411-Design of Highway Pavements

8/12/2019 411-Design of Highway Pavements

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411. Design of Highway Pavements

411.1. Equivalent Single Axle Load

For design of highway pavementsrigid and flexibleone of the most

significant inputs into the design process is the traffic volume and

composition. Heavier vehicle axles have significantly higher potential for

causing damage to pavements than lighter axles. Passenger cars and pickup

trucks are excluded from the calculation of wheel load impact on pavements.

In order to standardize the vehicular impact on the condition and life

expectancy of a pavement,AASHTO Guide for Design of Pavement

Structuresconverts all vehicle axles (single, double, and triple axles) of

various axle loads to an equivalent number of 18-kip single axles. The load

equivalence factor (LEF) is based on damage potential. For example, if the

LEF for a 12-kip single axle on a flexiblepavement with a structural number

(SN) of 4 is 0.213, this means that on a flexible pavement with SN = 4, a

12,000-lb single axle has the potential to cause about 21% of the damage that

would be caused by an 18-kip single axle.

The equivalent single axle load (ESAL) is the cumulative 18-kip equivalent for

a pavement over its entire design life. It is calculated as the summation of the

LEF values for the total number of axles expected to use the pavement over

the plan duration. If the axles are classified by type (single-axle, tandem-axle,

triple axle, etc.) and load, then the ESAL is calculated as

(411.1)

Design of Highway Pavements
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where N is the number of axles in a particular category and LEF is the load

equivalence factor for that category.

The truck factor (TF) is defined as

(411.2)

411.1.1. Load Equivalence Factors

LEF values were generated based on AASHTO road tests conducted in

Ottawa, Illinois. Test traffic consisted of thousands of single axles (ranging

from 2 to 30 kips) and tandem axles (ranging from 24 to 48 kips) being driven

over pavements composed of an asphalt surface course (three different

thicknesses ranging from 1 to 6 in), a well-graded crushed limestone base

course (three different thicknesses ranging from 0 to 9 in) and a uniformly

graded sand-gravel subbase (three different thicknesses ranging from 0 to 6

in).

Tables 411.6 to 411.11 show load equivalence factors for single, double, and

triple axles on flexible and rigid pavements for terminal serviceability index

p = 2.5.

The serviceable life of a pavement is related to the difference in present

serviceability index (PSI) between construction and end-of-life. Typical values

used for PSI are:

Post-construction: 4.0 to 5.0 depending upon construction quality,

smoothness, etc.

End-of-life (called "terminal serviceability" and designated "p "): 1.5 to 3.0

depending upon road use (e.g., interstate highway, urban arterial,

residential). This chapter tabulates load equivalence factors for terminal

serviceabilityp = 2.5.

Example 411.1

Traffic data for a section of two-lane, bidirectional roadway shows the

following truck axle loads. Number of average daily trips (heavy vehicles

only) is 8500 with a 60/40 directional split. What is the annual equivalent

i i

t

t

t
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single axle load for the design lane? Assume all trucks are two-axle vehicles.

SolutionSince the ADT is 8500, the number of axles = 17,000. Of these, 67%

+ 21% are single axles and 6% + 6% are tandem axles. The ESAL is calculated

as

Example 411.2

The annual ESAL (W ) for a highway is calculated to be 280,000 in 2005.

Expecting a 4% growth in traffic per year over the next 10 years, what is the

cumulative ESAL for this highway over the 10-year period?

SolutionThe situation described is a geometric series with the first term a=280,000 and the rate of increase r= 1.04. The sum of the first 10 terms is

given by

Note that the factor 12.0061 in the example above may be called a growth

factor and it is numerically identical to the F/A factor in the engineering

economics tables (Chap. 501) for n= 10 and i= 4%.

411.2. Flexible Pavements

Axle type Gross load (lb) LEF % ADT

Single 6000 0.017 67

10000 0.118 21

Tandem 14000 0.042 6

22000 0.229 6

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Flexible pavements are composed of a wearing surface, usually composed of

bituminous materials, underlain by a layer of granular material (base course)

and a layer of blended aggregates (subbase). This arrangement is underlain

by a well-compacted subgrade that serves as the foundation of the

pavement. Flexible pavements are also classified as high-type, intermediate-

type, and low-type. High-type pavements support the traffic loads without

any visible distress and are not susceptible to weather conditions. Low-type

pavements have wearing surfaces that range from untreated to loose

materials to surface treated earth. Intermediate-type pavements, as the name

suggests, have qualities between those of high- and low-type pavements.

The subbase course is the portion of the flexible pavement structure

between the roadbed soil and the base course. It usually consists of a

compacted layer of granular material or of a layer of soil treated with an

admixture. The subbase may be omitted from the pavement cross-section

design if the underlying soil bed is of high quality. In addition to contributing

to the overall structural strength of the pavement, the subbase course may

have the following secondary functionsimprove drainage characteristics,

prevent intrusion of fines into the base course, and minimize frost damage.

The base course is that portion of the pavement structure, which isimmediately beneath the surface course. It lies either above the subbase

course or if no subbase course is used, it may lie directly on the roadbed soil.

It usually consists of aggregates such as crushed stone, crushed gravel, and

sand, which may be untreated or treated with stabilizing admixtures such as

asphalt, lime, Portland cement, etc.

411.3. Stress Distribution Within the Pavement Thickness

Modeling the surface layer as a flexible beam subject to the wheel load, Fig.

411.1 shows typical distribution of vertical and horizontal stresses through

the pavement thickness.
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Figure 411.1. Stresses in a flexible pavement due to wheel loads.

411.4. Structural Number

Flexible pavements are characterized by the structural number (SN), which is

calculated as

(411.3)

where a , a , and a are strength coefficients for layers 1, 2, and 3, and m

and m are drainage coefficients for layers 2 and 3.

Default values for layer strength coefficients are

Asphalt concrete surface course a = 0.44

Crushed stone base course a = 0.14

Sandy gravel subbase a = 0.11

Coefficients m and m represent drainage coefficients of base course and

subbase, respectively. Values of these coefficients range from 0.4 to 1.4.

Values of mhigher than 1.0 are assigned where these courses have very

good drainage characteristics.

