok – Rangsit, Control section 1005)

Single – Axle, Dual Wheels (MT, HB) Tandem Axles, Dual Wheels (HT) % Axle Load

Tons (kips) MT HB Axle Load Tons (kips)

% HT

2.60 (5.73) 3.25 (7.16) 3.90 (8.60) 4.55 (10.03) 5.20 (11.46) 5.85 (12.89) 6.50 (14.33) 7.15 (15.76) 7.80 (17.19) 8.45 (18.62) 9.10 (20.06) 9.75 (21.49)

43.38 8.14 9.54 9.85 7.23 6.26 5.18 3.02 2.33 0.51 0.85 0.40

5.30 29.39 40.86 17.74 6.09 0.62

6.40 (14.11) 7.20 (15.87) 8.00 (17.63) 8.80 (19.40) 9.60 (21.16) 10.40 (22.92) 11.20 (24.68) 12.00 (26.45) 12.80 (28.210 13.60 (29.97) 14.40 (31.74) 15.20 (33.50) 16.00 (35.26) 16.80 (37.03) 17.60 (38.79) 18.40 (40.55) 19.20 (42.32) 20.00 (44.08) 20.80 (45.84) 21.60 (47.61) 22.40 (49.37) 23.20 (51.13) 24.00 (52.90) 24.80 (54.66) 25.60 (56.42) 26.40 (58.19) 27.20 (59.95) 28.00 (61.71)

39.74 1.41 0.97 1.13 1.02 1.10 1.04 1.93 2.06 1.36 6.25 3.33 7.66 19.08 2.34 0.84 0.35 0.45 0.71 0.45 1.36 3.29 0.22 0.32 0.41 0.76 0.22 0.04

Total 100 % 100 % Total 100 % Note: MT = Medium Truck, HB = Heavy Bus, HT = Heavy Truck Table 6.2 Load Safety Factors as recommended by PCA

Load Safety Factor Type of Road 1.2 Motorways and other multilane projects carrying uninterrupted

flows of high volumes of commercial vehicles, and where high levels of serviceability are required throughout the design period with minimum maintenance

1.1 Motorways, highways and arterial road projects with moderate volumes of commercial vehicles

1.0 Roads carrying low volumes of commercial vehicles.

52

Table 6.3a. Effect of untreated subbase on k values. Subbase k value, pci Subgrade k

value, pci 4 in. 6 in. 9 in. 12 in. 50 100 200 300

65 130 220 320

75 140 230 330

85 160 270 370

110 190 320 430

Table 6.3b. Design k values for cement-treated subbase.

Subbase k value, pci Subgrade k value, pci 4 in. 6 in. 8 in. 10 in.

50 100 200

170 280 470

230 400 640

310 520 830

390 640

- Note: 1 in. = 25.4 mm, 1 pci. = 271.3 kN/m3 Thickness Design Two distress modes considered in the thickness design procedure are:

- flextural fatigue cracking of the pavement base; - subgrade/subbase erosion arising from repeated deflections at joints and planned

cracks. The fatigue mode will usually control the design of light-traffic pavements (residential streets and secondary roads regardless of whether the joints are doweled or not) and medium traffic pavements with doweled joints. The erosion mode will usually control the design of medium and heavy traffic pavements with undoweled (aggregate-interlock) joints and heavy traffic pavement with doweled joints. Account is also taken of the presence or absence of doweled joints or concrete shoulders. For design purposes continuously reinforced pavements are treated as doweled jointed pavements. Information is required on both axle types and load distributions and the number of repetitions of each axle type/load combination expected to use the pavement during its design period. In principle, a trial thickness is selected and the total fatigue and erosion damage are calculated for the entire traffic volume and composition during the design period. If either fatigue or erosion damage exceeds 100 percent, the trial thickness is increased and the design process is repeated. The design thickness is the least trial thickness which has a total fatigue less than or equal to 100 percent and a total erosion damage less than or equal to 100 percent. Fig 6.2 and Fig 6.3 are the worksheets presenting the format for completing design problems. The step-by-step design is as follows:

1. Select a rigid pavement type, either jointed undoweled, jointed doweled or continuously reinforced concrete base. Also decide whether concrete shoulders are to be provided.

53

2. Determine the modulus of subgrade (k). This value can be determined from CBR value by the chart shown in Fig 2.1.

3. Select the 28-day flextural strength of the concrete. 4. Select the appropriate load safety factor. 5. Select a trial base thickness. 6. Enter the data of load distribution on axle groups in the first 3 Columns of

“Calculation of Expected Repetitions” sheet, together with the design traffic in Column 4. The expected repetitions of each load on each axle group type is then calculated as the product of the entries in Columns 2, 3 and 4 and the results are filled out in Column 5.

7. Transfer the expected repetitions and the corresponding axle load value to Columns 1 and 3 of “Calculation of Pavement Thickness” sheet.

8. Multiplied the axle load by Load Safety Factor and then enter the results into Column 2.

9. For each axle group, perform the Fatigue Analysis • Without concrete shoulder, use Table 6.4 and Fig 6.4 • With concrete shoulder, use Table 6.5 and Fig 6.4

Procedure steps 9.1. Enter as items 8 and 11 on the worksheet from the appropriate table the equivalent

stress factors depending on trial thickness and k value. 9.2. Divided these by the concrete modulus of rupture and enter as items 9 and 12 9.3. Using the stress ratio factor and the design load determine from Fig 6.4 the

“Allowable Repetitions to Fatigue”. Fill in Column 4. 9.4. Compute the ratio of expected fatigue repetitions to the allowable repetitions

(Column 5) by dividing Column 3 by Column 4, multiplying by 100. Then total the fatigue for all axle group types at the bottom.

10. For each axle group, perform the Erosion Analysis Without concrete shoulder

• Doweled joints or continuously reinforced pavement, use Table 6.6 and Fig 6.5 • Aggregate interlock (undoweled) joints, use Table 6.7 and Fig 6.5.

