Wai-Fah Chen.The Civil Engineering Handbook

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62-40 The Civil Engineering Handbook, Second Edition

analyses based on elastic theory to generate pavement thickness requirements against two failure criteria:

a fatigue-cracking criterion for the asphalt layer and a rutting criterion for the subgrade.

More comprehensive mechanistic procedures, capable of handling the following aspects in pavement

design, are available in the literature: (a) viscoelastic behavior of bituminous materials, (b) nonlinear

response of untreated granular and cohesive materials, (c) aging of bituminous materials, (d) material

variabilities, (e) dynamic effect of trafﬁc loading, (f ) effect of mixed trafﬁc loading, and (g) interdependency

FIGURE 62.22 Critical area ﬂexible pavement thickness for DC 10-30, 30CF, 40, and 40CF. (Source: Federal Aviation

Administration. 1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C. With permission.)

NOTE: CURVES BASED ON 20-YEAR

PAVEMENT LIFE

CONTACT AREA = 331 SQ IN.

DUAL SPACING = 54 IN.

TANDEM SPACING = 64 IN.

CENTER-LINE GEAR SPACING = 37.5 IN.

THICKNESS - BITUMINOUS

SURFACES

5-IN. CRITICAL AREAS

4-IN. NONCRITICAL AREAS

GROSS AIRCRAFT

WEIGHT, LB

600,000

500,000

400,000

300,000

200,000

1 in. = 2.54 cm

1 ib. = 0.454 kg

ANNUAL DEPARTURES

1200

3000

6000

15,000

25,000

345678910 1520 30

40 50

THICKNESS, IN.

345678910 15202530

40 50

CBR

Highway and Airport Pavement Design 62-41

of the development of different distresses, including pavement roughness. Unfortunately, quantiﬁcation

of necessary material properties and analysis of pavement response by these procedures are often com-

plicated, time consuming, skill demanding, and costly. Although there are great potentials for these

procedures when fully implemented, simpliﬁcations such as that adopted by the Asphalt Institute method

will have to be applied for pavement design in practice.

62.6 Structural Design of Rigid Pavements

Structural design of rigid pavements includes thickness and reinforcement designs. Two major forms of

thickness design methods are being used today for concrete pavements. The ﬁrst form is an approach

FIGURE 62.23 Minimum base course thickness requirements. (Source: Federal Aviation Administration. 1978.

Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C, p. 53. With permission.)

TOTAL PAVEMENT THICKNESS, IN.

(cm)

100

678910 15

MINIMUM BASE COURSE THICKNESS, IN.

20 25

(cm)

250

200

175

150

140

130

120

110

100

5045403530252017

SUBGRADE CBR

62-42 The Civil Engineering Handbook, Second Edition

that relies on empirical relationships derived from performance of full-scale test pavements and in-service

pavements. The design procedure of AASHTO [1993] is an example. The second form develops relation-

ships in terms of the properties of pavement materials as well as load-induced and thermal stresses and

calibrates these relationships with pavement performance data. The PCA [1984] and the FAA [1978]

methods of design adopt this approach. Thickness design procedures by AASHTO, PCA, and FAA are

discussed in this section. Reinforcement designs by the AASHTO and FAA procedures will be presented.

AASHTO Thickness Design for Rigid Highway Pavements

The serviceability-based concept of the AASHTO design procedure for rigid pavements [AASHTO, 1993]

is similar to its design procedure for ﬂexible pavements. Pavement thickness requirements are established

from data of the AASHO road test [Highway Research Board, 1962]. Input requirements such as reliability

information and serviceability loss for design have been described in the section on AASHTO ﬂexible

pavement design. Details for other input requirements are described in this section.

Pavement Material Properties

The elastic modulus E

and modulus of rupture S

of concrete are required input parameters. E

determined by the procedure speciﬁed in ASTM C469. It could also be estimated using the following

correlation recommended by ACI [1977]:

(62.26)

where f

= the concrete compressive strength in psi as determined by AASHTO T22, T140 [AASHTO,

1989] or ASTM C39 [ASTM, 1992].