Minimum pavement layer thicknesses recommended by AASHTO are shown in

Table 411.1.

1 2 3 2

3

1

2

3

2 3


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Table 411.1. Minimum Recommended Thickness of Flexible Pavement

Components (AASHTO)

Example 411.3

The design structural number of a flexible pavement is 5. The pavement

cross section consists of an asphalt surface course (minimum thickness = 4.0

in) underlain by a granular base course (maximum thickness 18 in). The

following layer coefficients are given:

Asphalt concrete surface course a = 0.45 in

Crushed stone base course a = 0.15 in

What is the minimum required thickness of the surface course (in)?

SolutionIn order for the surface course to have minimum thickness, we must

use the maximum permissible thickness for the base course, D = 18 in.

Assuming drainage coefficient m = 1.0, we can write

Since this is greater than the minimum requirement of 4 in, the required

thickness of the asphalt surface course is 5.5 in.

ESAL

[Minimum thickness

(in)] Asphalt

concrete

[Minimum thickness

(in)] Aggregate base

7,000,000 4.0 6.0

1-1

2-1

2

2


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411.5. Flexible Pavement Design

The following criteria are important guideposts for the overall design of

asphalt pavements:

Sufficient asphalt to ensure a durable pavement

Sufficient stability under traffic loads

Sufficient air-voidslower limit to allow room for initial densification due to

traffic and upper limit to prevent excessive environmental damage

Sufficient workability

411.6. Purposes of Compaction

To prevent further compaction and settlement

To increase shear strength

To improve water tightness of mixture

prevent excessive oxidation of the asphalt binder

The basic design equation for flexible pavements is given by

(411.4)

where W = number of equivalent single axle load applications over

design life (ESAL)

Z = standard normal deviation corresponding to a given reliability

S = overall standard deviation

SN = structural number of pavement

PSI = loss of serviceability index = p p

M = resilient modulus of subgrade soil (lb/in )

18

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o

i t

r2


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411.7. Asphalt

Hot mix asphalt (HMA) is a mixture of asphalt binder and well-graded, high-

quality aggregate heated and compacted. Asphalt is placed in multiple lifts

(layers). Using deep lifts has the following advantages: (1) thicker layers hold

heat longer and it is therefore easier to roll the layers to the required

density, (2) deeper lifts can be placed in cooler weather, (3) one deep lift is

more economical than multiple lifts, and (4) deep lifts suffer less distortion

due to rolling than thin lifts.

Asphalt mix design may be performed using the Hveem, Marshall, or

Superpave mix design methods.

411.7.1. Asphalt Grading

In the past, asphalt cement (AC) was graded by either penetration resistance

or viscosity.

Penetration Grading

Penetration graded asphalts were specified by a measurement by a

standardized penetrometer needle (mass = 100 g) under a standard load at a

standard temperature. Penetration graded asphalts were typically expressed

as "Penetration Grade 85-100," meaning that the needle penetration was

between 85 and 100 mm. Higher penetration signifies a softer AC. Five

different penetration grades ranging from hard (4050 mm penetration) to

soft (200300 mm penetration) are specified in this classification system.

Penetration grading describes only the consistency at an intermediate

temperature (25C). Low-temperature properties are not directly measured

by this grading system.

Viscosity Grading

Viscosity-graded asphalts were specified by determining the viscosity of

asphalt cement. A temperature of 60C (140F) was considered to be a typical

summer pavement temperature, and at this temperature, the unit of viscosityused was the poise. Standard terminology referred to AC-10 and AC-20,

meaning that the viscosity of the AC was 1000 or 2000 poise, respectively. AC-

20 was thicker or harder than AC-10. A temperature of 135C (275F) was


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considered the mixing and handling control point. At this temperature,

different laboratory equipment was used and the unit of viscosity used was

the centistoke (cS).

Although viscosity is a fundamental measure of flow, it only provides

information about high temperature viscous behavior, not about the low or

intermediate temperature elastic behavior.

Performance Grading

In 1994, a new system of design for asphalt paving materials known as

Superpave, which introduced a new concept called performance grading, was

introduced based on research done under the Strategic Highway Research

Program (SHRP). The performance grading (PG) system of specifying binder

is based on a complex series of performance-based tests.

The new system for specifying asphalt binders is based on performance at

specified temperatures. Physical property requirements are the same, but

the temperature at which the binder must attain the properties changes. For

example, the high temperature, unaged binder stiffness (G/sin ) is

required to be at least 1.0 kPa, but this must be achieved at higher

temperatures if the binder is to be adequate in a hot climate.

Binder physical properties are measured using four devices:

1. Dynamic shear rheometer The dynamic shear rheometer is used to

characterize the viscoelastic properties of the binder. It measures the

complex shear modulus (G) and phase angle (). For totally elastic

materials, there is no lag ( = 0) between the applied shear stress and the

shear strain response of the sample. For totally viscous materials, = 90.

The binder specification uses either G/sin at higher temperatures (T>

46C) or G sin at intermediate temperatures (7C < T< 34C) as a

means of controlling asphalt stiffness.

2. Rotational viscometerThis test characterizes the stiffness of the asphalt

at 135C, at which temperature it behaves almost entirely as a viscous

fluid. The RTV is a rotational coaxial cylinder that measures viscosity by

the torque required to rotate a spindle submerged in a sample of hot

asphalt at a constant speed. The binder specification requires that binders

have a viscosity of less than 3 Pa-s.


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3. Bending beam rheometer The BBR measures the creep stiffness (S) and

the logarithmic creep rate (m) by measuring the response of a small binder

beam specimen to a creep load at low temperatures. Binders with low

creep stiffness and/or higher mvalues will not crack in cold weather.

4. Direct tension tester A high creep stiffness (at low temperatures) may be

acceptable if a direct tension test shows that the binder is sufficiently

ductile at low temperatures.

