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
R
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
R
o
i t
c
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
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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
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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
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plot a point with these coordinates and estimate the required pavement
thickness.
Tables 411.6 to 411.8 show load equivalence factors for single, double, and
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
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Table 411.7. Axle Load Equivalence Factors for Flexible Pavements,
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
Pavement structural number (SN)
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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Table 411.8. Axle Load Equivalence Factors for Flexible Pavements,
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
Pavement structural number (SN)
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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Tables 411.9 to 411.11 show load equivalence factors for single, double, and
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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Table 411.10. Axle Load Equivalence Factors for Rigid Pavements,
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
Slab thickness, D (in)
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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Table 411.11. Axle Load Equivalence Factors for Rigid Pavements,
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
Slab thickness, D (in)
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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