With concrete shoulder • Doweled joints or continuously reinforced pavement, use Table 6.8 and Fig 6.6 • Aggregate interlock (undoweled) joints, use Table 6.9 and Fig 6.6

Procedure Steps 10.1. Enter the erosion factor from the appropriate table as items 10 and 13 in the

worksheet. 10.2. Using the erosion factor, determine from Fig 6.5 or Fig 6.6. “Allowable Number

of Repetitions for Erosion”. Fill in Column 6 10.3. Compute the ratio of expected erosion repetitions to the allowable repetitions

(Column 7) by dividing Column 3 by Column 6, multiplying by 100. Then total the erosion damage for all axle group types at the bottom.

11. The trial thickness is not an adequate design if either of the totals of fatigue or erosion damage are greater than 100 %. A greater trial thickness should be selected for another calculation. A lesser trial thickness is selected if the totals are much lower than 100 %.

54

Table 6.4 Equivalent Stress – No Concrete Shoulder (Single Axle/Tandem Axle)

k of subgrade – subbase, pci Slab Thickness,

Inch 50 100 150 200 300 500 700

4 4.5

825/679 699/586

726/585 616/500

671/542 571/460

634/516 540/435

584/486 498/406

523/457 448/378

484/443 417/363

5 5.5

602/516 526/461

531/436 464/387

493/399 431/353

467/376 409/331

432/349 379/305

390/321 343/278

363/307 320/264

6 6.5

465/416 417/380

411/348 367/317

382/316 341/286

362/296 324/267

336/271 300/244

304/246 273/220

285/232 256/207

7 7.5

375/349 340/323

331/290 300/268

307/262 279/241

292/244 265/224

271/222 246/203

246/199 224/181

231/186 210/169

8 8.5

311/300 285/281

274/249 252/232

255/223 234/208

242/208 222/193

225/188 206/174

205/167 188/154

192/155 177/143

9 9.5

264/264 245/248

232/218 215/205

216/195 200/183

205/181 190/170

190/163 176/153

174/144 161/134

163/133 151/124

10 10.5

228/235 213/222

200/193 187/183

186/173 174/164

177/160 165/151

164/144 153/136

150/126 140/119

141/117 132/110

11 11.5

200/211 188/201

175/174 165/165

163/155 153/148

154/143 145/136

144/129 135/122

131/113 123/107

123/104 116/98

12 12.5

177/192 168/183

155/158 147/151

144/141 136/135

137/130 129/124

127/116 120/111

116/102 109/97

109/93 103/89

13 13.5

159/176 152/168

139/144 132/138

129/129 122/123

122/119 116/114

113/106 107/102

103/93 98/89

97/85 92/81

14 144/162 125/133 116/118 110/109 102/98 93/85 88/78 Table 6.5 Equivalent Stress – Concrete shoulder (Single Axle/Tandem Axle)

k of subgrade – subbase, pci Slab Thickness,

Inch 50 100 150 200 300 500 700

4 4.5

640/534 547/461

559/468 479/400

517/439 444/372

489/422 421/356

452/403 390/338

409/388 355/322

383/384 333/316

5 5.5

475/404 418/360

417/349 368/309

387/323 342/285

367/308 324/271

341/290 302/254

311/274 276/238

294/267 261/231

6 6.5

372/325 334/295

327/277 294/251

304/255 274/230

289/241 260/218

270/225 243/203

247/210 223/188

234/203 212/180

7 7.5

302/270 275/250

266/230 243/211

248/210 226/193

236/198 215/182

220/184 201/168

203/170 185/155

192/162 176/148

8 8.5

252/232 232/216

222/196 205/182

207/179 191/166

197/168 182/156

185/155 170/144

170/142 157/131

162/135 150/125

9 9.5

215/202 200/190

190/171 176/160

177/155 164/146

169/146 157/137

158/134 147/126

146/122 136/114

139/116 129/108

10 10.5

186/179 174/173

164/151 154/143

153/137 144/130

146/129 137/121

137/118 128/111

127/107 119/101

121/101 113/95

11 11.5

164/161 154/153

144/135 136/128

135/123 127/117

129/115 121/109

120/105 113/100

112/95 105/90

106/90 100/85

12 12.5

145/146 137/139

128/122 121/117

120/111 113/106

114/104 108/99

107/95 101/91

99/86 94/82

95/81 90/77

13 13.5

130/133 124/127

115/112 109/107

107/101 102/97

102/95 97/91

96/86 91/83

89/78 85/74

85/73 81/70

14 118/122 104/103 97/93 93/87 87/79 81/71 77/67

55

Table 6.6 Erosion Factors – Doweled Joints, No Concrete Shoulder (Single Axle/Tandem Axle)