411.8. Superpave

The new specification system no longer refers to asphalt cement, but rather

to binder, which includes modified and unmodified asphalts. It specifies

asphalt binders as PG followed by two numbers, for example PG 66-20. Thefirst number is always higher and positive, while the second number is

smaller and negative. The first number represents the high pavement

temperatureand is based on the 7-day average high air temperature of the

surrounding area, while the second number represents the low pavement

temperatureand is based on the 1-day low air temperature of the

surrounding area. Both numbers referred to are in degrees Celsius. PG

asphalt binders are specified in 6C increments. If the sum of the twonumbers (absolute value) >90, then use of polymer-modified asphalt is

indicated.

The Superpave software calculates high pavement temperature 20 mm below

the pavement surface and low temperature at the pavement surface. Design

pavement temperature calculations are based on HMA pavements subjected

to fast-moving traffic. Pavements subject to slow traffic, such as at

intersections, toll booths, and bus stops should contain a stiffer asphalt

binder than that which would be used for fast-moving traffic. Superpave

allows the high-temperature grade to be increased by one grade (6C) for

slow transient loads and by two grades (12C) for stationary loads.

Additionally, the high-temperature grade should be increased by one grade

for anticipated 20-year loading in excess of 30 million ESALs. For pavements

with multiple conditions that require grade increases, only the largest grade

increase should be used. For example, for a pavement intended to experienceslow loads (one grade increase) and greater than 30 million ESALs (one grade

increase), the asphalt binder high-temperature grade should be increased by

only one grade.


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In Superpave, the high pavement design temperature at a depth of 20 mm is

calculated using Eq. (411.5)

(411.5)

where T = 7-day average high air temperature (C) of the surrounding

area

lat = latitude (degrees) of location

The pavement low temperature (C) is calculated using Eq. (411.6)

(411.6)

Example 411.4

For Topeka, KS (39.02N, 95.687W), the average 7-day maximum air

temperature is 36C with a standard deviation of 2C. The average coldest air

temperature is 23C, with a standard deviation of 4C.

SolutionAccording to Eqs. (411.5) and (411.6), for a high air temperature of

36C, the mean pavement high temperature is expected to be 56C and for a

low air temperature of 23C, the mean pavement low temperature is

expected to be 18C. For 98% reliability (2 standard deviations away from

the mean), these should be adjusted to 56 + 2 2 = 60C and to 18 2 4

= 26C. Therefore, the performance grading should be PG 64-34. To account

for slow transient loads, the designer should select one grade higher binder,

a grade of PG 70-34.

411.8.1. Mixture Volumetric Requirements

Voids in mineral aggregate (VMA) is the sum of the volume of air voids and

effective (unabsorbed) binder in a compacted sample. It represents the void

space between aggregate spaces. Table 411.2 shows Superpave VMArequirements.

Table 411.2. Voids in Mineral Aggregate (VMA) Requirements in

air
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Superpave

Voids filled with asphalt (VFA) is defined as the percentage of the VMA

containing asphalt binder. Table 411.3 shows Superpave VFA requirements.

Table 411.3. Voids Filled with Asphalt (VFA) Requirements in

Superpave

411.8.2. Dust Proportion

Dust proportion is computed as the ratio of the percentage (by weight) of

Nominal maximum aggregate

size (mm)Minimum VMA (%)

9.5 15

12.5 14

19.0 13

25.0 12

37.5 11

Traffic (ESALs) Design VFA (%)


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aggregate finer than no. 200 sieve (0.075 mm) to the effective asphalt

content, expressed as a percent of the total mix. Effective asphalt content is

the total asphalt content less the percentage of absorbed asphalt. In the

Superpave guidelines, acceptable dust proportion should be in the range 0.6

to 1.2.

The Superpave mix design method consists of seven basic steps:

1. Aggregate selection

2. Asphalt binder selection

3. Sample preparation (including compaction)

4. Performance tests

5. Density and voids calculations

6. Optimum asphalt binder content selection

7. Moisture susceptibility evaluation

411.9. Aggregates in Asphalt Mix

Desirable properties of aggregates in hot mix asphalt are toughness,

soundness, and good gradation.

The nominal maximum aggregate size is defined as one size larger than the

first sieve to retain more than 10%. The maximum aggregate sizeis defined

as one size larger than the nominal maximum aggregate size.

Coarse aggregate is that designated as retained on the 4.75-mm sieve andfine aggregate is that passing the 4.75-mm sieve.

Combined Specific Gravity of Aggregates

When various aggregates (1, , n) with specific gravities G , , G are

combined in proportions (percentages) P , , P (where P + + P =

100), the overall specific gravity of the mix is given by

1 n

1 n 1 n


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(411.7)

Apparent specific gravity of an aggregate is designated G . It is calculated

as

(411.8)

The bulk specific gravity of an aggregate mixture is calculated using bulk

specific gravity values for each component aggregate. Similarly, the apparent

specific gravity of an aggregate mixture is calculated using apparent specific

gravity values for each component aggregate.

Coarse Aggregate Specific Gravity Calculations (ASTM C127)

The standard test procedure ASTM C127 outlines the following steps for

determining parameters of a coarse aggregate:

From the test, the following measurements are made:

A= weight of oven dry aggregate

sa

Steps: Dry aggregate

Soak in water for 24 h

Decant water

Use dampened cloth to obtain

surface saturated dry (SSD)

condition

Determine weight of SSD aggregate

(B)

Submerge and determine weight of

submerged aggregate (C)

Dry to constant mass

Determine oven dry weight (A)


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B= weight of SSD aggregate

C= weight of submerged (water) aggregate

The bulk specific gravity is given by

(411.9)

The specific gravity of the SSD aggregate is given by

(411.10)

The apparent specific gravity of the aggregate is given by

(411.11)

(411.12)

Fine Aggregate Specific Gravity Calculations (ASTM C128)

The standard test procedure ASTM C128 outlines the following steps for

determining parameters of a fine aggregate:

Steps: Dry aggregate

Soak in water for 24 h

Spread out and dry to SSD condition

Add 500 g of SSD aggregate to

pycnometer of known volume

Add water and agitate to remove allair

Fill to line and determine mass of


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From the test, the following measurements are made:

A= weight of oven dry aggregate

B= weight of pycnometer filled with water

C= weight of pycnometer, SSD aggregate and water

S= weight of SSD aggregate (standard value 500 g)

The bulk specific gravity is given by

(411.13)

The specific gravity of the SSD aggregate is given by

(411.14)

The apparent specific gravity of the aggregate is given by

(411.15)

(411.16)

411.10. Hot-Mix Asphalt-Volumetric Relationships

pycnometer, aggregate, and water

(C)

Empty aggregate into pan and dry

to constant mass

Determine oven dry mass (A)


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The various constituents of total mass and total volume of an asphalt mix are

shown in Fig. 411.2.