TA BLE 62.13 FAA-Recommended Equivalency

Factors for Stabilized Base and Subbase

Material

Equivalency

Factor

(a) Equivalency Factors for Stabilized Base Course

Bituminous surface course 1.2–1.6

Bituminous base course 1.2–1.6

Cold-laid bituminous base course 1.0–1.2

Mixed-in-place base course 1.0–1.2

Cement-treated base course 1.2–1.6

Soil cement base course N/A

Crushed aggregate base course 1.0

Subbase course N/A

(b) Equivalency Factors for Stabilized Subbase Course

Bituminous surface course 1.7–2.3

Bituminous base course 1.7–2.3

Cold-laid bituminous base course 1.5–1.7

Mixed-in-place base course 1.5–1.7

Cement-treated base course 1.6–2.3

Soil cement base course 1.5–2.0

Crushed aggregate base course 1.4–2.0

Subbase course 1.0

Source: Federal Aviation Administration. 1978. Airport

Pavement Design and Evaluation. Reprinted from FAA

Advisory Circular. Report FAA/AC-150/5320-6C.

7 December 1978; NTIS Accession No. AD-A075 537/1.

psi() 57 000 f

()

0.5

Highway and Airport Pavement Design 62-43

is the mean 28-day modulus of rupture determined using third-point loading as speciﬁed by

AASHTO T97 [AASHTO, 1989] or ASTM C39 [ASTM, 1992].

Modulus of Subgrade Reaction

The value of modulus of subgrade reaction k to be used in the design is affected by the depth of bedrock

and the characteristics of the subbase layer, if used. Figure 62.25 is ﬁrst applied to account for the presence

of subbase course and obtain the composite modulus of subgrade reaction. Figure 62.26 is next used to

include adjustment for the depth of rigid foundation. It is noted from Fig. 62.25 that the subgrade soil

property required for input is the resilient modulus M

Example 62.15

This example entails computation of composite subgrade reaction. A concrete pavement is constructed

on a 6-in.-thick subbase with elastic modulus of 20,000 psi. The resilient modulus of the subgrade soil

is 7000 psi. The depth of subgrade to bedrock is 5 ft.

Entering Fig. 62.25, with D

= 6 in., E

= 20,000 psi, and M

= 7000 psi, obtain k

•

= 400 pci. With

bedrock depth of 5 ft., composite k = 500 pci, from Fig. 62.26.

Effective Modulus of Subgrade Reaction

Like the effective roadbed soil resilient modulus M

for ﬂexible pavement design, an effective k is computed

to represent the combined effect of seasonal variations of k. The procedure is identical to the computation

of effective M

, except that the relative damage u is now computed as

(62.27)

Instead of solving the above equation, u can be obtained from Fig. 62.27.

FIGURE 62.24 Typical plan and cross section for runway pavements. (Source: Federal Aviation Administration.

1978. Airport Pavement Design and Evaluation. Advisory Circular AC No. 150/5320-6C, p. 35. With permission.)

200’

(61m)

200’

(61m)

200’

(61m)

200’

(61m)

200’

(61m)

RUNWAY WIDTHS IN ACCORDANCE WITH

APPLICABLE ADVISORY CIRCULAR.

TRANSVERSE SLOPES IN ACCORDANCE

WITH APPLICABLE ADVISORY CIRCULAR.

SURFACE, BASE, PCC, ETC., THICKNESS

AS INDICATED ON DESIGN CHART.

MINIMUM 12" (30 cm) UP TO 30" (90cm)

ALLOWABLE.

FOR RUNWAYS WIDER THAN 150’ (45.7 m)

THIS DIMENSION WILL INCREASE.

NOTES

TRANSITIONS

RUNWAY WIDTH

6@ 25’ (7.6 m)

BASE

PCC

SUBBASE

THICKNESS = T

THICKNESS TAPERS = T O.7 T

THICKNESS = 0.9 T

THICKNESS = 0.7 T

LEGEND

SUBBASE

SURFACE

2"(1 cm) MINIMUM

SURFACE THICKNESS

TRANSITIONS

P1 P1

0.75

0.39k

0.25

–()

3.42

62-44 The Civil Engineering Handbook, Second Edition

Depending on the type of subbase and subgrade materials, the effective k must be reduced according

to Fig. 62.28 to account for likely loss of support by foundation erosion and/or differential soil move-

ments. Suggested values of LS in Fig. 62.28 are given in Table 62.14.