k of subgrade-subbase, pci Slab Thickness,

Inch 50 100 200 300 500 700

4 4.5

3.74/3.83 3.59/3.70

3.73/3.79 3.57/3.65

3.72/3.75 3.56/3.61

3.71/3.73 3.55/3.58

3.70/3.70 3.54/3.55

3.68/3.67 3.52/3.53

5 5.5

3.45/3.58 3.33/3.47

3.43/3.52 3.31/3.41

3.42/3.48 3.29/3.36

3.41/3.45 3.28/3.33

3.40/3.42 3.27/3.30

3.38/3.40 3.26/3.28

6 6.5

3.22/3.38 3.11/3.29

3.19/3.31 3.09/3.22

3.18/3.26 3.07/3.16

3.17/3.23 3.06/3.13

3.15/3.20 3.05/3.10

3.14/3.17 3.03/3.07

7 7.5

3.02/3.21 2.93/3.14

2.99/3.14 2.91/3.06

2.97/3.08 2.88/3.00

2.96/3.05 2.87/2.97

2.95/3.01 2.86/2.93

2.94/2.98 2.84/2.90

8 8.5

2.85/3.07 2.77/3.01

2.82/2.99 2.74/2.93

2.80/2.93 2.72/2.86

2.79/2.89 2.71/2.82

2.77/2.85 2.69/2.78

2.76/2.82 2.68/2.75

9 9.5

2.70/2.96 2.63/2.90

2.67/2.87 2.60/2.81

2.65/2.80 2.58/2.74

2.63/2.76 2.56/2.70

2.62/2.71 2.55/2.65

2.61/2.68 2.54/2.62

10 10.5

2.56/2.85 2.50/2.81

2.54/2.76 2.47/2.71

2.51/2.68 2.45/2.63

2.50/2.64 2.44/2.59

2.48/2.59 2.42/2.54

2.47/2.56 2.41/2.51

11 11.5

2.44/2.76 2.38/2.72

2.42/2.67 2.36/2.62

2.39/2.58 2.33/2.54

2.38/2.54 2.32/2.49

2.36/2.49 2.30/2.44

2.35/2.45 2.29/2.40

12 12.5

2.33/2.68 2.28/2.64

2.30/2.58 2.25/2.54

2.28/2.49 2.23/2.45

2.26/2.44 2.21/2.40

2.25/2.39 2.19/2.35

2.23/2.36 2.18/2.31

13 13.5

2.23/2.61 2.18/2.57

2.20/2.50 2.15/2.47

2.18/2.41 2.13/2.37

2.16/2.36 2.11/2.32

2.14/2.30 2.09/2.26

2.13/2.27 2.08/2.23

14 2.13/2.54 2.11/2.43 2.08/2.34 2.07/2.29 2.05/2.23 2.03/2.19 Table 6.7 Erosion Factors – Undoweled Joints, No Concrete Shoulder (Single Axle/Tandem Axle)

k of subgrade-subbase, pci Slab Thickness,

Inch 50 100 200 300 500 700

4 4.5

3.94/4.03 3.79/3.91

3.91/3.95 3.76/3.82

3.88/3.89 3.73/3.75

3.86/3.86 3.71/3.72

3.82/3.83 3.68/3.68

3.77/3.80 3.64/3.65

5 5.5

3.66/3.81 3.54/3.72

3.63/3.72 3.51/3.62

3.60/3.64 3.48/3.53

3.58/3.60 3.46/3.49

3.55/3.55 3.43/3.44

3.52/3.52 3.41/3.40

6 6.5

3.44/3.64 3.34/3.56

3.40/3.53 3.30/3.46

3.37/3.44 3.26/3.36

3.35/3.40 3.25/3.31

3.32/3.34 3.22/3.25

3.30/3.30 3.20/3.21

7 7.5

3.26/3.49 3.18/3.43

3.21/3.39 3.13/3.32

3.17/3.29 3.09/3.22

3.15/3.24 3.07/3.17

3.13/3.17 3.04/3.10

3.11/3.13 3.02/3.06

8 8.5

3.11/3.37 3.04/3.32

3.05/3.26 2.98/3.21

3.01/3.16 2.93/3.10

2.99/3.10 2.91/3.04

2.96/3.03 2.88/2.97

2.94/2.99 2.87/2.93

9 9.5

2.98/3.27 2.92/3.22

2.91/3.16 2.85/3.11

2.86/3.05 2.80/3.00

2.84/2.99 2.77/2.94

2.81/2.92 2.75/2.86

2.79/2.87 2.73/2.81

10 10.5

2.86/3.18 2.81/3.14

2.79/3.06 2.74/3.02

2.74/2.95 2.68/2.91

2.71/2.89 2.65/2.84

2.68/2.81 2.62/2.76

2.66/2.76 2.60/2.72

11 11.5

2.77/3.10 2.72/3.06

2.69/2.98 2.64/2.94

2.63/2.86 2.58/2.82

2.60/2.80 2.55/2.76

2.57/2.72 2.51/2.68

2.54/2.67 2.49/2.63

12 12.5

2.68/3.03 2.64/2.99

2.60/2.90 2.55/2.87

2.53/2.78 2.48/2.75

2.50/2.72 2.45/2.68

2.46/2.64 2.41/2.60

2.44/2.59 2.39/2.55

13 13.5

2.60/2.96 2.56/2.93

2.51/2.83 2.47/2.80

2.44/2.71 2.40/2.68

2.40/2.65 2.36/2.61

2.36/2.56 2.32/2.53

2.34/2.51 2.30/2.48

14 2.53/2.90 2.44/2.77 2.36/2.65 2.32/2.58 2.28/2.50 2.25/2.44

56

Table 6.8 Erosion Factors – Doweled Joints, Concrete Shoulder (Single Axle/Tandem Axle)

k of subgrade-subbase, pci Slab Thickness,

Inch 50 100 200 300 500 700

4 4.5

3.28/3.30 3.13/3.19

3.24/3.20 3.09/3.08

3.21/3.13 3.06/3.00

3.19/3.10 3.04/2.96

3.15/3.09 3.01/2.93

3.12/3.08 2.98/2.91

5 5.5

3.01/3.09 2.90/3.01

2.97/2.98 2.85/2.89

2.93/2.89 2.81/2.79

2.90/2.84 2.79/2.74

2.87/2.79 2.76/2.68

2.85/2.77 2.73/2.65

6 6.5

2.79/2.93 2.70/2.86

2.75/2.82 2.65/2.75

2.70/2.71 2.61/2.63

2.68/2.65 2.58/2.57

2.65/2.58 2.55/2.50

2.62/2.54 2.52/2.45

7 7.5

2.61/2.79 2.53/2.73

2.56/2.68 2.48/2.62

2.52/2.56 2.44/2.50

2.49/2.50 2.41/2.44

2.46/2.42 2.38/2.36

2.43/2.38 2.35/2.31

8 8.5

2.46/2.68 2.39/2.62

2.41/2.56 2.34/2.51

2.36/2.44 2.29/2.39

2.33/2.38 2.26/2.32

2.30/2.30 2.22/2.24

2.27/2.24 2.20/2.18

9 9.5

2.32/2.57 2.26/2.52

2.27/2.46 2.21/2.41

2.22/2.34 2.16/2.29

2.19/2.27 2.13/2.22

2.16/2.19 2.09/2.14

2.13/2.13 2.07/2.08

10 10.5

2.20/2.47 2.15/2.43

2.15/2.36 2.09/2.32

2.10/2.25 2.04/2.20

2.07/2.18 2.01/2.14

2.03/2.09 1.97/2.05

2.01/2.03 1.95/1.99

11 11.5

2.10/2.39 2.05/2.35

2.04/2.28 1.99/2.24

1.99/2.16 1.93/2.12

1.95/2.09 1.90/2.05

1.92/2.01 1.87/1.97

1.89/1.95 1.84/1.91

12 12.5

2.00/2.31 1.95/2.27

1.94/2.20 1.89/2.16

1.88/2.09 1.84/2.05

1.85/2.02 1.81/1.98

1.82/1.93 1.77/1.89

1.79/1.87 1.74/1.84

13 13.5

1.91/2.23 1.86/2.20

1.85/2.13 1.81/2.09

1.79/2.01 1.75/1.98

1.76/1.95 1.72/1.91

1.72/1.86 1.68/1.83

1.70/1.80 1.65/1.77

14 1.82/2.17 1.76/2.06 1.71/1.95 1.67/1.88 1.64/1.80 1.61/1.74 Table 6.9 Erosion Factors – Undoweled Joints, Concrete Shoulder (Single Axle/Tandem Axle)