Figure 411.2. Composition of an asphalt mix

The maximum specific gravity of the paving mixture is calculated using

(411.17)

where P = percentage of aggregate in the mixture

G = effective specific gravity of the aggregate

P = percentage of asphalt in the mixture

G = specific gravity of the asphalt

This can be also written as

s

se

b

b
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(411.18)

The total air voids (%) is given by

(411.19)

where G = maximum bulk specific gravity

G = maximum possible specific gravity

G = bulk specific gravity of aggregate mixture

P = percentage of aggregate in the mixture

Voids in mineral aggregate (VMA) is an indication of the film thickness on the

surface of the aggregate. The VMA (%) is given by

(411.20)

Voids filled with asphalt (VFA) is the percentage of VMA that is filled with

asphalt. The VFA (%) is given by

(411.21)

411.10.1. Unit Volume Approach to Calculating Asphalt Properties

For a total volume = 1.0, the following relationships are useful in calculating

all components of the asphalt mix:

Volume of bulk aggregate = mass of aggregate bulk SG of aggregate

Effective volume of aggregate = mass of aggregate effective SG of

aggregate

mb

mm

sb

s


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Volume of absorbed asphalt = volume of bulk aggregate effective volume

of aggregate

Effective volume of asphalt = total volume of asphalt volume of absorbed

asphalt

Volume of air = total volume total volume of asphalt effective volume ofaggregate which can also be expressed as:

Volume of air = total volume total volume of asphalt + volume of

absorbed asphalt volume of bulk aggregate

or

Volume of air = total volume (effective volume of asphalt + volume of

bulk aggregate)

VMA = volume of air + effective volume of asphalt = total volume volume

of bulk aggregate

VFA = effective volume of asphalt VMA

Example 411.5

A sample of compacted hot mix asphalt is known to have the following

properties at 25C

Mix bulk specific gravity = 2.329

Bulk specific gravity of aggregate = 2.705

Effective specific gravity of aggregate = 2.731

Asphalt binder specific gravity = 1.015

Asphalt content = 5% by weight

What are the (a) VMA, (b) VFA, and (c) maximum theoretical specific gravity?

Solution

Assume a total volume = 1.0 ft

Weight of asphalt mix = 2.329 62.4 1.0 = 145.33 lb

3


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Total weight of asphalt = 0.05 145.33 = 7.27 lb

Total volume of asphalt = 7.27/(1.015 62.4) = 0.115 ft

Total weight of aggregate = 145.33 7.27 = 138.06 lb

Volume of bulk aggregate = 138.06/(2.705 62.4) = 0.818 ft

Effective volume of aggregate = 138.06/(2.731 62.4) = 0.810 ft

Volume of absorbed asphalt = 0.818 0.810 = 0.008 ft

Effective volume of asphalt = 0.115 0.008 = 0.107 ft

Effective mass of asphalt = 0.107 1.015 62.4 = 6.78 lb

Effective asphalt content = 6.78/145.33 = 4.66%

Absorbed asphalt content = 5.0 4.66 = 0.34%

Volume of air = 1.0 0.115 0.810 = 0.075 ft

(a) VMA = 1.0 0.818 = 0.182 ft

(b) VFA = 0.107/0.182 = 0.588 = 58.8%

Maximum theoretical unit weight = (Weight of asphalt + weight of

aggregate)/(Effective volume of asphalt + Bulk aggregate volume) = (7.27

+ 138.06)/(0.107 + 0.818) = 157.11 lb/ft

(c) Maximum theoretical specific gravity = 157.11/62.4 = 2.518

Example 411.6

An asphalt mix contains the following constituents (see the table below). The

bulk specific gravity of the mixture is 2.34. The specific gravity of a voidless

mixture (i.e., the maximum specific gravity) is 2.55.

Calculate the following: (a) bulk specific gravity of the aggregate, (b) effective

specific gravity of the aggregate, (c) asphalt absorption, (d) air void content

of the asphalt mixture, (e) VMA of the asphalt mixture, and (f) the effective

asphalt content of the mixture.

3

3

3

3

3

3

3

3

ComponentPercentage (by

weight)Specific gravity

Apparent

specific gravity


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Solution

a. The aggregate is composed of the three components limestone dust,

sand, and gravel.

The bulk specific gravity of the aggregate is calculated as:

b. The effective specific gravity of the aggregate is calculated from Eq.

(411.18)

c. The asphalt absorption is calculated from

d. The air void content (VTM) is calculated from Eq. (411.19)

e. The voids in mineral aggregate (VMA) is calculated from Eq. (411.20)

f. The effective asphalt content (%) is calculated using

Asphalt 5.4 1.02

Limestone dust 14.2 2.66 2.80

Sand 29.5 2.61 2.68

Gravel 50.9 2.62 2.65
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411.11. Rigid Pavement Design

The design of a rigid pavement involves design of the thickness of the

concrete slab, choice of reinforcement, and load transfer devices for joints.

The basic materials in the pavement slab arePortland cement concrete,

reinforcement steel, either in the form of reinforcement bars or welded wire

fabric, joint transfer devices and joint sealing materials. There are four

primary types of concrete pavement. They are (1) jointed plain concrete

pavement (JPCP), (2) jointed reinforced concrete pavement (JRCP), (3)

continuous reinforced concrete pavement (CRCP), and (4) prestressed

concrete pavement (PCP).