Example 62.16

The value of composite k values determined at 1-month intervals are 400, 400, 450, 450, 500, 500, 450,

450, 450, 450, 450, and 450. Projected slab thickness is 10 in. and LS = 1.0. Determine effective k.

By means of Eq. (62.27) or Fig. 62.27, the relative damage for each k can be determined. Hence, total

u = 100 + 100 + 97 + 97 + 93 + 93 + 94 + 94 + 94 + 94 + 94 + 94 = 1144. Average u = 95.3 and average

k = 470 pci. Entering Fig. 62.28 with LS = 1.0 and D = 10 in., read effective k = 150 pci.

Load Transfer Coefﬁcient

Load transfer coefﬁcient J is a numerical index developed from experience and stress analysis. Table 62.15

presents the J values for the AASHO road test conditions. Lower J values are associated with pavements

with load transfer devices (such as dowel bars) and those with tied shoulders. For cases where a range

of J values applies, higher values should be used with low k values, high thermal coefﬁcients, and large

variations of temperature. When dowel bars are used, the AASHTO guide recommends that the dowel

FIGURE 62.25 Chart for estimating composite k

•

. (Source: AASHTO. 1993. AASHTO Guides for Design of Pavement

D.C. Used by permission.)

Subbase Elastic

Modulus, E

(psi)

•

(pci)

(Assumes Semi—

infinite Subgrade

Depth)

2000

1500

1000

800

600

500

400

300

200

100

Subbase Thickness, D

(inches)

Roadbed

Soil Resilient

Modulus, M

(psi)

18 16 14 12 10 8 6

15,000

30,000

50,000

75,000

100,000

200,000

400,000

600,000

1,000,000

1000

10,000

20,000

12,000

16,000

2000

3000

5000

7000

(Turning Line)

Composite Modulus of

Subgrade Reaction,

Highway and Airport Pavement Design 62-45

diameter should be equal to the slab thickness multiplied by 1/8, with normal dowel spacing and length

of 12 in. and 18 in., respectively.

Drainage Coefﬁcient

To allow for changes in thickness requirement due to differences in drainage properties, pavement layers,

and subgrade, a drainage coefﬁcient C

was included in the design. Setting C

= 1 for conditions at the

AASHO road test, Table 62.16 shows the C

values for other conditions. The percentage of time during

the year that the pavement structure would be exposed to moisture levels approaching saturation can be

estimated from the annual rainfall and the prevailing drainage condition.

Thickness Requirement

The required slab thickness is obtained using the nomograph in Fig. 62.29. If the environmental effects

of roadbed swelling and frost heave are important, they are considered in the same way as for ﬂexible

pavements.

Example 62.17

Apply the AASHTO procedure to design a concrete pavement slab thickness for ESAL = 11 ¥ 10

. The

design reliability is 95%, with a standard deviation of 0.3. The initial and terminal serviceability levels

are 4.5 and 2.5, respectively. Other design parameters are E

= 5 ¥ 10

, S

= 650 psi, J = 3.2, and C

= 1.0.

Design PSI loss = 4.5 – 2.5 = 2.0. From Fig. 62.29, D = 10 in.

FIGURE 62.26 Chart for k as a function of bedrock depth. (Source: AASHTO. 1993. AASHTO Guides for Design of

Washington, D.C. Used by permission.)

Subgrade Depth to Rigid

Foundation, D

(ft.)

Roadbed Soil Resilient Modulus, M

(psi)

50 100 200 300 400

500

600

700

800

1000

1200

1400

Modulus of Subgrade Reaction, k

•

(pci)

Assuming Semi-infinite Subgrade Depth

Modulus of Subgrade Reaction, k (pci)

(Modified to account for presence of

rigid foundation near surface)

20,000 15,000 10,000 5,000 500 1000 1500 20000

62-46 The Civil Engineering Handbook, Second Edition

AASHTO Reinforcement Design for Rigid Highway Pavements

Reinforcements are introduced into concrete pavements for the purpose of crack-width control. They

are designed to hold cracks tightly closed so that the pavement remains an integral structural unit. The

amount of reinforcement required is a function of slab length (or joint spacing) and thermal properties

of the pavement material.