k of subgrade-subbase, pci Slab Thickness,

Inch 50 100 200 300 500 700

4 4.5

3.46/3.49 3.32/3.39

3.42/3.39 3.28/3.28

3.38/3.32 3.24/3.19

3.36/3.29 3.22/3.16

3.32/3.26 3.19/3.12

3.28/3.24 3.15/3.09

5 5.5

3.20/3.30 3.10/3.22

3.16/3.18 3.05/3.10

3.12/3.09 3.01/3.00

3.10/3.05 2.99/2.95

3.07/3.00 2.96/2.90

3.04/2.97 2.93/2.86

6 6.5

3.00/3.15 2.91/3.08

2.95/3.02 2.86/2.96

2.90/2.92 2.81/2.85

2.88/2.87 2.79/2.79

2.86/2.81 2.76/2.73

2.83/2.77 2.74/2.68

7 7.5

2.83/3.02 2.76/2.97

2.77/2.90 2.70/2.84

2.73/2.78 2.65/2.72

2.70/2.72 2.62/2.66

2.68/2.66 2.60/2.59

2.65/2.61 2.57/2.54

8 8.5

2.69/2.92 2.63/2.88

2.63/2.79 2.56/2.74

2.57/2.67 2.51/2.62

2.55/2.61 2.48/2.55

2.52/2.53 2.45/2.48

2.50/2.48 2.43/2.43

9 9.5

2.57/2.83 2.51/2.79

2.50/2.70 2.44/2.65

2.44/2.57 2.38/2.53

2.42/2.51 2.36/2.46

2.39/2.43 2.33/2.38

2.36/2.38 2.30/2.33

10 10.5

2.46/2.75 2.41/2.72

2.39/2.61 2.33/2.58

2.33/2.49 2.27/2.45

2.30/2.42 2.24/2.38

2.27/2.34 2.21/2.30

2.24/2.28 2.19/2.24

11 11.5

2.36/2.68 2.32/2.65

2.28/2.54 2.24/2.51

2.22/2.41 2.17/2.38

2.19/2.34 2.14/2.31

2.16/2.26 2.11/2.22

2.14/2.20 2.09/2.16

12 12.5

2.28/2.62 2.24/2.59

2.19/2.48 2.15/2.45

2.13/2.34 2.09/2.31

2.10/2.27 2.05/2.24

2.06/2.19 2.02/2.15

2.04/2.13 1.99/2.10

13 13.5

2.20/2.56 2.16/2.53

2.11/2.42 2.08/2.39

2.04/2.28 2.00/2.25

2.01/2.21 1.97/2.18

1.98/2.12 1.93/2.09

1.95/2.06 1.91/2.03

14 2.13/2.51 2.04/2.36 1.97/2.23 1.93/2.15 1.89/2.06 1.87/2.00

57

Calculation of Expected Repetitions Project __________________________________________________________________ Axle Load,

kips Proportion of loads (%/100)

Proportion of Axle Group

(%/100)

Design Traffic Expected Repetitions

1 2 3 4 5 Single Axles Tandem Axles

Figure 6.2. Worksheet for calculation of expected repetitions

58

Calculation of Pavement Thickness Project__________________________________________________________________ Trial Thickness ____________________in. Doweled joints: yes ______ no ______ Subgrade-Subbase k ________________pci. Concrete shoulder: yes ______ no ______ Modulus of Rupture, MR ____________psi. Load Safety Factor, LSF _____________ Design Period ______ years

Fatigue analysis Erosion analysis Axle load,

kips Multiplied

by LSF Expected repetitions Allowable

repetitions Fatigue,

% Allowable repetitions

Damage, %

1 2 3 4 5 6 7 8. Equivalent stress___ 10 Erosion Factor____ 9. Stress Ratio Factor ______

Single Axles

11. Equivalent stress__ 13 Erosion Factor____ 12. Stress Ratio Factor ______

Tandem Axles

Total Total

Figure 6.3 Worksheet for thickness design of rigid pavements

59

Figure 6.4. Fatigue analysis – allowable load repetitions based on stress ratio factor (with and without concrete shoulder)

60

Figure 6.5. Erosion analysis – allowable load repetitions based on erosion factor (without concrete shoulder)

61

Figure 6.6. Erosion analysis – allowable load repetitions based on erosion factor (with concrete shoulder)

62

Road Note 29 Method Road Note 29 recommended the procedure of thickness design of both reinforced and unreinforced concrete pavements as follows.

Traffic Analysis The traffic analysis of the cumulative number of standard axles to be carried in the design lane of the pavement is estimated using the procedure described in Chapter 4.

Thickness Design For design of concrete pavement, the subgrade, the subbase and the concrete slab are each considered in turn. Subgrade Road Note 29 categorized the subgrade based on its qualities in to three groups as given in Table 6.10 As in design of flexible pavements, Road Note 29 recommended that the water table should be prevented from rising to within 600 mm of the finished subgrade level. This may be done by sub-soil drainage or by raising the finished subgrade level by means of an embankment. Subbase The minimum thickness of subbase recommended for the three types of subgrade is also given in Table 6.10. Table 6.10. Classification of subgrades for concrete roads and minimum thicknesses of

subbase required as recommended by Road Note 29

Type of subgrade Description Minimum thickness of subbase required

Weak All subgrades of CBR value 2 percent or less 150 mm Normal Subgrades other than those defined by the other

categories 80 mm

Very stable All subgrades of CBR value 15 percent or more. This category includes undisturbed foundations of old roads

0

Concrete Slab The required thickness for reinforced and unreinforced concrete slab in terms of the cumulative number of standard axles to be carried for the three types of subgrades is determined by the chart shown in Fig 6.7. The designs given by this chart are based on a minimum compressive strength for concrete of 28 MPa at 28 days.