411.11.1. AASHTO Method: Rigid Pavement Design

According toAASHTO Guide for Design of Pavement Structures , the basic

design equation for flexible pavements is given by

(411.22)

where W = predicted number of equivalent single axle load applications

over design life

Z = standard normal deviation corresponding to a given reliability

S = combined standard error of traffic prediction and performance

prediction

D= thickness of the concrete pavement (in)

PSI = loss of serviceability index = p p

E = modulus of elasticity of concrete (lb/in )

S ' = modulus of rupture of concrete (lb/in )

J= load transfer coefficient = 3.2

18

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2

c2


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C = drainage coefficient

k= effective modulus of subgrade reaction (lb/in ); the k-value, similar to

modulus of elasticity, is the primary performance indicator of the soil

The tensile strength of concrete is expressed as the modulus of rupture

(S ). This is similar to, but is not exactly f (as defined by ACI) but rather is

specified by AASHTO T97 or ASTMC78.

The modulus of elasticity of concrete E (psi) is given by

where f is the 28-day compressive strength (psi) of the concrete.

California bearing ratio (CBR) is correlated with subgrade modulus k.

411.11.2. Reinforcement

The purpose of reinforcement in a rigid pavement slab is to hold cracks

together, thus maintaining the overall integrity of the pavement. Cracking in

a slab-on-grade is caused by differential between the temperature and

moisture related contraction of the slab and the frictional resistance from the

material underlying the slab. For such slabs, the maximum tensile stresses

occur at mid-depth. If this maximum stress exceeds the tensile strength of

the concrete, cracks form, and the stress transfers to the reinforcement.

Short slabs (L


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411.11.3. Joint Sealing Materials

Three different types of joint sealing materials are used currently: (1) liquid

sealants, such as asphalt, silicone, hot rubber and polymers; (2) cork

expansion joint fillers; and (3) preformed elastomeric (neoprene) seals.

The purpose of using longitudinal joints in a concrete pavement is that

cracks form at known locations, so that such cracks may be sealed properly.

The maximum recommended spacing of longitudinal joints is 16 ft.

Table 411.4 shows Z values for various reliability levels.

Table 411.4. Standard Normal Deviation (ZR)

Table 411.5 shows overall standard deviation recommended for flexible and

rigid pavements.

Table 411.5. Standard Deviation Recommended for Pavement Design

Figure 411.3 shows a nomograph, reproduced fromAASHTO Guide for

R

Reliability (%) Z

90 minus;1.282

95 1.645

99 2.327

99.9 3.090

99.99 3.750

R

Pavement type Standard deviation, S

Flexible 0.400.50

Rigid 0.300.40

o
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411fig03http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411table05http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411table04


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Design of Pavement Structures, which can be used to solve Eq. (411.4).

Figure 411.3. Design chart for flexible pavements.

411.11.4. Resilient Modulus M

As adopted byAASHTO Design of Pavement Structures , the definitive

material property used to characterize roadbed soil is the resilient modulus

(M ), which is determined using AASHTO Test Method T 274. The resilient

modulus can be used directly for the design of flexible pavements but mustbe converted to the modulus of subgrade reaction (k) for the design of rigid

pavements. A correlation between the CBR value and the resilient modulus

has been established (Huekelom and Klomp, 1962) as

(411.24)

Similarly, the Asphalt Institute has developed the following correlation

between M and the R-value:

R

R

R
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411eq04


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(411.25)

whereA= 772 to 1155

B= 369 to 555

Figure 411.4. Design chart for rigid pavements (segment 1).

The pavement design guide recommends using

(411.26)

In the approach using the design charts and nomographs, the variables R,

S , and ESAL are used to determine the x-coordinate, whereas the variables

k, E , S ,J, C , and PSI are used to determine they-coordinate. A design

chart inAASHTO Guide for Desi n of Pavement Structures is then used to

o

c c d


27/41

plot a point with these coordinates and estimate the required pavement

thickness.


triple axles on flexible pavements of various structural number, andp = 2.5.

Table 411.6. Axle Load Equivalence Factors for Flexible Pavements,

Single Axles, pt = 2.5

t

Pavement structural number (SN)

Axle

load

(kips)

1 2 3 4 5 6

2 0.0004 0.0004 0.0003 0.0002 0.0002 0.0002

4 0.003 0.004 0.004 0.003 0.002 0.002

6 0.011 0.017 0.017 0.013 0.010 0.009

8 0.032 0.047 0.051 0.041 0.034 0.031

10 0.078 0.102 0.118 0.102 0.088 0.080

12 0.168 0.198 0.229 0.213 0.189 0.176

14 0.328 0.358 0.399 0.388 0.360 0.342

16 0.591 0.613 0.646 0.645 0.623 0.606

18 1.00 1.00 1.00 1.00 1.00 1.00

20 1.61 1.57 1.49 1.47 1.51 1.55

22 2.48 2.38 2.17 2.09 2.18 2.30

24 3.69 3.49 3.09 2.89 3.03 3.27

26 5.33 4.99 4.31 3.91 4.09 4.48

28 7.49 6.98 5.90 5.21 5.39 5.98

30 10.3 9.5 7.9 6.8 7.0 7.8

32 13.9 12.8 10.5 8.8 8.9 10.0

34 18.4 16.9 13.7 11.3 11.2 12.5
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411table08http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch411#ch411table06


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Tandem Axles, pt = 2.5

36 24.0 22.0 17.7 14.4 13.9 15.5

38 30.9 28.3 22.6 18.1 17.2 19.0

40 39.3 35.9 28.5 22.5 21.1 23.0

42 49.3 45.0 35.6 27.8 25.6 27.7

44 61.3 55.9 44.0 34.0 31.0 33.1

46 75.5 68.8 54.0 41.4 37.2 39.3

48 92.2 83.9 65.7 50.1 44.5 46.5

50 112.0 102.0 79.0 60.0 53.0 55.0


Axle

load

(kips)

1 2 3 4 5 6

2 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000

4 0.0005 0.0005 0.0004 0.0003 0.0003 0.0002

6 0.002 0.002 0.002 0.001 0.001 0.001

8 0.004 0.006 0.005 0.004 0.003 0.003

10 0.008 0.013 0.011 0.009 0.007 0.006

12 0.015 0.024 0.023 0.018 0.014 0.013

14 0.026 0.041 0.042 0.033 0.027 0.024

16 0.044 0.065 0.070 0.057 0.047 0.043

18 0.070 0.097 0.109 0.092 0.077 0.070

20 0.107 0.141 0.162 0.141 0.121 0.110

22 0.160 0.198 0.229 0.207 0.180 0.166


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24 0.231 0.273 0.315 0.292 0.260 0.242