Reinforcements are not required in jointed plain concrete pavements (JPCP) whose lengths are rela-

tively short. As a rough guide proposed by AASHTO, the joint spacing (in feet) for JPCP should not

greatly exceed twice the slab thickness (in inches), and the ratio of slab width to length should not exceed

1.25.

Reinforcement Design for JRCP

The percentage of steel reinforcement (either longitudinal or transverse reinforcement) required for

jointed reinforced concrete pavement (JRCP) is given by

(62.28)

FIGURE 62.27 Chart for estimating relative damage to rigid pavements. (Source: AASHTO. 1993. AASHTO Guides

Ofﬁcials, Washington, D.C. Used by permission.)

Projected Slab

Thickness

(inches)

Relative Damage, u

1000

500

100

10 50 100 500

Composite k-value (pci)

1000 2000

Projected Slab

Thickness

(inches)

LF◊

----------

100%¥=

Highway and Airport Pavement Design 62-47

where L = slab length in feet, F = friction factor between the bottom of the slab and the top of the

underlying subbase or subgrade, and f

= allowable working stress of steel reinforcement in psi. AASHTO’s

recommended values for F are given in Table 62.17. The allowable steel working stress is equal to 75%

of the steel yield strength. For grade 40 and grade 60 steel, f

is equal to 30,000 and 45,000 psi, respectively.

For welded wire fabric, f

is 48,750 psi. Equation (62.28) is also applicable to the design of transverse

steel reinforcement for continuously reinforced concrete pavement (CRCP).

FIGURE 62.28 Correction of effective modulus of subgrade reaction for potential loss of subbase support. (Source:

State Highway and Transportation Ofﬁcials, Washington, D.C. Used by permission.)

TABLE 62.14 Typical Ranges of Loss of Support

(LS) Factors for Various Types of Materials

Type of Material

Loss of Support

(LS)

Cement treatment granular base

(E = 1,000,000 to 2,000,000 psi)

0.0–1.0

Cement aggregate mixtures

(E = 500,000 to 1,000,000 psi)

0.0–1.0

Asphalt treated base

(E = 350,000 to 1,000,000 psi)

0.0–1.0

Bituminous stabilized mixtures

(E = 40,000 to 300,000 psi)

0.0–1.0

Lime stabilized

(E = 20,000 to 70,000 psi)

1.0–3.0

Unbound granular materials

(E = 15,000 to 45,000 psi)

1.0–3.0

Fine-grained or natural subgrade materials

(E = 3000 to 40,000 psi)

2.0–3.0

Source: AASHTO. 1993. AASHTO Guides for Design of Pavement

way and Transportation Ofﬁcials, Washington, D.C. Used by permission.

Effective Modulus of Subgrade Reaction, K (pci)

(Corrected for Potential Loss of Support)

1000

500

100

510 50100

Effective Modulus of Subgrade Reaction, K (pci)

500 1000 2000

LS=3.0

LS=2.0

LS=1.0

LS=0

(170)

(540)

62-48 The Civil Engineering Handbook, Second Edition

Example 62.18

Determine the longitudinal steel reinforcement requirement for a 30-ft-long JRCP constructed on crushed

stone subbase.

From Table 62.17, F = 1.5. Percentage of steel reinforcement P

= (30 ¥ 1.5)/(2 ¥ 30,000) = 0.075%.

Longitudinal Reinforcement Design for CRCP

The design of longitudinal reinforcement for CRCP is an elaborate process. The amount of reinforcement

selected must satisfy limiting criteria in the following three aspects: (a) crack spacing, (b) crack width,

and (c) steel stress.

CRCP Reinforcements Based on Crack Spacing: (P

min

)

and (P

max

)

. The amount of steel reinforce-

ment provided should be such that the crack spacing is between 3.5 ft (1.1 m) and 8 ft (2.4 m). The

lower limit is to minimize punchout and the upper limit to minimize spalling. For each of these two

crack spacings, Fig. 62.30 is used to determine the percent reinforcement P required, resulting in two

values of P that deﬁne the range of acceptable percent reinforcement: (P

max

)

and (P

min

)

The input variables for determining P are the thermal coefﬁcient of portland cement concrete a

, the

thermal coefﬁcient of steel a

, diameter of reinforcing bar, concrete shrinkage Z at 28 days, tensile stress

due to wheel load, and concrete tensile strength f

at 28 days. Values of a

and Z are given in Table 62.18.