63

Figure 6.7 Thickness of concrete slab as recommended by Road Note 29

64

Details of Joints Joints should be provided in concrete pavements so premature cracks due to temperature or moisture changes will not occur. There are four types of joints in common use: contraction, expansion, construction and longitudinal. Contraction joints Contraction joints are transverse joints used to control the crack due to shrinkage (contraction) of concrete. The joints are made by sawing concrete after it is set or by placing a strip on the fresh concrete, which is later removed. The cracks will be controlled to occur at the joints because at these points the thickness is thinner than that of surrounding concrete. Once the crack occurs, concrete will loss the load transfer. Therefore, dowels are usually needed to provide load transfer. Contraction joints are usually placed at regular intervals perpendicular to the centerline of pavements at 10 – 15 m spacing. Expansion joint Expansion joints are transverse joints for the relief of compressive stress due to thermal expansion of concrete. Smooth dowel bar lubricated at least on one side must be used for load transfer. An expansion cap must be installed at the free end to provide space for dowel movement. Expansion joints are placed perpendicular to the centerline of pavements at 100 – 150 m interval. Construction joint This joint is installed when the constructions work temporarily stop. The joint has the function the same as contraction joints and should be placed at the location of contraction joint. Longitudinal Joint Longitudinal joints are used in highway pavements to relieve curling and warping. In one-lane-at-a-time construction, the longitudinal joints are used to ensure load transfer and the pavements are tied together with tie bars. Detail of all joints mentioned above are shown in Fig 6.8

Dowels Dowel bars are to be plain steel bars with yield strength not less than 240 MPa and 500 mm long. Dowels should strength with one end free from burrs. Appropriate dowel diameter, for slab thickness of 200 – 250, is 25 mm. Dowels at a spacing of 300 mm should be installed at transverse contraction joints where appropriate. Dowels must be securely held parallel to each other, to the road centerline and to the centerline of the surface of the finished pavement.

65

Tie Bars Tie bars prevent separating of the pavement at longitudinal joints. Ties bars are to be 16 mm diameter, 500 mm long and have yield strength of 400 MPa. Place centrally in the joint at spacing 600 mm.

CapPainted & Greased

HH/2

Joint SealerJoint Filter

φ 25 mm smooth dowel bar500 mm long @ 300 mm c/c

Painted & Greased

HH/2

Sawed Joint 10.00 m c/cJoint sealer

φ 25 mm smooth dowel bar500 mm long @ 300 mm c/c

Painted & Greased

HH/2

Sawed Joint 10.00 m c/cJoint sealer

φ 25 mm smooth dowel bar500 mm long @ 300 mm c/c

First slab

Painted & Greased

HH/2

Sawed Joint 10.00 m c/cJoint sealer

φ 16 mm deformed bar 500mm long @ 600 mm c/c

First slab

(a) Contraction Joint (b) Expansion Joint

(c) Construction Joint (d) Logitudinal Joint

Figure 6.8 Detail of joints

Reinforcement Design Procedure The purpose of reinforcing steel in rigid pavements is not to prevent cracking of the concrete, but to hold tightly closed any cracks that do occur in such manner that the load carrying capacity of the slab is preserved. In jointed pavements the amount of steel is governed by the spacing of contraction joints. In case of continuously reinforced pavements, sufficient steel is provided to eliminate the need for contraction joints.

66

Reinforcement in Jointed Reinforced Pavements The required area of reinforcing steel in jointed reinforced pavements is given by the equation:

ss f2

LMghA μ=

where, As = the required area of steel (per width of slab) fs = the allowable tensile stress of the reinforcing steel. g = the acceleration due to gravity h = thickness of slab

L = the distance between untied joints and/or free edge of slab

M = the mass per unit volume of the slab μ = the coefficient of friction between the concrete base slab

and the subbase; this varies from 1.0 to 2.0 depending on the type of debonding layer applied to the subbase.

Typical concrete pavement in Thailand Typically, concrete pavement in Thailand is Jointed Reinforcement Concrete Pavement (JRCP) with the thickness of 230 – 250 mm. The length of slab (distance between contraction joints) about 7.5 – 10.0 m. Subbase is made of sand blanket 100 mm and soil aggregate 150 mm. Fig 6.9 shows typical cross section of rigid pavement constructed in Thailand.

Concrete Slab

Subbase

Shoulder (Paved)

Embankment or Subgrade

Logitudinal joint with tie bar

Figure 6.9 Typical cross section of rigid pavement in Thailand

67

REFERENCES The ASPHALT INSTITUTE (1970), Thickness Design – Full-Depth Asphalt Pavement

Structures for Highways and Streets, Maryland. AUSTROADS (1992), Pavement Design – A Guide to the Structural Design of Road

Pavements, Sydney, Australia. DEPARTMENT OF HIGHWAYS (2001), Analytical Design of New Flexible Pavements in

Thailand, Pavement Technology Project, Department of Highways, Thailand. HUANG, Y.H. (1993), Pavement Analysis and Design, Prentice Hall, New Jercey. JAPAN ROAD ASSOCIATION (1989), Manual for Asphalt Pavement, Japan. PORTLAND CEMENT ASSOCIATION (1984), Thickness Design for Concrete Highway

and Street Pavements. ROAD RESEARCH LABORATORY (1970), Road Note 29 – A Guide to the Structural

Design of Pavements for New Roads, London. SILAROM, P. (2001), “Presentation of Laboratory Test Methods and Findings”, Proceeding

of the Second Seminar on Pavement Technology, Department of Highways, Bangkok, Thailand. pp. 35 – 41.

ULLIDTZ, P. (1987), Pavement Analysis, Elsevier, New York. ULLIDTZ, P. (1998), Modelling Flexible Pavement Response and Performance, Polyteknisk

Forlag, Denmark.