26 0.327 0.370 0.420 0.401 0.364 0.342

28 0.451 0.493 0.548 0.534 0.495 0.470

30 0.611 0.648 0.703 0.695 0.658 0.633

32 0.813 0.843 0.889 0.887 0.857 0.834

34 1.06 1.08 1.11 1.11 1.09 1.08

36 1.38 1.38 1.38 1.38 1.38 1.38

38 1.75 1.73 1.69 1.68 1.70 1.73

40 2.21 2.16 2.06 2.03 2.08 2.14

42 2.76 2.67 2.49 2.43 2.51 2.61

44 3.41 3.27 2.99 2.88 3.00 3.16

46 4.18 3.98 3.58 3.40 3.55 3.79

48 5.08 4.80 4.25 3.98 4.17 4.49

50 6.12 5.76 5.03 4.64 4.86 5.28

52 7.33 6.875.93

5.38 5.63 6.17

54 8.72 8.14 6.95 6.22 6.47 7.15

56 10.3 9.6 8.1 7.2 7.4 8.2

58 12.1 11.3 9.4 8.2 8.4 9.4

60 14.2 13.1 10.9 9.4 9.6 10.7

62 16.5 15.3 12.6 10.7 10.8 12.1

64 19.1 17.6 14.5 12.2 12.2 13.7

66 22.1 20.3 16.6 13.8 13.7 15.4

68 25.3 23.3 18.9 15.6 15.4 17.2

70 29.0 26.6 21.5 17.6 17.2 19.2

72 33.0 30.3 24.4 19.8 19.2 21.3

74 37.5 34.4 27.6 22.2 21.3 23.6


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Triple Axles, pt = 2.5

76 42.5 38.9 31.1 24.8 23.7 26.1

78 48.0 43.9 35.0 27.8 26.2 28.8

80 54.0 49.4 39.2 30.9 29.0 31.7

82 60.6 55.4 43.9 34.4 32.0 34.8

84 67.8 61.9 49.0 38.2 35.3 38.1

86 75.7 69.1 54.5 42.3 38.8 41.7

88 84.3 76.9 60.6 46.8 42.6 45.6

90 93.7 85.4 67.1 51.7 46.8 49.7


Axle

load

(kips)

1 2 3 4 5 6

2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

4 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001

6 0.0006 0.0007 0.0005 0.0004 0.0003 0.0003

8 0.001 0.002 0.001 0.001 0.001 0.001

10 0.003 0.004 0.003 0.002 0.002 0.002

12 0.005 0.007 0.006 0.004 0.003 0.003

14 0.008 0.012 0.010 0.008 0.006 0.006

16 0.012 0.019 0.018 0.013 0.011 0.010

18 0.018 0.029 0.028 0.021 0.017 0.016

20 0.027 0.042 0.042 0.032 0.027 0.024

22 0.038 0.058 0.060 0.048 0.040 0.036


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24 0.053 0.078 0.084 0.068 0.057 0.051

26 0.072 0.103 0.114 0.095 0.080 0.072

28 0.098 0.133 0.151 0.128 0.109 0.099

30 0.129 0.169 0.195 0.170 0.145 0.133

32 0.169 0.213 0.247 0.220 0.191 0.175

34 0.219 0.266 0.308 0.281 0.246 0.228

36 0.279 0.329 0.379 0.352 0.313 0.292

38 0.352 0.403 0.461 0.436 0.393 0.368

40 0.439 0.491 0.554 0.533 0.487 0.459

42 0.543 0.594 0.661 0.644 0.597 0.567

44 0.666 0.714 0.781 0.769 0.723 0.692

46 0.811 0.854 0.918 0.911 0.868 0.838

48 0.979 1.015 1.072 1.069 1.033 1.005

50 1.17 1.20 1.24 1.25 1.22 1.20

52 1.40 1.41 1.44 1.44 1.43 1.41

54 1.66 1.66 1.66 1.66 1.66 1.66

56 1.95 1.93 1.90 1.90 1.91 1.93

58 2.29 2.25 2.17 2.16 2.20 2.24

60 2.67 2.60 2.48 2.44 2.51 2.58

62 3.09 3.00 2.82 2.76 2.85 2.95

64 3.57 3.44 3.19 3.10 3.22 3.36

66 4.11 3.94 3.61 3.47 3.62 3.81

68 4.71 4.49 4.06 3.88 4.05 4.30

70 5.38 5.11 4.57 4.32 4.52 4.84

72 6.12 5.79 5.13 4.80 5.03 5.41

74 6.93 6.54 5.74 5.32 5.57 6.04

76 7.84 7.37 6.41 5.88 6.15 6.71


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triple axles on rigid pavements of various thicknesses, andp = 2.5.

Table 411.9. Axle Load Equivalence Factors for Rigid Pavements,

Single Axles, pt = 2.5

78 8.83 8.28 7.14 6.49 6.78 7.43

80 9.92 9.28 7.95 7.15 7.45 8.21

82 11.1 10.4 8.8 7.9 8.2 9.0

84 12.4 11.6 9.8 8.6 8.9 9.9

86 13.8 12.9 10.8 9.5 9.8 10.9

88 15.4 14.3 11.9 10.4 10.6 11.9

90 17.1 15.8 13.2 11.3 11.6 12.9

t

Slab thickness, D (in)

Axle

load

(kips)