A value of a

= 5.0 ¥ 10

–6

in./in./˚F may be used. Steel bars of 5/8- and 3/4-in. diameter are typically

used, and the 3/4-in. bar is the largest practical size for crack-width control and bond requirements. The

nominal diameter of a reinforcing bar, in inches, is simply the bar number divided by 8. Meanwhile,

is the tensile stress developed during initial loading of the constructed pavement by either construction

TABLE 62.15 Recommended Load Transfer Coefﬁcient

for Various Pavement Types and Design Conditions

Shoulder Asphalt Tied P.C.C.

Load Transfer Device Yes No Yes No

Pavement Type

Plain Jointed and

Jointed reinforced

3.2 3.8–4.4 2.5–3.1 3.6–4.2

CRCP 2.9–3.2 N/A 2.3–2.9 N/A

Source: AASHTO. 1993. AASHTO Guides for Design of Pave-

State Highway and Transportation Ofﬁcials, Washington, D.C.

Used by permission.

TA BLE 62.16 Recommended Value of Drainage Coefﬁcient, C

for Rigid Pavement Design

Quality of

Drainage

Percent of Time Pavement Structure Is Exposed

to Moisture Levels Approaching Saturation

Less than

1% 1–5% 5–25%

Greater than

25%

Excellent 1.25–1.20 1.20–1.15 1.15–1.10 1.10

Good 1.20–1.15 1.15–1.10 1.10–1.00 1.00

Fair 1.15–1.10 1.10–1.00 1.00–0.90 0.90

Poor 1.10–1.00 1.00–0.90 0.90–0.80 0.80

Ve ry Poor 1.00–0.90 0.90–0.80 0.80–0.70 0.70

Source: AASHTO. 1993. AASHTO Guides for Design of Pavement

way and Transportation Ofﬁcials, Washington, D.C. Used by permission.

Highway and Airport Pavement Design 62-49

equipment or truck trafﬁc. It is determined using Fig. 62.31 based on the design slab thickness, the

magnitude of the wheel load, and the effective modulus of subgrade reaction. Likewise, f

is the concrete

indirect tensile strength determined by AASHTO T198 or ASTM C496. It can be assumed as 86% of the

modulus of rupture S

used for thickness design.

CRCP Reinforcements Based on Crack Width: (P

min

)

. Crack width in CRCP is controlled to within

0.04 in. (1.0 mm) to prevent spalling and water inﬁltration. The minimum percent steel (P

min

)

that

would produce crack widths of 0.04 in. can be determined from Fig. 62.32 with a selected bar size and

input variables s

and f

FIGURE 62.29 Rigid pavement thickness design chart. (Source: AASHTO. 1993. AASHTO Guides for Design of

Washington, D.C. Used by permission.)

TA BLE 62.17 Recommended

Friction Factors

Type of Material

beneath Slab

Friction

Factor

Surface treatment 2.2

Lime stabilization 1.8

Asphalt stabilization 1.8

Cement stabilization 1.8

River gravel 1.5

Crushed stone 1.5

Sandstone 1.2

Natural subgrade 0.9

Source: AASHTO. 1993. AASHTO

Guides for Design of Pavement Structures.

ciation of State Highway and Transpor-

tation Ofﬁcials, Washington, D.C. Used

by permission.

99.9 99 95 90 80 70 60 50

Concrete Elastic Modulus, E

(10

pci)

1200

1100

1000

900

800

700

600

500

800 500 100 50 10

Effective Modulus of Subgrade

Reaction, k (pci)

4.0

4.5

1.3

1.1

0.9

0.7

0.6

3.5

3.0

2.5

2.2

Load Transfer

Coefficient, J

Drainage Coefficient, C

100

Match Line

Design Serviceability Loss, ∆PSI

1000 500 100 50 10 5 10 5 1 05

Estimated Total 18−kip Equivalent Single Axle

Load (ESAL) Applications, W

(millions)

Mean Concrete Modulus of Rupture, S′

(psi)

NOTE : Application of reliablility

in this chart requires

the use of mean values

for all the input variables.

1.0

2.0

3.0

Design slab thickness, D (inches)

Reliability, R (%)

Overall Standard Deviation, S

13 12 11 10 9 8 7 6 5