69

APPENDIX

EXAMPLE PROBLEMS Design CBR value Example 1. Checking an extremely large maximum value The CBR values at 6 locations of a road section of a generally uniform soil quality have been found to be, in an increasing order, as follows: 4.4, 4.8, 5.2, 6.2 and 12.2

77.04.42.122.62.12

CBRCBRCBRCBR

minmax

1maxmax =−−

=−

−=γ −

From Table 2.2, for 6 samples, γ6 = 0.560 < 0.77. Thus, the value 12.2 should be ignored. Example 2 Checking an extremely small minimum value The CBR values at 5 locations of a road section have been obtained as follows: 2.4, 4.3, 4.7, 4.8 and 5.2

678.04.22.54.23.4

CBRCBRCBRCBR

minmax

min1min =−−

=−−

=γ +

From Table 2.2, for 5 samples, γ5 = 0.642 < 0.678. Thus, the value 2.4 should be ignored. Example 3 Determination of section CBR For a certain road construction project, the CBR values at 29 spots have been obtained as: 27.7, 26.7, 20.7, 17.7, 16.5, 14, 11.8, 11.5, 11.2, 10, 9.4, 9.4, 9, 8.9, 8.55, 8.5, 7.9, 7.9, 7.7, 7.6, 7.2, 6.7, 6.4, 6.4, 5.6, 4.9, 4.3, 4.3, 3.7

1) All CBR values are already in numerical order 2) Percent of CBR values equal to or greater than each different value.

CBR Number equal to or greater than Percent equal to or greater than 3.7 4.3 4.3 4.9 5.6 6.4 6.4 6.7 7.2

29

28 26 25

24 22 21

(29/29)100 = 100 (28/29)100 = 96.55 (26/29)100 = 89.66 (25/29)100 = 86.21 (24/29)100 = 82.76 (22/29)100 = 75.86 (21/29)100 = 72.41

70

7.6 7.7 7.9 7.9 8.5 8.6 8.9 9

9.4 9.4 10

11.2 11.5 11.8 14

16.5 17.7 20.7 26.7 27.7

20 19

18 16 15 14 13

12 10 9 8 7 6 5 4 3 2 1

(20/29)100 = 68.97 (19/29)100 = 65.52 (18/29)100 = 62.07 (16/29)100 = 55.17 (15/29)100 = 51.72 (14/29)100 = 48.28 (13/29)100 = 44.83 (12/29)100 = 41.38 (10/29)100 = 34.48 (9/29)100 = 31.03 (8/29)100 = 27.59 (7/29)100 = 24.14 (6/29)100 = 20.69 (5/29)100 = 17.24 (4/29)100 = 13.79 (3/29)100 = 10.34 (2/29)100 = 6.90 (1/29)100 = 3.45

3) Plot CBR vs Percent CBR equal to or greater than.

0102030405060708090100

0 1 2 3 4 5 6 7 8 9 101112 1314 151617 181920 212223 2425 262728 2930

CBR (%)

% e

qual

to o

r gre

ater

than

4) Design CBR = 5 % Flexible Pavement Design (Asphalt Institute (1970) Method) Design Parameters Four lane highway Design Subgrade CBR = 5 % Design period 15 years The average gross weight of heavy vehicles is 21 tons (46,000 lbs) The legal single-axle load limit is 8.2 tons (18,000 lbs) Traffic Data The average daily traffic from adjacent existing road are as follow:

71

Car Light

Bus Heavy

Bus Light Truck

Medium Truck

Heavy Truck

Total

5609 500 261 2248 473 620 9711 An annual growth rate of 6.5 % is expected. Thickness Design of Full-Depth Asphalt Structure Estimate the average daily traffic in the opening year, assuming that the road will open 3 years after the year that the traffic survey was done.

11730)065.01(9711IDT 3 =+= vehicles per day

Percent of heavy vehicles in both direction (A) = 100Total

HTMTHB×

++

= 1009711

620473261×

++ = 13.94 %

Percent of heavy vehicles in design lane (B) = 45 %

Number of heavy vehicles in design lane = 10045

10094.1311730 ×× = 736 vehicles

The ITN can be determined by entering Fig 4.1, with the average gross weight of the trucks and number of heavy trucks in design lane, joining these points on the C and D scales and project to line B. Single-axle load limit = 18,000 lbs is located on line E. Join points on lines B and E and project to line A. Read on line A, an Initial Traffic Number (ITN) = 700. ITN is more than 10, no correction for automobiles and light trucks necessary. From Table 4.3, for Design period = 15 years and annual growth rate = 6.5 %, Initial Traffic Adjustment Factor = 1.21 Therefore, DTN20 = 700 × 1.21 = 847 The minimum thickness of Full-Depth asphalt structure is determined by entering Fig 4.3, with DTN20 and CBR values, joining these points on the scales and projecting across to the Full-Depth asphalt thickness, TA. Read on the scale, TA = 10.9 inches (277.7 mm.) Substitution Asphalt Thickness by Granular Materials

Material Thickness (mm) Sr TA Asphalt surface and binder course Crushed rock base CBR > 80 % Granular subbase CBR > 25 % Selected material “A”

80 200 150 200

1.0 2.0 2.7 3.0

80 100 55.56 66.67

Total 302.23 > 277.7 OK

72

Odemark – Boussinesq Method A three layer system (subgrade is counted as a “layer”) with the thicknesses and moduli shown in Fig A1 is loaded by a uniformly distributed load with radius 150 mm and contact stress 0.7 MPa. Poisson’s ratio is assumed to be 0.35 for all materials.

h1 = 150 mm, E1 = 3000 MPa

h2 = 300 mm, E2 = 300 MPa

E3 = 50 MPa

300 mm

0.7 MPa

Figure A1

1) Horizontal strain at the bottom of the asphalt Equivalent thickness of asphalt corresponding to modulus of second layer,

he,2 = 3300

30001500.1 ×× = 323 mm

When,

z/a = 323/150 = 2.15 and r/a = 0

From Fig 5.2, q

zσ ×100 = 26

Thus, σz = 0.26 × 0.7 = 0.18 MPa

Similarly, from Fig 5.3 and Fig 5.4, q

tσ ×100 = q

rσ ×100 = 1.6

Thus, σr = σt = 1.6/100 × 0.7 = 0.01 MPa

Horizontal strain, )]([E1

ztrr σ+σν−σ=ε

)]18.001.0(35.001.0[300

1r +−=ε

= -0.0002 = - 200 με (minus sign indicates tension)

2) Vertical stress on subgrade

he,3 = 350

300)300323(8.0 ×+× = 906 mm

73

When

z/a = 906/150 = 6.04 and r/a = 0

From Fig 5.2, q

zσ ×100 = 4

Therefore, σz = 4/100 × 0.7 = 0.028 MPa

Analytical Design of Flexible Pavement Design Parameters Four lane highway Design period 10 years Design CBR = 3 % Strain criteria: AUSTROAD (1992) Traffic Data ADT = 7429 vehicles per day % Heavy vehicles = 28.32 % Annual growth rate = 5 % Assume average number of standard axle per heavy vehicle = 1.0 Design Traffic Number of heavy trucks in design lane = 7429 × 0.2832 × 0.45 = 946 vehicles Number of repetitions of heavy trucks during design period = 4.3 × 106 vehicles Number of repetitions of standard axle during design period = 1.0 × 4.3 × 106 = 4.3 × 106 ESAL Pavement Analysis The pavement structure will be designed as a five-layer structure on a subgrade. Each layer is modeled as elastic material which can be characterized by two parameters; Young’s modulus (E) and Poisson’s ratio (ν). A trial pavement is shown in Fig A2.