6 7 8 9 10 11 12 1

2 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.00

4 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.00

6 0.012 0.011 0.010 0.010 0.010 0.010 0.010 0.01

8 0.039 0.035 0.033 0.032 0.032 0.032 0.032 0.03

10 0.097 0.089 0.084 0.082 0.081 0.080 0.080 0.08

12 0.203 0.189 0.181 0.176 0.175 0.174 0.174 0.17

14 0.376 0.360 0.347 0.341 0.338 0.337 0.336 0.33

16 0.634 0.623 0.610 0.604 0.601 0.599 0.599 0.59

18 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

20 1.51 1.52 1.55 1.57 1.58 1.58 1.59 1.59


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Tandem Axles, pt = 2.5

22 2.21 2.20 2.28 2.34 2.38 2.40 2.41 2.41

24 3.16 3.10 3.22 3.36 3.45 3.50 3.53 3.54

26 4.41 4.26 4.42 4.67 4.85 4.95 5.01 5.04

28 6.05 5.76 5.92 6.29 6.61 6.81 6.92 6.98

30 8.16 7.67 7.79 8.28 8.79 9.14 9.35 9.46

32 10.8 10.1 10.1 10.7 11.4 12.0 12.3 12.6

34 14.1 13.0 12.9 13.6 14.6 15.4 16.0 16.4

36 18.2 16.7 16.4 17.1 18.3 19.5 20.4 21.0

38 23.1 21.1 20.6 21.3 22.7 24.3 25.6 26.4

40 29.1 26.5 25.7 26.3 27.9 29.9 31.6 32.9

42 36.2 32.9 31.7 32.2 34.0 36.3 38.7 40.4

44 44.6 40.4 38.8 39.2 41.0 43.8 46.7 49.1

46 54.5 49.3 47.1 47.3 49.2 52.3 55.9 59.0

48 66.1 59.7 56.9 56.8 58.7 62.1 66.3 70.3

50 79.4 71.7 68.2 67.8 69.6 73.3 78.1 83.0


Axle

load

(kips)

6 7 8 9 10 11 12 1

2 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.00

4 0.0006 0.0006 0.0005 0.0005 0.0005 0.0005 0.0005 0.00

6 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.00

8 0.007 0.006 0.006 0.005 0.005 0.005 0.005 0.00


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10 0.015 0.014 0.013 0.013 0.012 0.012 0.012 0.01

12 0.031 0.028 0.026 0.026 0.025 0.025 0.025 0.02

14 0.057 0.052 0.049 0.048 0.047 0.047 0.047 0.04

16 0.097 0.089 0.084 0.082 0.081 0.081 0.080 0.08

18 0.155 0.143 0.136 0.133 0.132 0.131 0.131 0.13

20 0.234 0.220 0.211 0.206 0.204 0.203 0.203 0.20

22 0.340 0.325 0.313 0.308 0.305 0.304 0.303 0.30

24 0.475 0.462 0.450 0.444 0.441 0.440 0.439 0.43

26 0.644 0.637 0.627 0.622 0.620 0.619 0.618 0.61

28 0.855 0.854 0.852 0.850 0.850 0.850 0.849 0.84

30 1.11 1.12 1.13 1.14 1.14 1.14 1.14 1.14

32 1.43 1.44 1.47 1.49 1.50 1.51 1.51 1.51

34 1.82 1.82 1.87 1.92 1.95 1.96 1.97 1.97

36 2.29 2.27 2.35 2.43 2.48 2.51 2.51 2.52

38 2.85 2.80 2.91 3.03 3.12 3.16 3.18 3.20

40 3.52 3.42 3.55 3.74 3.87 3.94 3.98 4.00

42 4.32 4.16 4.30 4.55 4.74 4.86 4.91 4.95

44 5.26 5.01 5.16 5.48 5.75 5.92 6.01 6.06

46 6.36 6.01 6.14 6.53 6.90 7.14 7.28 7.36

48 7.64 7.16 7.27 7.73 8.21 8.55 8.75 8.86

50 9.11 8.50 8.55 9.07 9.68 10.14 10.42 10.5

52 10.8 10.0 10.0 10.6 11.3 11.9 12.3 12.5

54 12.8 11.8 11.7 12.3 13.2 13.9 14.5 14.8

56 15.0 13.8 13.6 14.2 15.2 16.2 16.8 17.3

58 17.5 16.0 15.7 16.3 17.5 18.6 19.5 20.1

60 20.3 18.5 18.1 18.7 20.0 21.4 22.5 23.2

62 23.5 21.4 20.8 21.4 22.8 24.4 25.7 26.7


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Triple Axles, pt = 2.5

64 27.0 24.6 23.8 24.4 25.8 27.7 29.3 30.5

66 31.0 28.1 27.1 27.6 29.2 31.3 33.2 34.7

68 35.4 32.1 30.9 31.3 32.9 35.2 37.5 39.3

70 40.3 36.5 35.0 35.3 37.0 39.5 42.1 44.3

72 45.7 41.4 39.6 39.8 41.5 44.2 47.2 49.8

74 51.7 46.7 44.6 44.7 46.4 49.3 52.7 55.7

76 58.3 52.6 50.2 50.1 51.8 54.9 58.6 62.1

78 65.5 59.1 56.3 56.1 57.7 60.9 65.0 69.0

80 73.4 66.2 62.9 62.5 64.2 67.5 71.9 76.4

82 82.0 73.9 70.2 69.6 71.2 74.7 79.4 84.4

84 91.4 82.4 78.1 77.3 78.9 82.4 87.4 93.0

86 102 92 87 86 87 91 96 102

88 113 102 96 95 96 100 105 112

90 125 112 106 105 106 110 115 123


Axle

load

(kips)

6 7 8 9 10 11 12 1

2 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.00

4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.00

6 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.00

8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.00


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10 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.00