120 mm Asphalt

150 mm Crushed rock base

150 mm Granular subbase

160 mm Selected material "A"

E = 2500 MPa

E = 350 MPa

E = 150 MPa

E = 120 MPa

Subgrade E = 30 MPa

Poisson's ratio (ν) is assumed = 0.35 for all layers

Figure A2.

74

Dual wheel loading is represented by uniform vertical stress in two circles of equal area separated by 350 mm center to center. The contact stress is assumed to be 566 kPa (equal to tire pressure) as illustrated in Fig A3. Critical locations are:

• Horizontal tensile strain at bottom of asphalt layer • Vertical compressive strain on top of subgrade

Both of the above will be checked directly beneath one of the loaded wheels and midway between the loaded wheels.

Asphalt

Crushed rock base

Granular subbase

Selected material

Subgrade

1 1

2 2

350 mmUniform stress

566 kPa

1 Tensile strain at bottom of asphalt2 Compressive strain at top of subgrade

Figure A3

The modeled pavement is then analyzed by the aid of computer program KENLAYER. Critical strains from KENLAYER output are: Asphalt – Maximum tensile strain is 201.3 με directly beneath one of the loaded wheels Subgrade – Maximum compressive strain is 524.1 με midway between the loaded wheels Strain Criteria Asphalt Nf = [(6918(0.856Vb + 1.08))/E0.36 × με)]5 Nf = [(6918(0.856 × 12 + 1.08))/(25000.36 × 201.3)]5

= 6.9 × 106 Subgrade Nf = (8511/με)7.14

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Nf = (8511/524.1)7.14 = 4.4 × 108 Design repetitions = 4.3 × 106 ESAL < 6.9 × 106. Thus, trial pavement is acceptable. From the calculation, the allowable number of repetitions based on asphalt cracking and subgrade rutting are 6.9 × 106 and 4.4 × 108 repetitions respectively, indicating that after the passage of approximately 6.9 × 106 ESAL, the pavement will fail in the asphalt cracking mode. However, for this example, the designer may opt to repeat the analysis with reduce layer thicknesses. The pavement structure is acceptable as long as the controlled allowable number of repetitions is smaller than the expected repetitions. Rigid Pavement Design (PCA Method) Design parameters Four lane highway Design subgrade CBR 2 % The 28-day flextural strength of the concrete = 600 psi. The pavement is to be joint reinforced pavement without concrete shoulder Load safety factor = 1.2. Traffic data ADT = 1,893 vehicles per day Growth rate = 5 % ADTT = 30 % of ADT, which includes:

• HB = 3.80 % • MT = 6.61 % • HT = 19.59 %

The load distributions of axle groups are as shown in Table 6.1. Determination of subgrade-subbase k value CBR of subgrade = 2 %. From Fig 2.1, use subgrade k value = 50 pci. Use untreated granular subbase 30 cm thick (12 inches) From Table 6.3a, use Modulus of subgrade-subbase reaction = 110 pci. Calculation of expected repetitions 1) Number of commercial vehicles during design period

Repetitions = 36505.0

1)05.01(189320

×−+

×

= 22846755 Repetitions in design lane = 22846755 × 0.45 = 10281040

2) The data in Table 6.1 is enter in the first 3 columns of “Calculation of expected repetitions” worksheet, together with the design traffic in column 4. The expected

76

repetitions of each load on each axle group type (column 5) is then calculated as the product of the entries in column 2, 3, and 4. The axle load value and the corresponding expected repetitions are then transferred to columns 1 and 3 of “Calculation of Pavement Thickness” worksheet.

Fatigue and Erosion analysis For each load group type, the equivalent stress and erosion factor is read from Table 6.4 and Table 6.6, respectively. The stress ratio factor is determined by dividing the equivalent stress by the 28-day flextural strength. The allowable repetitions for fatigue (column 4) are determined by entering Fig 6.4 with design load and stress ratio factor, joining these points on the scales and projecting across to the allowable load repetition scale. The percentage fatigue (column 5) is the ratio of expected repetitions to allowable repetitions multiplied by 100 The allowable repetitions for erosion (column 6) are determined in similar manner to fatigue by entering Fig 6.5 with design load and the erosion factor. The percentage erosion damage (column 7) is the ratio of expected to allowable repetitions multiplied by 100. Having performed these calculations for all loads on all axle group types, entries in the Fatigue (%) column are summed to give Total percentage fatigue. Similarly, entries in the Erosion damage (%) column are summed to give Total percentage erosion. Evaluation of analysis For the example situation, the total fatigue and erosion percentages are 99.98 and 21.42 respectively, indicating that the trial pavement is expected to fail in fatigue after the passage of approximately 1.03 × 108 commercial vehicle axle groups. The total percentage fatigue and erosion damage are less than 100 %. Therefore, a slab thickness of 250 mm is adopted.