12 0.011 0.010 0.010 0.009 0.009 0.009 0.009 0.00

14 0.020 0.018 0.017 0.017 0.016 0.016 0.016 0.01

16 0.033 0.030 0.029 0.028 0.027 0.027 0.027 0.02

18 0.053 0.048 0.045 0.044 0.044 0.043 0.043 0.04

20 0.080 0.073 0.069 0.067 0.066 0.066 0.066 0.06

22 0.116 0.107 0.101 0.099 0.098 0.097 0.097 0.09

24 0.163 0.151 0.144 0.141 0.139 0.139 0.138 0.13

26 0.222 0.209 0.200 0.195 0.194 0.193 0.192 0.19

28 0.295 0.281 0.271 0.265 0.263 0.262 0.262 0.26

30 0.384 0.371 0.359 0.354 0.351 0.350 0.349 0.34

32 0.490 0.480 0.468 0.463 0.460 0.459 0.458 0.45

34 0.616 0.609 0.601 0.596 0.594 0.593 0.592 0.59

36 0.765 0.762 0.759 0.757 0.756 0.755 0.755 0.75

38 0.939 0.941 0.946 0.948 0.950 0.951 0.951 0.95

40 1.14 1.15 1.16 1.17 1.18 1.18 1.18 1.18

42 1.38 1.38 1.41 1.44 1.45 1.46 1.46 1.46

44 1.65 1.65 1.70 1.74 1.77 1.78 1.78 1.78

46 1.97 1.96 2.03 2.09 2.13 2.15 2.16 2.16

48 2.34 2.31 2.40 2.49 2.55 2.58 2.59 2.60

50 2.76 2.71 2.81 2.94 3.02 3.07 3.09 3.10

52 3.24 3.15 3.27 3.44 3.56 3.62 3.66 3.68

54 3.79 3.66 3.79 4.00 4.16 4.26 4.30 4.33

56 4.41 4.23 4.37 4.63 4.84 4.97 5.03 5.07

58 5.12 4.87 5.00 5.32 5.59 5.76 5.85 5.90

60 5.91 5.59 5.71 6.08 6.42 6.64 6.77 6.84

62 6.80 6.39 6.50 6.91 7.33 7.62 7.79 7.88


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64 7.79 7.29 7.37 7.82 8.33 8.70 8.92 9.04

66 8.90 8.28 8.33 8.83 9.42 9.88 10.17 10.3

68 10.1 9.4 9.4 9.9 10.6 11.2 11.5 11.7

70 11.5 10.6 10.6 11.1 11.9 12.6 13.0 13.3

72 13.0 12.0 11.8 12.4 13.3 14.1 14.7 15.0

74 14.6 13.5 13.2 13.8 14.8 15.8 16.5 16.9

76 16.5 15.1 14.8 15.4 16.5 17.6 18.4 18.9

78 18.5 16.9 16.5 17.1 18.2 19.5 20.5 21.1

80 20.6 18.8 18.3 18.9 20.2 21.6 22.7 23.5

82 23.0 21.0 20.3 20.9 22.2 23.8 25.2 26.1

84 25.6 23.3 22.5 23.1 24.5 26.2 27.8 28.9

86 28.4 25.8 24.9 25.4 26.9 28.8 30.5 31.9

88 31.5 28.6 27.5 27.9 29.4 31.5 33.5 35.1

90 34.8 31.5 30.3 30.7 32.2 34.4 36.7 38.5


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Figure 411.4. Design chart for rigid pavements (segment 2).

411.12. Frost Action

Frost action, which can be quite detrimental to pavements because of its


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effect on the underlying subgrade, can be divided into "frost heave" and

"thaw weakening." "Frost heave" is an upward movement of the subgrade

resulting from the expansion of accumulated soil moisture as it freezes, while

"thaw weakening" is a weakened subgrade condition resulting from soil

saturation as ice within the soil melts.

411.12.1. Frost Heave

Frost heaving of soil is caused by the formation of ice crystals within the soil

voids and the tendency of this ice to form continuous ice lenses, layers, veins,

or other ice masses. As the ice lens grows/thickens, the overlying soil and

pavement will "heave" up potentially resulting in a rough, cracked pavement.

Frost heave occurs primarily in soils containing fine particles ("frostsusceptible" soils), while clean sands and gravels (small amounts of fine

particles) are non-frost susceptible (NFS). Thus, the degree of frost

susceptibility is mainly a function of the percentage of fine particles within

the soil. Many agencies classify materials as being frost susceptible if 10% or

more passes a No. 200 sieve (0.075 mm opening size) or 3% or more passes a

No. 635 sieve (0.02 mm opening size).

The following rule-of-thumb criterion is widely used for identifying potentially

frost susceptible soils (Casagrande 1932):

"Under natural freezing conditions and with sufficient water supply one

should expect considerable ice segregation in non-uniform soils containing

more than 3 percent of grains smaller than 0.02 mm, and in very uniform soils

containing more than 10 percent smaller than 0.02 mm. No ice segregation

was observed in soils containing less than 1 percent of grains smaller than

0.02 mm, even if the groundwater level is as high as the frost line."

411.12.2. Thaw Weakening

Thaw weakening occurs when the ice contained within the subgrade melts.

As the ice melts, the water cannot drain out of the soil fast enough and thus

the subgrade becomes substantially weaker and loses bearing capacity.

Therefore, loading that would not normally damage a given pavement may

cause significant damage during spring thaw.


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411.12.3. Mitigating Frost Action

Frost action mitigation generally involves structural design considerations as

well as other techniques applied to the base and subgrade to limit its effects.

The basic methods used can be broadly categorized into the following

techniques:

Frost Heave

Limit the depth of frost into the subgrade soils . This is typically

accomplished by specifying the depth of pavement to be some minimum

percentage of the frost depth. By extending the pavement section well into

the frost depth, the depth of frost-susceptible subgrade under the

pavement (between the bottom of the pavement structure and frost depth)

is reduced, causing correspondingly less damage.

Removing and replacing frost-susceptible subgrade. Ideally the subgrade

will be removed at least down to the typical frost depth. Removing frost-

susceptible soils removes frost action.

Providing a capillary break . By breaking the capillary flow path, frost

action will be less severe because frost heaving requires substantially

more water than is naturally available in the soil pores.

Thaw Weakening

Design the pavement structure based on reduced subgrade support .

This method simply increases the pavement thickness to account for the

damage and loss of support caused by frost action.

Restrict pavement loading during thaw conditions . Permanent pavementdamage can be limited by limiting pavement loading while the subgrade

support is weak. Typically, a load reduction in the range of 40% to 50%

should accommodate a wide range of pavement conditions.

Citation

Indranil Goswami: Civil Engineering All-In-One PE Exam Guide: Breadth and Depth,

Second Edition. Design of Highway Pavements, Chapter (McGraw-Hill Professional,

2012), AccessEngineering

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411-Design of Highway Pavements

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Transcript of 411-Design of Highway Pavements