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Calculation of Expected Repetitions Project_________Example__________________________________________________ Axle Load,

kips Proportion of loads (%/100)

Proportion of Axle Group

(%/100)

Design Traffic Expected Repetitions

1 2 3 4 5 Single Axles (MT)

5.73 0.4338 0.0661 10281040 294801 7.16 0.0814 0.0661 10281040 55318 8.60 0.0954 0.0661 10281040 64832 10.03 0.0985 0.0661 10281040 66938 11.46 0.0723 0.0661 10281040 49133 12.89 0.0626 0.0661 10281040 42542 14.33 0.0518 0.0661 10281040 35202 15.76 0.0302 0.0661 10281040 20523 17.19 0.0233 0.0661 10281040 15834 18.62 0.0051 0.0661 10281040 3466 20.06 0.0085 0.0661 10281040 5776 21.49 0.0040 0.0661 10281040 2718 22.92 0.0120 0.0661 10281040 8155 24.35 0.0137 0.0661 10281040 9310 25.79 0.0023 0.0661 10281040 1563

Single Axles (HB)

11.46 0.0530 0.0380 10281040 20706 12.89 0.2939 0.0380 10281040 114821 14.33 0.4086 0.0380 10281040 159632 15.76 0.1774 0.0380 10281040 69307 17.19 0.0609 0.0380 10281040 23792 18.62 0.0062 0.0380 10281040 2422

Calculation of Expected Repetitions

78

Project_____________Example______________________________________________ Axle Load,

kips Proportion of loads (%/100)

Proportion of Axle Group

(%/100)

Design Traffic Expected Repetitions

1 2 3 4 5 Tandem Axles (HT)

14.11 0.3974 0.1959 10281040 800387 15.87 0.0141 0.1959 10281040 28398 17.63 0.0097 0.1959 10281040 19536 19.40 0.0113 0.1959 10281040 22759 21.16 0.0102 0.1959 10281040 20543 22.92 0.0110 0.1959 10281040 22155 24.68 0.0104 0.1959 10281040 20946 26.45 0.0193 0.1959 10281040 38871 28.21 0.0206 0.1959 10281040 41490 29.97 0.0136 0.1959 10281040 27391 31.74 0.0625 0.1959 10281040 125879 33.50 0.0333 0.1959 10281040 67068 35.26 0.0766 0.1959 10281040 154277 37.03 0.1908 0.1959 10281040 384282 38.79 0.0234 0.1959 10281040 47129 40.55 0.0084 0.1959 10281040 16918 42.32 0.0035 0.1959 10281040 7049 44.08 0.0045 0.1959 10281040 9063 45.84 0.0071 0.1959 10281040 14300 47.61 0.0045 0.1959 10281040 9063 49.37 0.0136 0.1959 10281040 27391 51.13 0.0329 0.1959 10281040 66263 52.90 0.0022 0.1959 10281040 4431 54.66 0.0032 0.1959 10281040 6445 56.42 0.0041 0.1959 10281040 8258 58.19 0.0076 0.1959 10281040 15307 59.95 0.0022 0.1959 10281040 4431 61.71 0.0004 0.1959 10281040 806

Calculation of Pavement Thickness Project______Example_____________________________________________________ Trial Thickness __10 inches (250 mm.)____ Doweled joints: yes ___/__ no ______ Subgrade-Subbase k ________110_____pci. Concrete shoulder: yes ______ no ___/__

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Modulus of Rupture, MR ____600_____psi. Load Safety Factor, LSF _____1.2_____ Design Period __20__ years

Fatigue analysis Erosion analysis Axle load,

kips Multiplied

by LSF Expected repetitions Allowable

repetitions Fatigue,

% Allowable repetitions

Damage, %

1 2 3 4 5 6 7 8. Equivalent stress_197.2 10 Erosion Factor_2.537 9. Stress Ratio Factor _0.329

Single Axles (MT + HB) 5.73 6.88 294801 Unlimited 0 Unlimited 0 7.16 13.20 55318 Unlimited 0 Unlimited 0 8.60 10.31 64832 Unlimited 0 Unlimited 0 10.03 12.03 66938 Unlimited 0 Unlimited 0 11.46 13.75 69840 Unlimited 0 Unlimited 0 12.89 15.47 157362 Unlimited 0 Unlimited 0 14.33 17.19 194834 Unlimited 0 Unlimited 0 15.76 18.91 89830 Unlimited 0 Unlimited 0 17.19 20.63 39627 Unlimited 0 Unlimited 0 18.62 22.35 5888 Unlimited 0 1000000000 0.01 20.06 24.07 5776 Unlimited 0 40000000 0.01 21.49 25.79 2718 Unlimited 0 22000000 0.01 22.92 27.51 8155 1600000 0.51 13000000 0.06 24.35 29.23 9310 330000 2.82 8000000 0.12 25.79 30.94 1563 125000 1.25 5400000 0.03

11.Equivalent stress 189.0 13. Erosion Factor_2.752 12. Stress Ratio Factor __0.315

Tandem Axles 14.11 16.93 800387 Unlimited 0 Unlimited 0 15.87 19.04 28398 Unlimited 0 Unlimited 0 17.63 21.16 19536 Unlimited 0 Unlimited 0 19.40 23.27 22759 Unlimited 0 Unlimited 0 21.16 25.39 20543 Unlimited 0 Unlimited 0 22.92 27.51 22155 Unlimited 0 Unlimited 0 24.68 29.62 20946 Unlimited 0 Unlimited 0 26.45 31.74 38871 Unlimited 0 Unlimited 0 28.21 33.85 41490 Unlimited 0 Unlimited 0 29.97 35.97 27391 Unlimited 0 70000000 0.04 31.74 38.09 125879 Unlimited 0 35000000 0.36 33.50 40.20 67068 Unlimited 0 20000000 0.34 35.26 42.32 154277 Unlimited 0 14000000 1.10 37.03 44.43 384282 Unlimited 0 9100000 4.22 38.79 46.55 47129 Unlimited 0 6600000 0.71 40.55 48.66 16918 Unlimited 0 5000000 0.34 42.32 50.78 7049 Unlimited 0 4000000 0.18 44.08 52.90 9063 Unlimited 0 3000000 0.30 45.84 55.01 14300 10000000 0.14 2400000 0.60 47.61 57.13 9063 1600000 0.57 1800000 0.50 49.37 59.24 27391 600000 4.57 1600000 1.71 51.13 61.36 66263 400000 16.57 1400000 4.73 52.90 63.48 4431 170000 2.61 1000000 0.44 54.66 65.59 6445 110000 5.86 820000 0.79

80

56.42 67.71 8258 70000 11.80 700000 1.18 58.19 69.82 15307 46000 33.28 600000 2.55 59.95 71.94 4431 29000 15.28 500000 0.89 61.71 74.05 806 17000 4.74 400000 0.20

Total 99.98 Total 21.42